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V. m“ A. _ . ‘ - -- -I- '4'. a _ A V‘“ ‘- O V v ‘ A-.. 4 fi .. cm “W. , '- - O ‘—r -. . ‘ -0 g - ‘. a , '- 0- . o J’ . -44 . . 4. J . . q-b. ‘ -. -l t - no-0 . I- ‘. y .. no " - - ' W.‘ . o. - .3 0- ° .. . O! — 0f O L I I: .2 A R Y Michigan State Univcnit)’ This is to certify that the thesis entitled PART I. NUCLEAR MAGNETIC RESONANCE STUDIES OF AMIDES PART II. THEORETICAL STUDIES OF AMIDES presented by Biing-Ming Su has been accepted towards fulfillment of the requirements for Ph.D. Chemistry degree in 7% 1/1"; / \LM1 /2 - 4] Major professo 0-7639 © 1978 BllNG-MING SU ALL RI GHTS RESERVED PART I. NUCLEAR MAGNETIC RESONANCE STUDIES OF AMIDES PART II. THEORETICAL STUDIES OF AMIDES BY Biing-Ming Su A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1978 “ nu' ‘1. ’ v ABSTRACT PART I. NUCLEAR MAGNETIC RESONANCE STUDIES OF AMIDES. PART II. THEORETICAL STUDIES OF AMIDES. BY Biing-Ming Su A variety of nuclear magnetic resonance (NMR) techniques has been used to investigate various physical properties of a series of amides, N-substituted amides, and both symmetrically and unsymmetrically N,N-disubstituted amides. The results are presented-in Part I in seven sections. I. Anisotropic molecular reorientation in a series of N,N-disubstituted amides (RCONR', R = H,CH3,C 2H5'C3H7 and R' = CH3,C2H5,C3H7, etc.) has been studied by measuring l3C spin-lattice relaxation times and NOE factors over a range of temperature. It is shown that the data can be satisfactorily treated on the basis of an approximate ellipsoidal model which leads to an axial diffusion tensor with Dll associated with a preferred rotation axis in the molecular plane. Values of the diffusion constants, DH and Di, the directions of the preferred rotation axes, the internal rotation rates of the N-methyl groups, the energy barriers_associated with the motions of the various carbons, Biing—Ming Su and the effective quadrupole coupling constants for 170, have been obtained and their significance discussed. 13C nuclear spin- II. The isomer ratios, and the. lattice relaxation times and NOE factors, have been measured for a series of N-monosubstituted amides and un- symmetrically N,N-disubstituted amides. The dipolar and other contributions to the 13C Tl values have been deter- mined along with the correlation times for overall rota- tional motion of the molecules, and for the internal TR, motions of individual groups, T The anisotropic re- G' orientational motions have been analyzed in terms of an approximate ellipsoidal model. The effects of structure and of intermolecular hydrogen bonding on the nuclear relaxation parameters have been evaluated. Effective quadrupole coupling constants for nitrogen have been estimated in four amides from the measured l4N relaxation times. III. The effects of phenyl substitution on the structures and molecular motions of amides have been in- vestigated in a series of formanilides and acetanilides. The 13 C chemical shifts, Tl values and NOE factors were 'measured for all carbons and the dipolar and other con- tributions to T1 calculated, along with the correlation times for overallanisotropic rotational motion of the molecules. The effects of carbonyl and nitrogen Biing-Ming Su substituents on the tumbling ratios for the benzene ring (with C the preferred axis) have been determined. IV. Chemical shifts for 13C, 14N, 15N and 17O 2 have been measured in a series of N,N-disubstituted amides and the effects of substituents on these shifts evaluated.' A number of linear correlations among them have been dis- covered including relationships between the chemical shifts of 14N (or 15N) and both 170 and the 13C of the carbonyl group; linear correlations between these and the energy barriers Ea restricting rotation about the central C-N bonds have also been obtained. The y and 6 effects used 13 in interpreting C NMR spectra have been shown to have analogues in the 14N, 15N and 170 NMR spectroscopy of the amides. V. The assignment of proton and carbon NMR signals in several amides has been accomplished by the use of off- resonance proton-selectively decoupled 13C NMR spectra along with 13C T1 measurements. From values of the residual one- 13 bond C-H coupling constants as functions of the separation between the applied decoupling frequency and the proton 13C and 1H NMR spectra were resonance frequency, the correlated for these amides and some errors in previous assignments of proton chemical shifts corrected. VI. Concentration dependence of the chemical shifts of the carbons of DMF in benzene and DNA in cyclo- hexane and formamide have been used to investigate the n-. I. I1- I 4 :v 1‘. \. 4 I I. u Biing-Ming Su nature of the species present in these solution VII. Solutions of Mn2+ in N,N-dimethylformamide have been studied by measuring the 13C T1 and T2 values for all the carbons of DMF over a range of temperature. The paramagnetic shifts and hyperfine electron-13C interaction constants have been evaluated, the relaxation mechanisms determined and the l3C-Mn2+ distances calculated for each 2+ . . has coordination carbon. The results indicate that Mn number eight in these solutions with weak bonding to the oxygens of four DMF dimers, which are tetrahedrally arranged about the metal ion. In Part II calculations by the INDO method of the theoretical energy barriers for-rotation about the central C-N bond in some selected amides are reported along with the bond orders for the C-N bonds. The variation of the partial charges on each atom in going from the ground equilibrium geometry to the transition state geometry was also studied. From the variation of the charges on the nitrogen and oxygen atoms, the observed decrease of the energy barrier resulting from the formation of hydrogen bonds to the carbonyl oxygen can be rationalized. The results obtained here for substituted amides using the INDO method are similar to those reported previously using the CNDO/Z method. TO MY PARENTS ii ACKNOWLEDGEMENTS The author would like to express his appreciation to Professor M.T. Rogers for his patient guidance and encouragement throughout this research. Gratitude is also extended to Dr. J.F. Harrison and Dr. W.G. Waller for allowing the author to use their INDO and MBLD programs. Many thanks go to my wife, Shin-Chin, and to my parents for their encouragement during these years. Finally, the author wishes to acknowledge the financial support of the Department of Chemistry through these years as a graduate student. iii TABLE OF CONTENTS PART I. NUCLEAR MAGNETIC RESONANCE STUDIES OF AMIDES INTRODUCTION . NUCLEAR MAGNETIC RESONANCE THEORY . . . . . . . I. II. III. HISTORICAL Introduction to NMR Theory . . . . . Nuclear Relaxation — General Theory Spin-lattice relaxation . . . . Spin-spin relaxation . . . . . . Comparison of spin-lattice and spin-spin relaxation times . . . Phenomenological Theory . . . . . . A. B. C. A. The Bloch equations . . . . . . l. The motion of the magnetiza- tion vectors in a laboratory coordinate system . . . . . 2. The motion of the magnetiza- tion vector in the rotating coordinate system . . . . B. NMR in the rotating frame of re- ference . . . . . . . . . . . . C. Nuclear induction . . . . . . D. Comparison between cw and FT NMR Theory of Chemical Shifts . . . . . A. Substituent effects on 1 C chemical shifts . . . . . . . . Double Resonance in NMR . . . . . . Nuclear Overhauser Effect . . . . . A. Theory for several important cases 0 O O O O O O O O O C O O 1. 2. 3. Isotropic reorientation . . 13C- {all H} double resonance Anisotropic rotation or groups with internal rotation REVIEW OF NUCLEAR RELAXATION STUDIES Statistical Mechanical Theory . . . Relaxation Mechanisms . . . . . . A. Dipole- dipole relaxation (DD) . B. Spin-rotation relaxation (SR) . C. Chemical shift anisotropy relaxation (CSA) . . . . . . . . iv Page .5 comma. l3 l3 l6 17 21 33 35 39 44 47 56 56 58 61 65 65 69 69 72 75 'In- 'l,. u... Page D. Scalar coupling relaxation (SC) . 76 E. Quadrupole relaxation (Q) . . . . 78 F. Electron-nuclear relaxation (e) . 79 G. Additivity of relaxation rates . 81 III. Some Experimental Results from the Literature . . . . . . . . . . . . . 82 A. Studies of Amides . . . . . . . . 82 B. Methyl group rotation . . . . . . 84 C. Anisotropic tumbling in mono- substituted benzenes . . . . . . 84 EXPERIMENTAL . . . . . . . . . . . . . . . . . . 88 I. Instrumental . . . . . . . . . . . . 88 A. 13C NMR spectrometer . . . . . . 88 B. Calibration of temperature for CFT—20 NMR spectrometer . . . . . 91 C. 13C Spin-lattice relaxation time measurement . . . . . . . . . . . 93 D. 14N NMR spectrometer (DA-60) . . 109 E. WH-180 NMR spectrometer . . . . . 112 II. Materials . . . . . . . . . . . . . . 116 AA. Compound preparation . . . . . . 116 B. Purification of compounds . . . . 120 C. Purification of solvents . . . . 121 D. Sample preparation . . . . . . . 122 SECTION 1. NMR STUDIES OF MOLECULAR MOTION IN SYMMETRICALLY N,N-DISUBSTITUTED AMIDES . . . . . . . . . . . . . . . 126 I. Background . . . . . . . . . . . . . 126 II. Results . . . . . . . . . . . . . . . 134 A. Studies of th anisotropic mole- cular motion in N,N-dimethylamides by an approximate ellipsoidal model . . . . . . . . . . . . . . 134 Determination of the energy barriers for the internal rota- tion of the NCH groups and for the segmental m6tion of the carbonyl substituents . . . . . . 150 Separation of the total spin- lattice relaxation rate into components . . . . . . . . . . . 161 --u-n . Ivo- na-‘ .y‘. SECTION 2. SECTION 3. III. SECTION 4. III. IV. V. VI. Page NMR STUDIES OF N-MONOSUBSTITUTED AND UNSYMMETRICALLY N,N-DISUB- STITUTED AMIDES . . . . . . . . . . 181 Results . . . . . . . . . ... . . . 181 A. Studies of cis-trans isomer ratios . . . . . . . . . . . 181 B. 13C chemical shifts of amides and the 15N-13C coupling con- stants in 15N-n- -butylformamide 187 C. 13C relaxation studies and nuclear Overhauser effects . . 188 D. 14N relaxation times and quadrupole coupling constants in some amides . . . . . . . . 199 B. Energy of the hydrogen bond in N-ethylformamide . . . . . . . 202 NMR STUDIES OF THE ANISOTROPIC MOLECULAR MOTION IN N-ALKYL ACETANILIDES AND FORMANILIDES . . . 205 Background . . . 205 Analysis of the 13C Chemical Shifts in N-Alkylacetanilides and N-Alkyl- formanilides . . . . . . . . . . . 207 Relaxation Times and NOE Effects . 213 CORRELATIONS AMONG 14N, 15N, 170, AND 13c CHEMICAL SHIFTS, AND BETWEEN THESE AND THE ROTATIONAL ENERGY BARRIERS IN SYMMETRICALLY N,N-DISUB- STITUTED AMIDES . . . . . . . . . . 221 Background . . . . .14 . . .15 . . . 221 Relationship between N and N Chemical Shifts . . . . . 224 Relationship Between the 15N and 13C(= 0) Chemical Shifts . . . . . 231 Relationship between the 15N and 13C 6 Values and E . . 233 Relationship betwegn 150 and 15N Chemical Shifts . . . . . . . . . . 237 14N Chemical Shifts of Some Other Amides Measured at High Temperatures 239 vi SECTION V. I.. II. SECTION 6. SECTION 7. I. II. III. SUMMARY(PARTI)................. PART II. I. OFF-RESONANCE PROTON-SELECTIVELY DECOUPLED 13C NMR SPECTRA AND SPIN- LATTICE RELAXATION TIMES A TOOLS FOR ASSIGNING THE 13C AND H CHEMICAL SHIFTS OF AMIDES . . . . . . . . . . . Background . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . SOLVENT EFFECT STUDIES OF N,N-DIMETHYL- FORMAMIDE AND N,N-DIMETHYLACETAMIDE BY 13C NMR . . . . . . . . . . . . . . . Background . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . A. The N,N-dimethylacetamide-cyclo- hexane system . . . . . . . . . . B. The N, N- dimethylacetamide-form- amide system . . . . . . . . C. The N, N-dimethylformamide benzene system . . . . . . . . . . . . . NMR STUDY OF THE SOLVATION OF Mn2+ IN N,N-DIMETHYLFORMAMIDE SOLUTIONS . . . Background . . . . . . . . . . . . . . A. Effects of paramagnetic ions on nuclear relaxation times . . . . . B. Effects of Chemical exchange . . . C. 13C relaxation data.ggd isotropic contact shifts 1n Mn -DMF mixtures . . . . . . . . . . . . . D. The dominant mechanisms of relaxation . . . . . . . . . . . . Results and Discussion . . . . . . . . A. Determination of the coordination number, To and the structure of the $01vat1on complex . . . . . B. Determination of She coupling con- stants between Mn and carbon . . C. Determination of AH*, AS*, E and T . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . THEORETICAL STUDIES OF AMIDES INTRODUCTION . . . . . . . . . . . . . THEORETICAL . . . . . . . . . . . . . General Survey . . . . . . . . . . . . vii Page 247 247 249 269 269 271 271 282 293 306 306 309 312 314 324 324 324 329 330 331 333 334 336 336 Page II. Standard Geometrical Models . . . . . 340 A. Bondlengths . . . . . . . . . . . 342 B. Bond Angles . . . . . . . . . . . 342 C. Dihedral Angles . . . . . . . . . 345 THEORETICAL . . . . . . . . . . . . . 346 I. Molecular Orbital Theories . . . . . 346 A. Roothaan self-consistent field procedure . . . . . . . . . . . . 346 B. Approximate molecular orbital theories . . . . . . . . . . . . 351 RESULTS AND DISCUSSION . . . . . . . 363 I. General Procedure . . . . . . . . . . 363 II. Dependence of INDO results on con- formation . . . . . . . . . . . . . . 372 A. Variation of energy with rotation about the N-C(O) bond . . . . . . 372 B. Energy variation with respect to the dihedral angle ¢ . . . . . . 379 C. Charge variation upon rotation about the N-C(O) bond . . . . . . 395 D. Variation of charges with respect to the dihedral angles ¢ . . . . 403 SUMMARY (PART II) . . . . . . . . . . . . 425 REFERENCES . . . . . . . . . . . . . . . . 426 viii I 1 I.. \L' Table LIST OF TABLES Page 13C Spin-lattice relaxation times and NOE data for some amides . . . . . . . . 83 Methyl internal rotational barriers from 13C dipolar relaxation rates . . . 85 Anisotropic tumbling in monosub- stituted benzenes . . . . . . . . . . . 86 Results of the determination of 13C spin-lattice relaxation times in N,N- dimethylformamide by different methods . 107 Physical properties of symmetrically N,N-disubstituted amides . . . . . . . . 117 Physical properties of unsymmetrically N,N-disubstituted amides . . . . . . . . 118 Physical properties of N-monosub- stituted amides . . . . . . . . . . . . 119 13C Chemical shifts, spin-lattice relaxation times (T1), and nuclear Overhauser enhancements (NOE), of several N,N-dimethylamides . . . . . . . 136 The calculated diffusion constants DH' Di and internal rotation rates for ' trans- and cis-N-methyl groups in some N,N-dimethyIamides . . . . . . . . . . . 146 Temperature dependence of the 13C spin- 1attice relaxation times of the carbons of N,N-dimethylformamide . . . . . . . . 151 Temperature dependence of the 13C spin- 1attice relaxation times of each alkyl carbon of N,N-dimethylformamide . . . . 153 Temperature dependence of the 13C spin— lattice relaxation times of each.alkyl carbon of N,N-dimethylpropionamide . . . 155 ix Table Page 10 Temperature dependence of the 13C spin- 1attice relaxation times of each alkyl carbon of N,N-dimethyl-n-butyramide. . . 157 11 Energy barriers for internal rotation about the threefold axes of the N-methyl group and carbonyl substituents in N,N-dimethylamides . . . . . . . . . . . 160 17 12 O Spin—lattice relaxation times (T1) and the quadrupole coupling constants of some amides . . . . . . . . . . . . . . 165 13C Chemical shifts,spin-1attice relaxa- tion times (T ) and nuclear Overhauser enhancements iNOE) of N,N-diethylamides 168 14 13C Chemical shifts, spin-lattice relaxa- tion times (T1) and nuclear Overhauser 13 enhancements (NOE) of other symmetrically N,N-disubstituted amides . . . . . . . . 171 13C Chemical shifts, spin-lattice relaxa- tion times (T1), cis-trans isomer ratios 15 and nuclear Overhauser enhancements of N-monosubstituted amides. Derived values of the effective correlation times To, and of the dipolar (T1(DD (T1(O)) contributions to T1, are included 183 13C Chemical shifts, spin-lattice relaxa- tion times (T1), cis/trans isomer ratios )) and other 16 and nuclear Overhauser enhancements (NOE) of N14-n-buty1formamide and le-n-butyl— formamide. Derived values of the effective correlation times Tc, and of the dipolar (T1(DD)) and other (T1(O)) contributions to T1, are included . . . 186 13C Chemical shifts spin-lattice relaxation times(T1) and nuclear Overhauser enhancements of unsymmetrically N,N-disubstituted amides . . . . . . . . 194 17 nu n IU-‘u A" All! I NA .5 nl‘ Table 18 19 20 21 22 23 24 25 26 27 14N Spin-lattice relaxation times (T1) and quadrupole coupling constants in some amides . . . . . . . . . . . . . . . Temperature dependence of the 14N spin— 1attice relaxation time in N-ethyl- formamide . . . . . . . . . . . . . . . . Experimental l3C chemical shifts, spin- lattice relaxation times T1’ and nuclear Overhauser enhancements NOE, in the N-alkylacetanildes. The derived . values of the dipolar and other contribu- tions to the spin-lattice relaxation t1mes, T1(DD) and T1(O)’ and of the effective correlation times, are also given 0 O O O O O O O O O O O O O O I O O 13C Chemical shifts spin-lattice re- laxation times(T1) and nuclear Overhauser enhancements(NOE) of N- alkylformanilides . . . . . . . . . . . . Anisotropic rotation of the N-phenyl group in N-alkyl acetanilides and formanilides . . . . . . . . . . . . .p. Chemical shifts of 14N, 15N, 17O and 13C = O in some symmetrically N,N-disub- stituted amides. Experimental values of the energy barriers (Ea) restricting rotation about the central C-N bonds of these amides are also shown . . . . . . . 14N Chemical shifts for some other amides 13C Chemical shifts and spin-lattice relaxation times of some amides as assign- ed in the literature . . . . . . . . . Proton chemical shifts in some amides . . Chemical shifts and spin-lattice relaxa- tion times of some amides measured in this work . . . . . . . . . . . . . . . . xi Page 201 203 208 210 220 225 242 250 252 254 Table 28 29 30 31 32 33 34 35 36 37 Page The dependence of residual C-H coupling constants Jr on the decoupler offset frequency, and the calculated hydrogen chemical shifts 6H in some amides . . . . 262 13C Chemical shifts of the carbons in N,N-dimethylacetamide (DMA) and in cyclohexane for solutions of DNA in cyclo- hexane of various concentrations . . . . 272 Calculated 13C chemical shifts(in the slow exchange region)between the NCH3 resonances in monomer and dimer,and the association equilibria,of some amides in nonpolar solvents . . . . . . . . . . . . 281 13C Chemical shifts of the carbons of N,N-dimethylacetamide (DMA) and of formamide in solutions of different con- centrations . . . . . . . . . . . . . . . 284 Concentration dependence of the 13C relaxation times of the carbons of DMA in N,N-dimethylacetamide-formamide mixtures . . . . . . . . . . . . . . . . 291 13C Chemical shifts of the carbons of N,N-dimethylformamide in various DMF- benzene mixtures . . . . . . . . . . . . 294 Calculated 13C Chemical shifts for DMF- benzene mixtures . . . . . . . . . . . . 303 Temperature dependence of the 13C spin- lattice relaxation times of the three carbons of DMF in a 2.77 x 10-4M solu- tion of MnCl2 in N,N-dimethylformamide . 316 Experimental 13C spin-lattice relaxation rates for the carbons of DMF in N,N— dimethylformamide solutions of Mn++ at 34.5°C . . . . . . . . . . . . . . . . 317 Temperature dependence of AvP and 1/T2P for the three carbons of DMF in a solution of MnClzin N,N-dimethylformamide which is 2.77'x 10'4M in an+ . . . . . . 321 xii Table 38 39 4O 41 42 43 44 45 46 47 Page Parameters calculated from the experi- mental relaxation and contact shift data for Mn++ in DM‘ 0 I O C O O O O O O O O O 32 6 Calculated charge distributions for formamide (in electronic units) . . . . . 338 Calculated charge distributions in N- methylacetamide (in electronic units), a model for the peptide bond . . . . . . . 339 Claculated energy barriers restricting rotation around the peptide bond (in kcal/mole). . . . . . . . . . . . . . . . 341 Standard bondlengths (in Angstrom units). 343 Standard atomic geometries and bond angles . . . . . . . . . . . . . . . . . 344 INDO input parameters . . . . . . . . . . 364 Total energies for various conformations of several amides by INDO method . . . . 368 Energy barriers for rotation about various bonds in some amides . . . . . . 377 Charge distributions in formamide and N-methylacetamide (in electronic units) calculated by the INDO method . . . . . . 396 xiii Figure 10 11 12 13 LIST OF FIGURES Page Precession of an ensemble of vectors without or with a radiofrequency field (H1) 0 o o o o o o o o o o o o o o o o 0 11 The effective field in the rotating co- ordinates:(A) off resonance,(B) at resonance . . . . . . . . . . . . . . . 18 Relaxation in the rotating frame of reference . . . . . . . . . . . . . . . 20 Free induction decay . . . . . . . . . . 23 The components v(t) and u(t) of the transverse magnetization in the rotating coordinates for the off-resonance case (ml-wo=m#0) o o o o o o o o o o o 27 Energy level diagram and transition probabilities for a two-spin system without J coupling . . . . . . . . . . . 50 CFT-ZO functional block diagram . . . . 92 Set-up for temperature measurement in the OFT-20 NMR spectrometer . . . . . . . . 94 Inversion-recOvery sequence . . . . . . 95 Computer fit of data for determining the 130 T1 of the trans-NQH3 in N,N-dimethyl- formamide by the inversion-recovery method 97 Homospoil pulse sequence . . . . . . . . 98 Measurement of T1 for 13C in the NCH3 groups of N,N-dimethylformamide by the inversion-recovery method . . . . . . . 102 Measurement of 13 C Tl values for the NCH3 groups in N,N-dimethylformamide by the homospoil pulse sequence . . . . . . 103 xiv Figure 14 15 16 17 18 19 20 21 22 23 24 25 Determination of the 13C Tl relaxation times for the NQH3 groups in N,N- dimethylformamide by the progressive saturation method . . . . . . . . . . . . l3C Tl relaxation times for the NQH3 groups in N,N- dimethylformamide by the -[90° - t - 90° - AT]- pulse sequence . . . . . . . . Measurement of the 13C relaxation times T1 for the N—CH3 groups of N,N-dimethyl- formamide by the variable-nutation- angle method . . . . . . . . . . . . . . Determination of the Nuclear Overhauser enhancement of coupled spectra by the gating technique . . . . . NOE measurement for 13C of the C = 0 group in N,N-dimethyl-n-butyramide . . . Block diagram of the DA-60 multi-nuclear NMR spectrometer . . . . . . . . . . . . Sample tubes for CFT-ZO NMR spectrometer Coordinates for the orientation of the relaxation vector r in the diffusion ellipsoid C O O O O O O O O O O O O O O 0 Estimated dimensions of various protein molecules as seen in projection . . . . . The relaxation in an axially symmetric ellipsoid compared to that in a sphere of the same volume as a function of the axial ratio 9 = b/a for particles obey- ing the Stokes approximation . . . . . . Relaxation rates of 13C in the trans- and Cis-NCH3 groups of N,N-dimethyl- formam1de . ' O O O O O O O O O O O O O O The preferred rotation axis for molecular motion in N,N-dimethylfcrmamide . . . . . XV Page 104 105 106 108 110 111 123 130 132 135 138 139 Figure Page 26 Preferred rotation axes for molecular motion of N,N-dimethylpropionamide and N,N-dimethyl-n-butyramide . . . . . . . . 140 27 Calculated ratio of the relaxation rates for 13C in the cis- and trans-NCH3 groups plotted versus p = DH/Dl for DMF . . . . 144 28 Calculated ratio of the relaxation rates 13 for C in the cis- and trans-NCH3 groups of N,N-dimethylpropionamide and N,N- dimethyl-n-butyramide plotted versus p = DII/D-L O O O O O O O O O O O O O O O O 145 29 Internal diffusion constants R for the trans- and cis-NCH3 groups of N,N- dimethylformamide, N,N-dimethylpropion- amide, and N,N-dimethyl-n-butyramide . . 148 30 Plot of ln(l/T1) versus 1/T x 103 for 13C of N,N-dimethylformamide . . . . 152 31 Plot of ln(1/T1) versus 1/T x 103 for 13C of N,N-dimethylacetamide . . . . 154 32 Plot of 1n(1/T1) versus 1/T x 103 for each carbon of N,N-dimethylpropionamide . 156 33 Plot of 1n(l/T1) versus 1/T x 103 for each carbon of N,N-dimethyl-n-butyramide 158 34 Various components of the total 13C re- laxation rates for the -NCH groups of N,N-dimethylamides plotted aersus mole- cular weight . . . . . . . . . . . . . . 163 17 eaCh each dimethylformamide by the inversion- recovery method . . . . . . . . . . . . . 166 36 Relaxation rates of 13C in the C = 0 group of N,N—dimethylacetamide, N,N- dimethylpropionamide, N,N-dimethyl-n- butyramide, N,N-diethylacetamide, N,N- diethylpropionamide, and N,N-diethyl- n-butyramide plotted versus molecular weight . . . . . . . . . . . . . . . . . 173 35 Determination of T1 for xvi _- p- I-n-n' oovlai .1. H I... '58 ‘QA A‘- ' ‘ll Figure Page 37 Relaxation rates of 13C in the C = 0 groups of N,N-dimethylpropionamide, N,N-diethylpropionamide, and N,N- diisopropylpropionamide plotted versus molecular weight . . . . . . . .4. . . . 175 38 Relaxation rates of 13C in the C = 0 groups of N,N-dimethylformamide, N,N- diethylformamide, and N,N-di-n— propylpropionamide plotted versus molecular weight . . . . . . . . . . . . 176 39 Relaxation rates of the a and B carbons of the carbonyl substituents of N,N- dimethylpropionamide, N,N-diethyl— propionamide, and N,N-diisopropyl- propionamide plotted versus molecular weight . . . . . . . . . . . . . . . . . 179 13C relaxation rates for the carbons-of the N-methyl groups of N-methylformamide, N-methylacetamide, and N-methylpropion- amide plotted versus molecular weight . 192 40 41 Relaxation rates of the a-carbon and B-carbon of the N-ethyl group of N- ethylformamide, N-ethylacetamide, and N-ethylpropionamide plotted versus mole- cular weight . . . . . . . . . . . . . . 193 42 Preferred rotation axis for the molecular motion of N-n-butyl-N-methylformamide in the conformer with the n-butyl group trans to the C = 0 group . . . . . . . . 197 43 Plot of 1n(1/T1)versus l/T x 103 for 14N in N-ethylformamide . . . . . . . . . . 204 44 Relaxation rates of the quaternary car- bon on the N-phenyl group and the carbon of the C = 0 group in N-methyacetanilide, N-ethylacetanilide, N-propylacetanilide, and N-n-butylacetanilide, plotted versus molecular weight . . . . . . . . . . . . 215 45 Relaxation rates of the carbonyl-EH3 carbon in N-methylacetanilide, N-ethyl- acetanilide, N-propylacetanilide, and N-n-butylacetanilide, plotted versus molecular weight . . . . . . . . . . . . 216 xvii Figure Page 46 Relaxation rates of the meta, ortho, and para carbons of the N-phenyl groups of N-methylacetanilide, N-ethylacetanilide, N-propylacetanilide, and N-n-butyl- acetanilide, plotted versus molecular weight . . . . . . . . . . . . . . . . . 217 47 Calculated ratios T p O 1(O,m)/Tl(p) versus R/D (for benzene ring geometry with 60°) 0 o o o o o o o o o o o o o o o 218 48 Correlations between the chemical shifts 615 and 614 for N,N-d1methylam1des and N,NEdiethylaNides . . . . . . . . . . . 226 49 Correlations between the chemical shifts 615 and 513 for the series of N,N- N C(=0) dimethylamides and N,N-diethylamides . . 232 50 Correlation between Ea and 615 for N,N- dimethylamides . . . . . . . .N. . . . . 234 51 Correlations between the chemical shifts 5 and 6 for a series of N,N-dimethy- 15N l7O amides and a series of N,N-diethylamides 240 52 The dependence of the residual C-H coupling constants J on the decoupler offset frequency D0 in N,N-dimethyl— formamide . . . . . . . . . . . . . . . 257 53 The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N,N-dimethyl- acetamide . . . . . . . . . . . . . . . 258 54 The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N,N-dimethyl- propionamide . . . . . . . . . . . . . . 259 55 The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N,N-dimethyl- n-butyramide . . . . . . . . . . . . . . 260 xviii Figure 56 57 58 59 6O 61 62 63 64 65 Page The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N-n-butyl-N- methylformamide . . . . . . . ',' . . . . 261 1H-NMR spectra (00: 60MHZ) of N-n- butyl-N-methylformamide (A) and N-n- butyl-N-methylacetamide (B) . . . . . . . 265 Completely decoupled 13C NMR spectra of N-n-butyl-N-methylformamide . . . . . . . 265 Off-resonance decoupled 13C NMR spectra of N-n-butyl-N-methylformamide . . . . . 267 Concentration dependence of the 13C chemical shift of the C = 0 group of DMA in cyclohexane solutions . . . . . . . . 273 Concentration dependence of the 13C chemical shifts of the cyclohexane and of the carbonyl methyl carbon of DMA in DMA-cyclohexane mixtures . . . . . . . . 274 Concentration dependence of the 13C chemical shifts for the carbons of the trans- and cis-NCH3 groups of DMA in various DMA-cyclohexane mixtures . . . . 275 Concentration dependence of thezcalculated and experimental chemical Shift differences (AmNCHB) between the two NCH3 carbon signals of DMA in cyclohexane-DMA mixtures.277 Concentration dependence of the 13C chemical shift of the carbonyl carbon of DMA in DMA-formamide mixtures . . . . . 285 Concentration dependence of the 13C chemical shift of the carbonyl carbon of formamide in DMA-formamide mixtures . . 286 xix sauna fbvv VF 1 Id: fp- Figure Page 13 66 Concentration dependence of the C chemical shifts of the carbons of the trans-NCHB, cis-NCH3, and carbonyl-CH3 groups of DMA in DMA-formamide mixtures 287 67 Concentration dependence of the 13C chemical shift difference between the carbons of the C = 0 groups in DMA and formamide, and the Chemical shift dif- ference between the carbons of the trans- and gistCH3 groups . . . . . . . 288 68 Concentration dependence of the 13C Chemical shifts of the carbon of the DMF C = 0 group and the carbons of benzene in DMF-benzene mixtures . . . . . . . . 296 69 Concentration dependence of the 13C chemical shifts of the carbons of the trans- and gistCH groups of DMF in . 3 DMF-benzene mixtures . . . . . . . . . . 297 70 Concentration dependence of the 13C chemical shift difference between the carbons of the trans- and cis-NCH3 groups of DMF in DMF-benzene mixtures . 298 71 Concentration dependence of the cal- culated and experimental chemical shift differences (AwNCH ) between the two- 3 NCH3 13C signals of DMF in DMF-benzene mixtures . . . . . . . . . . . . . . . . 301 72 Computer fit of the temperature variation of the experimental relaxation rate T.1 for the carbon of the trans- 1P NCH3 group in N,N-dimethylformamide . . 318 73 Computer fit of the temperature varia- tion of the experimental relaxation rate 1/T1P for the carbon of the cis-NCH3 group in N,N-dimethylformamide . . . . . 319 XX - v'r‘ uni-b Kl, Figure Page 74 Computer fit of the temperature varia- tion of the experimental relaxation rate -1 TlP in N,Pbdimethylformamide . . . . . . . . 320 for the carbon of the carbonyl group 75 Computer fit of the temperature variation of the experimental relaxation rate TI; for the carbonyl carbon in N,N- dimethylformamide . . . . . . . . . . . 322 76 Temperature variation of the experimental contact shifts, AVP, of the carbons of N,N-dimethylformamide in a solution 2.77 x 10'4 M in an+ . . . . . . . . . 323 77 Structure of the solvation complex of Mn2+ in N,N-dimethylformamide . . . . . 327 78 Conformations of various amides (6-1) for INDO calculations . . . . . . . . . 365 79 Comparison of the energy barriers for rotation about the peptide bond in N, N- dimethylformamide, N ,N-dimethylacetamide, and N ,N-dimethyltrifluoroacetamide . . . 374 80 Comparison of the energy barriers for rotation about the peptide bond in N,N- dimethylformamide and N-methyl-N-ethyl- formamide . . . . . . . . . . . . . . . 380 81 Comparison of the energy barriers for rotation about the peptide bond in formamide, N-methylformamide, and N,N- dimethylformamide . . . . . . . . . . . 381 82 Variation of the energy for rotation of -CH3 in the N-CH3 group of N- methylacetamide ... . . . . . . . . . . 382 83 Variation of the energy for rotation of -CH3 in the N-CH3 group of N-methyl- acetamide . . . . . . . . . . . . . . . 382 xxi nli I ...v it‘d 91 a d Ill“ A114 - 11- Figure Page 84 Energy variation for rotation of -CH3 in the N-CH3 group of N-methylacet- amide . . . . . . . . . . . . . . . . . . 383 85 Energy variation for rotation of -CH3 in the carbonyl-methyl group of N—methyl- acetamide . . . . . . . . . . . . . . . . 383 86 Energy variation for rotation ofi-CH3 in the carbonyl-methyl group of N- methylacetamide . . . . . . . . . . . . . 384 87 Energy variation for rotation of -CH3 in the carbonyl-methyl group of Nemethyl— acetamide O O O O O O O O O O 0 O O I O 0 384 88 Three-dimensional energy surface for N-methylacetamide as a function of the dihedral angles of the N-methyl (¢2) and the carbonyl-methyl (O1) group . . . . . 385 89 Variation of energy with rotation of the carbonyl-methyl group in N,N-dimethyl- acetamide . . . . . . . . . . . . . . . . 389 90 Energy variation for rotation of the carbonyl-CF3 group in N,N-dimethyl- trifluoroacetamide . . . . . . . . . . . 390 91 Energy variation for rotation of the N-ethyl group about the N-C(H2) bond in N-ethylfOrmamide in both the ground equilibrium geometry and transition geometry . . . . . . . . . . . . . . . . 391 92 Energy variation for rotation of the N-ethyl group about the N-C(H2) bond in N-ethylacetamide in both the ground equilibrium geometry and transition geometry . . . . . . . . . . . . . . . . 392 93 Energy variation for rotation of the N-methyl group about its threefold axis by angle ¢3 in N-methylformamide in the ground equilibrium geometry and in the last transition geometry. . . . . . . . . 393 xxii Figure Page 94 Energy variation for rotation of the N-CH3 group in the transition geometry and in the ground equilibrium geometry of DMF . . 394 95 Energy variation for rotation of the N-CH3 group in the transition geometry and in the ground equilibrium geometry of DMF . . . . . . . . . . . . . . . . . 394 96 Variation with 8 of the partial charges on the atoms of formamide . . . . . . . 398 97 Variation with 8 of the partial Charges on the atoms of N,N-dimethylformamide . 399 98 Variation with 8 of the partial Charges on the atoms of N,N-dimethylacetamide . 400 99 Variation with 8 of the partial charges on the atoms of the peptide bond in N,N-dimethyltrifluoroacetamide . . . . . 401 100 Variation with 8 of the partial charges on the atoms of the peptide bond of N-methyl-N-ethylformamide . . . . . . . 402 101 Variation with ¢3 of the partial charges on the atoms of the N-CH group of N,N- dimethylformamide,p’2 = 3° . . . . . . . 404 102 Variation with O3 of the partial charges on the atoms of the N-methyl group of N,N-dimethylformamide,‘82 = 60°. . . . . 405 103 Variation with ¢2 of the partial Charges on the atoms of the N-methyl group of N,N-dimethylformamide,‘83 = 0° . . . . 406 104 Variation with ¢2 of the partial charges on the atoms of the N-methyl group of N,N-dimethylformamide, g3 = 60° . . . . 407 105 Variation with ¢3 of the partial charges on the atoms of the N-methyl group of N-methylformamide . . . . . . . . . . 408 xxiii Figure Page 106 Variation with ¢1 of the partial charges on the atoms of the carbonyl-methyl group of N-methylacetamide . . . . . . . . . . 409 107 Variation with ¢l of the partial charges on the atoms of the carbonyl-methyl group of N-methylacetamide . . . . . . . . . . 410 108 Variation with ¢1 of the partial Charges on the atoms of the carbonyl-methyl group of N-methylacetamide . . . . . . . . . . 411 109 Variation with ¢2 of the partial charges on the atoms of the N-methyl group of N-methylacetamide. fll = 0 . . . . . 412 110 Variation with ¢2 of the partial charges on the atoms of the N-methyl group of N-methylacetamide. 81 = 30° . . . . . 413 111 Variation with ¢2~Of the partial charges on the atoms of the N-methyl group of N-methylacetamide. d = 60° . . . . . 414 112 Variation with ¢1 of the partial charges on the atoms of the carbonyl-methyl group Of DMA O O O O O O O O O O O O O O O O O 415 113 Variation with ¢1 of the partial Charges on the atoms of the carbonyl-CF3 group of N,N-dimethyltrifluoroacetamide. . . . 416 114 Variation with ¢3 of the partial charges on the atoms of the N-ethyl group of trans-N-ethylformamide . . . . . . . . . 417 115 Variation with ¢3 of the partial charges on the atoms of the N-ethyl group of cis-N-ethylacetamide . . . . . . . . . . 418 116 Qualitative description of the energy levels of a typical peptide bond in the conjugated and unconjugated geometries . 422 xxiv PART I NUCLEAR MAGNETIC RESONANCE STUDIES OF AMIDES INTRODUCTI ON Nuclear magnetic resonance spectrosc0py has developed rapidly into a major spectroscopic technique during the last ten years or so. The applications of high-resolution NMR in chemistry are numerous and are growing at an almost exponential rate. In recent years NMR has undergone a revolutionary Change in technique from swept continuous-wave to pulsed excitation. With the development of pulsed Fourier transform NMR tech- niques and the use of heteronuclear decoupling, the signal-to-noise of the observed nuclei can be increased by 2-3 orders of magnitude over the older methods. This increase in sensitivity has made 13C NMR almost routine work in many laboratories. Recently, the quadrature detection and the phase-alternating pulse sequence techniques have also been used to increase the sensi- tivity of 15N and 120 signals so that these nuclei can now be observed routinely in natural abundance. The properties of the amide bond have received considerable attention because of its importance in determining secondary and tertiary structure in peptides and proteins. In Part I of this dissertation, several 1 ~ v .0 \. :0- 5‘.. u 1" Ion‘ ... \ u.‘ :... (I) ‘1 1” (I! different properties of amides are studied by 13C, 14N, 15N and 170 NMR. A theoretical section is presented first to familiarize the reader with the basic theories of pulsed and continuous-wave NMR, the nuclear Overhauser effect, double resonance experiments, and Chemical shifts. The historical section covers the various known relaxation mechanisms and methods for extraction of the microscopic parameters of interest from the experimental measurements. A section describing the experimental techniques and methods for data interpretation follows. The main portion of Part I has been separated into seven sections. The first three sections comprise a study of the molecular motion of symmetrically N,N-disubstituted amides, of N-monosub- stituted amides and unsymmetrically N,N-disubstituted amides, and of N-alkyl anilides, respectively. To this end, the 13C spin-lattice relaxation times and NOE effects have been measured. In the fourth section, various correlations of 14 15 17 13 the Chemical shifts of N, N, O and C (of the Carbonyl group) in the amido groups of N,N-dimethyl amides rand N,N-diethyl amides are presented, as well as correla- 1Zions between the energy barrier restricting rotation about the C-N partial double-bond and the 15 13 N and carbonyl Silsoup C Chemical shifts. The fifth section outlines 13 title determination of proton chemical shifts by the C off- lteesonance technique and the reassignment of proton and Au» V g . D .3 H. .4. 8 u '\ carbon chemical shifts in some amides. The sixth section reports the solvent effects on some amides by 13C NMR. The last section in this part describes a series of experi- ments designed to investigatetfluasolvation of Mn2+ in N,N-dimethyl formamide. Part two of the thesis consists of theoretical studies of some selected amides by the intermediate neglect of differential overlap (INDO) method. In this part, a brief description of molecular orbital theories and approximate molecular orbital theories are presented initially. An historical section presents the bond length, bond angles and dihedral angles used in these calculations, along with some results of the CNDO/Z and EHT methods. The calculated results relate the energy barrier for rota- tion about the C-N bond to the charge distribution in the amido group as the amide is twisted from the ground state goemetry to the transition state configuration. NUCLEAR MAGNETIC RESONANCE THEORY 1. Introduction to NMR Theory It is well known from elementary nuclear magnetic resonance theory1 that the possession of both spin and charge confers on the nucleus a magnetic moment Er given by E=Ylfi=gslt (1) where Y is the magnetogyric ratio, which is charac- o a o o I -1 ter1st1c of each nucleus and 13 measured 1n radians sec gauss-l, g is the nuclear g factor and I is the nuclear spin quantun number . B is the nuclear magneton, which is equal to efi/ZMC, where e and M are, respectively, the charge and mass of the proton, C is the velocity of light, and‘h’is Planck's constant divided by 2n. When the nucleus is placed in an external magnetic field Ho' there are 21+l energy levels available, each correspond- .ing to a different component of the angular momentum. {Phe allowed components of angular momentum along Ho have 1:he values m = I, I-l,...,-I (in units of‘fi) and its energy levels have the values E = -y‘h m Ho. The Selection rule is Am = i 1 so the energy difference AE between two levels is (I: [ll (1 F! (D if A E = u Ho/I = y fi'Ho’ (2) Nuclear magnetic resonance occurs when transitions take place between these levels. This can occur by the absorp- tion of photons from an oscillating external field having the correct polarization and satisfying the frequency con- ditions in the above equation or Vo = y Ho/ZN, (3) where v0 is the frequency of radiation from an external field which is absorbed by the nuclear spin system. Con- tinuous irradiation by the rf field Hl would cause all nuclei to precess around Ho' and no further absorption of energy would occur if there were no other process at work to restore the energetically favored orientation of the spins. In fact, continuous energy absorption from radiofrequency fields due to nuclear magnetic resonance is observed over a long period if the rf power is not too high. The processes responsible for this are referred to as relaxation. At equilibrium, nuclei are distributed among the energy levels according to the Boltzmann distribution, ‘which favors the lower state. For the two orientations irelative to Ho of nuclei with I = 1/2, the spin popula- ‘tions may be symbolized Na and NB' The distribution Iqu/NB can be expressed by the Boltzmann factor, and re- calling that A E = u HO/I = ZuHO (I = 1/2). eAE/kT Na/NB = z 1 + AE/kT = 1 + ZuHo/kT . (4) For carbon nuclei in an external magnetic field of about 20 kG at room temperature, Na/NB is of the order of 1.00000345. Consequently the populations of the two spin states differ by only 3.5 ppm and so the nuclear resonance absorption is very weak. II. NUCLEAR RELAXATION - GENERAL THEORY A. Spin-lattice relaxation At resonance, the rf field H1 causes the transfer of spins from the lower to the higher energy level. The equilibrium distribution of the spins in the static field H0 is disturbed. Following any process that disrupts this distribution, the nuclear spins will relax to equili- brium with their surroundings (the lattice) by a first- order relaxation process characterized by a time constant T1, the spin-lattice relaxation time. Observed values of 4 to 10+4 sec. This constant T1 cover a range of about 10- reflects the efficiency of the coupling between the nuclear spin and its surroundings. The shorter this time, the faster equilibrium is attained and the more efficient this coupling is, and vice versa. For liquids with rapid molecular motions, T1 is a measure of the lifetime of a nucleus in a particular state. According to the Heisenberg uncertainty principle .11 \.\ )T > h (5) AE x At = h(Avl 1 _ /2 and the minimum width A V1/2 at half-maximum intensity of an NMR absorption line is 1/2 If W1 and W2 are the transition probabilities of absorp- tion and emission, respectively, and the total number of spins is N, then the approach to equilibrium is described by the following differential equations, ll 2 2 I Z S dNa/dt (7) dNB/dt = N w and at equilibrium dNa/dt = dNB/dt = 0. If n is the population difference between the two nuclear spin states then the following equation can be derived: dn/dt = 2 W N - 2 W 2 B 1Na = N(W2 - W 1) - n(W1 + W2).(8) This equation can be rewritten in the form dn/dt = (n - no)/T1, (9) if no = N(W2 - W1)/(W1 + W2) and 1/T1 = W1 + wz. The solution to Equation (9) is n = no(l - exp(-t/Tl)). (10) IEquation (10) describes the return of the Z component of the magnetization to equilibrium after it has been dis- turbed by the application of a pulse. This relaxation is a nonradiative transition between two energy levels. B. Spin-spin relaxation In solids and liquids with slowly tumbling mole~ cules, internuclear dipole-dipole interactions become important. Furthermore, energy quanta AB = 2uHo are ex- changed between nuclei to a certain degree. Both factors tend to shorten the lifetime of spin states, again leading to line broadening. This second type of first-order relaxation process is called spin-spin relaxation and is Characterized by a time T2. The spin-spin relaxation time reduces the life— time of a nucleus in a particular spin state to T2 5-T1' The linewidth at half-maximum intensity is expressed mOre precisely by AVl/Z = l/flTZ. The observed linewidth of an NMR signal depends additionally on the field in- homogeneity AHO, which contributes to Avl/Z so that ..1 * Av1/2(obs) ’ /"T2 ‘ Av1/2 + Av1/2(inhom ) = l/HT2 + yAHo/Zn. (11) * Thus T2 includes contributions from both the natural linewidth Avl/Z and from the magnetic field inhomogeneity ‘Avl/2(inhom )' C. Comparison of spin-lattice and spin-spin relaxation times (1) Spin-lattice relaxation of nuclei (e.g., 1H, 13C) in a molecule may be accelerated by interaction with (a) adjacent nuclei having spins I :_l (e.g., 2D, 14N, 170), since the electric quadrupole moments of such nuclei result in additional fields in the tumbling mole- cule, and (b) unpaired electrons in paramagnetic compounds (radicals or some metal Chelates). (2) Spin-spin relaxation of nuclei is accelerated when they are bonded to another magnetic nucleus (170-1H, l4N-lH, l3C-lH). This relaxation.involving dipole- dipole interaction.is very effective in solids and in viscous liquids in which molecular motion is slow, since the magnetic fields caused by slowly tumbling dipoles change very slowly. (3) Spin-lattice relaxation occurs via transi- tions which are stimulated by components of the local magnetic field seen by a particular nucleus and which fluctuate at its Larmor frequency. Fluctuations in the local magnetic field are generated by variations in Hdipolar caused by changes in r and 8 resulting from JBrownian motion. Hdipolar is given by H = u /4r3(3 cos28 - l) (12) dipolar z ' 10 where r is the distance of the first dipole from the second dipole and 8 is the angle between the axis of the first dipole and the line joining their centers. This dipole-dipole effect, due to the term r3, is a local one and the average value of the Hdipolar field is zero. However, at any particular time, the dipolar field is not necessarily zero. Spin-spin relaxation also occurs through local magnetic fields, but in a different way. If one nucleus undergoes a transition from one spin state to another, then changes of H10C at the correct frequency will in- duce a transition in a second nucleus. If at this particular time a second nucleus of the same type and the opposite spin state is close by, then the two nuclei can in effect exchange energy. Such a process is not of the spin-lattice type as the total syStem energy is conserved. A process of this type, however, does affect the lifetime of the excited state, hence the resonance linewidth. Spinespin relaxation is an entropy effect, as opposed to spin-lattice relaxation which is an energy effect. The spin-spin relaxation time can be defined as the lifetime or phase memory of the excited spin state. The relationship between T and T can be 1 2 ‘visualized by a vector model as shown in Figure 1. In ‘this model the nuclei are considered as vectors. In 'the presence of only an external field Hz, the spin .mpasmms soapMNHposwae .M ..x pm: a use cocouonoo amuse Sweeps op whosoo> on» momsmo .hoSosoonm economou one no monopou sown: .oao«H a: so no soapmonann< Amy .coepoonao N on» :a haze soupwaupocwos no: a mmozoosn Osman .m.x on» as manage scones new: muovoo> no masseuse so no cowomooonm A = = 0. If now an exciting field H is applied precisely at the Larmor 1 frequency of the nuclei, then resonance occurs and they attain phase coherence as shown in Figure l-B. MX and My become finite and M2 decreases appropriately. An alternative description, and perhaps a similar one, can be given using the idea of a rotating frame of coordinates which will be discussed later. On the removal of H1, Mz returns to its original value at the spin-lattice relaxation rate, however Mx and My relax exponentially at a different rate, responding to any process which changes phase coherence of the vectors but not the total energy of the system. The constant T2 can thus be defined by the following equations: dMy/dt = -My/T2 and de/dt = -Mx/T2. (13) Equations (9) and (13) illustrate the origin of the alternative names for T1 and T2 which are, respectively, the longitudinal and transverse relaxation times. So local magnetic fields fluctuating at the Larmor frequency can contribute to both T1 and T2 relaxation process. Static magnetic field, however, can only contribute to 13 transverse relaxation. It is thus not surprising that T must be equal to, or shorter than, T In normal 2 1' liquids T1 and T2 are often equal, though this depends in detail on the molecular motions involved. In solids, however, particularly at low temperatures, Tl may be very long due to the lack of any suitable molecular motion, while T may be short due to static dipolar 2 fields. In changing from liquids to solids there are changes in the absolute and relative values of T1 and T2. Hahn2 experimentally observed the effect of a single radiofrequency pulse applied to a spin system as had been suggested by Bloch3. The pulse experiment is basically quite different from the continuous wave (cw)4 experiment, since it depends upon the behavior of the spin system monitored just after the application of a single rf pulse, rather than its being observed duringthe con- tinuous application of low-level rf energy. Since pulse techniques are now used almost exclusively in sophiscated NMR instrumentation, the following discussion will mainly focus on the theory of pulse techniques. III. Phenomenological Theory A. The Bloch quations (l) The motion of the magnetization vectors in a laboratory coordinate system The earliest treatment of the magnetic resonance zahenomenon is that of Bloch3'4. He used a vector model 14 and treated the assembly of nuclear spins in macroscopic terms. The starting point in his theory is the classical equation of motion of a magnetic field Ho. Upon irradia- tion with a rf field H1 at resonance, transitions between the nuclear magnetic energy levels occur. The nuclear spins change their directions relative to H0. The direction of the angular momentum P is now time dependent, as shown in the equation dP/dt = g X H, (14) where H is the total field resulting from the static field Ho and the rf field H By multiplying Equation 1. (14) by the magnetogyric ratio y, one obtains d_u_/dt = Y g x a. (15) where E = yp. If M_is the vector sum of the E's, its time dependence is given by dM/dt = y M x g. (16) The vector product M'x H can be expressed in terms of the components along the three Cartesian coordinates (x,y,z) and the unit vectors along these axes (1,1,5), M.x Hx i y y = (MyHz — MzHy)i + (MZHX - Mtz)l (l7) l: x IE: II :1: IW F4 + (M H - M H )k x y y x — In TT 5. ‘s 15 and the time derivative of M is dM/dt = de/dt i + dMy/dt l + sz/dt k . (18) A comparison of Equations (17) and (18) yields de/dt = y (Msz - MzHy) dMy/dt = y (MZHX - MXHZ) (19) sz/dt = y (MXHY - MyHX) . The field components Hx’ Hy, and H2 can be expressed in terms of the static field HO and the alternating field H1: HX = Hl cos wt, Hy = -Hl Sin wt, Hz = Ho' (20) where w is the angular velocity of the rf field H1 in the xy plane. By combining Equations (19) and (20), one obtains Equations (21) describing the motion of the components of the magnetization vector produced by the fields HO and H1 (without considering relaxation) de/dt = y (MyHo + MzHl Sln wt) dMy/dt = y (MZH1 cos wt - MxHo) (21) sz/dt = y (Mle Sin wt + MyHl cos wt). In order to include spin-lattice relaxation and spin-spin relaxation, the Bloch equations in the final form are modified to give 16 de/dt sin wt) - Mx/TZ y (MyHO + MzHl dMy/dt = Y (MzHl cos wt - MXHO) - My/T2 (22) = - ' — ll — sz/dt y(MxH1 Sin wt + MyHl cos wt) (Lz Mo)/Tl° (2) The motion of the magnetization vector in the rotating coordinate system The path of the magnetization vector M subjected to magnetic fields will be simplified in a coordinate system rotating at the angular velocity w of the rf field H1. In the rotating coordinate system Equation (16) becomes (cit_n_a_/<3u:)r0t = Y M x A — 93 x pg . (23) where g_is the angular velocity of the three unit vectors in the rotating coordinate system. Rearranging Equation (23), we obtain (OE/Ot)rot = Y E! X £1- + ‘Y £4- x Q/Y = Y E x (a + _w_/'Y). (24) The term g/y has the dimensions of a magnetic field and can be treated as a "fictitious" field that arises from the effect of the rotation. If we define the effective = g + fl/Yr then field Eeff (GE/5t)rot = Y E x geff ' (25) 17 Thus, in the rotating frame of reference the net magnetiza- tion M precesses about Eeff' B. NMR in the rotating frame of reference Suppose the magnetization M precesses about the effective field Me in a coordinate system rotating with ff frequency w = 2nv about the z axis and symbolized as the x',y',z' frame of reference with rotating unit vectors i', '1', and M}. (A) In the absence of H the magnetization vector M keeps 1’ its equilibrium value and orientation MO in the z direc— tion. M is thus time invariant in the rotating coordinate system, so that Equation (25) is equal to zero, and con- sequently Me f = 0 since M = Mo # 0. If the frame rotates f at the Larmor frequency mo vao, then w/Y = wo/y, since the effective field is zero, and the Larmor equation is thus Eeff = (Ho + wo/y) = 0, so that mo = -y H0. This means that the rotational field w/y opposes Ho M1 in the rotating coordinate system, Figure 2(A), finally cancelling Ho M' when the coordinates rotate at the Larmor frequency, w . O (B) If an rf field Ml, with wl = 2nvl, pendicular to H0 along the z' axis, the effective field is applied per— Eeff in the coordinate system rotating at ml is = u i -'c fleff (Ho + wl/Y) 15. + H1 .1. - (26) 18 .oosasouou as A5 Jonas—ouch who ASESMCESOO msupmpoh 05 5.. came.“ 3.3005: 23. .N 0.3.»: >.FNfl3 (I 19 If the coordinate system rotates at an rf frequency 01 matching the Larmor frequency v0, the term (HO + wl/y) M' becomes zero. The remaining effective field at resonance is now H £1 so that Equation (25) becomes Eeffires) = 1 (GM/6t)rot = y M x H1 1 . (27) This relation tells us that at resonance the vector M precesses about the field vector H i', Figure 2(B). 1 Since the coordinate system and H1 are chosen to rotate at the same frequency, Hl lies along the rotating X' axis. According to Equation (27) the vector M will precess about the x' axis and the precession frequency ml of M about the X' axis is ml = y H1. Thus, an rf field Hl applied at resonance for tp seconds, causes the vector M_to precess about the X' axis by an angle 8, where wl tp = y H1 tp (rad). (28) If only H0 is applied, the nuclear moments will precess without any phase coherence. No resultant component of the magnetization in the x'y' plane will be observed and M2 will equal MO, Figure 3(A). A radiofrequency H1 applied perpendicular to Ho forces the nuclei to precess in phase, tipping the vector M0 by an angle 8 toward the y' axis, Figure 3(B). A transverse magnetization My,i' in the x'y' plane arises and the magnitude of M2, de- creases. To restore equilibrium, the nuclei exchange 20 (A) (B) M:’ ~ M0 M1" M0 (D) (C) Figure 3. Relaxation in the rotating frame of reference. (A) only the external field H is applieds(B) a radiofrequency H1 is applied Berpendicular to Ho: (C),(D) dephasing of magnetic moments in the x'y' plane and restoration of magnetic moments in the 2' direction. 21 energy with each other (spin-spin relaxation) and dephase, causing My,j' to spread out in the x'y' plane and finally decay to zero with time constant 1/T2, Figure 3(C,D). Dephasing may be accelerated by the field in— * homogeneity SO that 1/T2(inhom) is greater than 1/T2. Moreover, the nuclear moments lose energy to their surroundings (spin-lattice relaxation), causing MZM' to increase to M0' The decay of the magnitude of trans- verse magnetization My' due to spin-Spin relaxation (T2) * or due to field inhomogeneity (T2) may be faster but can- not be slower than the spin-lattice relaxation time (T1). C. Nuclear induction At resonance the magnetization vector M precesses about the vector Hlifof the rf field according to Equa- tion (27). As a result, a component of transverse magnetization My,jfrotates in the x'y' plane at the Larmor frequency v0. If a receiver coil is placed in the x'y' plane, the rotating magnetic vector My,jfinduces an electromotive force measurable as an induced current. This process is called nuclear induction. The orientation of coil axis will affect the phase relative to H13} but not the magnitude of the induction current. Following Equation (27), the magnetization vector M is rotated toward the y' axis by the oscillation of H1 i' in phase with the x' axis of the rotating frame. The current Iin due to the induced EMF opposes the d 22 inducing magnetization. At resonance, the magnetization vector rotates 90° behind H1 3'. The maximum induction current, however, is observed 90° ahead of H1 i'. In practice it is usual to study a spin system which,in an external field Ho' contains Chemically non- equivalent nuclei each with a different precession fre- quency. In a pulsed NMR experiment, the sample is irradiated by Short,intense rf pulses. The rapid switching necessary to generate such pulses generates Fourier components over the range v0 : l/tp, where v0 is the rf frequency of the instrument and tp is the pulse width. Every frequency component in the range v0 : l/tp is present and any nuclear spin which precesses at a fre- quency within the range is excited by the appropriate frequency. A short rf pulse is therefore equivalent to the simultaneous application of a wide range of rf fre- quencies to the spin system. According to Equation (28), the rf pulse width tp seconds, Figure 4(A), rotates the magnetization vector by an angle 8, Figure 4(B). A transverse component of magnetization My, results. The t as can be 1P seen in Figure 4(B). Following the rf pulse, the trans- magnitude of My' is given by My, = M0 sin w verse magnetization My, decays exponentially to zero via spin-spin relaxation, Figure 4(C). At resonance the magnetization My' always has a phase shift of n/2 relative to the rf field H1 in the 23 Ft?) '9 ”<1— input or. t A H II II II III II II II II I z' 1' sample Y' magnetization X, 2_ C’ H!) —1— F“) Vl'Vo ' a»: (4(- ' l : n I output ’ t q o V1'Vogo vl-VO'O p S. Figure 4. Free induction decay. (A) rf pulse as input signals (B) sample magnetization during the rf pulse: (C) free induction decay following the rf pulse; (D) output for rf at resonance: (B) output for rf off resonance. 24 rotating coordinate system. This is due to the experi- mental arrangement and is not affected by pulsing. Thus, a nuclear induction current Stemming from the decay of My' is built up in the receiver coil following the rf pulse, Figure 4(D). If the rf frequency differs from the Larmor fre- quency of the nuclei to be investigated ("off resonance") the transverse magnetization My' is rotating relative to the coordinate system after the pulse has ended. My' and H1 periodically rephase and dephase, Figure 4(E),1eading to a response analogous to the wiggles observed in cw high- resolution NMR spectra. The spacing between two best peaks is the reciprocal of the difference between the frequency of the pulse and the Larmor frequency l/(v1 - v0). Figure 4(E). The time domain function F(t) arising from the re- laxing spins following an rf pulse is called the free in- duction decay (FID) Signal or the transverse relaxation function (5). Due to Chemical shielding, each nucleus may come into resonance within a range of Larmor fre- quencies sw (sw = spectral width), 2n(sw) w - w, 0 depending on its chemical environment. In order to rotate all nuclear spins within that range by the same angle 8, the strength of the rf pulse must be yn >> 2n(sw). Furthermore, the pulse width must be 1 shorter than the relaxation times,tp << T1,T2, relaxation is negligible during the pulse. so that 25 For a liquid sample containing identical nuclei, the transverse magnetization My will arise from one Larmor frequency, which is actually the maximum of a very small frequency distribution caused by spin-spin relaxa- tion and slight field inhomogeneity. The FID signal F(t) of this sample decays exponentially according to -t/T2 F(t) = F(0)e , where F(O) is the amplitude of the FID signal at the time the pulse has stopped. If a sample contains equivalent nuclei A (e.g., l3C) subject to spin-spin coupling with nuclei X (e.g., 1H), the transverse magnetization will arise from two or more Larmor frequencies, depending on the multiplicity. The corresponding magnetization vectors periodically rephase and dephase with the field vector H1 as in the off- resonance case. The FID signal is thus modulated by the frequency of the coupling constant JAX' Similarly, in a sample containing two non-equi- valent nuclei A1 and A2, the transverse magnetization results from two components due to two Larmor frequencies. In this case, the FID signal is modulated by the chemical shift difference of Larmor frequencies, v = v FID l - v2. signals caused by rf pulses and modulated by spin-spin coupling and chemically shifted Larmor frequencies are referred to as pulse interferograms. In most pulsed NMR experiments, the rf pulse is applied off resonance. 26 Modulated pulse interferograms arise because the vectors of transverse magnetization do not precess with a con- stant phase shift of n/2 relative to the vector H as 1! shown in Figure 5. The transverse magnetization is then the resultant of two components, v(t) with a phase shift of n/2 relative to H1, and u(t) in phase with Hl' where v(t) MO sin 8 cos wt (29) u(t) Mo sin 8 sin wt . In mathematical treatments of FID and NMR signals, F(t) and F(w), it is convenient to use complex quantities. The time domain signal is then defined by F(t) = v(t) + i u(t): where i = +/:I . (30) Combining Equations (29) and (30) yields F(t) = M.o sin 8 (cos wt + i sin wt) (31) or, recalling that iwt e cos wt + i sin wt, (32) F(t) MO sin e elwt. (33) Since NMR spectra are not sequences of lines representing discrete Larmor frequencies but sequences of Lorentizian frequency distributions f(w), Equation (33) must be replaced by 27 Figure 5. The components v(t) and u(t) of the transverse magnetization in the rotating coordinates for the off-resonance case ( uJ1 - won w i O). 28 F(t) = M0 sin 8 f:: f(w) elmt dw, (34) iwt where M.o sin 8 e is multiplied by the frequency f(w), and w represents the difference between ml and the Larmor frequency distribution mo + Aw, w = ml - (mo + Aw). must be integrated over Furthermore, MO sin 8 f(w) elmt the Larmor frequency distribution with limits of integra- tion :9. Equation (34) can be solved by developing it as a complex series of sines and cosines according to Equation (32). This is a Fourier seriesG. Thus, we can say that an exponential in the time domain, F(t) and a Lorentzian in the frequency domain f(w) are Fourier transforms of each other7’8'9. Fourier transformations of pulse interferograms are normally performed in digital computers. Consequently, the FID analog signal must pass through an analog-to- digital converter (ADC). The sampling time during which FID data points must be collected in order to gain the true NMR spectrum after Fourier transformation depends on the spectral width (sw). According to information 10,11 theory , the sweep time per data point, called the dwell time (dw), must satisfy the relation dw ; 1/2(sw). (35) Multiplying the dwell time by the number of data points (dp) to be collected during the FID yields the acquisi- tion time (AT) required for recording the interferogram 29 digitally, AT = ((39) X (dW) ; (dP)/2(SW) - (36) When several pulse interferograms must be accumulated in order to improve the signal-to-noise ratio (S/N), AT is the minimum repetition time between two pulses or the minimum pulse interval. Sometimes, Larmor frequencies not included in sw contribute to the FID signal. This occurs only when partial spectra are desired. All frequencies outside of the spectral width given by Equation (35) at a certain dwell time will be "folded back" within the range sw of the Fourier transformed FID. This is also true for high- and low-frequency noise. In order to avoid folding back peaks in FT NMR spectra, frequency components higher than sw must be filtered be- fore digitization. In order to optimize the pulse interferograms for Fourier transformation, the rf pulse frequency must be set outside the Larmor frequency range to be observed. This requirement is due to the experimental arrangement, which measures frequency difference relative to the rf field using phase sensitive detectors. Positive and negative frequencies relative to the rf frequency cannot be dis- tinguished in the FID. Fourier transformation of an interferogram obtained by an rf pulse of frequency v', which is within the spectral width sw, yields a distorted 30 NMR spectrum in which the frequencies on both sides of the rf pulse overlap. To optimize the FID signal, the pulse width tp must be adjusted for a 90° pulse and the power must also be very strong without saturation, so that yHl << 2 (sw). Combining this relation with Equa- tion (28) gives tp << l/4(sw). (37) Routine Fourier transformations of the FID are achieved in digital computers with a memory size of 4-20 K. The transformation prOgram makes use of the Cooley-Tukey algorithm12'13r14 , which requires a minimum time for multiplications and efficiently uses the computer memory. This computation is called the fast Fourier transformation (FFT) and requires less than one minute for transforming an 8 K interferogram,depending upon the speed of the computer. FFT computation yields both real and imaginary FT NMR spectra, v(w) and iu(w), which are related to the absorption and dispersion modes of cw spectra. These two parts of the complex spectrum are stored in different blocks of the memory and can be dis- played on an oscilloscope to aid in further data manipula- tions. The real and imaginary spectra obtained by Fourier transformation of FID signals are usually mixtures of the absorption and dispersion modes. These phase errors 31 mainly arise from frequency independent maladjustments of the phase detector and from frequency dependent in- fluences such as the finite pulse length, delays in the start of data acquisition, and phaSe shifts induced by filtering frequencies outside the spectral width sw. One method of phase correction assumes a linear dependence of the phase ¢ on the frequency, ¢ = ¢a + ¢bvl (38) where ¢a is the phase at frequency difference zero, and ¢b is the phase shift across the total spectral width from zero to sw Hz. Correction of the real part for absorp- tion mode yields the dispersion mode in the imaginary part and vice versa. The S/N ratio, or resolution of the FID and its Fourier transformation, can be improved by digital filtering. This involves multiplication of the FID with an exponential eiat 15 Negative values of at will enhance the signal-to-noise ratio while causing some artificial line broadening. Positive values of at improve the resolution at the expense of sensitivity. For a dwell time (dw) limited by the spectral width according to Equation (35), the resolution dv of a FT NMR spectrum depends on the number of data points (dp) constituting the digitized FID signal to be transformed, dv = 1/(dp)(dw) = 2(sw)/(dp) Hz. (39) 32 For the S/N improvement of weak signals, FID'S are accumulated many times. According to Equation (36) the minimum repetitive time of an 8 K 13C interferogram at a spectral width 5 kHz is 0.82 sec. "Spin-lattice relaxa- tion times of some 13C nuclei such as quaternary 13C atoms are as long as 100 sec, so that T1 is greater than At. These nuclei cannot relax within the pulse interval. Using the Bloch equations, a steady state will be reached in this casel6, the magnetization is attenuated and the signal strength depends on the ratio of ATVZTl. The S/N ratio of the FID and its Fourier transform will decrease as a result. An obvious way to avoid this attenuation is to add a pulse delay (> 5T1). However, accumulation of pulse interferograms becomes time consuming. A more practical way is to decrease the flip angle 8 below 90° by reducing the pulse width. Restoration of the equili- brium magnetization then requires shorter periods. How- ever, the transverse magnetization is also decreased by reducing the flip angle. The best way to optimize the S/N is to usetfluaso-called driven equilibrium Fourier transform NMR (DEFT NMR). This method involves a three- pulse sequence, 90° - T - 180° - r - 90° with a repeti- tion time tr sec. This sequence refocuses the magnetization vector MO into its equilibrium position within the repetition time17'18'19. 33 D. Comparison between cw and FT NMR As is true of any time-domain function F(t), a square-wave rf pulse of width t can be approximated by P a Fourier series of sines and cosines with frequencies n/2tp (n = 1,2,...)5'6. A pulse of width tp thus stimulates a multifrequency transmitter of frequency range sw = l/4tp. Thus, a tp = 250 usec pulse simul- taneously rotates with MO vectors of all nuclei with Larmor frequencies within a range of at least sw = 1000 Hz. It stimulates at least 1000 simultaneous transmitters, the resolution in the Fourier transform depending on the number of FID data points (Equation (39)), not the stimulating time, tp. During the 250 usec, only 0.5 x 10.6 of a 1 kHz scan is stimulated in a cw experi- ment using a 500 sec sweep to cover 1 kHz. A more _realistic comparison takes into account the time re- quired for the Fourier transformation and the sweep time in a cw experiment at a spectral width of 1 kHz: (1) Fourier transformation of a 2 K FID takes about 10-25 sec, (2) Using a sweep of l kHz/500 sec the cw experiment needs 500 sec. Furthermore, the 500 sec re- quired for the cw experiment can be used to accumulate at least 1000 2 K FID signals. The S/N of FT NMR is thus increased by a factor lO/IO over the cw experiment. In summary, FT NMR is much more efficient for equivalent measuring time,and much less time consuming 34 for equivalent S/N ratio,in comparison to cw NMR. FT NMR follows the Fellgett princip1e20’21: The signal-to- noise ratio of any spectroscopic experiment increases if simultaneous multichannel excitatiOn is applied. In the FT NMR technique, rf pulses stimulate multichannel transmitters. If m transmitters are stimulated simul- taneously, the enhancement factor relative to one channel excitation (m = l) is (S/N)m = (S/N)l /fi . (40) The minimum number of simultaneously exciting channels m required for resolving a spectrum of width sw at a resolution dv is m = sw/dv . (41) Combining Equations (39) and (41), the number of simul- taneously exciting channels stimulated by a rf pulse is therefore m = dp/2, which depends only on the computer memory size, and yields an enhancement of factor /d§72. Thus, according to the Fellgett principle, a FT NMR spectrum obtained from an 8 K FID should give a S/N en- hancement factor of /4096 = 64 relative to a cw spectrum of equal width, resolution and measuring time. Due to this greatly enhanced sensitivity in com- parison to cw NMR, the FT method has made 13C NMR into a routine method of structure analysis for all molecules 35 containing 13C in its natural abundance of 1.1%. Additionally, phase-corrected FT NMR spectra contain all spectral details without the line-skewing and ring- ing observed in Cw spectra. Short-lived molecules can also be measured by FT NMR and sensitivity enhancement by accumulation of FID'S before Fourier transformation requires much less time than the accumulation of cw NMR spectra due to the small time required for acquisition of FID signals. IV. THEORY OF CHEMICAL SHIFTS When a molecule with a fixed geometry is placed in an external magnetic field M0, the electrons will produce a secondary field M' at any nucleus, where M} is not necessarily parallel to M0. The relation be- tween M‘ and M0 is given by the equation , (42) where g is a second-rank tensor which depends on the position of the nucleus in the molecule. In solution, molecules are rotating rapidly and randomly such that the chemical shift is determined by the mean component of Mf along the direction of Mo, averaged over many rotations. As a result of the averaging the tensor Q can be replaced by a scalar o, which is the mean value of the diagonal elements of the tensor, 36 o = l/3(oxx + Oyy + 022). (43) A general expression for the tensor components Uxx' Oyy and 022 has been derived by Ramsey22 for the case of an isolated molecule 2 2 (X y) 2 2 a a 022 =(e /2mc )<0|Z 3 |0> r a 2 2 2 2 -1 2La 2 -(e h /4m c ) 2 (E - E ) ( n o a,z n#0 a a r a 2La z + ). (44) a ra a where <0| refers to the unperturbed electronic ground state wave function and > IAvl, IJOI, then Equation (58) reduces to Jr = JOAv/xH2 . . (59) The off-resonance cw spin decoupling technique has been 13 widely applied to the assignment of C NMR signals and such experiments are reported in many articleszg. For measuring 13C - 1H coupling constants, broad- band decoupling and off-resonance techniques cannot be applied. However, the S/N ratio of coupled 13C NMR spectra is much lower due to signal splitting and lack of nuclear Overhauser effects. It is possible to achieve NOE signal—to-noise enhancements without decoupling effects by applying the decoupling power H2 only between H1 pulses (i.e., not decoupling during acquisition time). Coupling constants can then be measured without much loss of sensitivity. Intensities of 13C signals are affected to a vary- 13C - {H} NMR spectra due to different NOE ing extent in and T1 values, so that the relative numbers of non-equi- valent carbons cannot be determined by integration in 13C - {H} NMR spectra. To prevent this error, there are three ways to remedy the problem of different Tl values: (1) Set a long enough delay time between pulses to result in the complete repolarization of all nuclei, (2) Use a very short pulse which perturbs the populations of the 47 spin states very little, or (3) Add a small amount of paramagnetic material to make all T1 values short compared to the pulse repetition rate. There are also three ways of dealing with the problem of variable NOE effects: (1) Operate without proton noise-modulated decoupling.- This has the disadvantage that the reappearance of the multiplicities will cause severe overlap of 13C spectra. Furthermore, the usual gain in signal-toénoise due to NOE will not be realized, (2) Gate the decoupler on during the acquisition time and off during the rather long delay time, and (3) Add a small amount of a para- magnetic species which can quench the NOE for all of the carbons without unduly broadening the lines. VI. NUCLEAR OVERHAUSER EFFECT The nuclear Overhauser effect (NOE) is the change in the integrated intensity of the NMR absorption for one nuclear spin as a result of the concurrent saturation of another NMR resonance. The term "Overhauser effect" originally referred to the dynamic polarization of nuclei in a metal30 when the electron spin resonance was saturated. The first application of this effect in a system containing only nuclear spins was made by Solomon and Bloembergen31 in their study of chemical exchange in HF. Thereafter, the nuclear Overhauser effect found many applications such as the analysis of complex nuclear magnetic resonance spectra32, the study of chemical 48 exchange33, the study of nuclear relaxation34, and signal- to-noise improvement in NMR spectra35. The nuclear Overhauser effect is commonly observed in 13C - {H} experiments and arises from an intramole— cular dipole—dipole relaxation mechanism. Any nucleus with a spin is a magnetic dipole. Two such nuclei A and X in a molecule having intermolecular and intramolecular mobilities (rotations, vibrations, translations) give rise to fluctuating fields. Energy transfers between A and X may occur via fluctuating fields. In an A - {X} experi- ment, the transitions of nuclei X are irradiated while the resonance of nuclei A is observed. Since the irradiat- ing field is very strong, the homonuclear relaxation pro- cesses are not adequate to restore the equilibrium popula- tion of the nuclei X. The nuclei X may transfer their energy to the nuclei A via the internuclear dipole-dipole interaction. The nuclei A, receiving these transferred amounts of energy, behave as if they have been irradiated themselves and relax. By way of these additional heter- nuclear relaxation processes of the nuclei A, induced by double resonance, the population of the lower A level increases. As a result, the intensity of the A signal is enhanced. To consider mathematically how the NOE enhance- ment occurs, let us start with a system of two nuclei of spin 1/2 (e.g., I = 13C, S = 1H), without J coupling, in 49 an external magnetic field HO along the Z direction. The energy level diagram for this two-spin system is shown in Figure 6. If the spins are labelled as I and S, then the energy levels can be designated as follows: spin I is a, spin S is a ++ spin I is a, spin S is B +- spin I is 8, spin S is a —+ spin I is 8, spin S is 8 -- . The W's are the transition probabilities, which are: W the single quantum transition probability 11 that spin I will go from a to B (or B to a) while the state of spin S remains unchanged. Wls : the single quantum transition probability for spin S when I remains unchanged. W : the two-quantum transition probability for the two spins to relax simultaneously in the same direction, i.e., -- to ++ or ++ to --. W : the zero-quantum transition probability for a mutual spin flip, i.e., +— to -+ or -+ to +-. The Hamiltonian for this system of two nuclei of spin 1/2 (I and S) 1336 H= -fiYIHI-‘EYSHS+H', (60) HM o z o z where H is the Hamiltonian operator for the motion of M the two nuclei I and S, and commutes with the spin 50 W1: W2 ... — “'15 ° “’15 -+ “'1: ++ Figure 6. Energy level diagram and transition probabilities for a two-spin system without J coupling. 51 operators. The next two terms are the Zeemann energies of the spins in the constant magnetic field Ho‘ H' is the dipolar interaction term of nuclei I and S, which is considered as a perturbation, fig YI YS H'=—( 3 )[3(£-£)(§-_1:)-;-_S_]- (61) r If the populations in each energy level are designated N and N__, then the following rate laws as N++, N+_, _+ can be written: dN ++ __——=- + dt (W11 + wis + W2)N++ + WirN—+ WisN+- + W2N__ + const. dN+_ dt = "(WIT + wo + Wis)N+- + woN-+ + WisN++ + WlIN-- + const. dN_+ dE_— = -(Wll + Wo + wls)N_+ + WON+_ + WlSN-- (62) + W1IN++ + const. dN__ dt = “(W2 + W11 + Wism" + wlIN+- + WisN-+ + sz++ + const. The constants are obtained by considering the system at temperature equilibrium and inserting the proper Boltzmann factors, and are unimportant in the 52 computation of the relaxation times. The experimentally observable quantities are the macrosc0pic magnetic moments and , which are given by (N + N+_) - (N_ + N__) + K (12> ++ (63) (N + N_ ) - (N+_ + N__) K . ++ + Combining Equations (62) and (63) yields d dt = _(WO + 2W11 + W2) — (W2 - WO) + const. (64) d dE_—— = .(w2 - wo) - (WO + ZWIS + W2) + const. With respect to the equilibrium values Io and So we may write d dt = —(Wo + 2WlI + W2H - Io) - (W2 - WO)( - So) (65) d dt = -(W2 - Wo)( - Io) - (W0 + 2WlS + w2)( - so)' Equation (65) shows that the decay of the observed magnetizations and is not a simple exponential, but a linear combination of two exponentials. If we apply an intense rf field at the resonance frequency of 53 spin S, so that the populations in states l+> and l-> are equalized ("saturation"), we will have = 0 and the decay of becomes d dt = -(WO + 2wlI + W2)[ - IO(1 + n)]. (66) Here n is defined by 0 11 21’: where YS and Y1 are the gyromagnetic ratios of spins S and I, respectively. It follows from Equation (66) that decays exponentially with a time constant l/T1 given by l/T1 = WO + 2wlI + W2 . (68) Equation (66) also tells us that saturation of the S nucleus changes the equilibrium value of to (l + n), giving rise to the familiar nuclear Overhauser enhancement (NOE)37'38 Idecoupled NOE = = (l + n), (69) coupled where Idecoupled and Icoupled are the integrated in- tensities of the decoupled and coupled spectra, respec- tively. Calculation of the transition probabilities shows that the maximum enhancement occurs when the relaxation 54 mechanism of the I spin is dominated by dipole-dipole coupling to the S spin. Consider the interaction be- tween two nuclear spins (I = 1/2, S = 1/2) acting as magnetic dipoles with the internuclear vector having polar coordinates, r, 8, and ¢, with respect to space- fixed axes. The dipole-dipole interaction term in Equation (61) can be rewritten as39 I _ H — Y2,m Am r , _ (70) 2 m where Y2 m are second-order spherical harmonics normalized I to unit root-mean-square averages, Y2 0 = (5/4)1/2 (l - 3 c0528) Y _ + 15 1/2 . . 2'+1 - _( /2) cos 8 Sin 8 exp(: 1¢) (71) IL? = -(15/8)1/2 sin28 exp(j-_ 21¢). In the expressions for these functions, 8 and ¢ are time dependent due to molecular motions hithe liquid. The spin operators A.m in the dipolar Hamiltonian are _ 1/2 _ Ao — (4/5) K[IzSz l/4(I+S_ + I_S+)] _ - 1/2 Ail — (3/10) KIIiSz + 125:] (72) __ 1/2 A+2 — -(3/10) K 1:5: . where the spins are designated I and S, and K =‘fiy1ys. According to time-dependent perturbation theory the probability per unit time of a transition being induced 55 between states ¢l and ¢j (energies are Bi and E., respectively) by a stationary random interaction is Wij = ffm<<¢i|Hv(t)|¢j><¢j|H-(t+r)|¢i>>a .exp(-imijr)dr, (73) V where < >av indicates that an average is taken over a statistical ensemble. The transition frequency, E. - E. w.. = —lfifi——l, is expressed in radians sec 1. Substitu- tion of the dipolar Hamiltonian in Equation (73) leads to W.. 13 2 +oo -6 i[<¢i|Am|¢.> f m J _ .exp(-imijr)dr], av (74) since the autocorrelation function Gm(r) is defined as Gm(T) = av. . (75) The spectral density function Jm(w) of Y2 mr-3, which is I a measure of the spectral power available at angular fre- quency w from the fluctuating interaction, is also de- fined as +0o . _ +00 Jm(w) - f__0° Gm(T)eXP('1wT)dT - 2f_co Gm(T)COS(wT)dT. (76) It may be noted that J is the Fourier transform of G. The transition probability may then be written as 56 _ 2 wij - i <¢i|Am|¢j> Jm(wij). (77) It can be seen from the form of the operators that a given term Am allows transitions of the type Wm only. It can also be shown that wm = W_m. Then evaluation of integrals ¢i Am ¢j gives — 2 - Wo — (1/20) K Jo(ws ml) 2 W11 — (3/40) K Jl(mI) 2 (78) W13 = (3/40) K Jl(ws) _ 2 W2 — (3/10) K J2(wI + ms). Introducing Equations (78) into Equations (67) yields NOE - 1 + - l + :fi [6J ( + ) - J ]0-1 (79) — n — YI 2 ms. ml 0 and 1/T1 = (1/20) K2 , (80) where O = Jo(wS - wI) + 3Jl(wI) + 6J2(wS + wI). A. Theory for several important cases (1) Isotropic reorientation If the molecular motion can be described by means of a single rotational correlation time T (i.e., re- R orientation is isotropic), then Gm(TR), the spectral density function,becomes _ 2 2 —1 —6 Jm(w) - 2rR(l + w TR) r , (81) 57 where r is the distance between I and S. Introducing Equation (81) into Equations (79) and (80) yields Y 6T _ T I 1+(ws+wI) TR 1+(wS-wI) TR 2 -6 and 1/Tl = (1/10) K r x. (83) where x _ TR + 31R + 61R - 2 2 2 2 2 2 1+(mS-w1) TR l+wITR 1+(wS+wI) TR It should be noted that even though T is strongly de- l pendent on the I-S distance, the NOE is not a function of r, so that even for non-protonated carbons the NOE effect may be predicted by Equation (82). In the extreme narrowing limit, i.e., (ms + “1)2TR << 1, all the J values in the above spectral densities are in- dependent of the radiofrequencies under consideration and can be replaced by a single constant JD' where the sub- script D indicates that only the dipolar interaction is important. In this case, the ratio of the transition probabilities is, WO:W = 2:3:3:12 and the iI‘Wis‘w2 nuclear Overhauser effect is YS Tlmax - 2Y I (84) I which is independent of the actual value of J . For the D 58 13 - _ _ C {H} experiments, YH/YC — 3.976 so nC—{H} — 1.988 and NOE = 2.988. When other relaxation mechanisms con- 13C the observed NOE value tribute to the relaxation of is decreased, since only the dipOlar mechanism con- tributes to W2 and WO while other mechanisms will con- tribute only to W1. The effect of these other mechanisms can be illustrated by separating W into a dipolar com- 1 expressing the effect of all other * 1C mechanisms. Thus, for a two-spin system ponent and a term W 2 Y8 K J _ D nI-{S} - (2y1)( 2 . ). (85) K JD + 4W11 * Equation (85) shows that when K2JD 2 W11 the enhancement depends on the contribution of these other relaxation mechanisms relative to the dipolar term. 13C-{all H} double resonance (2) An important case is that of more than two spins, where the resonance of one type of nucleus is observed while those of all other types of nuclei in the sample are saturated, e.g., 13C-{all H}. This technique is very 13 important in C NMR because of (a) the common occurrence of CH3 and CH2 groups, and (b) the desirability of eliminating all indirect 13C - 1H Spin-spin couplings by irradiation of the entire proton spectrum for the mole- cule. 59 Consider a spin system consisting of a spin I of one species and n spins or another species, S(i) (i = 1,2,3,...,n), where all spins are supposed to have a quantum number 1/2. It has been shown that will not depend on which 8 spin is considered so we assume that the final expression for the multi-spin system differs from that for a single S spin merely by being a summation over independent contributions from each S spin: YS 2 nI-{all S} = 2y n * I JDi + 4 W11). (86) I i where Z is the summation over all 8 nuclei being i saturated. No distinction has been made in the above derivation between intramolecular and intermolecular dipole-dipole interactions. Clearly if dipole-dipole interaction in the 13C-{all H} case is dominant, i.e., * 4W1C << K22 JDi' then Equation (86) reduces to Equa- i tion (84). In such cases the number of protons involved is irrelevant. Thus, if dipole-dipole relaxation be- tween directly bonded carbon and hydrogen atoms provides the dominant mechanism, the same NOE value (i.e., 2.988) 13 will be seen for all C nuclei of CH, CH2 or CH groups. 3 However, if contributions from other relaxation mechanisms are appreciable the number of nearest protons can lead to variations in the values of nC-{H}° 60 It is of interest to consider the spin-lattice l3 relaxation time of the decoupled C nuclei. If it is assumed that all the protons are saturated, then d * dt 2 = "% KziJDi + 2W11H l (1 + nI-{S})Io] (87) and 1 _ 1 2 * T_ — 38K 2 JDi + 2 WII . (38) Measurement of T1 is thus a valuable complement to Overhauser effect measurement. Combination of Equations * (86) and (88) leads to separate solutions forWl and C 2 K EJDi: l KZZJ = 4 /( T ) (89) 1 Di Ycnc—{H} YH 1 * _ -1 Equation (88) tells us that if the dipolar interaction is dominant among the relaxation mechanisms then the relaxation rate is proportional to the number of hydrogens 13 bonded to C. Combining Equations (84), (86) and (88), we derive Tllobs ) = 1.22§__ T1(DD) n max . (91) where T and n l(obs ) are the experimentally (obs ) 61 determined spin-lattice relaxation time and NOE effect, and T1(DD) and ”(max) are the corresponding values con- tributed from the dipolar interaction alone. (3) Anisotropic rotation or groups with internal rota- tion If the rotational motion is anisotrOpiC (39), or if internal motion must be considered, the relaxation times and NOE values will depend on all components of the rota- tional diffusion tensor. Equations (78)-(80) are still valid but the spectral densities are functions of the various components of the rotational diffusion tensor. The only case we will consider here is that of a rotating group attached to a molecule undergoing isotropic re- orientation with TG and TR being the correlation times for internal motion and overall molecular motion, respectively. If the internal rotation is a stochastic diffusion process, i.e. , there are a large number of equilibrium positions, Woessner4o has shown that the spectral densities are given by J (w) = 2r-6f(r T w) (92) m R’ G' and TR T T f(T IT :03) = A "'""' + B + C I (93) R G l+w21R2 l+mer 1+w2102 where 62 -1 _ -1 -1 TB - TR + (6TG) —1 _ —1 -1 TC — TR + 2(3 TG) A = % (3c0528 - 1)2 ' (94) B = 3 sin28 C0528 sin48 0 II on» 8 = the angle between C-H vector and the axis of internal rotation. Introducing Equations (92)-(94) into Equations (79) and (80) yields: 1 NOE = 1 + R(A¢R + B¢B + C¢C)(AxR + BxB + cxc)- (95) _ ,-l -l -1 and l/Tl -.A11R + BT1B + CT1C , (96) where l/Tlj = 10 Kzr-6Xj, R = yflygl and T. 3T. 6T. Xj = J 2 2 + 2 + J 2 2 1+(wH-wc) Tj 1+wcrj l+(wH+wC) Tj 6T. T- V ¢j = J 2 2 " J 2 2 0 (j = RIBIC) 1+(wH+wC) Tj 1+(wH-wc) Tj Rearranging Equation (96) yields TlR/Tl = A + B(XB/XR) + C(XC/XR). (97) It should be noted that T and (l + R¢R/XR) are the T 1R 1 and NOE, respectively, in the absence of internal 63 rotation. In the extreme narrowing limit, + w )ZI? << 1, X. = 101.. If we introduce this rela- H C J J 3 tion and Equation (94) into Equation (97) we obtain (w 6T 3T G G ———1 + C[————— 6TG+TR 3TG+2TR TlR/Tl = A + B[ ]. (98) Thus, in the extreme narrowing limit T > T since 1 1R’ A + B + C = 1. If the internal rotation is much faster than the overall reorientation (TG << TR), Equation (98) becomes TlR/Tl = A + (GB + 3/2)TG/TR . (99) If 8 is appreciably different from the magic angle (for which A = 0) then Equation (99) becomes T1 = TlR/A . (100) The above equation gives the maximum increase in T1 from fast internal rotation when the overall reorientation satisfies the extreme narrowing condition. When the angle between the CH vector and the axis of rotation is tetrahedral, C0328 = 1/9, and T = 9 T A tetrahedral 1 1R“ methine carbon with one degree of internal motion has a T1 value up to nine times that of a methine carbon which is part of the rigid backbone in a large molecule under- going isotropic reorientation. In the very common case of a methyl group directly attached to a rigid backbone, 64 one must correct for the presence of three hydrogens. In this case the upper limit to the T1 of methyl carbon will be three times that of the T1 of a methine carbon on the backbone. This behavior has been confirmed experimentally41 HISTORICAL REVIEW OF NUCLEAR RELAXATION STUDIES I. STATISTICAL MECHANICAL THEORY The rapidly increasing use of 13 e e n 13 I o conSIderable interest in C relaxation mechanisms. 13 C NMR has generated The information derivable from C relaxation measurements is generally unobtainable from the chemical shifts, spin- spin couplings and peak area (integration) parameters. Relaxation data are related closely to overall and local molecular geometry, bonded and nonbonded interactions, and other factors controlling molecular motion. From relaxa- tion data, together with the nuclear Overhauser effect - observed on proton decoupling of 13C NMR spectra, the 13C relaxation mechanisms in a liquid can be obtained. Dif- 13 ferences between the T1 values measured for the C nuclei of a molecule can help in the assignment of 13C NMR spectra, particularly in cases of signal crowding and multiplet overlapping. In this section, the details of several re- laxation mechanisms will be discussed. The relaxation processes occur by the interaction of the nuclear spin system with fluctuating local magnetic fields. These fields are generated by other molecules in the sample and their fluctuation is governed by the motion 65 66 of these molecules. If the locally induced magnetic fields, which act as microscopic radiofrequency fields, have com- ponents at the appropriate Larmor frequency, they can interact with the given nuclei and cause spin relaxation. The larger such a component is, the quicker relaxation can occur. The frequency components of these motions in the 13C relaxation; fast motions, MHz region are important for e.g., electronic motions and molecular vibrations, are thus going to have components of insufficient magnitude and so of little importance. However, Brownian motion (rotational 13C relaxation, as are and diffusional) is important for certain molecular torsional and rotational motions. Since molecular motion is effectively a random pro- cess in solution, any property generated from it, e.g., h(t), will have zero average, (hloc(t)> = O ; (101) its mean square average, however, will not be zero, * # 0 . (102) Thus, this latter average will be a useful property to describe molecular motion. If the Fourier transform of hloc(t) is Hloc(v), then H C(v) is itself random With a lo 2 zero average but a non-zero square average. |H (v)| loc represents the total energy available at frequency v, and would be infinite unless one limited the time under 67 consideration (t). We can thus define a power spectrum * Hloc(v) ° Hloc(v) (103) o1: J(v) = lim t=—cx> J(V) is called the spectral density function and tells us the power (energy/unit time) available in the molecular motion as a function of v. A useful property in describing random molecular motion is the correlation time TC which can be defined as the average time for a molecule to rotate by one radian in reorientational motion. If a molecule is in one state of motion for TC sec, one would expect there to be frequency -1 C O The correlation time of a molecule in solution will components of the motion spread around T depend on many factors such as molecular size, symmetry and solution viscosity. If the molecule is small (M.W. < 100), then in solutions of normal viscosity 1 is about 10".12 - 10"13 sec; for larger molecules (M.W. = 100-300) TC may increase to as much as 10"10 sec. Mole- C cular geometry will obviously have an effect on the correlation time; a symmetrical molecule, causing less dis- ordering of the solvent as it rotates, will move faster than an asymmetric one. Viscosity describes the ease with which reordering can be achieved in the solution and de- pends on both the solute and solvent. The correlation time for molecular reorientation used here is equal to one third of the dielectric correlation time TD of the Debye 68 theory of liquids and can thus be expressed, using that theory, in terms of the solution viscosity n and the molecular radius a: TC = (1/3)rD = 4nna3/3kT. (104) By using the concept of a correlation time, one can set up a reasonable model for the auto-correlation function by assuming that the effect of molecular collisions decays exponentially with a time constant TC. The auto-correla- tion function will have the form m * G(T) = f_mh (t) - h(t) exp(|T|/Tc)dt . (105) Rewriting the above equation one obtains _ 2 G(T) — h10c exp(II|/TC). (106) Fourier transformation of Equation (106) leads to ' ——. 2T J(v) = h2 C 1°C 1 + (2nv)21é . (107) It is evident that J(v) is a maximum at v = 0 and begins to fall off with increasing frequency as va becomes comparable to l/TC. Any relaxation process can be repre- sented by an equation which has the general form _ 2 R - Hloc f(TC) . (108) loc and TC W111 depend on the Inechanisms under consideration. The value and origin of H 69 II. RELAXATION MECHANISMS Local magnetic fields in solution can be generated in many ways. Six possible relaxation mechanisms will be discussed here. A. Dipole-dipole relaxation (DD) The principal source of nuclear relaxation for spin-l/2 nuclei is via dipole—dipole interactions. Consider the relaxation of a nucleus I by a magnetic particle 8 (an unpaired electron or a nucleus). The local field gen- erated at I by S is given by the classical equation DD_ 2_ -3 H - :uS(3 cos 8 1)rIS ICC (109) DD loc nucleus 8, where H is the magnetic field produced at nucleus I by “S is the dipole moment of S, rIS is the nuclear separation of I and S, and 8 is the angle of the rIS vector relative to the applied magnetic field Ho' Thus, both inter- and intra-molecular interactions are possible, except that the former will tend to be attenuated more 3 readily as a result of the r- dependence. Local fields from this source may be as large as approximately 2 mT where 1T = 103G. In a rigid system of intramolecular dipoles, 8 shows a time dependence in liquids due to mole- cular tumbling while for intermolecular interactions rIS and 8 can both fluctuate with time owing to translational and rotational diffusion. 70 For the interaction of two Spins I and S, the per— turbing Hamiltonian is 42 Hb(t) =‘fi l Mloc(t) = fl £,- - S, (110) "D where Q is the dipolar coupling tensor and contains the time dependence of the system. When I and S are both spin 1/2 nuclei but different nuclear species, the expression for dipolar relaxation can be derived from Equation (83) and is 2 2 2 1 =__1__fiYIYS[ TR + 3TH T 10 6 2 2 2 2 1(DD) rIS 1+(ws wI) IR l+wITR 61R + l. (111) 2 2 1+(ws+wI) TR Under the extreme narrowing approximation, (u)I + wS)21§ << 1, Equation (111) reduces to 1 fizYiYS ______T = ___6 TR' (112) 1(DD) rIS where T is the reorientational correlation time which R varies exponentially with temperature as43 TR = r; exp(E/RT). (113) Equation (113) shows that T will decrease as the tempera- R ture increases and hence Tl(DD) becomes longer. Equation (112) holds for isotropic rotational diffusion which is 71 characterized by a single correlation time constant T R' To handle the case of multi-spin relaxation, Equation (112) can be modified to38 fiz YZYZ —— =1 :§—-——S— C. (114) Tl(DD) S rIS provided that S i I and that an effective isotropic correlation time T can be employed. This expression has C .often been utilized as a means of acquiring rough quanti- tative estimates of the correlated motion even though the motion may actually be anisotropic. Under such condi- tions, however, details of the motional features are obscured and care should be taken not to over interpret these approximate correlation times. Due to the rapid attenuation of the r22 obtained by summing S only over the directly-bonded nuclei term, a simplified form can be to yield 1 _ s I s T__——_'— 6 TC (115) 1(DD) rIS where nS is the number of directly bonded S nuclei. 13 Most of the C nuclei in organic molecules, especially those linked to hydrogens (i.e. CH CH2, CH), are re- 3! laxed mainly by internuclear dipole-dipole interactions and intermolecular dipolar relaxation has rarely needed to be considered since the carbons are in the backbone of the molecule. 72 B. Spin-rotation relaxation (SR) Electron and nuclear currents associated with overall molecular rotation can give rise to correlated fluctuating magnetic fields which can lead to spin relaxa- tion. These fluctuations in the local magnetic fields may result from a modulation of the magnitude (M-diffusion), or of both the magnitude and the direction (J-diffusion), of the angular momentum vector associated with the rotat- ing molecular system44. Although currents arising from completely symmetrical negative and positive charge dis- tributions can be expected to cancel one another, it is to be noted that any angular momentum possessed by electrons around a given nucleus, no matter how symmetrical the Charge distribution may be, will on the average lead to a local magnetic field at that nucleus. The spin-rota- tion mechanism is usually important for small, symmetrical molecules or small segments of larger molecules (methyl groups). The Hamiltonian for the spin-rotation interaction is: HéR(t) = -_I_ - g - _q_(t), (116) where g is the spin angular momentum, g is the spin-rota- tion interaction tensor, and J(t) is the time-dependent angular momentum associated with overall molecular rota— ‘tion. Although the above equation is relatively easy to 73 employ in the gas phase, where a set of good J quantum numbers can be used characteristic of such systems, only an approximate solution for liquids is possible because the states are rendered indistinguishable by lifetime broadening resulting from extensive intermolecular inter- 45 Thus, relatively simple ensemble averaging of actions. J(t) over all possible angular momenta is employed to estimate the magnitude of HéR(t) due to rotation. For spherically symmetric molecules T for a magnetic 1(SR) nucleus at the center of symmetry (and under the extreme narrowing limit) is given by l 2 IkT 2 —————— = C T , (117) T1 (SR) 462 SR where I is the moment of inertia, C is the isotropic spin- rotation interaction constant and TSR is the spin-rotation correlation time. If the nucleus lies in a cylindrically symmetric electronic environment, Equation (117) can be modified by replacing C2 by the relation 2 -.1_. 2 C - 3 (C , 2 H + 2 Cl), (118) where the parallel direction is that of the principal vector of the rotation axis. It may be shown that the angular momentum correlation time TSR is related to the molecular reorientation time TR by _ I 74 where k is the Boltzmann constant and T is the absolute temperature. This relation holds only at temperatures well below the normal boiling point of a liquid. The important distinction between TSR and IR is that TSR becomes longer as the temperature increases, whereas TR becomes shorter. As the temperature becomes very high and the sample becomes a gas, collisions become more in- frequent and the molecule remains in a given angular momentum state for a longer period of time. On the other hand, the higher the temperature the faster a molecule re- orients and the shorter TR becomes. The result of this is that for the spin-rotation interaction the relaxation time T1 becomes longer as the temperature decreases. This be- havior is opposite to that observed for the other relaxa- tion mechanisms. In general, the small, symmetric molecules with nuclei which have a large range of chemical shifts, i.e. 19F, 13C, 15N, will have important spin-rotation interactions. This relation between spin-rotation and chemical shifts arises because both the chemical shift and the spin-rotation tensor components of any given molecule depend on the electron distribution in a molecule and a distribution which results in large chemical shifts will also lead to large spin-rotation interactions. 75 C. Chemical shift anisotropy relaxation (CSA) Significant anisotropy in the shielding of a nucleus can give rise to fluctuating magnetic fields when the molecule tumbles in solution. As is well known, the local magnetic field at a nucleus in an external field H0 is given by H10C = (1 - o)HO (120) where o is the chemical shielding tensor. If the electron screening around the nucleus is not isotropic, Q will have directional components which vary with time as the molecules tumble relative bathe Ho axis. The linear coupling between HO and spin I is represented by the Hamiltonian I — _. e o HCSA(t) - is h g I- (121) In the extreme narrowing approximation limit, this yields the following expression for T the chemical shift 1(CSA)’ anisotropy relaxation time, 2 2 Y H T“;— = I5 0 (012 + 023 + 081)TR' (122) 1(CSA) where the oij's represent the anisotropic magnitudes (oi - oj)/3 of the three principal terms in the dia- gonalized shielding tensor g and TR is the reordintational correlation time for the dipole-dipole relaxation mechanism. If g is axially symmetric (C3V or higher symmetry), 76 Equation (122) reduces to 1 _2__ 2 -———-—— = Y T1(CSA) 15 I - Ol)2T , (123) 2 Ho(0 R H where o”, 01 are the components of g parallel and per- pendicular to the symmetry axis. A contribution of the CSA mechanism is apparent when the measured Tl values are proportional to the square of the applied magnetic field strength Ho‘ This contribution is usually negligible for 13C nuclei of organic molecules. D. Scalar coupling relaxation (SC) If the spins of two proximate nuclei I and S in a molecule undergo coupling, and the lifetime of these nuclei in their nuclear magnetic energy states is suf- ficiently long, then the signals for I and S will be split (scalar coupling). The interaction Hamiltonian is of the form t) = h I - H> Héc( - §_. (124) To produce a contribution to the relaxation of nucleus I, there are two possibilities, (a) S is time dependent, or (b) A is time dependent. If nucleus S relaxes very much faster than nucleus I, i.e., l/Ti < 1/A, then no signal splitting is observed. However, the fast relaxation of nucleus S will generate fluctuating fields which in turn contribute to the relaxation of nucleus A. Quadrupolar 77 nuclei with I Z l, i.e., nuclei whose charge distribution is not spherically symmetrical, relax so fast that they accelerate the relaxation of neighboring nuclei. This is the so-called scalar relaxation Of the second kind. The relaxation rate due to this mechanism is 2 T l _ 2A —I____ — —§— S(S + l) 2 2 Tl(SA) 1+(wI-ws) TS S I (125) where A is the spin-spin coupling constant expressed in rad sec"1 and TS is the relaxation time of nucleus S, i.e., T? = TS. Scalar relaxation can also occur when g becomes a function of time. This situation can arise when chemical exchange is present and is referred to as scalar relaxa- tion of first kind. In this case the local magnetic field at I is A(t)S/YI, when I and S are covalently bound in the same molecule, and zero otherwise. If the chemical exchange rate is much larger than either the coupling A, or l/T1 for either I or S, and if the time the nuclei are uncoupled is short compared with the time they are coupled, the multiplet structure disappears and only a single resonance line is observed. This is quite similar to scalar relaxa- tion of the second kind, and Equation (125) is still valid but 1 now becomes Te, the exchange time. The contribution S of the scalar mechanism can be recognized from a frequency and temperature dependence of T1 when the nuclei I and S precess with similar Larmor frequencies. 78 E. Quadrupole relaxation (Q; Nuclei with Spin I > 1/2, having an electric quadrupole moment, eQ, will interact with the field gradient, eq, produced by the surrounding electrons. This interaction provides a very efficient relaxation for the quadrupolar nuclei. The interaction Hamiltonian H'(t) is Q gé(t)=_I_-g-_I_. (126) where Q is the quadrople coupling tensor. The quadrupole relaxation rate in the extreme narrowing limit 1342 1 3 21 + 3 2 eZQ 2 1(0) I (21 - l) where n is the asymmetry parameter and (eZQq/h) is the quadrupole coupling constant. Since in mobile liquids the molecular correlation times T are in range of 10.11 to R ‘12 sec. the quadrupole relaxation rate is Primarily 10 determined by the magnitude of the quadrupole coupling constant. The quadrupole interaction is usually the dominant one for nuclei with spin I > 1/2 (unless, due to molecular symmetry, eZQq/fi = 0). Since it is almost entirely an intramolecular interaction, a measurement of the quad- rupole relaxation time provides an excellent means for measuring the molecular correlation time T if the quad- RI rupole coupling constant can be determined independently. 79 F. Electron-nuclear relaxation (e) The electron is a magnetic dipole and an unpaired electron will therefore generate a local magnetic field, which in general will have a nonezero average value and SO cause a Knight shift. This local field will be randomly modulated by molecular motion, providing a nuclear relaxation mechanism. The interaction is dipolar in nature and its efficiency therefore depends on the square of both the magnetic moment of the electron and of the nucleus. The electron's magnetic moment is about 103 times larger than that of the proton, which has the largest known nuclear moment. Electron-nulcear dipolar relaxation is thus a more efficient relaxation process by a factor of 106 than the nuclear dipolar relaxation discussed above. Against this, the increased efficiency is only partially offset by the larger characteristic mean inter—dipole dis- tance. The efficiency of this form of relaxation means that it has detectable effects even at very low con- centrations of the paramagnetic species. The most common example of this kind of interaction is that resulting from oxygen dissolved in the solution. Dissolved oxygen can lead to line broadening, particulary in proton spectra where linewidths below a few tenths of a Hertz normally cannot be achieved without degassing the sample. Even in 13 C spectra, where the mean distance of approach of oxygen to carbon is much larger than that to protons and 80 consequently the effects much weaker, oxygen still con- tributes significantly to the relaxation of quaternary carbons. Electron-nuclear relaxation is often produced in NMR by the addition of small quantities of paramagnetic ions to the solution. If the paramagnetism of the ion comes purely from spin angular momentum, its magnetic moment is u = yéfi(S(S + 1))1/2. If there are other contributions, an effective magnetic moment “eff has to be used. As a rule the relaxation rates l/T1 and l/T2 are directly pro- portional to N the concentration of paramagnetic species, 5! and roughly proportional to “iff' A detailed analysis of this mechanism is given later, but basically it fOllows the approach used in analyzing nuclear dipolar relaxation. In the extreme narrowing limit42, it is found that 1 4S(S + l)yzy2 = e I (128) T 2 6 TC l(e) 3h r l l S(S + DA2 and T = T—-—— + 2 Te , (129) 2(8) l(e) ‘5 where A is the electron-nuclear hyperfine interaction constant. The correlation time Te is related to the electron (T ) relaxation time, and also to the exchange ZS time Th of the molecular complex between the ion and the molecule being relaxed,44 l _ l .L_ ?— — T__ + . (130) e ZS Th 81 The effect of paramagnetic ions on nuclear relaxation has important applications in chemistry and biology, where they can be applied to the measurement of exchange reactions. The "relaxation reagents" used in 13 C NMR provide another example of the use of electron-nuclear relaxation. These reagents are usually transition complexes, the trisacetony- 1acetonates of chromium (Cr3+) and iron (Fe3+) being the most common, and their function is to dominate 13C re- laxation in the sample. In doing so they first shorten all the Tl's, thus speeding up a pulsed experiment, and secondly they eliminate the NOE effects. This is especially useful in quantitative l3C work. G. Additivity of relaxation rates Since the relaxation rate l/Tl, depending on several possible relaxation mechanisms, can be aSsumed to be addi— tive, $—-=;f—-]L—-+Fl——-+T—;——+E‘—;———+Tl +Tl +... 1 l(DD) l(SR) l(CSA) l(SC) l(Q) l(e) (131) the contribution from each mechanism can give different chemical information. Consequently, in order to gain the full value from a study of relaxation data, the contribution of each mechanism must be resolved. For carbon atoms bonded to one or more protons in medium and large molecules, relaxation is dominated by the dipolar interaction and 82 this contribution can be measured by determining the nuclear Overhauser effect, as shown in Equation (91). III. SOME EXPERIMENTAL RESULTS FROM THE LITERATURE A. Studies of Amides. The data available on13C relaxation times is quite limited and detailed separations into the contributing mechanisms are even less available. The majority of such 38,48-53 analyses are due to Grant and coworkers on small molecules, and to Allerhand and coworkers41 on large systems. The results of these investigations combine to 13 provide a consistent overview of C relaxation for mole- cules of diverse size at ambient temperatures and verify 13 the anticipated result that C Tl values are controlled mainly by the C-H intramolecular dipolar relaxation pro- cess. Thus, the dynamical information on liquid systems obtained from 13 C relaxation studies has, for the most part, been extracted from the effective reorientational correla- tion time associated with the C-H dipolar mechanism. A few 13C relaxation data and NOE values for amides have been reported so far, and these are shown in Table 1. The anisotropic molecular motion of N,N—dimethyl- formamide has been studied by Huntress et a1.54 by measuring the quadrupolar relaxation rates of deteurium, nitrogen, and oxygen. The anisotropic molecular motion of some symmetric-top molecules, e.g., CH3CN, CH3I, CH3C1, 83 Table l. 13C Spin-lattice relaxation times and NOE data for some amides o - 1‘ Compound T( C) Substituent Tl NOE Tl(DD) x1012 (sec) (sec) (sec) N,N-Dimethyl- formamidea 38.0 cis-NCH3 18.6 3 28.6 trans-NCH3 11.1 2 7 13.1 C = O 20.2 4 28.9 25.0 cis—NH3 17.8 trans-NCH3 10.5 C = O 19.5 72.0 cis-NCH3 19.0 2.2 32.0 trans-NCH3 18.0 2.3 28.0 Acetamideb (in D20) 30.0 C = O 72.0 2.0 139 . CH 12.3 2.3 18.5 . b c 3 Acetamide ’ (in H20) 30.0 C = O 37.1 2.2 61.0 . CH3 11.0 2.3 17.5 . acetamide 30.0 C = O 44.2 2.3 65.6 11.1 Carbonyl-CH3 9.6 2.6 12.2 11.1 N-CH3 9.5 2.6 12.0 11.1 N,N-Di-n-butyl- formamidea 38.0 N-a-C 1.0(trans) 1.2(cis) N-B-C 1.5(trans) 1.7(cis) N-y-C 2.4(trans) 2 . 3 (cis) N-G-C 3.1(trans, cis) aReference 58. b5.3 M, Reference 59. CD20 External lock. 84 have also been studied by measuring the 13C and the quadrupolar relaxation times.49'55”56 Quantitative calculations of the diffusion tensors for asymmetric-top molecules have been carried out on EEEgsfdecalin and norbornane,57 where symmetry now requires three diffusional parameters to diagonalize the diffusion tensor. Thus, l3C T1(DD) data from carbons with different geometrical arrangements of the C-H vector relative to the principal axis of the moleculewere required to solve the three simultaneous equations. B. Methyl group rotation Analysis of the internal reorientational effects upon dipolar relaxation have also been investigated. The 59 methyl rotational barriers in some compounds have been determined as shown in Table 2. C. Anisotropic tumbling_in monosubstituted benzenes Levy et al.47 have determined the anisotropic tumbling ratios of some monosubstituted benzenes as shown Table 3. They found that T1 for the para carbon is shorter than that for the TEES and Egg; carbons in all cases. This phenomenon results from anisotropic tumbling. The motional behavior of substituted benzenes can be used 13 to facilitate resonance assignments. The C Tl values can also give a new view of solvent effects such as 85 Table 2. Methyl internal rotational barriers from 13C dipolar relaxation rates Moleculeg DxlO-ll RxlO-l.l Ea(kcal/mole) (sec-1) (sec-l) (CH3)2SO 0.35h 4.0h 2.2a, 3.07b, 2.87c (CH3)2CO 1.6 29.9 0.92a, 0.76d, 0.78c (CH3)CC13 1.3 1.2 2.9a, 2.91C (CH3)3C-Cl 1.4 0.5 3.5a, 4.3C'e (CH3)COOCH3 1.4 49.4 0.673, 0.48C CH3COO(CH3) 1.4 21.0 1.13, 1.19C'f aReference 57. b Reference 60. cReference6l. Values represent gas phase data. d Reference 62. eValue for t-butyl fluoride. f Value for OCH in methyl formats. 9The methyl group for which data are given is in parentheses. hR is the tumbling rate (diffusion constant) for rotation . of the methyl group about the C V axis and D is the difquIOn constant for overall rotation of the molecules. 86 Table 3. Anisotropic tumbling in monosubstituted benzenes. Substituent T /T Approximate Reference l(o.m) l(p) .tumbling b ratio (R/D) CH3 1.3 2 47 C(CH3)3 1.8 3.5 47 (2::(31 1.7 3.2 47 Ph 1.8 3.5 47 CBCPh 2.4 7 63 CzCCaCPh 4.9 17 63 N02 1.4 2.2 47 OH 1.5 2.5 47 a Tl(o,m) is an average T1 for ortho and meta carbons and T1(p) is for the para carbon. bTumbling ratio, R/D, where R is the tumbling rate for motion about the C2v axis of the benzene ring and D is the diffusion constant for rotation about an axis perpendicular to C2v in the plane (or for the overall molecular motion). 87 hydrogen bonding and strong solvation of organic ions. For example, when phenol is diluted with CC14, the phenol molecular aggregates begin to dissociate; this effect is 13 reflected in the C Tl values of phenol by an increase in T1 for the protonated ring carbons and a decrease in T1(o.m)/T1(p)° EXPERIMENTAL I. INSTRUMENTAL A. 13C NMR Spectrometer A Varian CFT-20 high-resolution nuclear magnetic resonance spectrometer was used to obtain the 13C spectra. The spectrometer is computer controlled. After initial set up procedures, data are accumulated, transformed and plotted by entering commands through the console keyboard. There are three resonance experiments involved in the observation of 13C nuclear resonances: (l) The excitation and resonance detection of 2D nuclei (lock channel), 13 (2)12m3excitation and resonance detection of C nuclei (observe channel), and (3) The excitation of 1H nuclei (decouple channel). At a constant field of 18.7 kG, the resonance frequency of 2D is 12.0 MHz, 13 l C is 20 MHz, and H is 80 MHz. All these frequencies are derived from a master oscillator (18 MHz) and are phase-locked to each other. 13C and 2D frequencies generated in the spectrometer The are not applied in a continuous wave, but transmitter and receiver are pulsed on and off to achieve optimum operat- ing efficiency. The rate of pulsing is regulated by the computer and by the parameters entered. 88 89 The decoupler transmitter frequency may be applied either as a continuous wave or as a pulsed wave depending on the parameters entered. The power of the RF pulse is 13C transmitter but may be varied by the operator for the 2D and 1H transmitters. constant for the The CFT-20 is composed of separate magnet and operating consoles and a probe; all are connected by a harness containing various wires for signal generation, data transportation, and control of operational parameters. The magnet console contains a 6" electromagnet with a self-contained power supply and cooling system. The magnet is further regulated by flux stabilizing circuits in the operating console which control and stabilize the magnetic field through pick-up and buck-out coils located around the poles. Shim coils, mounted on the poles caps, adjust the homogeneity of the magnetic field at the sample. Adjustment of the current through the shim coils is con- trolled with the homOgeneity controls on the operating console. The operating console contains all of the operating electronics including the Varian 620L-computer, the data displaying devices (X—Y plotter and oscilloscope), computer keyboard, and various controls for homogeneity adjustments, field stabilization, and decoupling. The 12K computer controls most operations of the spectrometer by the use of CFT-20 Tl program tape. This 9O tape uses 4096 words of computer memory, leaving 8192 words for data storage. The keyboard provides the Operator/ computer interface for entering commands and parameters. The alphanumeric oscilloscope, X-Y plotter, and optional printer provide the computer/Operator interface for data and parameter display. An analog-to-digital converter (ADC) converts the electrical signal (analog) from parameters, commands, and data to the digital information for computer storage. Alternatively, a digital-to-analog converter (DAC) allows the stored digital information to be trans- mitted in analog form to the display devices mentioned above. The computer has two modes of operation: the Executive mode in which it is performing an instruction or routine, and the Waiting mode in which it is waiting for an instruction. The programmed 4K consists Of a series Of routines for: 1) Control of accumulation Of data, 2) Transformation Of data by several methematical functions in- cluding Fourier transformation, phasing and integrating, 3) Transmission of data to several devices, 4) Referencing of data to internal standards, and 5) T1 and NOE determina- tion. In order to select one Of these operations or routines, the Operator communicates with the computer via the keyboard in the operating console. The communication 91 consists of one and two letter mnemonics which may stand for either a command, a parameter, a flat or an interrupt.79 The temperature at the 8 mm sample tube may be varied from -80°C to +200°C by use of the NMR variable temperature accessory. The sample is placed in a tempera- ture-controlled nitrogen gas stream which maintains the selected Operating temperature at the sample. During Operation below ambient temperature, the nitrogen gas is cooled by liquid nitrogen, then the gas is heated to the selected temperature by a heater in the probe. When Operating at ambient temperature and above, the air flows directly into the probe and is heated to the selected temperature. 13 The C NMR spectrometer functional block diagram is shown in Figure 7. B. Calibration of Temperature for CFT-20 NMR Spectrometer (1) Calibration Of the temperature was accomplished by using the chemical shift thermometers, (A) TMS:CH I = 3 1:3, v/v,for -60°C to +20°C, and (B) Cyclooctane:CH 64 212 1:5, v/VIfor +20°C to +100°C. Temperatures in the low temperature range were found from the expression l/T = 0.0161165 - 0.000570057 x A6(TMS:CH3I==1:3, v/v): where A6 is the chemical Shift dif- (TMS:CH3I==1:3, v/v) ference between the 13C chemical shifts of TMS and CH I at 3 92 .S<¢0<_n 390.: ..(ZO-hUZq-u Quit—U .N. 0.3m?" good 5552 £200 ., HONO - $235. :00. - , 30081)— uooz ZOE a......11 .0.— a Egan. v. 90.. . 93 20 MHz and T is the absolute temperature. In the high temperature range, +20°C to +100°C, the calibration equa- tion is l/T = 0.0220027 - 0.000223362 x A5(cycoct ,CH I _ 1,5 v/V), o o '— o p 2 2 where A5(cycoct =CH212=.135, v/v) 18 the chemical shift difference between the 13C chemical shifts in cyclooctane and CH2I2. (2) In measuring the spin-lattice relaxation time, the spectral width used is sometimes smaller than the chemical shift difference of the chemical shift thermo- meters, so temperature measurement was accomplished by using a copper-constantan thermocouple to determine the temperature at the start and at the end of each experiment. It usually takes about 30 to 50 minutes to obtain tempera- ture equilibrium in the probe. Temperature measurements were obtained by use of the set-up shown in Figure 8. C. 13C §pin-Lattice Relaxation Time Measurement Four techniques are used with the 16 K CFT-ZO Tl program and these are summarized in the following para- graphs. (1) The Inversion-Recovery Method 65 The inversion-recovery method uses the pulse sequence (Figure 9) -(PD - Pl - t — P2 — AT)n- , 94 TO { THERMOCOUPLE TEFLON SPACER '35. .3 E; f. '9”, SOLVE NT II": t " 19’" COIL CENTER . . . 2mm GLASS was +>| Z 5 mm T-bO NMR tun! +| 8 mm cn-zo NMR was Figure 3. sn-up son I'EMPERATURE MEASUREMENT IN THE CFT-20 NMR SPECTROMETER. 95 2 g .. ’\ o ,I 180 __ I ‘ y’ INVERTING V PULSE l / I UI 'M x : ° 2 c 2 I, I I” 0 I, t , Y' 90 i ___ ’ --I 05 t 5 5': -Mm OBSERVATION : : PULSE ' I x’ x’ . Figure 9. INVERSION-RECOVERY SEQUENCE. 96 where PD is the pulse delay time, P1 is the first RF pulse, t is a delay time which is experimentally varied, P2 is the RF pulse, AT is the acquisition time, and n is the number of times this sequence is repeated. In this method P1 is a 180° pulse and P2 is 90° pulse, PD should be at least greater than five times the longest Tl value to be measured. In order to get more accurate Tl values, the 66 1' equation for the Z component of the magnetization vector value of t is usually varied from 0 to 2T The Bloch is sz(t) [MO - Mz(t)] dt Tl and integration of this equation will give Mz(t) = MO[1 - 2 exp(—t/Tl)] . Rearranging the above equation and taking the logarithm gives ln[MO - Mz(t)] = ln(2MO) - t/Tl A plot of ln[MO - Mz(t)] versus t gives a line of slope l/Tl (Figure 10). (2) The Homospoil Sequence (or Saturation Recovery Sequence) 67,68 The homospoil sequence uses the pulse sequence (Figure 11) 97 .h wpamp an x apamc wEdm mnp CH mum pcfiom poemHSOHmo paw HMPCmEfiummxw cm pmcp mamme u .pcfiom cmPMHSOHmv w mQMmE o .Pcflog HapCmEHpmmxm cm mcmwe x “nonpme hum>oompncOfimhm>Cw map hp moflsmnomahspmsflcuz.z Cw mmoz-mcmnp map no as omH map mcflzfienmpmo pom mpme no pun noPSQEOU Aommv mafia “l1 1 i 1 q 1 4 1 6 1 1 1 1 u q d d u d mmom OX ML Ho.m .oa musmflm (1w - OW)UI 98 A 9. I ’ APPLY A FIELD- ’, ___ I’ Y, —+ --— I Y, E GRADIENT PULSE : ' FROM 2 AXIS ' X APPLY A FIELD- GRADIEN'I' PULSE ___... Y FROM 2 AXIS xi 2 E DELAY TIME ,’ I I I —-> Y 90° —-> OBSERVATION PULSE Figure llHOMOSPOIL PULSE SEQUENCE. 99 -(PD-HS-Pl-HS-t-P2-AT)n-, where H8 is the homospoil pulse applied to the Z-axis shim coil and all other symbols are the same as those for the inversion-recovery method. In this sequence, PD is set equal to HS. For this sequence to work properly, it is essential that the net magnetization in the X'Y' plane be zero. Using this method, there is no wait for the establishment of thermal equilibrium. Therefore, this sequence has the potential of being a very fast method for the determination of spin-lattice relaxation times. By using the equation ln[MO - Mz(t)] = ln(MO) - t/Tl, a semi-log plot similar to that used for the inversion-re- covery data will yield the T1 value. (3) The Progressive Saturation Sequence The progressive saturation sequence69 uses the pulse sequence -[Pl - (AT + t)]n- If the sample is subjected to a series of 90° pulses more frequently spaced than 3T1, the line intensities are de- tectably reduced by saturation. By studying line intensities as a function of the interval between the 90° pulses, Tl can be extracted by use of the equation ln[MO - Mz(t)] = ln(MO) - (AT + t)/Tl. 100 The main limitation of this sequence is that the smallest interval between pulses which can be chosen is limited by the data acquisition time. (4) The variable-nutation-angle Sequence This method70 uses the pulse sequence variable nutation “(PD ' HS ' rf pulse(6) - AT)D- I where the rf pulse angle is varied manually and n should be a big number (> 100). The spin system is subjected to rapid repetitive pulses of nutation angle 0, with a con- stant T between pulse cycles (T = AT + PD). A steady state of magnetization is achieved after about the first 71 The resulting steady-state NMR signal four pulses. obtained by Fourier transformation is lower in amplitude than the equilibrium value Mo' due to incomplete recovery of magnetization, as in the progressive saturation method. The amplitude of this steady-state signal is a function of T, e, and T1 as shown below M -T/T M -T/T = e l 9 sin 6 tan 6 l + Mo(1 - e ) . By systematically varying e, the pulse nutation angle, in the range 20° to 110° at an appropriately chosen constant interval between pulse cycles, T1 can be evaluated by a linear regression analysis. A linear plot of Me/sin-Jg/T1 versus Me/tan 0 will give a line of slope equal to e . Knowing T, the time interval between pulse cycles, Tl can 101 be calculated. In an actual experiment, T is chosen approximately equal to 0'5T1° Due to the restriction of data memory size (8K), spectral widths used were 500 Hz or 1000 Hz. When larger widths were required, separate experiments were run on each spectral region. For each experiment, 7-14 sets of measurements were taken. Some determinations were run two or three times. All the T1 values were calculated by use of the KINFIT program72 by using appropriate equations. Reproducibility of T1 values was better than 5%. T1 values of the C = 0 group carbon, and of the a-carbon of the N-N- butyl group in 15N-n-butylformamide were determined by taking the average value of the pair of signals split by J . One set of the partially relaxed Fourier trans- 15N_13C form spectra (PRFT) obtained by application of each of the four methods is shown in Figures 12-16 and the results obtained by each method are given in Table 4. (4) Nuclear Overhauser Effect Measurement The NOE is determined by using the NOE-suppress procedure. Two pulse sequences are recorded, one with the decoupler on all the time, the other with the decoupler on only during the 90° pulse and acquisition time, as shown in Figure 17. Due to the decoupling of protons during the acquisi- tion time in both sequences, the final results are that there is only one peak for each carbon. This prevents 102 t(sec) 0.5 E 6.5 9-5 12.5 15.5 I m. Figure 12. Measurement Of T1 for 130 in the -NCH3 groups of N.N-dimethy1formamide by the inversion- recovery’method. 103 .oonozvmm awash Haonmoaon on» an ocwsasnomahnvmsdcuz.z cw mnzoum nmoz «:9 non mosam> H9 and mo vcmaunammoz .nH Unawam ma . ma a23L>4§2L<ér3 ma ma €153.54 E 253 .. 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In this sequence, T1 is the estimated spin- lattice relaxation time,-entered via the teletype, P1, P2 are the 180° and 90° pulses, which are varied from 1-100 usec in two ranges by three-turn 'potentiometers, n is an integer varied by the program from 1 3 n i NP, t = 4T1/NP, and NP is the number of data points desired. Before the experiments, the probe and image filter were carefully tuned to the N-l4 resonance frequency. The homogeneity was also maximized. The magnetic field is fixed by the proton external lock at the H O upfield sideband. 2 The temperature was regulated by the heater-sensor and V-4343 variable temperature controller and the tempera- ture was determined using a copper-constantan thermocouple. During the experiments the temperature is very stable. E. WH-180 NMR Spectrometer A Bruker WH-180 multinuclear NMR spectrometer was used to obtain the 15N and 170 chemical shifts and the T 1 values of 17O. The spectrometer consists of a supercon- ducting solenoid, a Nicolet 1180 computer, and the necessary accessories such as plotter, disk system, etc. The spectro- meter is computer controlled as are the CFT-20 and DA-60. Like the CFT-20, there are three RF frequencies involved in the observation of the desired nucleus (e.g., 15N, 17O): (1) The lock channel frequency-2D(45 MHz), (2) The decouple channel frequency-1H (180 MHz), and (3) The observe channel frequency-the resonance frequency for the observed nucleus 113 (e.g., 15N or 17O). The 15N (or 17O) and 2D frequencies are pulsed on and off instead of using continuous waves. The observe or look channel receiver is gated off during each pulse and then on for phase-sensitive detection be- tween each pulse. This technique can (1) eliminate the leakage between transmitter and receiver, (2) eliminate the field modulationanuiunwanted side bands, (3) optimize lock and observe channel separately for improved sensitivity, and (4) improve efficiency in the decouple channel since power is not dissipated in side bands. 15 In order to improve the sensitivity for N and 170 spectra in our experiments, the phase-alternating- pulse-sequence (PAPS) and quadrature-detection techniques are employed. Conventional time-averaging techniques (e.g., those used on the CFT-ZO and DA-GO) normally will result in a reduction of incoherent noise but are in- effective in removing coherent noise. Such coherent noise usually comes from the computer, A/D converter and pulse generator. In the WH-180 NMR spectrometer, all such effects can be removed by the PAPS technique which employs phase alternation of the observe RF pulses (180° phase shift). The input signals produced will then have alter- nating phases (+ and -); the + signals are added to memory and the - signals are subtracted. In this manner the desired signal is coherently added, coherent (phase-inde- pendent) noise is cancelled out, and incoherent noise is 114 averaged. In addition, the PAPS technique can prevent Spin-echoes, which occur when the pulse repetition rate is faster than the time required for complete free induction decay. This effect will produce phase and intensity dis- tortion in transformed spectra. In conventional FTNMR, a single phase-sensitive detector (such as used on the CFT-20 and DA-60) can only determine the magnitude of the frequency difference between the signal and the rf pulse, but not the sign of this dif- ference, so the rf pulse is usually set at one end of the Spectral region to avoid folding back of the resonance. This gives rise to two problems: (1) The power bandwidth of the rf pulse must be equal to twice the total spectral width (i.e., yHl > 20(sw)), and (2) Noise from the unused side of the carrier frequency is folded into the spectral region decreasing S/N by 40% (a factor of /2). Quadrature detection can solve both of these problems directly. The incoming sample signal is fed to two identical phase- sensitive detectors whose reference signals differ by 90°. The resultant audio signals are passed through identical low-pass filters digitized by a multiplexed A/D converter, and stored in separate data memory blocks. Quadrature Fourier transformation produces a real and imaginary spectrum in a manner analogous to normal detection with the exception that now + and - frequencies (relative tothe RF carrier) can be carried. Thus, the rf pulse may be 115 applied at the center of the spectral region with the following advantages: (1) Audio filters can be optimized at half the bandwidth necessary for normal detection giving a S/N improvement of /2, or a time saving factor of 2, and (2) The transmitter power is now symmetrically distributed about the center of the spectral region, allowing twice the normal usable spectral width at any given pulse width. Since the rf power requirement varies as the square of the spectral width, quadrature techniques bring an effective gain of a factor 4. Switching from normal to quadrature detection is performed by a single program command. In addition to the above two advanteges, the WH-180 can also perform a wide variety of experiments: (1) Homo- nuclear decoupling experiments for proton FTNMR, including cw and gated decoupling, and (2) Heteronuclear decoupling including broadband, single-frequency on- or off-resonance, gated decoupling and inverse-gated decoupling. The Nicolet-1180 computer is incorporated into the spectrometer with the 8K program FTQUAD located in 400- 17777 with starting address 1000; FTQUAD includes a sophisticated microprogram. The data memory available in this computer is 16K. With the FTQUAD program the follow- ing experiments can be carried out by entering the commands through the teletypewriter: (1) T1 experiments, (2) NOE determination, (3) Solvent peak suppression and sample homodecoupling experiment, etc. 116 The FTQUAD program can also leave the central pro- cessor of the computer free to perform any calculations and output commands while the spectrometer performs the auto- mated experiments. In the 170 T1 experiments, the inversion-recovery procedure is used. The 180° pulse is about 72 usec. Due to the quadrupole moment of 17O (I 3/2), the spin—lattice relaxation times of most amides are rather short so it is convenient to use this pulse sequence. II. MATERIALS A. Compound Preparation All of the amides used in this work are listed in Table A (symmetrically N,N-disubstituted amides), Table B (unsymmetrically N,N-disubstituted amides) and Table C (N-monosubstituted amides). Boiling points are also given in these tables. (1) N-thhyl-N-t-butylacetamide In order to prepare this amide, N-methyl-N-t- butylamine was first prepared76 by adding t-butylamine (73.14 g; 1.0 mole) to ice cold formic acid (160 g; 3.0 mole, 85% purity) in a three-neck flask. The three-neck flask was then equipped with a reflux condenser, a thermo- meter and a separatory addition funnel and the contents were stirred with a magnetic stirrer. The reaction mix- ture was brought to 50°C by means of a heating mantle. jFormaldehyde solution.tl.25 mole) was added dropwise (2 drops per 117 Table A. Physical properties of symmetrically N,N-disubstituted amides. Amide B.P Source (°C/mm) N,N-Dimethylformamide 31.5-34.0°/25 mm A N,N-Dimethylacetamide 44.0-45.0/3 B N,N-Dimethylpropionamide 51.0-52.0/3 C N,N-Dimethyl-n-butyramide 47.0-47.5/0.5 C N,N—Dimethylacrylamide 46./3 D N,N-Diethylformamide 177-179/760 E N,N-Diethylacetamide 60.5-6l.5/2 C N,N-Diethylpropionamide 53.0-54.0/l.5 C N,N-Diethyl-n-butyramide 61.0-64.0/l.0 C N,N-Diethylacrylamide 106-107/? D N,N-Di-n-propylformamide 60.5-61.5/2.5 F N,N-Diisopropylpropionamide 6.20-62.5/0.5 C N,N-Diphenylacetamide M.P. = 103°C C 3-Methyl-2-phenylbutyramide M.P. = 111-112°C B A: Fisher Scientific Company, Fair Lawn, N.J. B: Aldrich Chemical Co., Milwaukee, Wisconsin. C: Eastman Organic Chemicals, Rochester, New York. D: The Borden Chemical Co., Philadelphia, Pennsylvania. E: Matheson Coleman and Bell, East Rutherford, N.J. F: Prepared by L.A. Laplanche in this laboratory.78 118 Table B. Physical properties of unsymmetrically N,N-disubstituted amides Amide B.P. Source (°C/nun) N-Methyl-N-n-butylformamide 55.0-56.0/l.0 A N-Methyl-N-ethyltrimethylacetamide 62.0-65.0/5.0 A N-Methyl-n-butyltrimethylacetamide 75.0—76.0/2.0 A N-Methylformanilide M.P. = 8-13 B B.P. = 243-244 N-Ethylformanilide C N-methylacetanilide M.P. = 102—104 B B.P. = 258/731 N-Ethylacetanilide M.P. = 55 B B.P. = 266/712 N-n-Propylacetanilide M.P. = 49 D B.P. = 266/712 N-n-Butylacetanilide M.P. = 24.5 B.P. = 281/760 C or 141/10 N,N'-Dipheny1urea M.P. = 238 N-Methyl-N-t-butylacetamide 262/760 (decomp) 56.5/5 E A: Prepared by L.A. Laplanche is this laboratory. B: Eastman Organic Chemicals, Rochester, New York. C: Aldrich Chemical Co., Milwaukee, Wisconsin. D: City Chemical Corporation, New York, New York. E: Prepared in this work as described in the text. 119 Table C. Physical properties of N-monosubstituted amides Amide B.P. Source (°C/mm) N-Methylformamide 56°/6 mm A N-Ethylformamide 63.2-64.0/l.0 A le-n-Butylformamide - B N14-n-Butylformamide 81/5 C N-t-Butylformamide 67/l.5 B N-Methylacetamide 80.0-81.0/2 C 204-206/760 N-Ethylacetamide 80-83/l.5 A N-Methylpropionamide 89.0-90.3/2.0 A N-Ethylpropionamide 78.5-79.5/2.5 B Thioacetamide M.P. = 76-79 A A: Eastman Organic Chemical Co., Rochester, New York. B: Prepared by L.A. Laplanche in this laboratory (Reference 78). C: Aldrich Chemical Co., Milwaukee, Wisconsin. 120 minute) through the separatory addition funnel to the mix- ture. The reaction mixture was then treated with 50 m1 concentrated hydrochloric acid and 100 ml of liquid was distilled from the mixture. The residue was made strongly basic with a 50% NaOH solution and this mixture was fractionally distilled through a 3-foot Vigreux condenser. The purity of N-methyl-N-t-butylamine was checked by proton NMR until no impurity signal existed in the distillate. A solution of NaOH (89 (0.2 mole) in 25 ml water) was added slowly to N-methyl-N-t-butylamine (17.49) in 35 m1 of water.77 The resulting solution was cooled in an ice bath for about 3 hours, then 0.2 mole of acetyl chloride was added at such a rate as to keep the temperature below 10°C. The mixture was then allowed to come to room temper- ature and the amide layer was decanted.. The aqueous layer was extracted three to four times with 12.5 ml portions of ether. The ether extract and the product were combined and dried over potassium carbonate and the ether was evaporated. The amide was collected by vacuum fractional distillation. B. Purification of Compounds (1) Liquid Amides All the amides which were liquid at room temperatute were dehydrated by 4A molecular sieves (Matheson Coleman and Bell, Norwood, Ohio) for about 2-3 days then distilled under vacuum. 121 (2) N,N-Dimethylformamide N,N-dimethylformamide was mixed with potassium metal (a small piece) to dehydrate it and then distilled under vacuum. (3) Solid Amides These were purified as follows: N,N-Diphenylacetamide, N-methylacetanilide, N—ethylacetanilide, thioacetanilide and benzamide were recrystallized from hot distilled water three times and then dried under vacuum. The crystals were sublimed and collected on a cold finger. The pure crystals are colorless. N—n-Prgpylacetanilide was recrystallized from a mixture of ligroin and ether (50:50,v/v) three times and then dried under vacuum. The pure crystals are colorless. Thioacetamide was sumblimed onto a cold finger. The pure crystals are pale yellow. C. Purification of Solvents (l) Dimethylsulfoxide was dehydrated by 4A mole- cular sieves for about 1 week, then distilled under vacuum. (2) Carbon tetrachloride was passed through an (solid) activated alumina column, then mixed with KMnO4 and distilled at atmospheric pressure. (3) Deuterated chloroform was purchased from Merck, Sharp and Dohme of Canada Limited, Montreal, Canada,in a sealed, coated vial and was not further purified. 122 (4) Deuterium oxide for NMR use was purchased from Mallinckrodt Chemical Co., St. Louis, Missouri, and was fractionally distilled. (5) Cyclohexane was distilled over potassium and benzophenone to remove water and oxygen. All these pro- cedures were carried out under nitrogen. (6) Benzene was distilled over sodium,and benzo- phenone under nitrogen,to remove water and oxygen. D. Sample_preparation (l) 13C Samples All the 13C NMR chemical shifts, Tl values and NOE data were obtained by placing the amides in a 5 mm inner tube with the deuterated compound in the outer tube as the external look, as shown in Figure 20. The restriction at point A serves both to reduce diffusion at the liquid- 43 vapor interface, which provides an additional source of relaxation through spin-rotation in the vapor phase, and also to restrict the sample to the most homogeneous region. of the magnetic field. The oxygen in the samples was re— moved by bubbling N2 through the solutions for 1-5 minutes and then degassing by the freeze-pump-thaw cycle at least 5 times until no gas bubbles were visible. The samples were sealed off in vacuo. The 13 C chemical shifts of the pure liquid amides were determined by using TMS as a reference in the outer tube, and CDCl3 as an external lock. In order to measure 123 6% Seal ? Teflon spacer llfllllll JIIIHIIE Deuterated compound for external lock Sample l4-r——5 mm o.d Inner tube ->l |<-8 mm o.d. Outer tube Figure 20. Sample tubes for OFT-20 NMR spectrometer. 124 the relative amounts of the EEEEE and gig forms in some amides, a 90° pulse and a sufficient pulse delay were used. The corrections to the chemical shifts due to the bulk dia- magnetic susceptibilities of the liquids are about 0.1- 0.2 ppm. Since most of the susceptibilities of the amides were not known, this correction was neglected. In the variable temperature studies of T1 the external lock signals used were as follows: CDCl3 for low temperatures: 10°C to -60°C D20 for medium temperatures: 10°C to 80°C DMSO-d6 for high temperatures: 80°C to 150°C. (2) 14 The N Samples 14N chemical shifts and T1 values were deter- mined in a 15 mm NMR tube. The samples were not degassed. (3) 15N and 170 Samples 15 17 The N and 0 chemical shifts were determined in 25 mm and 20 mm NMR tubes, respectively. The samples were not degassed. (4) 13C Samples with added paramagnetic salt To prepare the solutions containing different amounts of MnCl ~4H 0 had been 2 2 dehydrated under vacuum, at a temperature over 300°C, for 2 in N,N-dimethylformamide, the MnCl 3-4 days. Then the solutions were carefully prepared, de- gassed and sealed. 13 (5) C Samples for solvent-effect measurements In the preparation of samples of N,N-dimethylacetamide 125 in formamide, N.N-dimethylformamide in benzene, and N,N-dimethylacetamide in cyclohexane, the solutions were all degassed and sealed. SECTION 1. NMR STUDIES OF MOLECULAR MOTION IN SYMMETRICALLY N,N-DISUBSTITUTED AMIDES I. BACKGROUND Amides have been studied more extensively by NMR spectroscopy than any other class of compounds. The substantial stimulus arises from the importance of the amide linkage in the peptide chain and in proteins. For the last twenty years or so, most of the NMR studies of the amides have been concerned with determination of the energy barrier for rotation about the central C-N bond and its relationship to the C-N partial double- bond character. However, only a few papers have been reported concerning investigation of the overall molecular motion in amides 39’54'58’59’80'81. The difficulties arose from the complicated molecular motion in amides, including overall anisotropic molecular reorientation, internal rota- tion, and segmental motion. Several studies of anisotropic molecular motion using quadrupolar relaxation have been made82’83. Nuclei with spin I > 1/2 will possess an electric quadrupole moment, which can be relaxed by the interaction of the quadrupole moment with the molecular electric field gradient at the nucleus. The electric field gradient at the nucleus results from the distribution of electrons in the 126 127 molecule and fluctuates in orientation in the spaceffixed axis system owing to molecular tumbling. Translational motion does not affect the orientation or magnitude of the electric field gradient at the nucleus and thus does not contribute to the relaxation. Furthermore,the quadru- pole interaction is so large that it is usually the dominant relaxation mechanism. The complication of including several mechanisms for relaxation, and account- ing for relative translation, in an expression for the relaxation time can thus be neatly avoided. By using quadrupolar relaxation, Huntress et al.39’54, have studied the anisotropic molecular motion of N,N-dimethylformamide in the liquid. However, some disadvantages have arisen, since most of the quadrupolar nuclei have very low natural abundance and their NMR linewidths are very broad. As a result, enriching of the isotope is necessary in some cases and the measurement of T1 by pulse sequences is more difficUlt due to the broad signals. 9 13 Since natural abundance C NMR Spectra have become available, there are several advantages to using 13C NMR to investigate the molecular motions: (l) The intermolecular interactions can usually be neglected since the carbons are in the backbone of the organic molecules, (2) The . . . 13 main relaxation mechanism for C iS the dipole-dipole inter- action, which can be separated from other mechanisms by measurement of the NOE effect,and (3) T1 data for several 128 carbons in the molecule can be determined simultaneously. In 1962, Woessner40 developed an expression for T1 in a symmetric-top molecule with no internal rotation in terms of the two unique parameters Dll and Di. These specify, respectively, the rotational diffusion about the C3 axis and about the two perpendicular axes perpendicular to C3: 2 '1'1 = néfi YI:YSZ ( 63 + SD B + D + 20 E 4D )° (132) l(DD) r18 1 1 H 1 H Here A,B, and C are geometrical constants ub||-‘ (31,2 - 1)2 B = 31:2(1 - £2) _ 3 2 _ 2 4 (Z 1) . O I £ is the direction cosine of the angle between the C-H vector and the C3v axis. YI and Y8 are the gyromagnetic ratios of nuclei I and S, n is the number of 8 nuclei S bonded to I, r is the distance between I and S, and‘fi IS is Planck's constant divided by 2n. Treatment of internal rotation by a methyl group attached to a rigid symmetric-top molecule has also been developed by Woessner et al.84 giving 2 1 = néfi Y121‘s2 ( A1 +Az'+ A3 + Bl T1(DD) r136 6D1 601 + R 5Dl + DH + B? + B3 + C1 + C2 + C3 ) (133) SDl + DH + R ZDl + 4DH 2Dl + 4DH + R ° 129 In this equation A = (l - 3cosza)2(l - 3coszA)2 1 con-- _ EL . 2 . 2 3L . 4 . 4 A2 + A3 - 16(Sin 2a)(31n 2A) + 16(Sin A)(Sin a) Bl = -g-(sin22a) (3cosZA - 1)2 B2 + B3 = %(c0322a + cosza)(sin22A) + %(sin2a + %sin22a)sin4a C = 2(3coszA - l)zsin4a l 8 _ ;1_ 2 2 2 . 4 C2 + C3 - 16[(1 + cos a) + 4cos a131n A + %(sin2a + %sin22a)(sin22A), where A is the angle between the C-H vector and the internal rotation axis, a is the angle between the internal rotation. axis and the symmetry axis of the ellipsoidal molecule (as shown in Figure 21), R is the internal rotation rate of methyl group, and all the other symbols have the same meaning as in Equation (132). However, the expression for an inter- nal top attached to a completely asymmetric rigid molecule has not been developed yet. The symmetric-top formulation, Equation (132), for dipole-dipole spin relaxation has already received 13 49,50,52,85 attention in C studies ; however, Equation(133) for a methyl group attached to an ellipsoidal tumbler has 13C relaxation data. To not yet been utilized to interpret be precisely applicable, this formulation requires that the D2h symmetry group of the diffusion ellipsoid holds and that 130 exile synun tq - tlzip;oid.ry " Ofe Figure 21. Coordinates for the orientation of the relaxation vector r in the diffusion ellipsoid. X, Y, and z are the principal axes of the ellipsoid while X', I.. and Z. are the internal rotation axes. a is the angle between the Z and Z. axes. and A is the angle between 0 the r vector and z axis. 131 the molecule possesses three uniquely different carbon atoms with attached protons whose C-H vectors manifest linearly independent sets of directional cosines. Such conditions allow diagonalization of the rotational diffu- sional tensor and provide sufficient data to specify its three diagonal components. Unfortunately, these conditions are so restrictive as to eliminate any extensive application of the theory, and, therefore, we have used the equations to give an approximate treatment of molecules with slightly lower symmetry. Levy et a1.57,63,86--88 have utilized the symmetric- top equation for planar molecules, such as substituted benzenes, and have estimated the approximate tumbling ratio for the benzene ring rotating about the preferred rotation axis and about the other two perpendicular axes. In their systems, the molecules are treated as being axially symmet- rical, although all the nuclei in the benzene ring are in one plane. Most of the macromolecules in proteins may also treated as ellipsoids (as shown in Figure 22). Since amides are planar in the ground state, due to the C-N partial double-bond character, and their proper- ties are like proteins, an ellipsoidal molecular model may also be assumed if a preferred rotation axis in the molecular plane can be found in the amides. Equation (133), treating the methyl group relaxa- tion in an ellipsoidal molecule, has never been utilized 132 RELATIVE DIMENSIONS OF VARIOUS PROTEINS Scale ’——_;_* + a- 0 100A No C‘L Glucose , ._ ' x , _ .. . Q.. .... e ’) ( I (‘- xx v ', qu albumin Insulin B-Lactoqlobulin 42, 000 36. 000 40. 000 W-~—‘_ (fl , ..,..,.... 'H“ (WW...) «-.....a (111.-....1» Albumin Hemoglobin B, -Globulin 69. 000 1 68,000 90. 000 . K .... .. 9..-. -.., ', ‘ ’ “as . - lg ion-1.0!?“ W .. :n‘ ‘ . I” l _ .-. , u. ' .. {i . .0" C I r u ‘* -—...'- '~ ---' "" WM“, ... — ar- Lipoprotein \ .7 y-Globulin 200,000 ‘ . _,- 156.000 )8. - Lipoprotein l. 300.000 _~¢ av r-v-‘i ....~-r "'“" ' - " .- ' ' ”'9” 'r ‘ ‘O -- fir ‘ «...- ‘. . n ‘ .. ...“ """""N~-‘.. :. ...; _.._. -.._..L. .. . Q- ' J Fibrinogen 400,000 «infirm ' ’i‘ 1 L‘ :1" gm, Edestin Zein 310. 000 50. 000 “WWW Gelatin (undegraded) 3 50. 000 Estimated dimensions at various protein molecules as seen'in projection. Most of the proteins are represented as ellipsoids of revolution. fi-lipoprotein is a sphere [J. L. Oncley, Harvard University]. The molecular weight M. is given under each name. Figure 22. 133 since it was published. In order to apply Equation (133) to the amides, an ellipsoidal molecular model should be assumed, and to further simplify the problem, the condition It>> V D1 is assumed. We also define p = B—— , so that DI Equation (133) can be reduced to 2 1:“8“ YIZYSZ ._1_(§1._51__.__‘31___) T1(DD) r 6 D 6 5 +r> 2 + 4p SI 1 (134) If there are two methyl groups whose C3v axes make different angles with the preferred rotation axis, then the tumbling ratio for rotation around the preferred rotation axis relative to rotation about the perpendicular axis can be obtained from the ratio of their relaxation rates, as shown by the following equation: __1__ B c Ala la la "71(na)a_ (T + 5_+ 0+2C_+ 4"p' ) , (135) __1__: , —— ( A11: +_ Blb Tlrnnib T 5+p ”'C12+4J where subscripts a and b denote the methyl groups in the a and b p051tionsand A , B , C , Alb' Blb’ and C1b are all la la la defined as in Equation (133). The effect of the motional anisotropy resulting from the shape of the molecule, approximated as an axially symmetrical ellipsoid, has been given by Woessner4q.who compared the relaxation rates corresponding to rotation about the principal axes of an ellipsoid to that for a 134 sphere of the same volume (Figure 23). It can be seen from Figure 23 that in an ellipsoidal molecule with p = b/a < l, the C-H vector having a larger angle with the principal symmetry axis of the ellipsoid will have a smaller relaxa- tion rate. This effect is especially enhanced in a rod- shaped molecule (p << 1), as shown in the left part of Figure 23. II. RESULTS A. Studies of the anisotropic molecular motion in gLN-dimethylamides by an approximate ellipsoidal model Table 5 shows the 13C chemical shifts, spin-lattice relaxation times Tl’ nuclear Overhauser enhancements NOE, dipolar relaxation times T effective correlation l(DD)’ times 16, and the relaxation times due to other mechanisms Tl(0) for several N,N-dimethylamides. 13C relaxation times for the trans- and The different gig-NCH3 group carbons, relative to that for the C = 0 group, indicate that the overall molecular reorientation of the N,N-dimethylamides is anisotropic. This anisotropic ef- fect is especially important in N,N-dimethylformamide, as compared with other N,N-dimethylamides, as shown in Figure 24. To describe this anisotropic motion, we will assume that there are two axes in the molecular plane, one the pre- ferred rotation axis, as shown in Figure 25 and 26, the other perpendicular to this preferred rotation axis but still in the molecular plane. The third axis is perpendicular to the molecular plane, and 135 23 23.5.2 ammo-somfiwammammmumwmwomaw mm” mmpwwsommmwosfimem can 0 u .q pm oopasam>o v coapnadxonnna moxovm on» wsaauno moaowvuan non a\n u a owpnn amass as» no :oapocsu a on assao> mean one no change a Ca page op canonsoo oaomowaao oaupoaahu hHHdwxa ad :« coavdxaaou one .mm unawam Almaa m6 :6 n6 «.0 H6 undid-l1: a .3 0.: o.m o.m I u q I 1 d u O J O N ON.Q L O M H u .s I 00 OO O O 0 00050 ‘n d’ H aaeu dsrTr/ri . “Tarts/r) 136 mH.eoa i mw.HNH no.m vm.H H mo.mm mm.mha o u o mm.H Hm.mm Hm.n mh.~ NH.o H Hw.m em.m Utmt nomlamsonnmo Hw.m oo~.A HH.m vm.m mH.o H mm.m mm.mm H oral nsmtamsmnumv Nh.o mw.mm om.o~ vm.~ om.c H mo.~a ~m.em onahnuofitz uoHEmsowmonm vm.o mm.om Ho.hm mo.~ mm.o H ov.ea mv.mm Auvamnuwfirz HmnquHUIw.% U r mm.mma mm.mmH vo.~ on.m H mm.mw mm.oha o u U va.a mv.hw mm.~H no.~ mm.o H mn.oa ~w.om manlamconumo mm.o nm.a¢ hm.am Hm.m wv.o H m~.va aa.vm AUVHmSHuEIZ mowfimumom hm.o ma.vm nm.am HN.N mH.o H hm.ma mm.hm AuvamnumErz ahnuoawvrz.z :5 mn.a hv.mma mm.m~ nw.~ mm.o H mH.HN mm.ama o u U mm.o mm.om vm.m~ mm.N mv.o H mm.mH mm.m~ “ovahnuofirz mowaoEHOM mo.H sm.mn mm.ma hm.m em.o H em.HH mo.mm AuvahnuoErz HanumEHoiz.z Ls» com com com o moz H “eddy uHHam unusuHumnsm ecsodsoo «Hoax p AOVHB AQQvHB Aommv a HMOHEonu e.mooHEmH»zumEHv4€;gHmum>wm mo .Amozv musoaooconqm Hansonuo>o Homaoss can .AHBV maEHH sowuoxoawu mOHuumHIGHmm .mumwnm HMUHEmnu U .m manna ma 137 .conumo Hmconumo so HamsuflumnSm Hagan any mo conuoo a map muumowpsH Urornsmraasonumoee .saa No.0 H was HHHam HmoHsmao :H mucosa manmpona was .asoum o u u on» on m>HHmaoH moon» n H .mmm u o .Uomm mode 0Hm3 musofimHsmon one .cmeHHsm mums mocsomEoo one HH< .onHmc3ov mwumoHosH + .mze ou obfluoamu who mHMHnm HMUHEanoe va.v no.mm mw.oH on.m maso H Ha.m mm.moH o u U mcHEmEHom i mm.mma Hp.hnar nm.a ~m.m H an.mm ov.mma o u o Amv nm.m nm.ova mm.o om.m vm.o H v~.w Hm.mma vim insmerCOQHoU mo.m mm.mm mm.va om.m mm.o H om.HH Ho.m~H Uta . insuramsonumo Hm.wH ma.em xocHsauosiz moHsmHHHom Hm.aH mm.mm xuvHHsuusiz HasumsHoiz.z Ame mv.o NN.mm mm.mm oc.N mv.H no.0 om.ov mm.om mH.N mo.H +l +l r . .NH.mNH na.~m mH.N na.~ H mn.mm mm.ama o u U ov.H vm.mm om.oa mm.m Hm.o H mm.> mm.mH or» insmiflasonumu wn.m oa.mm em.n mm.m v~.o H ma.m wa.ma 01m insuramsonumo mv.m nm.mm mm.o mm.m mH.o H mo.m Hm.vm Uio rbsmrH>c0meo «N.NH m~.em locassumsiz uanmmuusaiai mm.~H em.om AuvHsnumsiz. HanumsHoiz.z .bav 0mm 0mm 0mm onoe onHe Aeneas moz “canvas leads ustm unusuHumnsm . ocsoasoo . Hmowfionu mm.o mo.hN mN.NN mo.m Nh.o wm.o wo.m~ mN.wN hm.H mm.o +| +l A.©.ucoov m mHQMB 138 .09 r m .08I- a l/Tl(sec-l) 0 .06. I .05 l 1 L l J I 60 7O 80 90 109 110 120 130 Molecular Weight Figure 2h. Relaxation rates of 130 in the trggg- and ci - NCH3 groups of N,N-dimethylformamide (Oltfii N.N-dimethylacetamide (OH I) , N .N-dimethyl- prepionamide ((D)( Z), and N,N-dimethyl- n-butyramide (9H 8) o plotted versus the molecular weight of the amides. .‘ .\° .. ..e \\ , e' \ __ g \V i?!— 70.5 ‘ (15) 1.47A 88.7°‘ .3° .47A (15) 1.32A (16V '4. 1.22A 1.08A (1) Figure 25. The preferred rotation axis for molecular motion in N.N-dimethylformamide(arrow). The bond angles and internuclear distances used in the calculations are shown. 140 .33 Houseman on» 3 m .-mmommommo a m no.“ .mwxo.oosnomosn on» pH m .imxommo u m new .ooassuhvsnrsraasvoaHoiz.z can ooHBMSoHAoHQHthoEHoiz.z Ho soHvoa unasooaos you mean soHpnvon cunnououm .om onsmHm . m (fir..— (Av.— < «n.— «N.— (NV.— 141 rotation about this axis will not affect the difference between the relaxation rate of the trans: and gig-N-methyl groups, since it makes the same angle (90°) with both N-methyl groups. Thus, the difference between the relaxa- tion rates for the trans- and cis-N-CH groups is attributed 3 to rotation of the molecules around the axes in the molecu- lar plane. However, in N,N-dimethylamides, the diffusion rate around the preferred rotation axis will be much faster than that about the other axis in the molecular plane, since rotation around the preferred axis will affect the neighboring molecules less than rotation about the other axis in the molecular plane. Therefore, the relaxation rate of trans- and cis-NCH groups will be mainly dependent 3 on the direction of the preferred rotation axis in the molecular plane. For the approximate ellipsoidal model, we will assume that the symmetry axis of the ellipsoid is along the preferred rotation axis in the molecular plane. Thus, on the ellipsoidal model, the considerably larger relaxation rate of the EEEEE‘NCH3 group in N,N-dimethyl- formamide (DMF) is attributed to the angle between the preferred rotation axis and the N-C bond of the Eggnng-CH3 group being considerably smaller than the angle between the preferred rotation axis and the N-C bond of the gig-N- CH3 group (Figure 23). In N,N-dimethylacetamide (DMA) the difference in the relaxation rates between the carbons of the trans- and cis-NCH groups is greatly reduced, which 3 142 shows that the preferred rotation axis has been shifted until it is approximatly parallel to the central C-N bond of the amide. However, in N,N-dimethylpropionamide (DMF) 13 and N,N-dimethyl-n-butyramide (DMB), the C relaxation rate of the cis-NCH carbon is greater than that of the 3 EEEEE‘NCH3 group, indicating that the preferred rotation axis makes a larger angle with the N-C bond of the trans- NCH3 group. These results show that the preferred overall molecular reorientation axis has been shifted from being nearly parallel to the N-O direction in N,N-dimethyl- formamide to the direction shown in Figure 25 in N,N- dimethyl-n-butyramide. Since the variation of the 13C spin-lattice relaxation rates for trans- and gig-NCH3 groups in going from N,N-dimethylformamide to N,N-dimethyl- n-butyramide is mainly attributed to the change of the substituents on the carbonyl group (from -H to -C3H7), we can see that the change in the direction for the preferred rotation axis in the molecular plane is mainly determined by the relative masses of oxygen and of the carbonyl sub- stituent (R). This means that the inertial effect is an important factor in determining the direction of the pre- ferred rotation axis. In N,N-dimethylformamide the atomic weight of oxygen is sixteen times that of hydrogen,so we can assume that the preferred rotation axis is along the N-O direction, as shown in Figure 25. However, in N,N- dimethylpropionamide and N,N-dimethyl-n-butyramide, the 143 masses of the carbonyl substituents are greater than that of oxygen, so the preferred rotation axes are shifted to the directions indicated in Figure 26. The directions of the preferred rotation axes in our models are determined by the ratios of the masses of the carbonyl substituents (R) and oxygen. In order to apply Equation (132) to (135) to our compounds, the bond lengths and bond angles for the amides are required, and the standard values89 for the amides shown in Figures 25 and 26 were used. The 13C relaxation rates for the carbons of the nonequivalent EEEEET and giseNCH3 groups can be used to calculate the ratio 0 = DII/Dl of the diffusion constants. From Equations (135) and the molecular dimensions given in Figure 25, the 13C relaxation relationship between D and the ratio of the rates for the gig: and trans-NCH3 groups in DMF was ob- tained and is plotted in Figure 27. Similar relationships were obtained for DMP and DMB by use of Equation (135) and the information in Figure 26; the results are plotted in Figure 28. From the experimental values of T for the 13 l(fl» methyl C's of DMF, DMF and DMB given in Table 1,the values of p were calculated and are shown in Table 6. These p values can be used as an estimate of the anisotropy of the overall molecular motion -- the larger 0, the more anisotropic the motion. Also, once the values of p have been determined, the absolute values of DH and D1 can be 1.0 (l/Tl)cis 3 (l/Tl)trans 144 l I I I I I I I I I I I I I l I I I I - l I l i J .1 1 1 1 1 I '1 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 p—> Figure 27. Calculated ratio of the relaxation rates for 13C in the cis- and trans-NCH versus p: ”7131 for DMF. 3 groups plotted (l/Tl)cis (l/Tl)trans 145 2.0 1.8 f’. o- N o- O O I 1 l_ L- n 1 1 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 p» Figure 28. Calculated ratio of the relaxation rates for 130 in the cis- and trans-NCH3 groups of N,N-dimethylpropionamide (--—-) and N,N-dimethyl-n-butyramide (----) Plotted versus 9 = DH/Dl. 146 mcmuu mHoAH AHB\HC \ .msonm Hmnuuaiz so mo mums coHHmuou Hmauuusw asu.mH m .Hawoe ecu sH oussmmm cHommHHHu .Hn\_o u a can B\HV oHHoH on» mmumoonH H\o coHumuos one Q oHHHmfismm mHHmem ecu mo mem muumeshm on» OH HmHsOHocmmnom can Hmaamumm mucmumsoo conDMMHU HmHsooHOE HHmHm>o map mum 40 can :0 .Uomm Hm cmHSmmmE mum3 mwowfid as» Adda oaxom.s m.H luxucmH.H meHsmususniansnumsHeiz.z «Hoaxa.e Naosxm.m oaoaan.e OH NHonv.m NHonm.e oaoaxaa.m oaoaxem.s o.~ Ao\uVeH.H uoHEHaoHdoustanmsHeiz.z NHOme.e NHOHxa.e oHOHHOH.m oaoaxom.m o.H Auxuvao.H moHsmuuomHmnumsHoiz.z «HOme.m NHOHxH.e OHOerm.m HHOHme.~ m.s Au\uvme.H moHsmsHoHHssumaHoiz.z AHioumv AHHWWHV xHiommv AHiommc a AnacwHumu ecsoasoo mcmuum mHUm HQ __Q n B\H m.mooHEth£quHorz.z meow :H masonm HhSHoEIZImHo was imsmuu How mmuoH sowuouou HosHchH can Ho . :o museumsoo sonSMMHo ouumasoasu one .w manna 147 obtained from Equation (132) and the experimental relaxa- tion rates of the non-spinning carbons, i.e., the formyl carbon in DMF and either the carbonyl carbon or the a carbon in DMF and DMB. The internal rotation rates for the N-methyl groups can then be obtained by use of Equation (133). These values were calculated for DMF,DMP and DMB and are shown in Table 6. Since the masses of the four substituents (oxygen and the three methyl groups) on the central C-N bond of DMA are nearly equal, its overall motion is almost isotropic3 as seen from the ratio of the relaxation rates of the methyl carbons. Since there are no non-spinning carbons in N,N- dimethylacetamide, Equation (132) cannot be used. If Equation (133) is used for the three methyl groups in DMA, then difficult and tedious work is required to solve for the three unknowns from the three equations. In order to avoid this problem, we usedauiinterpolation method shown in Figure 29 to find the internal rotation rate of the trans- and cis-NCH groups in DMA, and then calculated the 3 diffusion constants by Equation (133). So far, only N,N-dimethylformamide has been studied in details? The reported diffusion constantswat 280°K are 2.0 i 0.4 x 1011 sec-1, a = 6 1 3 x 109 sec-1, and Y 2.90 i 0.7 x 1010 sec-1; the reported DX value is D x D 2 very close to our DH value (Table 6). This is reasonable, 148 5.6 5-2 .. 5.0 L 4.8 4.6 .. 4.4 P 4.2 " 4.0 - . 3.8 b 3.6 P R x 10'12 (sec-l)-*>’ 3.4 - 3.2 l l l I l l _I 1 60 70 80 90 100 110 120 130 140 150 Molecular Weight—D» Figure 29. Internal diffusion constants R for the trans— and gig-NCH3 groups of N,N-dimethylformamide ( I ) ( O ), N,N-dimethylpropionamide ( ) ( O ), and N,N-dimethyl-n-butyramide ( Cl ) ( O ). The dotted‘line gives the interpolated values of R for DMA. 149 since the x axis chosen by Huntress corresponds to our preferred overall molecular rotation axis. The D1 value in our result is an effective diffusion constant perpen- dicular to the preferred overall molecular rotation axis and is some average of the Dy and D2 values (which have been reported in Reference 54). Although individual values of Dy and D2 are not obtained using our approxima— tions, we believe that the Di value obtained by our method should be closer to the larger of the two values Dy, Dz. In the case of N,N-dimethylformamide, Dl is found to be closer to Dz. It might also be expected that the D1 values for DMA, DMF and DMB would be closer to D2 at room tempera- ture since rotation about D2, which corresponds to spinning of the molecule in its molecular plane, should be easier than rotation about Dy. These results show that the 13 C dipole-dipole spin- lattice relaxation rate provides as powerful a method for investigating anisotropic motion as the quadrupolar relax- ation method used by Huntre3354. In calculating the diffusion constants of N,N- dimethylpropionamide and N,N-dimethyl-n-butyramide, the relaxation ratesrxfa carbons on the carbonyl substituents have been used and this may introduce some experimental error due to the segmental motion of the carbonyl substi- tuents. The choice of the direction for the preferred rotation axis may also introduce about 10% error by intro- ducing an uncertainty in the angle of about 10°. 150 B. Determination of the energy barriers for the internal rotation of the NCH3 groups and for the sggmental motion of the carbonyl substituents The energy barriers for the internal rotation of NCH3 groups and for the segmental motion of the carbonyl substituents in N,N-dimethylamides have been determined from the experimental values of the 13 tion times. 13C Tl values for the cis- and trans-N-CH C spin-lattice relaxa- 3 groups and the C = 0 group of DMF are shown in Table 7. Values of £n(l/Tl) are plotted versus reciprocal tempera- ture in Figure 30 for the three carbons and the energy barrier corresponding to each was determined from the slope of the linear portion of the curve by use of the Arrhenius relationship 1/Tl = AeEa/RT . (136) 13C'spin-lattice relax- The temperature dependence of the ation for each carbon of DMA, DMF and DMB is given in Tables 8-10, respectively, and the values of £n(l/Tl) are plotted versus reciprocal temperature for each in Figures 31-33, respectively. The values of Ea obtained from the lepes of the curves are also given in Figures 31- 33. The energy barriers for internal rotation about the threefold axes of the trgns- and gig-NCH3 groups are consistent with the internal rotation rates R and trees Rois in Table 6, except in the case of the high value 151 Table 7. Temperature dependence of the 13C spin-lattice relaxation times of the carbons of N,N-dimethyl- formamide. Ergng-N-methyl gig-N-methyl Q,= O T(°C) (T1)sec (Tllsec T(°C) (T1)sec -51.2 2.78210.128 6.507:0.302 -52.4 3.136:0.106 -30.0 4.384t0.l60 lO.l49iO.l7l -36.0 7.32410.129 -l4.6 5.28110.150 12.151i0.212 -21.0 11.180 t.423 + 2.2 8.183zt.193 16.655 t.26l - 4.0 17.204 i.980 +23.5 ll.lO7:t.378 19.5192t.332 14.0 16.7061:.838 +34.5 13.0802t.368 l9.ll9:t.320 +34.0 20.262 t.364 +50.4 l7.278:t.651 18.755:t.550 +52.2 25.510 t.927 +66.2 21.680:l.070 20.104 1.433 +70.3 27.269zt.621 +83.3 21.53211.680 25.757il.460 88.6 20.2621:.364 +98.0 20.814 t.540 19.071 1.585 101.5 19.790i1.120 +116.0 22.703i1.410 18.965il.060 .120.7 25.333il.900 3.0 N O 4 + Inn/Tl) 1.0 152 II (I L L L l I I l I I 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1 4.3 4.5 u.7 l/T x103 ( ° K’l ) Figure 30. Plot of ln(l/T1) versus l/T x 103 for each 130 of N.N-dimethylformamidei 0 denotes trang-NCHB, C] denotes the 0:0 group. and C denotes ci - NCH3; Ea(t-NQH3) = 2.60 kcal/mol. Ea(c-NCH3) = 2.12 kcal/mol. and Ea(Q=O) = 4.10 kcal/mol. 153 Table 8. Temperature dependence of the 13C spin-lattice relaxation times of each alkyl carbon of N,N-dimethylacetamide. Erggst-methyl ging-methyl Carbonyl-EH3 T(°C) T1(sec) T1(sec) Tl(sec) -16.2 - 10.318 1 0.277 - ~15.9 12.747 i 0.414 10.554 i 0.234 6.507 t 0.289 - 4.6 - 15.595 i 1.480 8.430 i 0.155 + 1.7 15.180 1 0.185 - 11.800 i 0.785 +18.l 18.575 2 0.371 20.597 i 0.789 12.286 i 0.275 +17.3 18.653 2 0.571 18.588 i 0.829 11.925 i 0.444 +26.8 23.168 i 1.860 - 16.461 i 1.160 +55.0 24.624 1 2.490 21.489 1 1.930 18.290 1 0.690 154 3.0 2.5- 005 " L 1 J I l 1 J 1 1 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0 l/T x 103 ( 0 K-1 ) 0.0 Figure 31. Plot of ln(l/T1) versus 1/T x 103 for each alkyl 13c of N.N-dimethylacetamidei 0 denotes carbonyl- 2H3' 0 denotes gig-N9HTD denotes m-NQl-Iat Ea(t-N§H3) . 1.66 kcal/mol, Ea(c-NQH3) = 2.55 kcal/mol, and Ea(0aC-QH3) = 3.27 kcal/mol. Table 9. Temperature dependence of the 155 13C spin-lattice relaxation times of each alkyl carbon of N,N-dimethylpropionamide. trans-N-methyl cis-N-methyl Carbonyl substituent T(°C) T1(sec) T1(Sec) a-C B-C T1(sec) T1(sec) -58.7 .502:.013 .451i.025 .124i.005 .332i.016 -42.6 1.198:.045 .989i.092 .404i.020 .777i.074 -30.2 2.600:.150 3.0561.142 .723i.036 1.549i.063 -l3.8 4.408i.233 5.997i.249 l.576i.027 2.477i.l32 1.0 7.290:.301 6.845:.315 2.530i.161 3.116i.l71 +17.5 10.514i.476 10.104:.480 4.778:.220 5.456i.159 +34.0 l4.400¢.680 12.6601.600 5.96 i.150 6.6101.120 +51.5 18.672i2.220 15.64lt.888 12.618i.625 9.4281.499 +66.5 19.323i.508 19.482i.456 ll.7002.287 11.030i.321 156 5.0 '- u + 1n(1/T1) F O I u o I 1 1 1 1 1 1 1 1 1 1 2.? 3.0 3:2 3.11 3.6 3.8 11.0 11.2 11.11 11.6 11.8 r/T x103 (_° K’l ) Figure 32. Plot of ln(l/T1) versus l/T x 103 for each alkyl carbon of N.N-dimethylpropionamider A denotes 0=C-a-§,. C denotes 0:0-6-21 0 denotes gig-NEH? and Eldenotes trang-NQHB; Ea(0=C-a-Q) = 5.97 kcal/mol. Ea(O=C-B-§_) = 4.37 kcal/mol, Ea(t-NQH3) = 4.38 kcal/mol. and Ea(c-NQH3) = 5.19 kcal/mol. 157 mum.OHmHm.n Hem.OHmmm.m mvH.OHoom.h omm.HHon.- Hme.ovam.>H m.~m+ omv.oHonm.n ov~.oHomH.m omH.oHowo.m omh.OHomm.~H omm.OHomm.Na ~.¢m+ mmm.0Hm~m.v nma.onmv.m mmm.onmo.m oma.ovam.m mom.oH~mm.m ¢.~N mmH.OHva.N moo.OHm>H.m moo.OHmvn.~ omm.onmm.v mmm.onhh.n m.m + boa.OHenm.H mmH.OHmvh.H HhH.onNm.H «mH.onhv.v Hmm.oHa~m.v m.h 1 hmo.0th~.H mvo.onow.o mmo.onmm.o mNH.oHHmv.N mmH.oHoom.H ~.HN1 mmo.lomm.o ~vo.onvm.o mao.onHv.o omo.oH~mv.H mno.0Hm~m.o o.mm1 lommcea rummage Anemone 166.139 Anemone 16.1 01> 01m 015 HhfiHoEIZIHHo HanquIZtmsmuu musuoummfima usosHHHmnsm Hmconuwo .mcflemnzpsnisiahsmeHoiz.z no Congas Hhxam come no muEHu QOHmenHoH moHHHmHIGHmm o as» NO mosucsuauo musumnomsma .oH manna ma 158 l a 3.0.. 4 + ln(1/T1) 2.0 P /‘. 0.0 1 1 1 1 1 l J I 2.8 3.0 3.2 3.11 3.6 3.8 11.0 111.2 11.1111.6 l/T x 103 (O K ) Figure 33. Plot of ln(l/T1) versus l/T x 103 for each alkyl 13C ‘ of N,N-dimethyl-n-butyramidei Cl denotes the a carbon of the carbonyl substituent. n denotes the 3 carbon of the carbonyl substituent. I denotes the y carbon of the carbonyl substituent. 0 denotes m-NQHB. and 0 denotes gig-N915; Ea(0=C-a.-Q) =- 5.71 kcal/mol, Ea(0-C-B-9_) = 5.21 kcal/mol. Ea(0=C-y-Q) :- 4.30 kcal/mol, Ea(t-N9_H3) :- 5.20 kcal/mol, and Ea(o-N9_H3) :1 4.72 kcal/mol. 159 Ea = 5,20 kcal/mole for the trans-NCH3 group of DMB. This value may be attributed to the strong steric effect of the n-C3H7 group, as has been found also in the INDO calcula- tions (Part II). The values of Ea for the carbons on the carbonyl substituents decrease in going from the a to the B or y carbon. This is the expected behavior since the motion becomes freer toward the end of the chain. In the case of the formyl carbon of DMF, and the a carbons of the carbonyl substituents of DMF and DMB, the Ea values may be mainly attributed to the overall molecular motions since the internal rotations for those carbons are not important. The theoretical values of Ba for the N-CH3 groups of DMF and DMA have been calculated and show the same trends as the experimental values,as seen in Table 11. For N,N-dimethylformamide, the ratio of Rtgggg/Dflis equal to 11.34, Table 6. By using the experimental energy barriers of the trgngéNCH3 group and the formyl carbon, the calculated exp[Ea |I/RT]/exp[E /RT] is equal to I aIE£22§ 11.9, which is close to 11.34, indicating that the energy barrier determined for the Egang-NCH3 group is mainly due to the internal rotation of -CH3 while that for formyl carbon (C = o) is mainly contributed from the aniso- tropic overall molecular motion around the preferred rota- tion axis (if the frequency factor is assumed to be the same). This assumption is reasonable since the trans-NCH3 160 Table 11. Energy barriers for rotation about the internal rotation axes of the N—methyl groups and of the carbonyl substituents in N,N-dimethylamides ... ‘I' Compound Substituent Ea Ea A (kcal/mol) (kcal/mol) (sec- N,N-Dimethyl formamide (DMF) trans-NCH 2.60 2.07 0.0247 g;§;NCH 2.12 1.40 0.0178 c=o 4.10 0.00745 N,N-Dimethyl ~ acetamide (DMA) trang-NCHB 1.66 2.03 0.0097 gig-NCH3 2.55 2.99 0.0128 Carbonyl-CH3 3.27 4.69 0.0114 N,N-Dimethyl propionamide (DMF) trang-NCH3 4.38 0.0182 gig-NCH3 5.19 0.0166 Carbonyl-a-C 5.97 0.0302 Carbonyl-B-C 4.37 0.0474 N,N-Dimethyl . n-butyramide (DMB) trang-NCHB 5.20 0.0212 gig-NCH3 4.72 0.026 Carbonyl-a-C 5.71 0.050 Carbonyl-B-C 5.21 0.0498 Carbonyl-y-C 4.30 0.0623 *Calculated values from Reference 90, obtained by the BET method. +The probable errors in Ea are + 0.5 kcal/mol. 161 group is nearly parallel to the preferred rotation axis, as seen in Figure 25. However, the ratio of Rois/DH is equal to 26, and the calculated value of expEEa'”/RTJ/expEEa'glg/RT] 18 equal to 14.1, which indi- cates that the frequency factors for the cis-NCH group and 3 for overall anisotropic molecular motion are different. The energy barrier for the cis-NCH3 group is contributed from its internal rotation and the overall molecular motion. The frequency factor for the cis-NCH group is about twice that 3 of the trans-NCH3 group as can be seen from Figure 25, where the cis-NCH group is almost perpendicular to the 3 preferred rotation axis. In N,N-dimethylacetamide, N,N-dimethylpropionamide, and N,N-dimethyl-n-butyramide, the calculated values of Rtrans/DH and R££§/DH are quite different from those of exPEBa,a-c/RTLéXP[Ea,trans/RT] and expEEa’a_c/RTJ/ exPEEa,giéRT]' which indicates that the measured energy barriers for the Egggg- and gig-NCH3 groups contain contri- butions from both the internal rotation and the overall molecular motion.‘ This can be seen from the values of D and of the diffusion constants D” and D1 for these three amides, which indicate that the overall molecular motions about the three principal axes are each important. C. Separation of the total spin-lattice relaxation rate into components Once the internal rotation rates of the trans- and cis-NCH3 groups have been obtained, the spin-lattice 162 relaxation rates (l/Tl) can be separated into several contri- butions: .1. — __1___.+.___1___.. 1 'rltobsi- T1(00) T1(DI) T1(SR) (137) where l/T1(DO) is the dipole-dipole relaxation due to the overall molecular motion, l/T1(DI) is the dipole-dipole relaxation due to the internal rotation of the methyl group and 1/T1(SR) is the spin-rotation relaxation. These were separated by calculating the second term using _ 2 2 2 6 1”1031) ‘ [n85 Yc YH /r JTC ' with TC = l/6R, and obtaining the first term as the differ- ence 1/T1(DO) = 1/T1(DD) - l/T1(DI)' w1th l/T1(DD) values taken from Table 5. Values of 1/T are obtained from 1(DD) the experimental spin—lattice relaxation times and NOE values using the relationship nmax T1100) = Tltexp) nexp ° Finally, values of l/T1(SR) were obtained from Equation (137) by difference. Values of 1/T l/T 1/T l(obs)’ 1(DI)’ J(DO) and 1/T1(SR) are plotted versus molecular weight for four N,N-dimethylamides in Figure 34. The results show that the variation of the total spin-lattice relaxation rate for the N,N-dimethylamides can be mainly attributed to the variation of the dipolar over- all molecular reorientation relaxation rate. The contribu- tion of Spin-rotation relaxation due to the internal l/T1 (sec-l) 163 e09 l/T (c) l(obs) l/T (t) .08_ l(obs) 0 0 .07—1 1 e .06P e05? .04.. .03r- .02.. t .01- l1/T1(DI)(“) l/T1(DI)(C) .00 l J 1 IE 1 i l 60 70 80 90 100 110 120 130 Molecular Weight Figure 34. Various components of the total 130 relaxation rates for the -NCH groups of N.N-dimethylamides plotted versus molacular weight: obs: observed total relaxation rate: D0 and D1 are the dipolar relaxation rates due to overall molecular motion and to internal rotation of the methyl groups. SR is the spin-rotation relaxation rate.(A11 at 35° C) 163a .0 6mm 90 0029220900 0203 020 000 29 020 mosa0> Ha 000290 0000.0 0000.0 00000.0 0200.0 000z-HH0 0000.0 0000.0 0H000.0 0000.0 0002100000 020 0000.0 0000.0 00000.0 0000.0 000zimmm 0000.0 0000.0 00900.0 0000.0 000zimmmmm 020 0000.0. 0000.0 00000.0 0000.0 000zimww 0000.0 0000.0 0H000.0 0000.0 0002100000 020 00H0.0 0000.0 00000.0 0900.0 000zimwm 0090.0 0000.0 00000.0 0000.0 000zimmmmw 020 Ammvam Aonvam AHQva Annvam 9202999mnsm 0230m800 9.0000950002902901z.z 020920> 29 0209200 0800 90 200202008 Ammv 20990902 12900 020 AQQVHm 00902 2009000002 2000m90 DMA 20050000202929 H0909 029 09 2099092092002 200500905 99020>0 .AHQV 20090902 00220929 029 90 0209939929200 .090 00909 164 rotation of NCH3 groups is also important but the contribu- tion of the dipolar relaxation resulting from internal rotation of the NCH3 groups is small. The narrowing of the difference between the relaxation rates 1/T1(obs)' for the EEEEE‘ and gig-NCH3 groups in N,N-dimethylpropionamide and N,N-dimethyl-n-butyramide, compared with the dipolar overall molecular relaxation 1/T1(DO) , is attributed to the contribution of the spin-rotation relaxation, as may be seen from Figure 34. 170 Spin-lattice relaxation times and quadrupole coupling constants in some N,N-dimethylamides The 17O spin-lattice relaxation times for formamide, N,N-dimethylformamide, N,N-dimethylacetamide, and N,N-dimethylpropionamide were determined by the inversion- recovery method, as shown in Table 12. One set of partially relaxed FTNMR spectra for N,N-dimethylformamide is shown data with the T * values 1 2 calculated from the 1inewidths,we find that they are almost in Figure 35. Comparing the T equal within the experimental error. Table 12 shows that the 170 T1 values decreased in the order DMF > DMA > 0MP. This decrease is mainly due to changes in the overall molec- ular reorientation, since the larger the molecule the more difficult the overall molecular motion will be. The 17O spin-lattice relaxation time of formamide is shorter than that for N,N-dimethylformamide, although its molecular weight is smaller than that of DMF. This can be rationalized by 165 .920902 ~\9 90 00920008 003 290930299 029 09023 .9290930299v 9 N NE 20990200 029 no 002 09 0090920900 003 ~82 9 s _ * .002908 m90>00091209m90>29 029 09 00920008 003 9B0 09wm9 mmm900.0 0.000 009ooo.0 H «00900.0 0098020920929029089o1z.z 0m.09 Nvmmoo.o N.ma 099ooo.o H mvomoo.o 0098090009029089olz.z 09.0 900moo.o m.mm «09000.0 H m9vmoo.o 0098089099029089alzez 1 009000.o 0.009 «09000.0 H 0mm~oo.o 009808902 90220 90000 9020 92\00~00 owe 290930299 90000 099 02202800 000980 0800 no 092090200 02992200 0902290020 029 020 9990 00899 2099020909 0099909129mm 009 .09 09909 166 ..000 09000.0 9 ~0m00.0 u n209090>29 029 an 00920090990290290nz.z 29 009 909 9 9 a .0on9ua_h90>ooo9 a no :o9pac9auopan .mn ouzm90 167 postulating the formation of hydrogen-bonded polymers in liquid formamide, which give it a longer effective 17 correlation time than that of DMF. By using the O relaxation time and the equation for the quadrupolar relax- 83,114 ation in an ellipsoid , the effective quadrupole coupling constant (equ/h) can be obtained by use of the equation 3(D -D ) fl— = 5% 7323—3 (eZqQ/fi)2 Din 9313—1—54)- sinzeu 1 I (ZI- l) l 1 ll 3(D -D ) l | . 2 + Zle+D 5 Sin 6)] ' (138) where e is the angle between the preferred rotation axis and the C = 0 bond, assuming that principal axis of the field gradient tensor at oxygen is along the C = O bond54. The calculated effective quadrupole coupling constants for some amides are assembled in Table 12. The values are close to the effective quadrupole coupling constant for gaseous formaldehyde, 9.42 MHz, obtained by microwave 17 spectroscopygl. No experimental measurements of the O quadrupole coupling constants in amides have been reported. Comparison of the 13C spin-lattice relaxation times for N.N-dimethylamides, N,N-diethylamides and ELN-di-n-propylamides. 13 The C chemical shifts and values of T1, Tl(DD)' Tc, and T1(O) propylamides are shown in Tables 13 and 14. Examining the 13C T1 values for the trans and cis carbons in the for the N,N-diethylamides and N,N-di-n- 168 : 00.009 00.009 09.0 00.0H00.00 00.009 0 u 0 00.0 90.90 09.09 00.0 90.0Hm9.99 00.90 000:90202900 00.0 00.09 00.0 09.0 00.0H09.0 09.09 2000:0: 220:2 00.0 00.09 90.0 00.0 00.0H00.0 00.09 9900:0: 200:2 00.0 00.00 00.0 00.0 90.0H00.0. 00.00 AUVUIG: 220:2 009809000 00.0 00.09 00.0 00.0 00.0H00.0 00.00 A900:0: 220:2 :9»29090:2.2 200 00.0 .00.00 00.0 00.0H00.0 09.0H90.0 00.909 0 u 0 00.9 00.0 00.0 09.0H00.0 00.0H00.0 00.09 9000:0: 220:2 00.0 00.00 90.0 09.0H00.0 00.0H00.0 00.09 2900:0I 220:2 00.0 00.09 00.0 00.0H00.0 00.0H00.0 00.00 9000:0: 220:2 009808900 09.0 000A 90.0 00.0900.0 09.0H90.0 00.90 A900:0: 220:2 :9029090:2.% 2 000 000 000 _o 2009 20009 9 2200000920 09090" 9 B B 002 20000 9 «90098020 92029990220 02200800 .0009809029090:2.2 90 90020 092080020220 90020290>o 9009022 020 9990 00899 2099020909 0099909:2900_09M920 90098020 0 .09 09209 09 169 : 00.00 00.00 90.0 90.9900.00 00.009 0 u 0 00.0 000 A 00.0 00.0 09.0900.0 00.09 0:»: 220 90202900 00.0 00.909 00.0 00.0 00.0900.0 00.09 0:0: 220 90202900 90.0 000 A 00.0 00.0 09.0900.0 00.00 0:0: 220:90202900 00.0 00.09 00.0 00.0 90.0909.0 00.09 9000:0: 220:2 00.0. 00.99 00.0 00.0 00.0H00.0 00.09 9900:0I 220:2 00.0 00.09 00.0 00.0 09.0900.0 00.00 9000:0: 220:2 0098090922I2: 09.0 00.0 90.0 00.0 00.0900.9 00.90 A900:d: 220:2 :9029090:w.% Q : 00.009 00.90 00.0 00.0900.90 00.909 0 u 0 00.9 00.09 00.0 00.0 09.0900.0 00.0 0:0: 220:90202900 09.0 00.00 00.0 00.0 00.0H00.0 00.00 0:0: 220:90202900 00.0 00.0 00.0 90.0 09.0900.0 00.09 2000:0: 220:2 09.0 00.0 00.0 00.0 09.0900.0 00.09 9900:0I 220:2 00.0 00.0 00.0 00.0 09.0900.0 00.00 9000:0: 220:2 009802092092 mm.m 90.0 00.0 00.0 o9.owmm.~ 00.90 2900-5: 220:2 n9mnuw9cuz.z 900 000 000 000 9 2200090900 0909x09 90098 922099 002 90000 9 «90098020 92029990220 02200800 9.0.92000 09 09209 170 0903 002200800 029 990 .0 mm “M ”UME 00903 mflfimemHflmwm—E 09.3”. .00HMfiHDQ .09099 2300 0090090m9 + 020 029 09 0>990909 090 090920 90098020 .i : 00.909 00.00 00.0 00.0900.00 90.009 0 u 0 00.0 000A 00.0 00.0 00.0H00.0 00.009 0:0: 220 90202900 90.0 00.09 00.0 00.0 09.0H90.0 00.009 . 0:0: 220:90202900 00.0 00.0 00.0 00.9 09.0900.0 00.09 2000:0: 220:2 00.0 00.0 00.0 00.0 99.0900.0 00.09 9900:0: 220:2 09.09 000_A 09.0 00.0 09.0909.0 00.00 2000:0: 220:2 0098090900 90.0 00.0 00.0 00.0 00.0900.9 00.90 2900:0: 220:2 :9029090:2.2 200 000 000 000 9 2200090900 0909x09 20099 200099 002 90000 8 090098020 92029990220 02200800 9.0.92000 09 09209 .090 u 0 .02099 n 9 .0000 90 0008 0903 092080920008 02E .090902300 009009029 + 020 029 09 0>990909 090 090920 90098020 fl 171 : 00.00 00.00 09.0 00.0900.00 00.009 0 u 0 00.0 00.00 00.0 00.0 00.0900.0 90.0 0:0 :.220:90202900 00.0 000 A 00.0 00.0 00.0900.0 90.00 0:0 :.220:90202900 09.0 00.00 90.0 00.0 00.0909.0 00.00 90.900:0: 220:2 990020 00.00 onouun 220:2 00.00 2000.5. 000.2 009smno90090 :9009000990:2.2 200 00.0 00.00 00.0 00.0 09.0900.0. 09.009 0 u 0 90.0 00.09 09.0 00.0 00.0H00.0 00.09 2900:»: 220:2 00.9 00.00 09.0 00.0 00.0900.0 00.09 2000:»: 220:2 09.0. 00.00 00.0 00.0 09.0900.0 00.00 2000I0: 220:2 00.0 90.99 00.0 00.0 09.0H90.0 00.90 2900:0: 220:2 290020 00.0 00.00 00.0 00.0 00.0H00.0 09.00 9000:0: 220:2 00.0 00.99 00.0 00.0 00.0900.0 00.00 2900:0: 220:2 009808900 :900090:2:90:2.2 A00 000 000 o 9 9200090920 0909x 9 20098 222099 002 90000 9 «90098020 92029990220 02200800 000980 0092999022090:2.2 0990099908800 90290 00 90020 092080020220 90020290>O 9009022 020 9990 00899 20990x0909 0099909I2900 .090920 90098020 0 .09 09209 09 172 N-methyl substituents of these two series of amides,we find that a preferred rotation axis still exists, although the effect of anisotropy is greatly reduced. Since in these two series of amides the choice of preferred rotation axis becomes more difficult, only a qualitative discussion will be presented. Several general properties of the T1 data can be deduced from these three series of symmetrically N,N-disubstitued amides (i.e., the N,N-dimethyl-, N,N-di- ethyl- and N,N-di-n-propyl- amides): l. The 13C T1 values of the non-protonated g = 0 groups are normally longer than those of the protonated carbons. Their values range from 25 to 87 sec, depending upon the size of 13 the molecule. Since the C relaxation is mainly attributed to the dipole-dipole interaction between 13C and 1H, in 0 groups this dipolar interaction the non-protonated C can only come from the nonbonded protons and will be very small because the dipolar interaction is inversely proportional to r6. In this case, spin-rotation interac- tion may become an important mechanism for the relaxation of the 139 = 0 group as seen in the NOE values, which are around 2.0. Variation of the relaxation rates with molecular weight for the non-protonated C = 0 groups in N,N-dimethyl- amides and N,N-diethylamides is shown in Figure 36. Both curves show that the relaxation rate is increased as the l/Tl (sec) 173 0.031 00029- 0.027.. 0.025- 0. 023+ 0.021- 0.014, 0.01%- 0.01 l l : 1 I l 80 90 100 110 120 130 ll+0 150 loleeuler Height Figure 36. Relaxation rates of 13C in the C=O group of N.N-dimethylacetamide (I). N.N-dimethyl- propionamide (D). N .N-dimethyl-n-butyramide (I). N.N-dieth lacetamide (O). N.N-diethylprogion- amide (O , and N,N-diethyl-n—butyramide 0) plotted versus molecular weight. 174 carbonyl substituent is changed from -CH to -C H This 3 3 7' is understandable since the relaxation rate is inversely pr0portional to the mobility of the molecule; thus, the larger the molecule the faster the relaxation rate will be. The variation of the 9 = O relaxation rate for N,N—diethyl- amides is more sensitive to change of the carbonyl substit- uent than is that for the N,N-dimethylamides. This is attributed to the larger size of the ethyl group, which introduces a larger moment of inertia for the overall molecular motion of N,N-diethylamides. The relaxation rates of the carbons of C = 0 groups in the propionamides are also increased as the nitrogen sub- stituents are varied from -CH to -CH(CH3)2, as shown in Fig- 3 ure 37. Again, this is due to the increase in the moment of inertia when the size of the nitrogen substituents become larger. 13 2. The C T values for the prononated C = 0 groups in 1 these three series of amides are usually smaller than those for the non-protonated C = 0 groups, since there is one hy- drogen directly bonded to them. Their values range fromnl.0 13 to 21 sec. The variation of the C relaxation rate for these protonated C = 0 groups is almost inversely propor- tional to molecular weight, as depicted in Figure 38. The 13C spin-lattice relaxation time of the C = 0 group in form- amide is shorter than in DMF. This is again attributed to the formation of hydrogen-bonded polymers in liquid forma- 17 mide, as was postulated in discussing the O relaxation times. 175 0.037 0.035 - 0.033 I 0.031 00029 b 0.027 P l/Tl (sec-l) 0.025 9 0.023 0.021 _ 0001.9 b 0.017 1 I 1 1 L 1 l J 90 100 110 120 130 140 150 160 170 Molecular Weight Figure 37. Relaxation rates of 13c in the 0:0 groups of N,N-dimethylpropionamide (O ). N.N-diethyl- propionamide (CD), and N.N-diisopropylpropion- amide (O) plotted versus molecular weight. 1 6 0.40 7 O'BSD 0.30L 0.20 l/Tl (sec-l) 0.15 0.1 0.0 0.0 l J 1 L 1 70 80 90 100 110 120 130 Molecular Weight Figure 38. Relaxation rates of 13C in the 020 groups of N .N-dimethylformamide (O). N.N-diethylformamide (O), and N.N-di-n-propylpropionamide (O) plotted versus molecular weight. 177 3. Values of the 13C relaxation times for the trans: and gig-N-substituentsenxausually determined by the relative directions of the preferred rotation axes (if they exist). The predictable result is that the larger the angle between the preferred rotation axis and the N-substituent, the longer its relaxation time will be. This effect of motional anisotropy can sometimes be used to distinguish the chemical shifts of the trans— and gig—N-substituents if their Tl values are determined. As we have already seen, the over- 41 as the all molecular motion will become more isotropic molecular weight (or size) of the amides becomes larger, and thus this anisotropic effect will be diminished. 4. In the nitrogen substituents of N,N-diethyl and N,N-di- n-propyl amides, the 13C Tl values increase in going from an a carbon to a B or Y carbon. This is a result of a combination of the segmental motion of the methylene carbons and the internal rotation of the methyl carbons. These motions are also reflected in the NOE values and those of the effective correlation time TC. The same segmental motion is also observed for the carbonyl substituents of N,N-disubstituted propionamides and n-butyramide in that T increases from the a carbon 1 outward. Although their 13C T1 values vary widely, they are normally shorter than those for non-protonated C = 0 groups or quarternary carbons. Due to the internal rotation of the -CH3 group, and the segmental motion of -CH2-in the 178 substituents, their NOE values are usually below the maxi- mum value, 2.988, since spin-rotation begins to make an important contribution. 5. In N,N-dimethylacrylamide and N,N-diethylacrylamide, the T1 value for the a carbon on the carbonyl substituent is about twice the value of T1 for the 8 carbon, and so is nearly inversely proportional to the number of directly bonded hydrogens, indicating that the overall molecular motions of these two unsaturated amides are nearly isotrOpic. 6. Due to steric effects, the NOE values for the carbons of the nitrogen substituents in N,N-di-n-propionamide tend to be random. 7. The relaxation rates of the a and B carbons in the carbonyl substituents of N,N-disubstitued propionamides, as shown in Figure 39, also increase as the size of the nitrogen substituent groups becomes bigger. This is, again, due to a decrease in the molecular mobility as the molecule becomes larger. The variation of the a-carbon relaxation rate is more sensitive than that of 8 carbon since its motion is only dependent on the overall molecular motion. However, that of the 8 carbon is also dependent on the internal rotation of methyl group. 8. The direction of the preferred rotation axis in the plane of N,N-dimethylamides is mainly determined by the masses of the carbonyl substituents and of oxygen, which indicates that the inertial effect is an important factor 179 O. 21" 0.20 l/Tl (sec'l) 046+ 0.15 I l I 1 n 41 90 100 110 120 130 140 150 160 170 loloeulsr Height Figure 39. Relaxation rates of the a carbons of the carbonyl substituents of N.N-dimethylpropionamide (I ), N.N-diethylpropionamide (C3). and N.N-diiso- propylpropionamide (ll) plotted versus molecular weight; (0). (O). and (o) are for the B carbons of the corresponding amides. 180 in determining the direction of the preferred rotation axis. The effect of the anisotropic motion will be greatly reduced as the size (or mass) of the molecule is increased. In N,N-diethylamides and N,N-di-n-propylamides, the differ- ence between the relaxation times of the trans- and gig- carbons is greatly reduced, although some effects of anisotropyenxastill observed. Anisotropic molecular motion is also observed in unsymmetrically N,N—disubstituted amides and will be discussed in next section. SECTION 2. NMR STUDIES OF N-MONOSUBSTITUTED AND UNSYMMETRICALLY N,N-DISUBSTITUTED AMIDES I. RESULTS The 13C chemical shifts, Spin-lattice relaxation times T1' and NOE values determined experimentally for a series of N-monosubstituted and unsymmetrically N,N- disubstituted amides are presented in Tables 15-17. The dipolar contributions to the spin-lattice relaxation times T1(DD)' the total contributionscfifthe remaining mechanisms T1(0), and the effective correlation times TC are also given along with the cis-trans isomer ratios as determined from the integrated intensities. A.Studies of cis-gragg isomer ratios N-monosubstituted amides may exist as the QgI-A) or E£§n§(I-B)isomers in which the nitrogen substituent R2 is gig or trans to carbonyl oxygen. If an amide in solution c—N/R2 \ Rl/ I\H R/ l (I-A) (I-B) occurs as a mixture of cis and trans isomers, separate 0 / __./” \a. signals will be observed for the isomers if rotation around the C-N bond is slow, i.e., if TA >> /2/2'n(vA - 03), where 181 182 TA is the mean lifetime at site A and 0A and 03 are the resonance frequencies at sites A and B, respectively. If separate cis and trans resonances can be observed, cis/trans isomer ratios can be determined. However, if only one set of signals is observed, it does not necessar- ily indicate that rapid rotation around the C-N bond is occurring, or that only one isomer is present, since other factors may cause chemical shift degeneracy of the trans and gig signals. By using the relative integrated intensities of the 13C NMR lines, the ratioscfifgig to trans isomers for some amides were obtained and are shown in the first column of each table. Some of the cis/trans ratios for these amides have been determined by proton NMR and the values reported (as percentages) are as follows: N-methylformamide93, 92%; N-ethylformamide93, 88%; N-t-butylformamidegB, 70-82%; 94. 97%; N-ethylacetamide93, 100%; N-methylpropionamide93, 100%; N-ethylpropionamide93, 100%; N-methyl-N-n-butylformamideg5, 39%. These are close to the N-methylacetamide values reported in Tables 15 and 16, except for N-ethylpro- pionamide. No values had been obtained by proton NMR for 14 15 N-n-butylformamide or N-n-butylformamide. For N-alkyl- formamides the percentage of trans isomer increases as the size of the N-alkyl substituent increasesg3, as shown by the values for N-methyl-N-ethylformamide and N-t-butylformamide 183 mm.mm mN.m Hm.a mo.oavh.m ~o.oama.~ onmo.HmH mo.m~ wo.oa mh.a Hm.oamm.~ mo.oaom.a Auvam.mwa O u 0 Hum u mama mac om.m no.m mm.H oo.oaon.~ Ho.oaam.a onmm.m~ u\ . mo.w mo.¢_ mo.m No.oHHm.N mo.oa>m.a Auvhv.om 01m: ndmlz I ov.m¢ mm.ma ma.oumm.m mm.oahm.oa onov.om moflEmEHOM . Ho.mm ~m.mH eo.oemm.~ om.oe~e.aa Auvam.me one- namuz nasusnuwuz UV om.m av.na m>.m mo.oamv.m ma.oamm.¢ oncm.ama Auvva.mma o u o I 1 Huh u mm.H hm.mH om.oa v~.o+w~.m «m.o+mh.w onhm.ma . Auvma.ea cum- nemuz meeuu\mao em.m mm.vm om.h vo.oamm.~ ma.oumfl.w onbv.~m w©HEmEHom Auoem.om one- nemuz namsueuz Am: m>.m mm.mm ma.ma mo.oaav.m mm.oamv.HH onmw.mma Huoa u Anvmm.mma o u U mcouu\mwo mv.o Hm.mm ma.om mo.oamm.a hm.oamm.va onmn.m~ m m I moflEmEHOM Auvaa.s~ H :0 s z uflssuesuz Adv com com com H AEQQV#Mflnm oax e AOVHB AQQVHB moz Aommv B «HMOflEmco ucwsuwumnsm UGDOQEOU NH )1 .omcsaocw mum .HB cu mcowusnfinucoo AAOVHBV Hmnuo can AADQVHBV Hoaomflo esp mo can . e mofiwu coaumHmuHoo m>wuommmm can mo mosHm> om>fluoa .mmcflfis cousuflumosmocoelz mo mucmeocmnco ummsmnnm>o Humans: 6cm mofiumu nmEOmH mcmuulmwo .AHBV moEHu cofiumxmawu mowuumalcwmm .mumwam amowswnu 0 .ma canoe ma 184 I w~.Hv om.mm Ha.oanm.m nm.o mm.vH ~¢.vha o ".0 H¢.H mm.wa ww.oa mo.oam~.~ om.oaov.w m~.m UIm IQSmIHmconuoU h>.m om.oa mm.m oa.oam~.m na.oahb.m vm.m~ UIo Insulamsonumo mcwfimcowmonm oo.~ mm.mm om.h mo.oamm.m Hm.oumm.m mo.m~ HanumEIz IaasuoEIz .5 I mm.av om.ma no.oamm.~ m¢.oaem.ma o~.ohH o u o ov.H ww.bm om.oa ma.ow¢v.m mm.oaaw.h Ho.wa mmoIamconumu HH.m Ho.mm mh.v mo.owmm.m mm.oahv.v mm.am UImI anIz ocwsouoom mm.m mm.va oo.m mo.oamv.m vo.oaho.v mh.mm UIcI namIz IamcmoIz S: I an.m~H va.o~ No.oamn.m vm.oamv.ha va.ona o u U vh.H mo.wv me.m ma.oamm.m ma.ow~a.h mm.Hm mmoIamconHmo wowfiouoom N@.H om.m~ mo.m NH.oH¢v.m na.oamm.m oa.m~ HmauoEIz IaxsuodIz av com com com a AEQQVHMHam awn a m csomfio 0 iota manta moz lemme a .Heoflsmno u u.» new 8 o Naoax P a B i.e.uqooo mH wanes 185 .ucosuflquSm somouuwc on» no common a may mmumowocw UIoImsmIz cam .mcmuu u u .mflo u o .memmmmo can mnsm,mnt monsomeoo on» HH< .Uemm um come wum3 mucmEmusmmoE one .oamflmcsoo moumoflocw + one mza ou w>flumHou who mumwSm HmowEmnu .1 I . ee.mm em.ma mo.oee~.m m~.oeam.m movmm.msa I mm.eH mH.HH ma.oema.~ mm.oeem.o Auvmm.mha o u o mm.m so.mH eo.e no.oemm.m mo.oeam.m Aoooe.m oImI Auvem.m nemIasconueo mo.ma ee.ma me.a so.oe~m.~ eo.oemm.a onmn.m~ 102mm.m~ UIeI admIamconumu mm.m mo.e mm.m so.oe-.m oa.oumm.~ 10.0vho.ea oImI nsmIz we.HH em.e am.H ao.oeem.~ «H.00he.a onmo.mm measeeoadoum Auvvm.mm UIeI nsmIz IasnumIz :3 com com H AEQQVuMflnm commV AOVHB AQQVHB moz Aoomv B «HoowEmnu pawsuflumnsm ccsomeou x p. NHOH A.U.ucoov ma magma 186 ah.hm mm.vm mm.H No.0 om.m mo.owmm.H onmm.HmH movem.~mH Auvco.mmH Auvmm.moH o u o oH.~ mo.~H me.e OH.oee~.m MH.oaem.e 10.0me.MH oIsI nsmIz mH.m «0.x mm.e OH.oHom.m mo.oemn.~ onom.mH Auvem.mH oI>I nsmIz mm.m Hm.mH NN.N OH.ouen.m NH.oeem.H moos~.Hm leeway HUVOH.mm oImI nemIz . . . . I . . I . loco~.hm HHOH u mo 0H 5H HH mm H OH 0.55 N mo o+- H looms.em maeuu\mH0 AuVmH.He Auvem.He oIeI nsmIz IqusnIcImHz mm.o~ HH.NH mH.m mo.oame.~ mo.oe~m.H onmm.HmH Ame Auvmm.emH o u o mH.~ mm.MH oe.m eH.oeem.~ pH.oe~m.e Ao.uvH~.MH oIsI nsmIz . mwc mm.e m~.eH Hm.e mo.oeHm.~ MH.oeme.m lovah.mH Au V Huvmm.mH oI»I nsmIz Hum n OH.m e~.HH ms.m eo.oeoe.~ no.oamH.~ movem.Hm meeuu\mHo Auva.mm oImI nsmIz ma.HH mo.mH mm.H mo.oeom.~ mo.oaoe.H movmm.em IHmmmwwauom . Auvm~.He oIeI nsmIz eH lav 00m 00m 0mm H AEQQV uwaflm NHOHxnw movHa AoovHa moz lemma 9 «HeoHsuso ucmsuHumnsm oesomsoo .cmcDHOGH mum .HB ou mcowpsnfluucoo HHOVHBV Hmnuo can AAQQVHBV Hoaomfio msumfiuoco . &.mmeu coaumHmnuoo m>fluommmw map No mosao> ww>wnmo .mowEMEHOMHmuanIGImHz can moflEmEHOMH>uSQIcIsz mo Amozv mucmEmoconcw Homamsum>o Howaosc can mOfluoH umEOmH mcmuu\mflo .AHBV mmep sowumxoamn wofluumalcwmm .mHMHsm Hmowfimno 0 .ma magma ma 187 given in Table 15. This trend has been explained in terms of simple steric interactions between the N-alkyl group and the carbonyl oxygen. However, no satisfactory explana- 93 tion has been given for the predominance of the cis isomer in N-alkylformamides,such as N-methylformamide, in which no steric interactions favoring the cis isomer are present, or in amides in which steric interaction would seem to favor the trans form, such as N-t-butylformamide93. B. 13C Chemical shifts of amides and the 15 15N_13C coupling constants in 13 N-n-butylformamide The C chemical shifts of the trans isomers in N-monosubstituted amides are normally downfield relative to the gig isomers just as in the symmetrically N,N-disub- stituted amides. However, exceptions are observed in the case of the a carbon of the N-t-butyl group in N-t-butylformamide and the a carbons of both the N-ethyl group and the carbonyl substituent in N-ethylpropionamide. The reason for these results is not clear. Due to the 13 96 31 13 C Y effect and 6 effect , the C chemical shifts of the cis y and 0 carbons are usually downfield relative to the transg7, as seen in 14N-n-butylformamide, 15N-n-butyl- formamide, and N-methyl-N-n-butylformamide. The coupling 15 13 constants between N and C in the trans and gis forms are the same. The results are J = 13.8 Hz and 15 _ N, C-O J = 9.6 Hz. 15N, N-a-carbon 188 C. 13C Relaxation studies and nuclear Overhauser effects Most of the N-monosubstituted amides exist as trans and cis isomers at room temperature. However, the percentages of the trans isomer at room temperature are so 13 low that measurement of their C Tl values become impos- sible. Thus, only the T values for the cis isomers are 1 reported, except in certain cases where the peaks for the gians isomers are intense enough to be measured, such as N-methyl-N-n-butylformamide, N-t-butylformamide and the carbonyl group of N-ethylpropionamide. (1) N-monosubstituted amides Comparing the T data of N-monosubstituted amides 1 with those of the corresponding N,N-disubstituted amides in Tables 11-13, we find that the 13 C relaxation times of C_: = 0 groups in N-monosubstituted amides are shorter than those of the corresponding N,N-disubstituted amides even though the molecular weights of N-monosubstituted amides are smaller than those of the corresponding N,N-disubstituted amides, as seen in the pairs N-methylformamide, N,N-dimethylformamide; N-methylacetamide, N,N-dimethylacet- amide; N-methylpropionamide, N,N-dimethylpropionamide; N-ethylformamide, N,N-diethylformamide; N-ethylpropionamide, N,N-diethylpropionamide; and N-n-butylformamide, N-n-butyl- N-methylformamide. This effect is especially enhanced in.the 13 C T data for non-protonated C = 0 groups, i.e., all but 1 189 the substituted formamides. All of these results indicate that hydrogen bonds are formed in N-monosubstituted amides, which become impossible in the N,N-disubstituted amides. The internal,rotational rates of N-methyl groups in N-monosubstituted amides are still very fast, as seen in the NOE values, since this internal rotation is not affected by the hydrogen bonding very much. The segmental motion of the long chain substituents on nitrogen and on the C = 0 groups is also reflected in the T1 values,which show increases in going from the heavy end to the free end. Let us assume that98 (139) where TR is the correlation time for the overall reorienta- tion of the molecule and is approximately equal to the effective correlation time of the C = 0 group in N-alkyl- formamide; TC is an effective correlation time for the internal motion of some group in the molecule. It follows that the I value for the N-methyl group in N-methylforma- G mide is 0.59 x 10'12 sec, while the To values for the a and B carbons of the N-ethyl group in N-ethylformamide are 5.38:< -12 sec and 1.77 x 10.12 sec, for the a, B, y, and 0 car- bons of the N-n-butyl group in 14N-n-butylformamide and 15N- 12 sec, 13.32 x 10"12 sec, sec, 2.45 x 10’ sec and 38.31 x 10‘12 sec, 15.45 x 10"12 sec, 6.37 x 10‘12 sec, and 2.34 x 10"12 sec, 10 n-butylformamide are 27.05 x 10- 6.39 x 10'12 12 190 respectively. The effective correlation times TG increased about 11 to 17 times in going from the a to the 0 carbon in N-n-butylformamide. In 15N-n-butylformamide and-*4N-n-butylformamide, the gyromagnetic ratios of 15N and 14N are very small compared with that of the proton, so the relaxation of the carbon of the C = 0 group, and of the a carbon on the N-n-butyl group, due to the dipolar interaction with the nitrogen,is not important and can be neglected. The 13C T values for l4N-n-butylformamide are a little longer than 1 those for 15N-n-butylformamide, presumably due to the difference in the atomic weights of 15N and 14N. In N-t-butylformamide, the T1 values for the car- bons in both the giggg and gig isomers have been measured and it is seen that the T1 values for the giggg carbons are longer than those for the gig carbons.» This effect is believed to result from the direction of the preferred overall molecular rotation axis which, for the 2522? form, lies roughly along the direction of a line joining carbonyl oxygen and the tertiary carbon of the t-butyl group (struc- ture JI-A). The TG value for the cis 8 carbon is CH . \3\ [0113 °\ /C\CH c... 3 (II-B) 191 13.44 x 10.12 sec. which is considerably longer than that of the 8 carbon in N-ethylformamide (5.38 x 10-12 sec) indicating that the steric effect and mass effect are both importantfku:the 8 carbon of N-t-butylformamide. In the gig isomer (Structure II-B) the motion is more nearly isotropic. In the series of N-alkyl formamides (compounds A, B, C in Table 11 and compounds A, B in Table 16), N-alkyl acetamides (compounds D, E in Table 15) and N-alkyl propion- amides.@ompounds F, G in Table 15), the relaxation rate of the carbon of the C = 0 group increases as the molecular weight of the amides increases. This mass effect is also shown by the relaxation rates for the carbons of the N-methyl groups of N-methylformamide, N-methylacetamide and N-methylpropionamide (as shown in Figure 40), and for the a and B carbons of the N-ethyl groups in N-ethyl- formamide, N-ethylacetamide, and N-ethyl propionamide. Again, the relaxation rate of the a carbon is more sensitive than that of the 8 carbon (Figure 41), since the a carbon is more dependent on the overall molecular motion. The T1 values for the carbons of the C = 0 groups. in N-alkylformamides are considerably smaller than those of the corresponding N-alkyl acetamide or propionamide, since there is one hydrogen directly bonded to the C = 0 group in N-alkylformamides. ' (2) Unsymmetrically N,N-disubstituted amides Only four unsymmetrically N,N-disubstituted amides were studied, as shown in Table 17. 192 0.20 0.18 0.12)- L/Tl (sec-l) 0.10 _. 0.04 l J l l I 50 60 70 80 90 100 110 Molecular Weight Figure #0. 13C relaxation rates for the carbonsof the N-QH3 groups of N-methylformamide (O). N-methylacetamide (D). and N-methylpropionamide (0) Plotted versus molecular weight. 193 0.90 0.80 n 0.70 .. g 0.60 I- 0.50).- l/Tl (sec'l) 0.40“ 0.30): 0.20.... 0.10 l 1 1 l j 60 70 80 90 100 110 120 Molecular Weight Figure #1. Relaxation rates of the a-carbon and B-carbon of the N-ethyl group of N-ethylformamide (O) ( I ), N-ethylacetamide ( O )( U ) I and N-ethyl- propionamide (O )( D) plotted versus molecular weight. 194 I mm.mm mv.vh mo.ouhm.H mm.oa¢m.H~ Ho.05H o u U em.v oomh mm.m mH.oaoo.m mo.oamm.m ~m.w~ UIqusnIuIz I mn.wm mm.om HH.oaHm.N oo.~avm.mm mh.mm UIeIpsnIuIz I I ocHEmuoom vv.H mm.mH mH.0H mo.o+HN.N wm.o+om.m em.v~ mUIHmconHmu IHmusnIu Hm.o m~.o~ mm.mm no.0HNm.H Hm.oamm.HH me.~m HhsumEIz IZIHanumEIz mm.h mm.mm mn.> mo.oam¢.~ m~.oHHm.m Ho.uvmm.HwH o u U Hmv mo.~ mm.mv me.m No.0amh.~ h~.oamm.w HuVON.MH AOVmN.MH UIqusnIch om.m mm.mH No.0H HH.oaN~.~ Hv.oamH.w Hovmm.mH sv.~ mo.mH om.m mo.owmm.~ m~.oumm.m Huvmm.mH UI>IusnIch ov.~ mm.HH mH.m Ho.oaoH.~ mo.oflmo.m Hovmm.mm . Humb.o n ma.m mm.MH me.m OH.oaem.~ mH.eaeo.e Aevmm.a~ oIsIusnIsIz mseau\mHo mh.m mH.>H nm.m mo.oamv.m ~m.oahm.v Hovvm.~v mH v we mH om m mo o+mv N hm o+mm m Huvmm mv UIeIusnIch moHEmEHom no.0 me.m~ mm.m~ mo.oaoo.~ mm.oaes.HH lovem.m~ IHausnIsI mo.~ coma eH.s HH.oasm.~ em.QHOH.s levee.mm HmsumeIz IzIHsnumsIz Hdv owmo AWWM Homww H Hammv uMHnm NHOHx e a a moz Hommv B HMUHEmno unwauHquDm pcsomaou mopHEm pmusuHquDmeIz.z MHHmoHuumfiahmcd mompcwawocwnsm Hmmsosnm>o HmoHosa paw HHvamEHu :OHumeHmH onuuMHIcHQmamuMHnm HMOHEoso U .nH oHQma MH 195 .0 can 0 mocsomaoo MOM omuomump on pHDoo anon mHo can ch0 onMHusm mch: oomm um come one: mucmEousmmmE was .mocsomsoo .mza ou 0>HumHmH one mUMHsm HMUHEonU m I e~.me se.me mo.eaeH.~ se.eaHm.s~ NH.msH o u o mH.m He.HH mm.m mo.oaam.~ ee.oam~.~ HH.m~ oIeInsmIoue I sm.am Ho.He ~o.oaea.H ae.Haao.om empmm oIeIssmIoue eo.m mm.e om.e mo.eamm.~ mo.oae~.m so.MH oIeIusnIsIz ~s.e em.a m~.m mo.oaae.~ mo.eame.~ mm.aH oI>IusnIsIz NH.HH He.eH mm.H so.owse.~ mo.oaee.H mm.m~ oIeIussIsIz aH.mH sm.e me.H Ho.oaee.~ se.eae~.H a~.ae oIeIusnIsIz 0eHseueoeHmsuesHau me.H Hm.eH Na.m mo.oam~.~ m~.oaas.m me.mm HssumsIz IHsusnIsIzIHssumwmw I ee.mm aH.sm mo.oaoo.~ ea.HhHa.me sm.msH o u o os.m me.eH sa.m OH.oaoe.~ eo.eao~.m ee.m~ oIeInsmIouo I e~.mm oe.~e sH.eamH.~ ae.Haem.e~ e~.mm oIeInsmIoue e~.m me.mH me.e mo.oaem.~ eH.oaae.m mm.~H oIqueIsIz eH.OH com mH.~ mo.easa.~ mo.eaeH.~ 5H.ee UIeIueIsIz 0eHseumoeHmsumaHuu mm.H ee.mm me.m mo.oamm.m He.oa~s.a om.em HanemsIz IHssumIzIHssuewwm oemo ANN“ momww moz mommvHa memwwwwmw usmseHumnsm essodsoo NHeHx e a a A.U.#GOOV NH $HQMB 196 In N-methyl-N-n-butylformamide, all the carbons in both the trans and cis isomers are observed except those in the C = 0 group. The T1 value of the cis-N-methyl group carbon (Structure III-A) is longer.than that of the gigggf NCH3 group (Structure III-B), indicating that an anisotropic molecular rotation axis approximately along a line joining the C = 0 group and the N-n-butyl group may exist in the molecular plane, as shown in Structure III-A. However, when the NCH3 group is Egggg to the C = 0 group, as shown in Structure III-B this preferred rotation axis will not exist and the motion will be nearly isotropic. (\0\\\ /CH3 __ng 0\C N/CHZ—Z 0115- 0112 CH3 C—Nm H/C--- NC\H LD 1:. .‘L-Z H {C 2 QflZ‘CHBH CH3 12 \ 21.6 er 10 8906.12 L5 1.2 £2.22 . (III-A) (III-B) Based on the INDO calculations of N-ethyl-N-methyl- formamide (see Part II of thesis), we predict that the most stable conformation of Structure E for N-n-butyl-N-methyl- formamide is that shown in Figure 42. Using the approxi- mate ellipsoidal molecular model, the diffusion constant along the preferred rotation axis D|Iis approximately 1.82 x 1010 sec-1, and the diffusion constant D1 for motion around the axis perpendicular to the molecular plane is about 4.23 x 1010 sec-1, which is about equal to the D1 197 .onum Ono one 0» mfimhfi Qsoum.th=nIc on» :pHs HeEHOHCoo on» :H ocHsmeuow IthmeIzIHmpspIch Ho soHpos umHzoeHoE one new mem :oHpmpou venuemenm .m: euzmHm $10 f‘ #4 v emoH smmH 05mm one n H .Uonuwe >Hm>oomuIconno>cH way an consumme was so mo.m m.nm NHIOH x mh.H mnHooo.o a mommoo.o moHEoEH0m IHmsumsHeIz.z He.m m.nm NHIOH x om.m nvoooo.o a emhooo.o oUHEoEHom IngumIz mm.m m.wm NHIOH x mn.m OOHooo.o H Hmomoo.o prEmEH0m kasumaIz Hm.~ mm.>m NHIOH x vH.v OOHooo.o u VOHNoo.o .mUHEmEuom Humzv H:\qumv w: Hommv ow Hommv MHB UGDOQEOU meHEo meow :H mucmumcoo mzHHmsou mHomsupmsw cam AHBV onHu COHumeHmH GOHuuwHIcHQm .z .mH anma vH 202 E. Energy of the hydrogen bond in N-ethylformamide In order to estimate the energy of the hydrogen bond in liquid N-ethylformamide, the variation of the 14N relaxation rate with temperature was measured, as shown in Table 19 and Figure 43. The energy barrier for the overall molecular motion of N-ethylformamide is about 5.58 kcal/mol, which compares with the value 4.10 kcamefl. for N,N-dimethylformamide which has the same molecular weight as N-ethylformamide. The estimated energy of the hydrogen bond is the difference between these values, approximately 1.48 kcal/mol The enthalpy of formation of the hydrogen bond for N—methylformamide in benzene is 3.4 kcal/molloz. Klotz and Franzen103 found that the energy of the hydrogen bond in N-methylacetamide decreased as the solvent became more 102 also found that the formation polar. Davis and Thomas constant of the hydrogen bond will decrease as the N-alkyl group becomes more bulky. All these results indicate that our value of 1.48 kcal/mol for N-ethylformamide is very reasonable. 203 Table 19. Temperature dependence of the 14N spin-lattice relaxation time in N-ethylformamidea. Temperature ~ Tl(l4N)b (°C) (sec) 28.0 7.84 x 10’4 3o 0 8.58 x 10'4 40 0 1.00 x 10‘3 51 0 1.40 x 10‘3 62.0 1.63 x 10’3 70.0 1.87 x 10’3 83.0 2.19 x 10'3 95.0 _ 2.43 x 10'3 104.0 2.78 x 10'3 aThe sample was purified but not degassed. bThe Tl value at each temperature is the average of at least five measurements. The probable errors of T1 values are within 5 %. 204 2.6- .1 2.2 I. 2.0 1.8 1.6 1.1+ 1.2 1.0 4 . 1n(1/T1) 0.8I 0.6 00“ j 1 1 l 1 1 L I 2060 207 208 209 300 301 302 303 Be“ 305 1/r x 103 (°x'1)-> Figure 43.Plot of Inn/Tl) versus l/T x 103 for luN in N-ethylformamide; Ea - 5.58 kcal/mol for the overall molecular motion. The probable error is i 0.5 kcal/mol. SECTION 3. NMR STUDIES OF THE ANISOTROPIC MOLECULAR MOTION IN N-ALKYL ACETANILIDES AND FORMANILIDES I. BACKGROUND Many small molecules tumble anisotropically in the liquid phase or in solution. Preferential tumbling modes occur, resulting from the inertial, frictional, and electrostatic effects, as well as from the intramolecular and intermolecular interactions. Anisotropic molecular motion may also occur with large molecules, although localized electrostatic and inertial effeCts tend to cancel out in these systems. For large polycyclic molecules,41 the central molecular framework may orient isotropically, while peripheral molecular fragments have Shorter effective correlation times Tc resulting from internal motions that are comparable with, or faster than, overall molecular reorientation. The effect of the anisotropic overall, or internal, motion on T1 values for the different carbons in a molecule which are bonded to hydrogen depends on the angular rela- tionships between each C-H vector and the preferred rota- tion axis. Anisotropic molecular motion of monosubstituted benzenes around the C2 axis has been thoroughly 205 206 studied47’63'88’104. Levy et al.47 found that, if the substituent is large and heavy, or highly polar, rotation around the C2 axis may be 20 to 50 times faster than rota- tion around the remaining two perpendicular axes. Rota- tion around the C symmetry axis does not lead to any 2 modulation of the dipole-dipole interaction for the para 13 C and its directly attached hydrogen. However, such a rotation does lead to the relaxation of the ggthg and mggg carbons since the C-H vectors in these two positions make angles 60° and 120° with the C2 axis. Therefore, the relaxation times of ggthg and.mg£g carbons are longer than those of BEES carbon. The steric effect of the grthg or gg£g_alkyl substituent on the rotation of biphenyls has 105 and it was found that the relaxation also been studied times of meta and para carbons are nearly equal, indicat- ing that the rotation around the C2 axis in 2,2', 6,6'- tetramethylbiphenyl is more difficult than that in biphenyl. Levy86 also studied the internal motion of the five—membered rings in monosubstituted ferrocenes and found that a sub- stituent can effectively reduce the rotation rate of the substituted ring, simultaneously allowing relatively free spinning of the unsubstituted ring. Allerhand, Doddrell, and Komorowski41 have developed the relaxation equation for a group (—CH3, benzene ring, etc.) attached to a rigid isotropic tumbler and undergoing internal rotation. 207 n 462 2 2 ——-——l - S YIYS (Zi— + ——B + ————C I. (141) T 6 6D 5D + R 2D + 4R l(DD) rIS Here, R is the internal rotational diffusion constant and D is the overall molecular diffusion parameter. The above equation is similar to Equation (132) except that D Iis I replaced by R and D1 replaced by D. All the other symbols are the same as for Equation (132) except that 1 is now the direction cosine of the angle between the C-H vector and the internal rotation axis. Replacing R/D by p in in Equation (141) , Equations (134) and (135) will be obtained. II. ANALYSIS OF THE 13C CHEMICAL SHIFTS IN N-ALKYLACETANILIDES AND N-ALKYLFORMANILIDES 13C chemical shifts, relaxation The experimental times T1' and NOE values are shown in Tables 20 and 21 along with the derived values of the dipolar and other contributions to the spin-lattice relaxation times (T1(DD) and T1(O))' and the effective correlation times, TC' for N-alkylacetanilides and N-alkylformanilides. At room temperature, most of the N-alkylacetanilides and N-alkyl- formanilides exist predominantly as the ggg isomers106-111, i.e., the phenyl group is giggg_to the C = 0 oxygen. l3C chemical shifts with In order to compare the those for previously studied amides,the following series of amides are examined: (1) N-Methylacetanilide, N-methylacetamide, N,N-dimethyl acetamide, N-methyl-N-t-butylacetamide. 208 I Hm.me oo.em mo.owme.H sm.HHso.mm ma.meH o u u I mm.me ee.me mo.oHem.H mm.oHem.~m Ha.meH oIeIHssesdIz oe.eH se.m eo.m so.owse.~ mo.oHe~.~ Hm.a~H oIeIHxsmseIz ss.m~ com A me.H eH.oHoo.m NH.one.H sm.s~H oIdIHssmsaIz AMHoao ms.HH mm.HH ms.m mo.oHem.~ OH.onm.~ eH.m~H oIoIHssmsdIz ea 2H.ee mm.m e~.~H as.m HH.oH~m.~ eH.oHae.~ mm.~H oIeIHasueIz . em.OH com A Ho.~ eo.one.~ eH.oHHo.~ mm.me moIeIHmsumIz meHHHsmueoe Hm.H ~m.sm ae.s MH.o+me.~ se.o+mm.e ee.- moIHssonaeo IHssuqu m I se.ma em.MHH OH.oHHm.H me.eHmm.Hm oa.aeH o u o I mm.es ms.MMH eH.oHHs.H eH.mHes.se me.eeH oIeIHxsmsdIz oe.m mm.mH NH.m eH.oHae.~ so.onem.m ee.mmH oIaIHmsmsdIz Hchao o~.eH es.sa me.~ OH.eHem.~ NH.oHem.~ mm.s~H oImIHmsmsdIz ea 2s.mv mo.s mm.a m~.e OH.onH.~ mH.oHea.m Ho.s~H oIoIHmsmsmIz . em.H wo.aH as.OH eo.owsm.~ mm.onm.e ma.em m HmsuosIz meHHHeeeeoe ~H.H aH.mH eH.MH eo.o+mH.~ mm.o+om.s m~.- moIHssonaeo IHmsuezIz :3 0mm 0mm 0mm AEWB 0 lovH AeoeH H umHsm NH+OHx e a a moz Homes 9 sHeoHsmso usmsuHqusm ecsoesou .cm>Hm omHo mum .meHu coHumeHHoo m>Huommmm 0:» Mo was .HOVHB pas HQQVHB .mmEHu coHummeoH mUHHHMHIcHQm mnu on mQOHHSQHHpcoo Hmnuo was HMHome.m£u mo mwsHm> om>HHmp one .meHHHcmuoUMmeHmIz 0:» CH .moz mucwfimocmscm mesmnuw>o HmmHosc pas . a meHu coHummewu GUHuuMHIcHQm .mHMHnm HMUHEmno U HmucmEHummxm .om mHnme MH .Oomm 98 some one: mPCmeHSmme one .pHHQm onHmczoo m momeHccH + was .msa ow o>HPMHmH ohm mPMHnm HMoHEwno b 209 NH I mm.mm se.MH so.o+e~.~ ~m.oHem.m m~.meH o u o I mm.eH em.sH mo.oHHm.H mm.oweo.e me.meH oIeIHmsesaIz em.me mm.mH ee.o mo.oHHa.~ mo.oHHe.o ee.a~H oIsIHmsesdIz ee.es ma.m am.o me.eHms.~ He.oHHm.o eH.m~H oIoIHssmnEIz ss.mm aH.e se.o mo.owme.~ ~o.owme.o Hm.s~H mIdIHssmsaIz Hs.m o~.m sm.m mo.owmm.~ eo.owms.H e~.- moIHmsonaeo AmHoao ee.e ee.eH a~.m me.eHme.~ H~.ons.~ me.MH oIeIqusnIsIz ea 2H.ee me.eH mm.m mm.H mo.owsm.~ eo.owme.H es.aH oIaIHsusnIsIz . Hm.e~ m~.e Hm.o mo.owas.~ me.owmm.e mm.m~ oImIHsusaIsIz 0eHHHseemoe m~.Hm com A me.o mo.o+ma.~ me.o+me.e eH.me oIeIHsusnIsIz IHsusmIflIw a I Hm.mm mm.~m ao.eHHe.~ H~.one.eH H~.meH oIeIHmseseIz I mm.ss es.m~ eo.ewme.~ mm.HHmm.o~ ee.aeH o u o mo.sH mm.e mm.m He.oHem.~ eo.ewme.H ee.m~H oIsIHssmsdIz me.om am.e MH.~ eH.oHae.~ eo.ewoe.H ma.s~H oIoIHssmseIz as.~e com A mo.H ~o.eHmm.~ so.ono.H ee.a~H IdIHmsmsaIz Achoo om.~ ma.sH so.m eH.onm.~ mH.onm.m em.e~ moIHmsonaeo ea 2H.ee oe.e so.s em.m eH.onm.~ OH.oHs~.~ ma.oH UIaIHmdoHEIsIz . ms.HH mm.s mm.H eo.oHHe.~ we.oH~m.H mm.m~ oImIammoadIsIz eeHHHseueoe mm.s~ com A ma.o H~.o+oo.m mo.o+ms.o a~.em oIeIamdoudIsIz IHsmoaaIflIm . 0 com com com Hammfl o loVH AeovH H HHHsm . OHx e B B moz Howey B HMUHEmno ucmsuHumnsm pasomfioo H.p.ucoov om mHnma 210 mucmEmHSmmmE 0:8 .umHsm eHmHussoe e mmeeoHesH + use .Uemm us come muo3 .mSB on m>HusH0H was mustm HMUHEmno .1 Ho.m~ com A Ha.H ao.oHaa.~ mH.eHHa.H HH.HeH o u o I Ha.oa o~.Hm eH.oHae.m ea.eHH~.m~ No.HeH oIeIHmsmsaIz se.mH ee.a em.m ee.onm.~ mo.onm.H me.amH oIaIHmsesaIz mm.ee em.m ea.o me.one.m mo.eumm.e me.emH oIaIHssmseIz He.eH ~N.H mH.N No.0Hee.m H~.eHaa.H em.m~H oIoIHssmseIz leeway ma.e H~.a em.~ eo.oHHm.~ m~.owm~.~ mH.~H oImIHssemIz meHHHsesuom HH.HH ma.e we.H me.o+oe.~ mo.o+mH.H 8H.am oIeIHasumIz IHxsumIz Hmv ea.OH Hm.em mo.e eH.eHms.~ ~H.QHom.m we.HeH o u o I me.em HH.oe HH.onH.H Hm.eHeH.- Hm.~eH oIeIHaseseIz Hm.mH Ho.OH e~.m mo.eHem.~ eH.eHee.~ mm.a~H oIsIHssmsaIz Hm.mm HH.e es.H me.eHmm.~ ee.oHem.H mm.m~H oIaIHmseseIz Hemmse mo.m Hm.m me.e NH.eHeo.~ ao.ewoe.~ ee.H~H oIoIHmsesaIz meHHHsesuom HH.H ae.sm a~.m mH.o+mm.~ em.o+em.e He.em HmsumsIz IHssudez 3 00m 0mm 06m Afima u loeH HeeeH H eHHsm mHon e a a moz Howey HeoHsmso usmsqumnsm essodaoo .1. .mmpHHquEHommeHMIz mo Hmozvmusmfimocmncm mesmnum>o HmmHosc one A HevmmEHu coHummemH moHuumHIcHQm.mumHnm HMUHEmSU U .HN GHQMB 211 (2) N-Ethylacetanilide, N-ethylacetamide, N,N-diethyl- acetamide. (3) N-n-Butylacetanilide, N-n-butyl-N-methy1acetamide. (4) N-Methylformanilide, N-methylfOrmamide, N,N-dimethyl- formamide, N-methyl-N-n-butylformamide. (5) N-Ethylformanilide, N-ethylformamide, N,N-diethyl- formamide. We find in each series that the 13 C chemical shifts of the carbons of the C = Ogroups in N-alkyl acetanilides and formanilides are normally at higher fields compared with their analogs. This is atrributed to the cross con- jugation of the C = 0 group with the nitrogen lone pair electrons and the benzene ring n electrons, as shown in 0 N.J./“2 (0 Structure (IV). (IV) 13C chemical shifts of the carbons of However, the the carbonyl-CH3 groups in N-alkylacetanilides and formanilides are normally to lower field, relative to their analogs in each series. Since the carbonyl-CH3 group in N-alkyl acetanilides and formanilides is in the deshielding 212 zone of the benzene ring, a downfield shift would be ex- pected due to the ring-current effect. A similar ring- current effect is also observed for the N-alkyl group car- bons of the N-alkylacetanilides and N-alkylformanilides thus introducing a downfield shift relative to that of 13C in the ging—alkyl groups of their analogs without the phenyl substituent. The quaternary carbons in the benzene rings of the N-alkyl acetanilides and formanilides are usually at lower field relative to the ortho, meta, and pg£g_carbons, as expected. The 13C chemical shift of the para carbon in the N-phenyl group can be distinguished from those of the 13 meta and ortho carbons by measuring their C spin-lattice relaxation times, since the relaxation time of the para carbon is usually shorter than that of ortho or meta car- bons. The 13 C chemical shifts of the gg£g_carbons in the N-alkylacetanilides change only very slightly as the N-alkyl group is varied from N-methyl to N-n-butyl since the resonance effect remains about the same. Spiesecke 113 13 and Schneider have found that the C chemical shifts of meta carbons in aniline and N,N-dimethylaniline are normally at lower field due to resonance involving the nitrogen lone pair electrons and the benzene ring. They also found that the mggg_carbon chemical shift changed very slightly,even the properties of the substituent group are quite different. Thus, they concluded that the 213 contribution to the 13 C chemical shift of the mgig_carbons from the magnetic anisotropy and inductive effects of the substituent is negligible. Since acetanilides and formanilides are analogous to aniline and N,N-dimethyl- aniline, we have determined the 13C chemical shifts of mggg and ortho carbons by comparing our values with those of Spiesecke and Schneiderll3, as shown in Table 16. The 13 C chemical shifts of the ortho and meta carbons in 112 N-methylacetanilide have been assigned, and their assignment agrees with ours. III. RELAXATION TIMES AND NOE EFFECTS The T1 values of the gggg carbons in the phenyl groups of the N-alkyl acetanilides and formanilides are shorter than those of the gggg_and gg£g_carbons, since the preferred rotation axis passes through C-1 and the gggg. carbon of the benzene ring and so will not lead to any modulation of the dipolar interaction between the pg£g_ carbon and C-H vector. The NOE value for the pg£g_carbon is very close to the maximum value of 3.0, indicating that dipolar relaxation makes a very important contribution to its relaxation. The relaxation times of the N-alkyl group carbons in these two series of anilides increase in the order a < B < y < 6 due to the segmental motions and internal rotations. 214 Due to the inertial effect, the 13C relaxation rates of the carbons of the benzene ring, the carbonyl-CH3 group and the C = 0 group in N-alkylacetanilides and N-alkylformanilides increase as the N-alkyl group is varied from CH3 to N-n-butyl, as shown in Figures 44, 45, and 46. The relaxation times of the carbons of the C = 0 group, and of the quaternary carbon of the phenyl group, are very long, since there is no hydrogen directly bonded to them. The variation of the relaxation rates for these C = 0 group carbons nearly parallels that for the quaternary carbons of the N—phenyl group, as shown in Figure 44, indicating that the relaxation of these car- bons is governed by nearly the same overall molecular motion. The variation of the relaxation rates for the vmeta carbons is nearly identical with that for the ortho carbons, since both are dependent on the overall molecular motion and on the internal rotation of benzene ring. How- ever, the relaxation rate of the para carbon is quite dif- ferent from that of meta and ortho carbons, since it is almost independent of the internal rotation of the benzene ring. According to Equations (141), (134), and (135), the relationship between the ratio of the relaxation time of the ortho or meta carbon to the para carbon and p = R/D is shown in Figure 47. Since some deviation between the 215 0.12; 0.11 - 0.10 * 0.09 L 0.08 0007 P 0.06 @ l/Tl (sec-l) 0002 F- 0.01 I J I I I I I 130 140 150 160 170 180 190 200 210 Molecular Weight Figure #4. Relaxation rates of the quaternary carbon on the N-phenyl group and the carbon of the 0:0 group in N-methylacetanilide (O )( I), N-ethyl- acetanilide ( O )( I ) , N-prOpylacetanilide ( O ) ( ll ) , and N-n-butylacetanilide ( O)( D ) , plotted versus molecular weight. 216 0.7 0.6 - 0.4 - 003 )- l/Tl (sec—l) 0.2 0e]. ‘ 0.0 l l 1, 11 l 180 150 160 170 180 190 200 Molecular Weight Figure #5. Relaxation rates of the carbonyl-QR3 carbon in N-methylacetanilide (O ), N-ethylacetani- lide (O), N-propylacetanilide (O). and N-n-butylacetanilide (0), plotted versus molecular weight. 217 2.4 1.6 1 leu' 1" 100 D 1/T1 (sec‘l) 0.8 - 0.6 - 0.4 - J I 1 1 L l 130 140 150 160 170 180 190 200 210 Molecular Weight 0.2 Figure #6. Relaxation rates of the gglg. ortho. and Egg; carbons of the N-phenyl groupsof N-methyl- acetanilide ( I )( D )( I ) , N-ethylacetanilide (I )( I )( O), N-propylacetanilide (Q )( D H © ). and N-n-butylacetanilide ( )( D )( O ) . plotted versus molecular weight. 218 3-5 3.0- 1 2.0 I- ’5. :: E-I \ I E O I: 92-! 1.0 - D CABE F I H l l A l l 0 1 2 3 1+ 5 6 7 8 9 10 p-> Figure #7. Calculated ratios Tl(o,m) /'T1(p) versus P:= R/D. (for benzene ring geometry with 0 = 60°). A-F are the compounds listed in Table 22. 219 relaxation times of mg£g_and giigg_carbons is observed, the average value of the relaxation times for these two carbons is used for the Tl(o,m) value. From the value of the tumbling ratios 0 of the diffusion Tl(o,m)/Tl(p)' constant R of the benzene ring around its C2 axis (relative to D) in N-alkyl acetanilides and formanilides were calculated and are shown in Table 22. In monosubstituted benzenes, Levy has found that the tumbling ratio increases as the substituent group be— comes larger or heavier. However, Imanari et al.105 also found that the tumbling ratio decreases as the steric effect becomes important, as in the case of 2,2', 6,6'— tetramethylbiphenyl. In N-alkylacetanilides and formanilides, these two effects, i.e., the inertial effect and the steric effect, will compete with each other. In N-methylacetanilide, N-ethylacetanilide, N-methylformanilide, and N-ethylformanilide, the inertial effect will be more important than the steric effect, since the sizes of the N-ethyl and N-methyl groups are not large enough to overcome the inertial effect. However, in N-n-propylacetanilide and N-n-butylacetanilide, the steric effect becomes more important than the inertial effect, and thus a lower tumbling ratio results. The tumbling ratios of N-methylformanilide and N-ethylformanilide are also larger than those of N-methylacetanilide and N-ethylacetanilide and this may also be attributed to the steric effect of the carbonyl methyl group. 220 .eHxs mo esp assays wch mamucmn 0:9 Ho PCoHoHHHeoo :onSHHHc 0:9 mH m use coHpoa hdeooHoa HHeae>e was He eseHeHHHeeo seHasmeHe as» 8H a apes; .a\m u._ eHema wsHHpsse ass a .Conhmo mumm on» Ho_eeHP :OHpmmeeu one wH AQVHB .gsouw HmcmngIz one CH meopamo apes can ospuo Ho oaHp :oHpmstou owmuo>m on» mH A s.e.He m mm.m sm.H eHm.o sm.~ eeHHHcesnemHssemIz .m Ho.~ eHm.o oe.m em.H eeHHHsesueeHaepezIz .m sm.o HeH.o we.H on.H eeHHHsspeoaHspsmIsIz .n sH.H Hem.o ee.~ oe.H eeHHHsseeesHaaeumIsIz .o oa.H mnm.o es.n Ns.H eeHHHsepeeaHssmez .m oe.m smm.o oo.m He.H oeHHHcmpeomHzneezIz .< omm x 0mm X A OHOHm v AHI QOHOH v pa aAana\Aa.ovHe mossonaoo aeeHHHsasuee new meuHHHcmpoom meHmIz cH macaw HanonnIz one Ho :oHpmpou 0Hnoupoch< .Nm oHnma SECTION 4. CORRELATIONS AMONG 14N, 15N, 170, AND 13C CHEMICAL SHIFTS, AND BETWEEN THESE AND THE ROTATIONAL ENERGY BARRIERS IN SYMMETRICALLY N,N-DISUBSTITUTED AMIDES I. BACKGROUND Relatively little work has been done so far on the 14 15N 17 13 systematic measurement of N, , O, and C chemical shifts for amides. The reason for this lies in the low signal-to-noise ratio for these nuclei. Owing to a low nuclear moment, low natural abundance, or presence of a nuclear quadrupole moment, the signal strength for each of these nuclei is normally lowered by a factor of about 10-3 from that for the same number of protons in the same magnetic field. Moreover, in most compounds of oxygen and nitrogen there is a large electric field gradient at 14 17 the N nucleus (I = l) or O (I = 5/2) nucleus and the interaction of this with the electric quadrupole moments 14 of the N and 170 nuclei leads to considerable broadening of their NMR signals. 14 The variation of the N chemical shifts in primary and secondary amides and thioamides had been qualitatively 115 in terms of the de- 116 explained by Hampson and Mathias localization of the nitrogen lone pair. Siddall et a1. had failed to observe the predicted correlation between 221 222 14N downfield shifts and the increase of barrier heights Ea to rotation about the central C-N bond in N-alkyl sub- stituted amides and explained their results as arising I from the dominant role of steric effects. However, 117 Martin et al. found that there is a good linear correla- tion between the energy barriers Ea hindering rotation about the central C-N bond and the 15N chemical shifts in N,N- dimethylamino derivatives (amides, thioamides, and related compounds). Unfortunately, they were unable to correlate the 15 13 N and carbonyl C chemical shifts in the amido groups of amides. However, since amides are generally considered to be resonance hybrids of the two structures (V-A) and (V-B), there should be some relationships R R R 1\\\0____N//// 2 l\\\C==== 3 3 (V-A) (V-B) among the chemical shifts of nitrogen, carbon, and oxygen in the amido groups of amides. In order to probe these relationships, two series of symmetrically NJJ-disubstituted amides were studied: (1) Formamide,N,N-dimethylformamide (DMF), N,N-dimethylacetamide (DMA), N,N-dimethylpropionamide (DMF), and N,N-dimethyl-n-butyramide (DMB); and (2) N,N-Diethylformamide (DEF), N,N-diethylacetamide (DEA), 223 N,N-diethylpropionamide (DEP), and N,N-diethyl-n- butyramide (DEB). 13 The C chemical shifts were determined by use of the CFT-ZO NMR spectrometer. This has a very stable l3C chemical shifts was less than 0.02 ppm per month. The 14N chemical magnetic field and the variation of the shifts were measured by use of the DA-60 NMR spectrometer 14 with an external lock; the variation of the N chemical shifts was about 3-5 ppm, which is mainly a result of the large linewidth of the 14 the 15N and 17 N signals. The determination of 0 chemical shifts was carried out on the WH-180 NMR spectrometer which, like the CFT-20, has a very , stable magnetic field so the variation of the 13N shifts was less than 0.05 ppm. However, the variation of the 17O shifts was about 1.0 ppm as a result of the broadl’7 118 O signals. Saika and Slichter had proposed that chemical shieldings Mdth.respect to isolated nuclei can be broken down into three components: due to the diamagnetic an, effect of the electrons on the nucleus concerned, GP due to the paramagnetic effect caused by asymmetries in the electronic distribution about thenucleus Produced by the bonding in the molecule, and 0 due to long-range effects A produced by other atoms or groups in the molecule. In the 14N, 15N, 17O, and 13C cases, contributions to the chemical shifts due to 0A can be considered too small for considera- tion at present. Since the s electrons will dominate GD 224 in these nuclei, and these electrons are affected little by chemical bonding, 0 will not be the main factor con— D trolling the variation of the chemical shifts in a series of related compounds such as the amides. The experimental evidence support the dependence of the chemical shifts of these nuclei upon the remaining term op. The overall variations of the chemical shifts of these nuclei can be understood qualitatively from the nature of the bonding involved. The results for the 15N, 14N, 17O, and 139 = 0 chemical shifts for the symmetrically N,N-disubstituted amides are shown in Table 23. Various relationships among these chemical shifts have been obtained in the amides and will be discussed in detail separately below. II. RELATIONSHIP BETWEEN 14N AND 15N CHEMICAL SHIFTS There is an almost linear relationship between 15N and 14N chemical shifts for N,N-dimethylamides and N,N- diethylamides, as shown in Figure 48. These results further 14 15 supporttflmaequivalence of N and N chemical shifts, which had been proposed before for various other nitrogen-con- 119,120 14 taining compounds. The relationship between the N and 15N chemical shifts can be expressed by the following equation: 615 = 0.8487 (: 0.0456) 614 + 46.1536 (ppm). (142) N N 225 .emm No.0H mam AUMHvo .AzmHvo CH was 899 HH mum AomHvo .A23Hvo :H whomuo oHnmnonm one o .uxwu memo .Uom.¢m #0 OUME wHw3 mfifimEOHUmme 0S“ USN .U.O 53 m 0H®3 60mg mmflflfl fizz 05“ “WEB EOHH CHOHH Ic30U mumHsm msHumOHch mosHo> + £#H3 .m:& on o>HMMHwH mum mHMHsm HMOHEwno o u .UomN Hm OUME OHTB mHCOEmHDmMQE 0&9 MGOflflm>HmeO wwwfifl HON Umm5 meDU mzz GE“ “NOZ .m m m m UMH can .MH0>Hpowmmmu ..p.o EE mm was .65 cm .EE mH mums mo 0» m>HuonH pHmHmms wHMHnm mcHuMOHp IcH m852.5 + nuHB oz mu ou mwauHHeHe.H HHm one 05H .ZmH .ZvH mo mumHSm HooHEmco 059m Hues mHse eme.eH mm.osH m.e~H mo.em~ m.ee~ eeHseuxusnIsIHssueHoIz.z sacs mHse eHm.eH mm.HHH H.e~H ma.em~ s.me~ meHseeoHaoaaHssueHoIz.z mmH a.eH me.aeH m.eHH e~.mm~ m.me~ meHseueoeHssumHaIz.z mmH m.mH mm.HmH m.mvH No.nem N.Hv~ opHEmEuomenuoHoIzsz mmH oo.o~ mm.HnH m.mmH mn.mm~ m.>hm opHEoumusnIcIHanuoEHoIz.z mmH.mmH.HmH mm.mH mm.m>H m.mmH Ho.mmm h.Hm~ ocHEmconoumHacuoEHoIz.z >MH.mmH.mmH.HMH oe.o~ mm.onH n.mHH oo.mw~ n.Hm~ mpHEmumosH>numEHnIz.z mMH.mmH emH.HmH.mmH.HmH mm.mm mm.HmH m.mMH mm.mhm o.Hh~ oUHEoEHOHHmsuoEHoIz.z I mm.mmH m.an om.wm~ o.mom mpHEmEuom H08 0 m c on o e s 0H m HHeosv m onomH esH zmH zeH HmHHHmmINmumcm Hemmv uMHam HMOHEmsU pcsomeou nggfigonm omHm some mopHEm omonu mo munch ZIO Hmuucwo on» usonm coHumuou mcHuoHuummH A my mHoHHHMb moumcm esp mo mosHm> HmucoEHHomxm .mopHEs pwusuHumnsme IZ.Z mHHmoHuumfifimm 050m :H o u UmH was 05H .3 .ZVH mo mHMHSm HMOHszu .mm wHQMB 226 290. 280. ->' 615N (ppm)/CH3N02 m N O\ \1 o o 250. 240 . 1 1 L l 240. 250. 260. 270. 280. 290. oluN (ppm)/CH3N02 —> Figure #8. Correlations between the chemical shifts 615 and 61“ for N.N-dimethylamides and N.N-di- N ethylamgdes. 227 The above relation is obtained by use of the KINFIT‘program, 15 14 where 6 and 6 are the chemical shifts of N and N 15N 14N in amides, with respect to the reference CH3NOZ. The linear relationship between 14N and 15N chemical shifts indicates that there are no intrinsic differences of any importance between the electron distributions and that the deviations from Equation (142) are the result of experimental errors. The qualitative description of the variations in the nitrogen chemical shifts among the amides can then be based on either 15 6 or 6 values but, since the N chemical shifts have 15N 14N smaller experimental errors, the discussion of nitrogen 15 chemical shifts will be mainly based on N chemical shifts. The 14N and 15N chemical shift range is known to cover about 800-1000 ppm. The variations can be under- stood on the basis of the nature of the. bonding involved. Normally, as the bonds to nitrogen become stronger (i.e., increasing partial double bond character of the C-N bond), the contribution of the paramagnetic term will become more 14 15 important and a downfield shift of N and N resonances will result. In the case of amides, the change of'oP for nitrogen is governed largely by the effect of sub- stituents on the nitrogen lone pair electrons. According to resonance theory, the barrier hinder- ing internal rotation in amides is due to the contribution of resonance form (V-B) to the ground state of the system. As seen from examination of the resonance structures, the 228 15N and 14N chemical shifts of form (V-B) would be expected to occur at lower field than those of form (V—A). Richards121 noted that low-field shifts are found when the nitrogen lone pair electrons become involved in bonding. Fraenkel 122 have shown that protonation takes place and Franconi preferentially on the oxygen and the larger internal rota- tional barriers found for protonated DMF, compared with the non-protonated species, indicate that there is appreciable contribution of canonical form.(VI) in acid solution. (VI) 14N and 15N chemical shifts in Table 23 Shows that all the the N,N-diethylamides examined are shifted downfield rela- tive to the corresponding N,N-dimethylamides by about 30— 36 ppm, which is about twice the shift.in N-ethylformamide relative to N-methylformamide, 15.4 ppm.115 This is reasonable since there are two substituent groups in the N,N-diethylamides. These big downfield field shifts can be reasonably explained123 by the structural changes which occur involving an increase in n bonding of the nitrogen atom through its lone pair electrons when either a stronger electron donor is introduced (Me + Et) or the fl-orbital 229 system is extended over the R2 and R3 groups. These struCtural changes should result in an increase in the absolute value of the paramagnetic term, inducing a down- field shift of the nitrogen resonance. 15 By examining the 14N and N chemical shifts within the series of N,N-dimethylamides and of N,N-diethylamides, we find that a similar trend in the variation of the 14N 15 and N chemical shifts is observed as the substituent group on the carbonyl carbon is varied from —H to -C3H7. The nitrogen chemical shift moves to higher field as the group a to carbonyl group is changed from -H to -C2 5, then to lower field as it is varied from -C H to -C H This 2 5 3 7' type of variation is attributed to the steric effect. 124 Microwave studies of formamide indicate that there is an angle of 12° between the planes defined by the H -C-0 1 bonds and the HZ-N-C bonds. If this twist increases, the overlap between nitrogen lone pair electrons and those of the C = 0 group would decrease, and the increased localization of the nitrogen lone pair would be expected to produce an 14N and 15N resonances. The upfield upfield shift in the shifts found in the series of N,N-dimethylamides and N,N-diethylamides with larger Rl groups could therefore be due to such an effect. These conclusions are supported by the lower energy barriers observed for rotation about the central C-N bonds in the series of N,N-dimethylamides125 as the size of the R1 group is increased. Models also show 230 that increased twisting about the N-CO bond might be ex- pected in order to facilitate normal rotation about the bond between the a-carbon and the carbonyl carbon in these larger molecules. In N,N-dimethyl-n-butyramide and N,N-diethyl-n- 14 butyramide the N chemical shift is to slightly lower field than that in their analogs, N,N-dimethylpropionamide and N,N-diethylpropionamide. The actual reason for this re- 13 sult has never been reported. However, in studies of C NMR spectra, a downfield 6 "steric effect" has been ex- 126-128 tensively probed , although its actual cause is still 14N and 15N chemical unknown. The downfield shift for the shifts in N,N-dimethyl-n-butyramide and N,N-diethyl-n- butyramide may be due to a similar 6 effect on the nitrogen atom, since in these two compounds we have introduced a 6 methyl group (structure‘VII). This appears to be the first O§\\§a ////R2 C-—-N a 5 H CH R 2 (VII) example of a downfield 6 "steric effect" which has been ob- served in the NMR spectra of nuclei other than 13C. This 6 effect is also observed in the 14N spectra of the compounds n-C3H7CONH2 and i-C H CONHZ, which had 3 7 been reported by Hampson and Mathias but not explained115 231 by them. The 14N chemical shift of i-C3H7CONH2 is slightly upfield relative to that in n-C3H7CONH2, since there is no 6 methyl group in i-C H CONH 3 7 2 but there IS a 6 methyl group in n-C3H7CONH2. The large low field 14 N chemical shift in formamide can be attributed to the formation of hydrogen bonds which stabilize structure (V-B). III. RELATIONSHIP BETWEEN THE 15N AND 13Q(= 0) CHEMICAL SHIFTS Since structure(V-B) corresponds to overlap be- tween the C = 0 group and nitrogen lone pair electrons, we expect to find a relationship between the 13C chemical shift of the C = 0 group carbon and the nitrogen chemical shifts:h1these two series of amides. A completely linear relationship between the 13C = 0 chemical shift and 15N chemical shift is indeed obtained, as shown in Figure 49. 13C = 0 The relation between 15N chemical shifts and chemical shifts for N,N-dimethylamides and N,N-diethylamides can be expressed by the following two equations: 6 (p.p.m.) = 0.6997 (+ 0.0100 ) 6 + 163.7070 15 — 13 N g_= o (143) for N,N-dimethylamides, and 6 (p.p.m.) = 1.0126 (+ 0.0111) 6 + 83.6074 ._ (144) for N,N-diethylamides. Here 613 is the 13C chemical 9=0 232 moHMom map How AOHVUWH ‘II was .\ 253 o ccm om zmH eeHsaHHeeeHeIz.z use meeHsaHaspeeHeIz.z me o mHHHAm HsoHEego on» coozvon meoprHeuuoo .m: oustm OHUMHO ssH msH msH HRH osH eeH meH seH eeH meH seH meH meH HeH oeH H q 1 d d h QED mmm .4 H 1 IHI q « .OdN mmm .omN mmm CH2 Y CH3 (X) show the same trend of variation with carbonyl substituent in both the series of N,N-dimethylamides and the series of 17 N,N-diethylamides. The 0 chemical shift moves downfield ,as the group a to the C = 0 group is varied from -H to -CH3, since a big structure change is introduced and the molecule may be twisted from the planar form. Structure (V-A) would then make a larger contribution and a downfield shift would be expected. However, when the group a to the C = 0 group is varied from -CH to - C2H the effect will be less than 3 5' for the change from H to -CH3. However, an upfield y steric effect (structure (XI)) begins to produce an upfield 17O .0 R X} §§\§ ///’ 2 CH C N y 3 ////d \\\\ \CHZ R3 8 (XI) chemical shift in N,N-dimethylpropionamide and N,N-diethyl— propionamide relative to their analogs with a methyl 239 substituent on carbonyl carbon, N,N-dimethylacetamide and N,N-diethylacetamide. In going from N,N-disubstituted propionamides to N,N-disubstituted-n-butyramides, the 170 chemical shifts move downfield again, since a downfield 6 steric effect of the terminal methyl group has been introduced. This is also the first example of a 6 down- field effect in oxygen NMR spectroscopy. An approximate linear relation between the 15N 17 and 0 chemical shifts is also observed, as shown in Figure 51. The small deviations from linearity may be 170 chemical shifts, since quite broad signal are obtained in 170 NMR attributed to experimental errors in the Spectra. These linear relations can be expressed by the following two equations: 1 + 339.443()(l49) 6 (p.p.m.) = -0.4451 (+0.0952) 6 15N — O 17 for N,N-dimethylamides, and 615N = -0.3172 (:0.131) 6170 + 294.4710 (150) for N,N-diethylamides. VI. 14N CHEMICAL SHIFTS OF SOME OTHER AMIDES MEASURED AT HIGH TEMPERATURES 14N NMR resonances are so broad at room 14 Some of the temperature that measurements of their N chemical shifts are impossible. In order to circumvent this problem, the temperature was raised to a constant high temperature. 240 290. re-DMP ©"‘ re'IDMB 1 280. I- DMF cu O z: m :n U \ ’g 270. P E F 2. m H “O 260. " 250. ' 240. I I I I 110 120 130 140 150 160 170 (ppm)/CH3N02 —-> Figure 51. Correlations between the chemical shifts 615 and 617 for a series of N,N-dimethylamides and g serges of N.N-diethylamides. 241 The signal then became sharper, although the linewidths re- mained quite broad, as shown in Table 24. For the amides listed in Table 24, only a qualitative discussion of the 14N chemical shifts will be presented. The 14N chemical shifts for N,N-dimethylacrylamide and N,N-diethylacrylamide are at higher fields relative to those of their analogs with alkyl substituents on carbonyl carbon in the series of N,N-dimethylamides and N,N-diethyl- amides, as shown in Table 23. This is attributed to "cross conjugation" in these two acrylamides which results from additional contributions of resonance structures Of the type of structure (XII). As a consequence, the contribution I, C-——C R \___N/2 / \I of structure (V-A) will be lowered, the nitrogen lone pair electrons will become more localized and the observed 14N chemical shifts for these two compounds will be at higher 127 field. Rogers and Woodbrey , had suggested this effect to account for the lowering of the energy barrier in N,N- dimethylacrylamide. The downfield shift of 14N in N,N-diethylacrylamide relative to that in N,N-dimethyl- acrylamide is about 35 ppm, which is in the range ob- served for their analogs, the saturated N,N-dimethylamides and N,N-diethylamides, 30-36 ppm. 242 Table 24. 14N Chemical Shifts for some other amides+ Compound Temper- Chemica1* Linewidth ature Shift (°C)- (ppm) (HZ) N,N-Dimethylacrylamide 96.0 289.6 - N,N-Diethylacrylamide 97.0 254.7 350.0 N,N-Di-n-propylacetamide 97.0 260.3 540.4 N,N-Diisopropylpropionamide 97.0 236.7 489.2 N-Methylformanilide 97.0 246.8 411.0 N-Ethylformanilide 98.0 232.1 459.9 N-n-Butylacetanilide 135.0 224.8 1314.4 N-thhyl-N-n-butyl- trimethylacetamide 96.0 273.7 855.4 N-MEthyl-N-n-butyl- isobutyramide 97.0 271.5 540.5 N-Methylformamide 28.0 270.5 245.0. N-Ethylformamide 28.0 252.4 372.0 N-n-Butylformamide 28.0 173.0 1199.6 N-n-Butylformamide 98.0 256.9 350.0 N-t-Butylformamide 97.0 241.2 347.2 N-Methylacetamide 28.0 269.3 532.2 N-thhylpropionamide 96.0 277.2 347.6 N-Ethylpropionamide 96.0 261.4 - * The chemical shifts are relative to CH3N02, with + values indicating shifts upfield relative to CH N02. The NMR tubes used were 15 mm o.d. All compounds were purified. +Measured at 4.335 MHz on the DA-60. The probable errors in 1""N chemical shifts are i 4 ppm- 243 The 14N chemical shift for N,N-di-n-propylacetamide is between that of N,N-dimethylacetamide and that of N,N-diethylacetamide. This is a result of the upfield Y steric effect in N,N-di-n-propylamide, illustrated in the 14 . conformation of Structure (XIII). SO the N chemical 5/ H2 0 y 0H3 082 o. >—-< 0113 y CH /CH2 0. (XIII) shift of N,N-di-n-propylacetamide is upfield relative to N,N-diethylacetamide. The 14 N chemical shift in N,N-diisopropylpropion- amide is at lower field than in N,N-diethylpropionamide, since there are two 3 carbons in each nitrogen substituent and so isopropyl is a stronger electron donor group. The 14N chemical shifts for N-methylformanilide, N-ethylformanilide, and N-n-butylacetanilide are at rather low fields compared with those for N-methylformamide, N-ethylformamide, and N-n-butylformamide. This is because the N-phenyl substituent in these compounds gives rise to contributions of additional resonance forms of the type of Structure (XIV). 244 This leads to a decrease in the double-bond character for the central C-N bond and a lowering of the energy barrier for internal rotation about that bond. The 14N chemical shift in N-methyl-N-n-butyl- trimethylacetamide is at higher field than that in N-methyl— N-n-butylisobutyramide, since there are three Y methyl groups in N-methyl-N—n-butyltrimethylacetamide. The strong steric effect of the tertiary butyl group substituent on C = 0 may also force the molecule out of the planar form, which would increase the localization of the nitrogen lone 14N chemical shift. 14 pair electrons and cause an upfield At room temperature (28°C) the N chemical shifts for N-methylformamide, N-ethylformamide, and N-n-butyl- formamide are lower, as expected. However the very low chemical shift for N-n-butylformamide may be due to an unusually large experimental error, since the linewidth of 1199 Hz is unusually large. 14 The downfield shift of N in N-ethylformamide relative to that in N-methylformamide is 15 ppm, which is just half of the downfield shift in going from N,N-dimethyl- formamide to N,N-diethylformamide. 14 At 98°C, the chemical shift of N in N-n-butyl- formamide is 256.9 ppm, which is at higher field than the 14N resonance in N-t-butylformamide (241.2 ppm). This is attributed to the tertiary butyl group being a stronger electron donor group, which would shift the 14N resonance in N-t-butylformamide to lower field. 245 The downfield shift of 14 N in N,N-dimethylacetamide relative to that in N-methylacetamide is about 12 ppm, which is considerably greater than the downfield shift in N-methylacetamide relative to that in acetamide, 0.9 ppm. 14 Comparing the N chemical shifts in N-methyl- propionamide and N-ethylpropionamide, we find that the 14N chemical shift in N-ethylpropionamide is at lower field, since the ethyl group is a stronger electron donor than the methyl group. This downfield shift is about 15 ppm, which is half the value obtained for N,N-diethylpropionamide relative to N,N-dimethylpropionamide. From the above results we can conclude that the linear relationships between the 14N, 15N, 17O, and 13g_= 0 chemical shifts in the amido groupschemical shift was because the carbonyl substituent groups in their system, which included unsaturated groups, changed the properties 13 of the C = 0 group. However, in our system the carbonyl substituents are all saturated alkyl groups so the varia- tions in the chemical shifts of 139.: O, 15N, 14N, and 70 mainly arise from overlap of the nitrogen lone pair electrons with those of the C = O groupl conditions are therefore favorable for the existence of linear relation- ships between the chemical shifts of those nuclei. The reason that Martin et al. were able to find a linear 246 relation between Ea and the 15N chemical shift is that the nitrogen is far away from the carbonyl substituents so their effect on the nitrogen chemical shift is small. We can predict that if an amide system has the same carbonyl substituent, and the same number of substituents on the nitrogen, then the energy barrier for rotation about the C-N bond will be related linearly to the 139(= o) and 170 chemical shifts as the nitrogen substituent groups are changed. However, a linear relation between Ea and 6 15 N may not exist. The second result obtained in these studies of the 14N chemical shifts is that when one of the nitrogen substituents is varied from -CH3 to -C2H5 a 15 ppm down- field shift will result, and this shift is additive when two nitrogen substituent groups are introduced. However, in going from primary amides to the corresponding N-methyl 14 secondary amides, the variation in N chemical shifts is small. SECTION V. OFF-RESONANCE PROTON-SELECTIVELY DECOUPLED 13C NMR SPECTRA AND SPIN-LATTICE RELAXATION TIMES AS TOOLS FOR ASSIGNING THE 13C AND 1H CHEMICAL SHIFTS OF AMIDES I. BACKGROUND The use of the heteronuclear off-resonance de- coupling technique, and of the application of graphical 13C and 1H 69,139,140 and other methods, in the interpretation of NMR spectra has been extensively demonstrated. Not only can the chemical shifts of quaternary carbons, CH-, CH2-, and CH3- be determined but also the residual one-bond13C-1H coupling constant Jr measured in these partially decoupled spectra may be used to interrelate carbon and proton chemical shifts. The relation between Av, the separation of the proton signal from the applied decoupling frequency, and Jr is141 I 2 Av = ——— J (151) Jo r at very strong decoupling fields, i.e., for |¥H2| >> [Jo] and IAvl. Here Jo is the coupling constant of the un- decoupled multiplet in the observed spectrum, and xHZ is the decoupling field strength. In 13C - {H} experiments, a plot of the proton irradiation frequency versus the corresponding residual coupling constant Jr will yield a straight line with a 247 248 slope equal to YHz/JO, and the exact position of the de- coupling field H2 in the proton spectrum corresponds to J = 0. r Therefore, if the chemically different protons or carbons have already been assigned from the proton or 13C NMR spectra, then corresponding carbons or protons can be readily assigned. This method is particularly useful for assigning 13 29,142-147 closely spaced C and 1H signals. Any wrong assignments of carbon resonances will result in deviations from the straight line relationship of Equation (151). 13C NMR chemical shifts is larger than 13 Since the range of that of proton NMR shifts, the C NMR spectra usually can be easily assigned by simply comparing spectra of similar compounds97 whereas the corresponding proton NMR spectra may be broad, highly split, or overlapped. For some 13C NMR spectra with closely spaced lines, the spin-lattice relaxation times may be very helpful in assigning the 148 signals, in case they have quite different T values. 1 By using these two techniques, off-resonance cw 13 13 proton decoupling and C T1 determination, the C and proton chemical shifts of N,N—dimethylformamide (DMF), N,N-dimethylacetamide (DMA), N,N-dimethylpropionamide (DMP), N,N-dimethyl-n-butyramide (DMB), and N-n-butyl-N-methyl- formamide (NnBNMF) have been assigned. 249 II. RESULTS 13 The C chemical shifts of the carbons in these 131 five compounds have been determined before, as shown in Table 25, where the 13 C chemical shifts have been measured at 0°C with TMS as the reference. The proton chemical shifts have also been reported (Table 26). Using the 13C chemical shifts from Reference 131 assignments of the (Table 25), we have determined the spin-lattice relaxation times of each of the carbons in the amides and these are shown in Table 25. The T1 values for DMF, DMA, and DMP are very reasonable, while those for DMB and NnBNMF are abnormal in the case of certain carbons. In DMB, the 13 C chemical shifts of the gig-N- methyl group carbon and the a carbon of the carbonyl sub- stituent (35.5 and 35.2), and in NnBNMF, of the gingtmethyl group carbon and of the 8 carbon of the gigfn-butyl group (29.5 and 29.1), are so close that they have been in- correctly assigned in the literature. Following the scheme of 13C spin-lattice relaxation times in Table 25, we find that if the chemical shifts in the above pairs of carbons in DMB and NnBNMF are exchanged, then the spin-lattice re- laxation time data can be explained in a reasonable manner. Due to the segmental motion of the long chain sub- stituents in organic molecules, the spin-lattice relaxation times of methylene carbons usually increase in going from the heavier end to the free end149'150, i.e., from the a 250 Table 25. 13C Chemical shifts and spin-lattice relaxation times of some amides as assigned in the literature. Amide SubstituentC Chemical Shifta T1(sec)a ‘ (ppm) N-N-Dimethyl- N-methy1(t) 36.2 11.64:0.34 fOrmamlde N-methyl(c) 31.2 l9.38:0.49 C = 0 162.8 N,N-Dimethyl- N-methyl(t) 38.0 13.37:0.19 acetamlde N-methyl(c) 34.9 14.28i0.46 Carbonyl-CH3 21.9 10.79:0.29 C = 0 170.2 63.89:2.70 N,N-Dimethyl- N-methyl(t) 37.3 14.40:0.68 pr091°namlde N-methyl(c) 35.4 12.66:0.60 Carbonyl-sub 26.8 5.96:0.15 -a-C ' Carbonyl-sub 9.8 6.61:0.12 _B_C c = 0 173.8 56.08:l.34 N,N-Dimethyl- N-methy1(t) 37.3 12.83:0.39 ‘n'butyramlde N-methyl(c) 35.5 5.06:0.15 Carbonyl-sub 35.2 12.22:O.72 -a-C Carbonyl-sub 19.2 6.19:0.24 _B_C Carbonyl—sub 14.6 7.29:0.20 C ==O 172.6 53.78:}.17 N-n-Butyl-N- N-methyl 34.4(t) 7.10:0.54 methyl- 29.5(c) 5.08:0.05 formamide N-n-butyl-a-C 48.9(t) 3.95:0.37 43.8(c) 4.37:0.52 N-n-butyl-B-C 30.8(t) 4.04:0.13 29.1(c) ll.74:0.58 N-n-butyl-Y-C 20.6(t) 5.96:0.26 20.2(c) 6.15:0.41 251 Table 25 (cont'd.) Amide Substituent Chemical Shifta T1(sec)a (ppm) N-n-butyl-6-C l4.4(t,c) 4.92:0.27 C = O l63.3(t,c) 5.81:0.23 aFrom Reference 131. bThis work. CCarbonyl-sub-a-C = carbonyl-substituent a carbon. 252 Table 26. Proton chemical shifts in some amides Substituent Amide H(C=O) N - CH _ R(C = O) N-n-butyl 3 trans cis a—C B-C Y-C N,N-Dimethyl-a formamide 7.90 2.98 2.81 N,N-Dimethyl-b 3.01 2.83 1.98 acetamide 3.01 2.83 1.98 N,N-Dimethyl-C propionamide 3.01 2.95 2.37 1.15 N,N-Dimethyl-d -n-butyramide 3.11 2.94 2.41 1.59 0.96 N-n-Butyl-e N-methyl- formamide 8.02 2.96 2.81 aSolvent CCl Sadtler 9287M. 4' bSolvent cc1 Sadtler 8875M. 4’ CSolvent c0013, Sadtler 19929M. dSolvent D20, Sadtler 19021M. eOnly a partial set of proton chemical shifts is reported in Reference 95. 253 to the B, Y,... carbons. After exchanging the assignments of the chemical shifts in the pairs of carbons in DMB and NnBNMF discussed above, the new 13C chemical shift assign- ments shown in Table 27 are obtained. The spin-lattice relaxation times of the carbons of the carbonyl sub— stituent in N,N-dimethyl-n-butyramide and of the carbons of the N-n-butyl group in N-n-butyl-N-methylformamide now increase in going from the a carbon to the Y or 6 carbon in the correct order. And the expected longer T1 values for the carbons of the gig-N-methyl groups compared to the methylene carbons of the n-butyl groups in both compounds may also be rationalized by assuming that there is free internal rotation of the methyl groups plus segmental motion of the n-butyl chain.85 The observed T1 value for the carbon of the gig-N-methyl group is shorter than that of the carbon of the giggng-methyl group in DMB while the opposite result is observed for NnBNMF. All these results are expected since there is a preferred rotation axis in each molecule which governs the overall anisotropic mole- cular motion. 13C chemical shifts of In order to prove that the all these five compounds are actually assigned correctly in Table 27, the off-resonance decoupling technique was used to calculate the corresponding proton chemical shifts, since the experimental hydrogen NMR spectra have been correctly assigned before. By using graphical methods and 254 Table 27. Chemical shifts and spin-lattice relaxation times of some amidesa’b measured in this work. Amide Substituent Chemical Shift T1(sec) (ppm) N,N-Dimethyl- N—methyl 35.09(t) ll.64:0.34 formamide 25.99(c) 19.38:0.49 C = 0 161.88 21.19:0.68 N,N-Dimethyl- N-methyl 37.25(t) l3.37:0.19 acetamide 34.l9(c) 14.28:0.46 Carbonyl-CH3 20.62 10.79i0.29 C = 0 170.53 63.89i2.70 N,n-Dimethyl- N—methyl 36.43(t) l4.40:0.68 propionamide 34.52(c) 12.66:0.60 Carbonyl-sub -a-C 25.89. 5.96:0.15 Carbonyl—sub -B-C 8.84 6.61:0.12 C = 0 173.25 56.08:}.34 N,N-Dimethyl- N-methyl 36.36(t) 12.83i0.39 -n-butyramide 34.25(c) 12.2210.72 Carbonyl-sub ‘ -a-C 34.51 5.06:0.15 Carbonyl-sub -B-C 18.16 6.19:0.24 Carbonyl-sub” -Y-C 13.39 7.29:0.21 C = 0 171.68 53.78i2.17 N-n-Butyl- N-methyl 33.40(t) 7.10+0.54 N-methyl 28.26(c) 11.74:0.58 formamide N-n-butyl-a-C 48.28(t) 3.95:0.37 42.94(c) 4.37:0.52 N-n-butyl-B-C 29.95(t) 4.04:0.13 28.59(c) 5.08:0.05 N-n-butyl-Y-C l9.23(t) 5.96:0.26 19.66(c) 6.15:0.41 255 Table 27 (cont'd.) Amide Substituent Chemical Shift T (sec) 1 (ppm) N-n-buty1-6—C l3.28(c) l3.20(t) 4.92+0.27 C = O 16l.89(t,c) 5.81:0.23 aAll the chemical shifts are relative to TMS. The measure- ments were made at 35°C. bThe assignments differ from those in Table 25 in some cases based on the arguments given in the text. 256 the KINFIT program, the proton chemical shifts of all these five amides have been determined in this work as shown in Figures 52-56. The proton chemical shifts calculated using Equation 151 are also shown in Table 28. Comparing the proton chemical shifts of all the symmetrically N,N-dimethyl- substituted amides - DMF, DMA, DMP, and DMB - we find that all the calculated results are matched with the experimental values, Tables 26 and 28. The chemical shift deviations between calculated and experimental results are mainly attributed to the bulk susceptibility factor (since our compounds were placed in an inner tube and the reference TMS in the outer tube, as described in Experimental Section). The matching of all the proton chemical shifts provides further proof that the 13 C chemical shifts of DMF, DMA, and DMP are correctly assigned in Table 27. .In addition, the matching of the proton chemical shifts in DMB tells us that our assignment of 13 C resonances for the ging-methyl group and the a carbon of the carbonyl substituent in N,N- dimethyl-n-butyramide is correct. Some of the proton chemical shifts for N-n-butyl- N-methyl formamide had been reported a long time ago and are given in Table 26. The reported proton NMR spectra of N-n-butyl-N-methylformamide and N-n-butyl-N-methylacet- amide are also shown in Figures 57-A and B. Since the chemical shifts of the trans and cis Y protons in the N—n-butyl group are so close to the limit of the resolving (Hz) Jr Figure 257 20h- 10)- ‘5'? fit‘ T’ ’ DO ( x 100 Hz ) 52. The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency ' D0 in N,N-dimethylformamide: TMS ( O ), NCH3(c_i§) (D), NCH3(m) (0), and 0:0 (I). 258 20 - , , I A 10+ III! 2 / v I- 1’ ’ l I l I 50’ 60’ DO (xlOOHz) Figure 53. The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N,N-dimethylacetamide: TMS ( 0 ), NCH3(trgg§) (A ). NCH3 (_cig) (0 ). and carbonyl-CH3 (o ). 259 30F 20 W IO- (Hz) '10 P -20 I- . 30 l J I l 30 4° 50 60 DO (xlOOHz) Figure 54. The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N,N-dimethylpropionamide: TMS ( 0 ), NCH3(trans) ( 0 ). NCH3(gi_§) (4 ), a carbon of the carbonyl substituent ( I ), and B carbon of the carbonyl substituent (0 ). 260 IO (Hz) Jr -N>+ II I I so 45 50 po(xlOOHz) Figure 55. The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N.N-dimethyl-n-butyramideI TMS ('.)O NCH3‘3EEQE) (")o NCH3(£;§) (‘9). a carbon of the carbonyl substituent (‘3). B carbon of the carbonyl substituent (<3). and Y carbon of the carbonyl substituent ( 0 ). 261 30F (Hz) Jr l I l l I ‘05 4o 45 SD 55 60 no (xlOOHz) Figure 56. The dependence of the residual C-H coupling constants Jr on the decoupler offset frequency D0 in N-n-butyl-N-methylformamideI TMS (0 ), trans- and _c:_i_§-NCI-I3 groups (0 )(---), a carbons of the tran and c N-n-butyl groups (0 )(.'_). B-carbons ( 0 )( 0 . y-carbons ( A )(y, ). and 5-carbons (A )( ). C=0 (0 )- 2 6 2 mo.o vm.o mevo.oHemmm.me 5H.Hm on.n mm.m I mH.mHI OImIQSm IHHGOQHMU mH.m on.H nmmo.oHemmh.mv mH.m~ oo.m OH.m I mo.nHI OIaInsm IHhconHmu os.~ eH.H ommo.oHsewH.me He.om me.e mm.m I HH.H~I HovmmoIz mm.~ m~.m bemo.oHemmm.mv om.om mv.v oh.m I hm.HmI HuvmmOIz oo.o oo.o smoo.onomo.mv me.om mm.m oo.~ I mv.MHI mza mzo en.H mm.H oHH.onHmm.nv n.mm v.m H.mHI m.emI mmUIHhconumu om.m mo.m .mmH.onm>a.nv m.o~ m.v m.>HI n.mmI HovmmOIz mn.~ o~.~ HoH.oH~mmo.mv m.om m.m ~.mHI >.mMI HuvmmUIz oo.o oo.o mmoo.onmmm.mv v.mm m.n m.HHI ¢.mmI mze <20 mm.> No.m vemo.onmmo.Nm om.m~ H.mI o.o~I oo.va o u U mv.m em.H mmHo.ovamm.nv mm.Hm om.m cm.h I h>.o~I HovmmOIz Ho.m mo.m mome.oHnNOH.mv mm.om om.v pH.m I hn.omI HuvmmOIz oo.o 00.0 ase.oHH~Ho.ee om.om om.m em.H I sm.mHI was man HeaaeHNmomH Ham OOH xv oeuoo mmuoa emuoa meuoa oenoo omuoa 0mm sow HoopmHsoHsov.oo Humvuo ucmsuHumnsm moHem meow cH m . .m.mmooHEs . @ mumHnm HMUHEono comouo»: oousHsono may one museums m umummo Honsoooo can so no mncmumcoo mcHHQsoo mIO HosonTH mo cosmocmmoo 0:9 .mm THQMB 3 6 2 oe.H mN.H Hom.oHsmsm.se me.e~ e.mH I a.m H.mHI Hoe ma.~ mm.m mme.e+eoem.me m.~m H.eH I I N.HHI Hue oIm IHmusnIsIz Ho.m He.~ ammo.omemoe.me m.e~ mm.eH I H.H m.mHI Hoe mo.m se.~ mmeoo.o+msme.me ma.e~ ma.mH I mm.» e.mHI Hue UIe , IHsusnIsIz em.~ mo.~ mamo.omemeo.ee mm.e~ e.mH m.e H.s m.HHI loom es.~ aH.~ memo.o+memH.me me.e~ me.mH sa.m mm.e H~.mHI Hue moIz oo.o oo.o .emo.o+mmam.me me.e~ e~.HH me.s m.H H.HHI was mzzmsz mm.o ee.o amm.oHomoe.ee ma.s oe.~ me.mHI oI>Insm IchonusO mm.H e~.H mmH.oHemHN.se mo.e mm.e me.eHI OImInsm IchonHmu e~.~ Hm.H mOH.oHemss.He oo.m mH.e mH.mHI cIsInsm IHmconHmu ee.m HH.~ memo.oneso.me mH.m om.m m.o~I HovmmoIz mm.~ em.~ amHo.onmmm.me mm.e ee.m Hm.H~I HevmmoIz oo.o oo.o eoao.oHemea.oe mmIm oa.H sm.mHI was man HemaeHNmOOH 1m: xv Ham OOH xv oenoo mmnoo omuoo meuoo oenoo emuoa my . 0 =00 HooumHsonov.OQ Humvnb ucmsuHumnsm ooHE< A.o.ucoov mm mHQnB 264 I HHeCmHm moHEev .msoum o n O we» on m>HueHmH mHo no mCeHu museum mueoHoCH o oCe u o u Ch He umooumuCH may mH .OD oce IoH x um CH NUCqumum ummmmo .Hmzev.oa .oo n soc see was 09 meHueHmu HHHsm HeoHamso scheme was mH 0.0\=oa III 300 n .HemImm measmamv umHmCoomo ecu mH one N Os.s HN.O HmH0.0HOmO~.Nm m.e~ H.O 0.0 s.m~I H.mmI H0.uO o u o O0.0 mm.O HmH.OmmsHm.Oe O.sm ~.sH m.s I mO.mHI HuO . OO.H O0.0 OHH.O+OOOH.OO N.O~ 0.0H H.O I O.mHI H0O OIe IHmusnIsIz mm.~ OO.H Omm.OmmmOm.He m.O~ s.mH m.m I H.OHI H0O em.m HO.H mamo.o+esem.se O.ON s.mH 0.0 I m.HHI H0O OI» IHmusnIsIz HemaOHNmOOH Iml xv Ham OOH xO OOuon mmuoa omuoo meuoo oeuoo .H o O son HeeueHeoHeee.oe HemO O usesuHemssm mOHss A.U.UCOOV mm mHneB 265 l3> III-CH. (B) N-CH. (A) 5'7 ECO N-C EfC,H7 N‘CH. Ct). CE. C5. 'mlfild ’- Figure 57. lH-NMR spectra (v a 60 MHz) of N-n-butyl-N- methylformamide (R) and N-n-butyl-N-methyl- acetamide (B). The internal reference is TMS. The NCgifiat higher field (A) is the methyl group c to the 080 group. N-Chzc n7 "'5529525255 . . N-c3h6283 TMS 3 5'CZHIIEHZC5'3 , (c.t) C-C' ‘ #41 LAM vv—‘w’F—F—H *7 v—W ‘— I I 3237.8 _ 0. cps Figure 58. Completely decoupledlac NMR spectra of N-n-butyl- N-methylformamide (bottom, full spectrum, sw'= 4000 Hz and (top) the region of upfield signals expanded). 266 power of the instrument, the signals fortflmeN-CHZ-CHZ-CHZ- CH3 protons observed in the proton NMR spectrum form a single broad line. The three signals observed in the N-Cflz-C3H7 region also have not been explained. Since the 13C chemical shifts of N-n-butyl-N-methylformamide are well resolved, as shown in Figure 58, and had been assigned by us by comparison with the 13 C NMR spectra in similar compounds and by use of spin-lattice relaxation data, it is worth using the off-resonance decoupling method to assign all the proton chemical shifts in this compound. The off-resonance decoupled 13 C NMR spectra of N-n-butyl— N—methylformamide are shown in Figure 59. The residual C-H coupling constants are plotted versus decoupler off- set in Figure 56 and the values of the proton chemical shifts calculated from the 13 C data are given in Table 28. As shown in Table 28, the three signals observed in the N-C§2C3H7 region are assigned to Eganng-n-butyl-a—H, the gig-N-n-butyl-a-H, and the Egggng-n-butyl-B-H, respectively (from low field to high field). Within the broad bump, there are two protons, the transt-n-butyl-y-H and the ging-n-butyl-y-H. The calculated chemical shift for the ging-n-butyl-B-H is rather low (1.60 ppm), and was assigned to the second signal in the spectrum (Figure 57(A)) as counted from the high field.‘ The signal at highest field is attributed to the trangf and gig-N-n-butquifl's, as shown by the signal intensity, which is about twice 267 I D_O= Ujk~j . (x100 Hz) ”3W“ WWWUMWMIJJJ W ULJLM‘QO ! i JWWwmeMg-Mwwww - Jc—JLJLHJL... 1+ 5 M 5 M. .b J” wemwaWb, mwmwwwwmgu JWJJ JJ'JPJJJJJMMJAM 6 0 Figure 59. Off-resonance decoupled 130 NMR spectra of N-n-butyl-N-methylformamide- The assignments and the scale are the same as in Figure 58. «warn WW“! "MWMMMJmMWMWw Mum»; WM“ 268 that for the gig-N-n-butyl-B-H. In N-n—butyl-n—methylacet- amide, Figure 56(b), the trans- and gig-G-hydrogens of the N-n-butyl group are separated; this further indicates that there are actually two protons in the peak at highest field in the N-n-butyl-N-methylformamide spectrum (Figure 57(a)). All the above results show that the off-resonance decoupling technique, and the use of T measurements, are 1 really powerful methods in solving the difficulties met in 13C and 1H chemical shifts, especially the assignment of when the signals in the spectra are complex, broad, or overlapped. One point that should be mentioned is that if the condition |¥H2| >> [AV] is not met, then the linear rela- tionship between Au and Jr will break down at values of Av/xH2 ~ 0.5. Under those conditions it has been suggested29 that the equation ¥H2 Jr Av = (152) (J2‘_ J2)l/2 o r be used instead of the previous equation (Equation (151)). The symbols in the above equation have the same definitions as those in Equation (151). A plot of Jr/(J: - J:)l/2 versus Av will therefore yield the exact decoupling field 2 2 1/2 H2 in the proton spectrum corresponding to Jr(Jo - Jr) = 0. SECTION 6. SOLVENT EFFECT STUDIES OF N,N- DIMETHYLFORMAMIDE AND N,N-DIMETHYLACETAMIDE BY 13C NMR I. BACKGROUND Hindered rotation around the central C—N bond in amides is a well-known phenomenon. It was detected by proton NMR and first reported in 1955 by Phillips151 and by Gutowsky152 for N,N-dimethylformamide. At sufficiently low temperatures, most N,N-dimethylamides show a doublet in the proton NMR spectrum and at higher temperatures this coalesces to a single line permitting measurement of rota- tion rates about the central C-N bond. Several proton NMR studies of this type had been carried out on N,N- dimethylformamide and N,N-dimethylacetamide.153"161 Al— though the studies were made primarily for the purpose of making spectral assignments, concentration dependence of the chemical shifts of the amide protons in different sol- vents was noted.162 It has been reported that when the pure amide is diluted with a nonpolar solvent, coupling 154 across the C-N bond decreases and the energy barrier Ea for rotation around the C-N bond decreases.162 In N,N- dimethylamides, dilution produces a larger downfield shift of the cis proton signal than of the trans,154 where cis and trans are taken relative to the C = 0 group. These results have been interpreted as indicating that in the 269 270 pure liquid the dipolar resonance form V-B is stabilized by 154'162 In dilute CCl head-to-tail dipolar association. 4 solution, ABC and AS0 values of —6 kcal/mole and -14.5 eu, respectively, have been reported for the dimerization 153 equilibrium. Hydrogen-donating solvents also increase the contribution of the dipolar form by hydrogen bonding to the amide through the amide oxygen.156 Several workers have extended the studies of Hatton and Richards of the interaction between amides and aromatic solvents.163_167 Sandoval and Hanna studied the complexes of DMF with benzene, toluene, p-xylene, mesitylene, and durene and obtained equilibrium quotients for association and the chemical shifts of the N-methyl groups in the pure complex. They found, in agreement with earlier work, that the proton N-CH3 upfield shifts decreased as the number of aromatic methyl groups was decreased. However, since the equilibrium quotient for association increased in the same order, they concluded that the decrease in chemical shifts was due to a reduction in the aromatic ring current rather than to a weakening of the complex of amide with aromatic solvent. Matsuo has studied the effects of the solvent cyclohexane upon the chemical shifts of the protons in some N-substituted imides.”6 As a result of the appearance of FT NMR spectro- 13 meters, C NMR has become a popular tool for probing the interaction between.solutesand different solvents. However, 271 only a few papers have been reported in which solvent effects of amides are investigated by 13C NMR.168 Here, we have studied the solvent effects in three different systems by use of 13C NMR: (A) N,N-Dimethylacetamide in cyclohexane, (b) N,N—Dimethylacetamide in formamide, and (C) N,N-Dimethylformamide in benzene. II. RESULTS A. The N,N-dimethylacetamide-cyclohexane system The concentration dependence of the chemical shifts for each carbon of N,N-dimethylacetamide and of cyclohexane in solutions of various concentrations are shown in Table 29 and Figures 60-62. From Figure 60 we see that the variation of the chemical shift for carbonyl carbon with the concentration of DMA is strongest, and that this resonance is shifted to low field as the concentration of DMA is increased. The chemical shifts at concentrations below 30% are not observed because the signals are too weak to be observed. The chemical shift of the carbon of the carbonyl methyl group as shown in Figure 61, is also strongly dependent on the concentration of DMA. The down- field chemical shift for carbonyl methyl group from infinite dilution to 100% DMA is about 0.64 ppm. The chemical shifts of the carbons of the trans and gigeN-methyl groups are also moved downfield, but their variations are smaller than those of the carbons of the C = 0 group and of the carbonyl methyl group. The variation of the chemical shifts 272 CH muonumo m moIzImflo new mass» may cow3umn oocmeMMHp unflnm Hmowfimno may mmuocmp .flZQ oma 3<«« .Uomm um mcmfi mum3 wucmfimusmmmfi map was commmmmp wum3 mousuxflfi may .mSB on m>flumHmH who mamasm HMUHEmno one i Ho.m mo.m~ Hm.om mm.mm wo.mm I moa . wo.m mm.om mm.om mm.mm Hh.mm I wow ma.m mm.m~ H¢.o~ hotmm om.mm me.mwa mom HH.m mm.mm mv.o~ mh.mm mm.om mm.mma woe Ha.m nm.m~ mm.om vh.mm mm.mm ~>.mma mom NH.m mm.wm mm.o~ h>.mm mm.mm ms.mwa mom NH.m mm.m~ mm.o~ ms.mm om.mm Hm.mma won mH.m vm.om em.om Hm.mm va.mm oo.moa wow oa.m sm.sm ms.o~ mm.mm mm.om va.mma. woo Ha.m I «5.0m mm.mm oo.hm H~.mma wooa mmosa mmnouo onmmoIz lawnmouz o u m es ocmxmnoHomu mpHEmumomesumfionz.z mcmxmsoHomU mocmeMMHa ou «Zn «0 pussm Hmosamao Insane swarm Hmossmao osumm >\> .mcoflumnncmocoo msoflum> mo msmxmnoHomo cw €29 mo mcowusHOm How mcmxmnoHoau as was lasso mossmnmomamnumsflsuz.z as muonumo 0:» mo mumssm Hmoflsoao 0 .mm THQMB 273 169.304 169.20l- 169.10r 169.00b 168.90L 168.8c» 168.70? 6C30 (ppm) 168.60- 168.50 168.h0 I 168.30 168.20 163.10 I I I I I I I I II 0 10 20 30 #0 50 6O 70 80 90 100 % of DMA (v/v) Figure 60. Concentration dependence of the 13C chemical shift of the 020 group of DMA in cyclohexane solutions. yclohexane 60 (ppm) 20.80 20.70 20.60 20.50 "‘20.u0 20.30 20.20 20.10 20.00. I r \‘j 11 ‘l‘ 274 I I I I ' I r I _I I 0 10 20 30 40 50 60 70 80 90 100 5 of DMA (v/v) Figure 61. Concentration dependence of the 13C chemical shifts of the cyclohexane carbons(top) and of the carbonyl-methyl carbon of DMA (bottom) in DMA-cyclohexane mixtures. 275 33-50 I I I I I 0 10 20 30 no 50 60 70 00 90 100 % of DMA (v/v) Figure 62. Concentration dependence of the 130 chemical shifts for the carbons of the tgggg- and ci - NCH3 groups of DMA in various DMA-cyclohexane mixtures. ‘ l 1 l l 276 for the cyclohexane carbons is only slight, which indicates that the intermolecular interaction between DMA and cyclo- hexane is not strong. This result is reasonable since cyclohexane is a nonpolar solvent. From the above results l3C chemical shifts we see that the strong variation of the in DMA is mainly attributed to the interaction of DMA with itself, i.e., self-association. The chemical shift dif- ference between the carbons of the trans- and gig-N—methyl groups is found to increase by about 0.18 ppm, as shown in Figure 63, as the concentration of DMA is increased from zero at infinite dilution to about 30% (by volume) and at concentrations above 30% the chemical shift only varied slightly. One would predict from these data that the energy barrier for rotation about the C-N bond would increase with an increase in the concentration of DMA up to about 30% (by volume) and then remain almost constant with further increases in DMA concentration. A rapid increase within the range from 0 to 30% DMA corresponds to the rapid increase in the chemical shifts of the carbons of the carbonyl methyl and tranng-methyl groups, which suggests that the solution structure changes rapidly in this concentration range and that it may be interpreted in terms of an association of the DMA mole- 153,157. cules. Woodbrey and Rogers162 and Neuman and Young169 suggested the cyclic structure (XV-A) for the dimer. The drawing (XV-B) of this dimer shows the regions of positive 277 .z spams an x spams 06mm on» Ca ohm wagon covmasoamo can aspsoswuonxo so Page mopmoacsn u can .Pswoa coPmHSoamo a o .pc«oe ampsosduomxo as mopmowcsa x .mmumpxas \\ \\\ __3§// 5- 3 (SVI-A) (XVI-B) to increase the C-N rotational barrier over that for the non-hydrogen-bonded molecule by stabilizing the charge separation in the polar ground state. Since the hydrogen bonding interaction between N,N-dimethylamide and formamide represents a 283 model for the hydrogen-bonding interaction between dif- ferent peptide groups of a protein, we have investigated the variation of 13C chemical shifts in this system as the concentration of DMA is changed. The results are shown in Table 31 and Figures 64-67. One main difference, com- pared with the chemical shifts of DMA in cyclohexane, is 13 that the C chemical shifts of all the carbons in this system are shifted upfield as the concentration of DMA is increased. This result is just the opposite of that ob- tained for the DMA-cyclohexane mixtures. In addition, the curves showing the variation of chemical shift with concentration in these two systems are completely different, as shown in Figures 60-67, indicating that there is a specific interaction between solute and solvent for solutions of DMA in formamide. In the DMA l3C chemical cyclohexane system, the variation of the shifts is interpreted in terms of a monomer-dimer self- association equilibrium. However, in the DMA-formamide system, there is an additional solute-solvent interaction which competes favorably with DMA self-association, i.e., + DMA + F + (DMA ° F). Neuman et al. have investigated solutions of DMA 159 in CCl4 and in formamide by proton NMR and obtained 13 similar results to those obtained using C chemical shift data for DMA-cyclohexane and DMA-formamide mixtures in 284 .mowsmfinom was <20 ca mononm o u.w cooBumn museumMMMo unflam Hmowfimno on» mm o u 03< xix .dza GA mmUIZImHO paw Imcmuw COOBUOQ OUGOHOMMflv Hmafim HMOflEmno 05¢ wwwocmc 3< es .Uomm um moms mucoEmusmmmE we» can oommcmmo mums monsuxwfi one .mZB ou m>flumamumhmmumficm Hmowfimso one i mm.s me.m Hm.meH mm.o~ mm.vm me.sm ma.asa mos mm.m mm.~ mo.mma mm.o~ as.sm me.am mo.asa wow em.o om.~ mm.vos em.o~ em.¢m oe.sm mm.HeH mom os.o. om.m mm.ess mm.o~ me.¢m mm.em m~.HsH woe oa.m mm.~ mm.vsa mm.o~ ~e.¢m mm.am m~.HsH mom ma.s sm.m em.soa mm.o~ sm.¢m mm.sm mo.aaa mom mm.s No.m Hm.mmH oo.om s~.vm m~.am ma.oas wow I so.m I mm.o~ ma.¢m m~.sm mm.osa woos o u.I mac 0 u.w szono lovflssuosIz AuvamsumsIz o u.m are, .3! (II msasmsuom mcasmuoomamnumsanuz.z mwasmsuom mocwumumaa as «so «0 swarm Hmossmzo reams sumaam Hmoasmao oaumm 0H0: .mcoflumupcwocoo psmuwmmwo mo mGOflpsHOm.sw moflameuom MO was Amzav moHEmumomahnmeHoIz.z mo mconnmo on» no mumwcm Hmowfimno U .Hm manna ma 285 171.90‘ 171.80 171.70 171.60 171.50 171.40 171.3- . 171.20 171.10 171.00 6c=0(DMA)(PPmJ 170.90 170.80 170.70. 170.60p 170.50b 0 10 20 30 #0 50 60 70 80 90 100 Mole fraction of DMA (%) Figure 6#. Concentration dependence of the 13C chemical shift of the carbonyl carbon of DMA in DMA-formamide mixtures. 286 165.00 ' 165.30 P 165.20 P 165.10 - 165.00- 164.90" 1614.80 P 6c=0( formamide) (PPmJ 16h.h0_ 164.30 164.2 164.1 16h.0 163.90, 163.80L 0 l L l l I l l J I 10 20 30 1+0 50 60 70 80 90 100 Mole fraction of DMA (%) Figure 65. Concentration dependence of the 13C chemical shift of the carbonyl carbon of formamide in DMA-formamide mixtures. 287 37-50 37.40 (u‘ppm) CH I 37.30 °N 37.20 34.80 34.70 34.60 O 20.50 1 J 1 1 1 1 1 1 1 o 10 20 3o 40 50 60 70 80 90 100 Mole fraction of DMA (%) Figure 66. Concentration dependence of the 13C chemical shifts of the carbons of the trans-NEH3 (top). cis-NEH3 (middle). and carbonyl-QR3 (bottom) groups of DMA in DMA-formamide mixtures. 288 2071 ' 2.6 f. 1 1 1 1 1 1 1 o 10 20 30 no 50 60 70 W00 Mole fraction of DMA (%) Figure 6?. Concentration dependence of the 13C chemical shift difference between the carbons of the C20 groups of DMA and formamide (top). and the chemical shift difference between the carbons of the jggng- and ginggfia groups (bottom). 289 this work. Neuman et al. also have determined the energy barrier for internal rotation in DMA in formamide and find that it increases as the concentration of formamide increases. From Figures 64 and 65 we find that the variation of the 13 C chemical shifts for the C = 0 groups of DMA and of formamide are sharp and almost linear, indicating that the intermolecular interaction between DMA and formamide is very strong. This is different from the concentration dependence of the carbonyl carbon in DMA-cyclohexane mixtures, since hydrogen bonding is important in the DMA- formamide system. In the DMA-cyclohexane system, the dimers formed by the self-association of DMA are held together by dipole- dipole interactions. This type of interaction should also be possible between DMA and formamide molecules to form DMA-F complexes. However, we would expect that the 13C chemical shifts in such a complex would be essentially similar to those for (DMA)2. since the relative shielding of the two NCH3 groups in DMA should be mainly a function of the respective positions of the two amide linkages. Such dipolar interactions should lead to little concentra- 13C chemical shifts for DMA in 13 tion dependence of the formamide. However, a large dependence of C chemical shifts in DMA is observed, so the structures of DMA-F and (DMA)2 must be quite different. A hydrogen—bonded DMA-F linear complex (Structure (XVI-3)) would satisfy this criterion. 290 13C chemical shift for carbon The variation of the in the carbonyl-methyl group is only slight, which in- dicates that the carbonyl methyl group of DMA must be E£a§§_to the C = 0 group of formamide, as shown in Structure (XVI-B), instead of gig to the C = 0 group of formamide as suggested by Neuman.159 The variation of the 13 C chemical shift of the carbon of the Eranng—methyl group is smaller than that observed for the ging-methyl group in DMA, which indicates that Structure (XVI-B), suggested here for DMA-F, is correct, since in this structure the trans NCH3 group in DMA is far away from the C = 0 group of formamide. Comparing the system DMA-formamide with the system DMA-H2804,168 we find that the change of 13 C chemical shifts in both systems is similar. This provides further support for the hypothesis that hydrogen bonding between DMA and formamide is important. 1 13C relaxation times for the carbons of DMA The in various concentration solutions in formamide were also determined and are shown in Table 32. The results show that as the concentration of formamide increases, the re- laxation times of the carbons in DMA decrease. This in- dicates that hydrogen bonds are formed between DMA and formamide. Since the molecular weight of formamide is smaller than that of DMA, if only the DMA~F complex is formed in the DMA-formamide system, as suggested by Neuman,159 then 291 .oomém we come 0.33 musoEousmmoe one .moflumu mace mm commoumxo mum mcowumuusoosou ¥ e~.oHem.m mH.oHHH.m Amtesmsuomv non m. modwmmée afimwmmam o .... m mm.ofime.m om.oHeo.OH mm.oHeH.oa u mm.onm.oH mmmrasconumo ee.oueo.HH oe.oumm.mfl I me.one.~H e~.oumm.ma Ammmv mmmrz om.oHHa.oa ee.oues.ma . mm.oun~.mH oe.on~.ma Ammmmmv mmmrz wom mom wow wow wooa uemsuhomnsm Adzav soflumsucmocoo .mousuxflfi opflfimahowImpweouoomHmnuoEflclz.z cw fizn mo msonumo mnu mo mosflu soflummeoH UmH on» no mocwpsmmmw cowumuucmosou .Nm magma 292 the 13C relaxation times of the carbons of DMA in this system should be almost equal to, or even longer than, those in neat DMA, which contains a high concentration of dimer, (DMA)2, in the pure liquid state. This result then indicates that other species, such as DMA-En, may exist in the DMA-formamide system. One possibility is the forma- tion of DMA complexes containing more than one formamide molecule DMA+F Z DMA-F, n n where n is greater than or equal to 2, and Fn can be cyclic dimers , chain dimers, or even trimers of formamide. The structure of such a complex might be written as in (XVI-C) additional molecules of formamide interacting with the first one by hydrogen bonding to the C = 0 group or by dipole- dipole interactions. Alternatively, additional molecules of formamide might interact with the DMA molecule of the DMA°F complex through dipole-dipole interactions as in Structure (XVI-B). (XVI-C) 293 Because of the uncertainty concerning the actual species present in this system we have not attempted quantitative determination of constants. C. The N,N-dimethylformamide-benzene system The structure and chemistry of n molecular complexes have been extensively investigated in the last three decades. Information about the equilibrium between n complexes and their components, and about the structures of w complexes, has come from many different experimental methodsl7o_l72 including visible, uv, and IR spectroscopic techniques. Proton NMR studies of these complexes have also 9S,161,164,l73,174 been carried out and, by using proton NMR, some formation constants of the n complexes have been de- termined. The determination of the formation constant of the complex between DMF and benzene have been in- vestigated by Hanna et al. and by Sandovall74’161. Hanna et al. were unable to determine the formation constants of the DMF-benzene and DMF-toluene complexes; however, Sandoval obtained these by the same method and the same equation.161 Since Hanna's equation can only be applied under restricted conditions, i.e., the concentration of donor should be much 13C NMR and develop a general equation to fit the experimental l3C greater than that of the acceptor, we tried to use chemical shifts. The results for the DMF-benzene system are shown 13 in Table 33 and the C chemical shifts are plotted 294 Table 33. 13C Chemical shifts of the carbons of N,N- dimethylformamide in various DMF-benzene mixtures. V/V Ratio . Chemical Shift* (ppm) gaggicgif- ginggieto N,N-Dimethylformamide- Benzene ference Aw (%) g = O N-g:_H3 (t) N-QH3 (c) CH3 100 161.92 35.13 30.03 - 5.10 95 161.89 35.11 30.04 128.06 5.08 90 161.86 35.10 30.04 128.02 5.07 85 161.83 35.09 30.03 128.02 5.06 80 161.80 35.08 30.03 128.03 5.05 75 161.77 35.07 30.04 128.02 5.03 70 161.71 35.04 30.02 128.00 5.02 65 161.66 35.02 30.02 127.97 5.00 55 161.59 34.95 29.99 127.94 4.96 50 161.52 34.92 29.99 127.92 4.93 45 161.49 34.88 29.97 127.91 4.91 40 161.50 34.90 30.01 127.92 4.89 35 161.41 34.82 30.01 127.90 4.81 30 161.42 34.84 29.98 127.91 4.86 25 161.26 34.70 29.93 127.83 4.77 20 161.17 34.61 29.89 127.78 4.72 15 161.11 34.54 29.84 127.76 4.70 10 161.02 34.44 29.83 127.72 4.61 * The chemical shifts are relative to TMS, the mixtures were degassed and the measurements were made at 35°C. ** AwCH denotes the chemical shift difference between the 3 trans-and cis-N-CH carbons in DMF. 3 295 graphically as functions of concentration in Figures 68-70. We find that the variation with concentration of the 13C chemical shift for the C = 0 group of DMF is again sharpest. The shapes of the curves are similar for each carbon and the chemical shifts are moved downfield as the concentra- tion of DMF is increased, which is similar to the case of DMA in cyclohexane solutions. However, the change of the 13C chemical shift of benzene is also relatively large. This indicates that the interaction between DMF and benzene is strong, which is opposite to the result obtained in the case of the DMA-cyclohexane system. As the concentra- tion of DMF decreases, both the Egg-and gig-NCH3 carbon reasonances are shifted upfield but the Erang signal shifts by a much larger amount. These observations can be explained by assuming that the amide molecule associates with benzene in such a way that the nitrogen atom, with its fractional positive charge, is situated close to the region of high n electron density of the benzene ring and the negatively—charged oxygen atom of the carbonyl group stays as far from the center of the ring as possible. The DMF molecule pre- sumably retains its planar configuration so that the planes of the solute and solvent molecules become parallel as in Structure (XVII). In this arrangement the trans-NCH3 group will be near the center of the ring and, consequently, the 0(DMF)(ppm) 60: 6benzene (ppm) 162.0 296 161.9 161.8 161.7 161.6 161.5 161.4 161.3 161.2 161.1 161.0 128.1. 128.0 127.9 127.8 p P 127.70 I l l l 10 20 3o FWD 0 o % of DMF (v/v) Figure 68. Concentration dependence of the 130 chemical shifts of the carbon of the DMF 920 group and the carbonsof benzene in DMF-benzene mixtures. 297 35.20 35.10 35.00 U 9 8 I C) (D ..." 29.90- 29.80. 1 1 1 l I I I 1 0 10 20 30 40 50 60 70 80 90 100 % of DMF (v/v) Figure 69. Concentration dependence of the 13C chemical shifts of the carbons of the IEEBE' and gig: NQH3 groups of DMF in DMF-benzene mixtures. 298 5.50 5.40.— 5.30- 5.20p A“’cnj‘ (ppm) Ic-fkcu, HA? (A) ref—1x I H , : \c—u ”I ' 1‘.) {‘6 A w v b.......... J I 1 l b L L l Figure 70. 0‘s)— 0 '10 20 30 no 50 7’6 of DMF (v/v) Concentration dependence of the 130 chemical shift difference between the carbons of the 3:533- and gig-NCH3 groups of DMF in DMF-benzene mixtures. The structures shown indicate the complexes which are postulated as the dominant species in the four concentration regions (4)-(D). 70 80 90 100 299 CH °\.._.../ ’ / H (XVII) diamagnetic anisotropy of benzene will affect the trans- NCH3 group more than the cis-NCH group, tending to shift 3 both the proton and 13C resonance to higher magnetic field. The formation of the n complex between DMF and benzene may be expressed by the equation DMF+@2(DMF-@ ). By using proton NMR, Hanna et al.174 had developed an expression for calculating the formation constant of the N complex. Due to the limitations of that expression, i.e., that the concentration of benzene should be much greater than that of DMF, we have developed a general expression as outlined below. Let us assume that A moles of DMF, B moles of benzene and C moles of 1:1 n complex are produced by mixing a total of 1 mole of DMF plus benzene, i.e., X moles of DMF and l-X moles of benzene. Then the mole fraction of each species corresponds to A, B, and C divided by A + B + C, and hence the equilibrium constant K is given by _ C(A + B + C) K — AB . (158) 300 Since the total number of DMF and benzene molecules, in- cluding both free and complexed molecules, is constant before and after mixing, the following two equations hold: X = A + C 5 (159) l - X = B + C . (160) The 13C chemical shifts can be expressed as the weighted sum of the shifts in the free 6 and complexed 6c states f XIO 5 = (g 5f + g 5 ) = 5 + cal c f (6c - 6f)' 13 where 6C is the calculated C chemical shift. From a1 Equations 158 to 160, the following equation may be derived: 2 _ 2* 5 = 5 + (5 _ 5 (K+1) + /(K+1) - 4K(K+1)(X-X ) f c f) 2X(K + 1) ' (161) 13C chemical shifts to The best fit of the experimental Equation (161), which is based on the 1:1 n-complex model, was obtained by use of the KINFIT program. One set of values calculated for the chemical shift difference 6 between the two NCH l3 NCH3 3 for DMF in benzene solution are shown in Figure 71 along C signals with the experimental values of Am The calculated NCH3 curve is based on the assumption that a 1:1 n complex is formed. The calculated chemical shifts of DMF in the free and complexed state, 6c and 6f, are also shown in 301 .h space an x mpaoc came 0:» ca one wagon copwasoamo use ampsosauonxo so was» movmowosn u can .pswon oovwasoamo w o .psfiom Hapsoafluomxo so monsodosfimxl.mousvst osousoonmzn a“ man mo Hmsmam oma nmmz: 03» on» soozpon A moze. (163) 3 2 e 2 2 ‘5 1."uL’STe where S is the electron spin of the paramagnetic ion, YI is gyromagnetic ratio of the observed nucleus, g and B are the g value for the paramagnetic ion and the Bohr 310 magneton, respectively, r is the distance between the para- magnetic center and the observed nucleus, A is the hyper- fine coupling constant between the paramagnetic electrons and the observed nucleus and Tc and Te are the correlation times for the dipolar interaction and the hyperfine inter- action, respectively. The latter are given by the equa— tions195 1/1 c l/Ts + l/TM + l/Tr (164) l/T e l/TS + l/T M I (165) where Tr is the correlation time for the molecular rota- tional reorientation, TS is the electron spin-lattice re- laxation time, and T is the mean residence time of the M 196 nucleus in the first solvation sphere, which char- acterizes the rate of ligand exchange. At room temperature, for Mn2+ in various complexes which have been studied,the experimentally found values for the electron relaxation times T8 are in the range 10-8 188-191 to 10"9 sec, while the correlation time for the molecular rotational reorientation Tr is approximately -10 11 10 to 10- sec for complexes with molecules of the size of N,N-dimethylformamide, therefore l/TS << l/Tr. Further- more, for Mn2+ complexes it is observed that187'197'198 l/TM < l/Ts at room temperature or slightly above this temperature. Subject to these inequalities, the correla- tion time for the electron-13C dipolar interaction TC 311 will be equal to Tr. When one can use this effective correlation time, combined with the ratio wS/wI 2 2600 be- tween the Larmor frequencies m 13 and w of the electron and S I C nucleus, respectively, as well as the inequalities (all of which apply at the magnetic field strength used in this work, 13 2 2 2T2 ~ 1 and wzrz >> 1 18.7 kG for C) wITr << 1. ms r S e 1 the Solomon-Bloembergen equations reduced to 2 S(S+1)yig282 7Tr l/T1M — I5 6 3Tr + 2 2) (166) r l + w T S r S(S+1)Y29282 13T 1/T = l— I (7T + r ) 2M 15 r6 r 1 + wZTZ S r 1 S(S + 1)::2 + — T . (167) 3 ‘62 e We see that the scalar relaxation term contributes only to 1/T2M. This implies that the order of magnitude for the scalar coupling constant A for Mn++ in these complexes is not significantly larger than 106MHz, the same order of magnitude as found for similar couplings to protons.l75’190 The recently reported Mn2+ - 13C coupling constants are in agreement with this assumption.182-184 It has been shown that electron relaxation in dilute aqueous solutions of the paramagnetic ions is controlled by the modulation of the quadratic zero field splitting (ZFS) interaction. + . Therefore, for an aqueous an complex, the correlation time for electron relaxation is given.to a good approximation, 312 by the equation 2 Tv 4Tv A (4S(S + l) - 3) x ( + ), (168) 1+22 1+427 1_ l/T = 5 S N where A is the zero-field splitting parameter and TV is a time constant for the modulation of the ZFS interaction. For the Mn2+-hexaaquo complex, where the Mn2+ ions are in an isotropic environment, it has been found199 that the ZFS interaction, as well as its time modulation, results from collisions between the Mn2+ and the bulk solvent molecules. If the paramagnetic ions are in an asymmetric environment there will, in addition, be a static ZFS interaction. The and T temperature dependence of T can be approximated by v r the Arrhenius expression _ o . _ Ti — Ti exp (Bi/RT), 1 f r or v (169) while TM is usually given by the more elaborate Eyring equation kT AH* AS* l/TM = H'— exp(- -—R-,i; + R ). (170) B. Effects of Chemical Exchapge To observe the signal from the nuclei in the ligand, it is necessary to observe the resonance using a solution with a very low concentration of the paramagnetic ion relative to the ligand to avoid line broadening. In addi- tion, a temperature must be selected to give a ligand ex- change rate between the coordination sphere and the bulk 313 solution which is sufficiently fast on the NMR time scale to average the spectral features of the complex with those of the unbound ligand. Under these conditions, the follow- ing expressionsZOI’202 are apprOpriate for relating TlM' TZM' TM, wM, and pq to the experimental observables: _ 0 = = u 199 1/1‘1'obs 1/Tl 1/T1P 1/T1A + TlM + TM (171) -— O = = ' 1/T2,obs l/T2 l/T2P l/T2A + * 2 (1/T2M + l/TM) 1/T2M + AwM ES I 2 1 . (172) TM (l/T2M + l/TM) + Am 2 M where T T and T2M have the same definitions as given m' lM' previously, AwM is the contact shift, p is the ratio of metal ions to ligand molecules and q is the number of co- ordinated ligands per metal ion. l/Ti and l/Tg are the relaxation rates of the nuclei in the free ligand while the adjusted rates 1/T1P and l/T2P measure the para- magnetic contribution to the observed averaged relaxation rates l/T l I and l/T l/T1A and 1/T2A are the l,obs. 2,obs.' contributions to the relaxation of the nuclei outside the first coordination sphere due to dipolar interaction with 201 the paramagnetic ions. For protons this contribution has been found to be less than 10% to l/T1 obs' while it I is a Significantly smaller fraction of 1/T2,obs when l/T2M 13 is dominated by scalar relaxation. For C relaxation, 314 these contributions are expected tolme even smaller fractionsofl/Tl’obs and 1/T2,obs , and thus may be neglected. Assuming a Curie law of temperature dependence, and an isotropic 9 value for the system, the isotropic con- tact shift AwM between the nuclei of the first coordina- tion sphere and those of the bulk solution is given by193'207 A93“. _ Ad = S(S __1+ 119181 A (173) wI — H 3kTYifi ’ where the symbols have their usual meanings. In case of chemical exchange, the experimental frequency shift Am 202 P is given by the equation AwM 7' 2 (l/T2M + l/TM) + AwM Amp = 23 [ T 2 ] , (174) M where the symbols are the same as defined above. The ex- perimental values of T were determined assuming 2,obs Lorentzian line shapes and using the relationship Avl/Z = 1/(NT2) . (175) C. 13C Relaxation data and isotropic contact shifts in 2+ MN ‘DMF mixtures Each 13C Tl value was extracted from 7-10 partially relaxed Fourier transform spectra by fitting the data to the equation ) = -t/Tl (176) 315 using the KINFIT program.72 In this way values of l/Ti and l/T were obtained for all three carbons of DMF l,obs from temperatures of about -60°C to +75°C and the results are given in Tables 7 and 35. Due to extensive broadening of the 13 2+ C signal from the C = 0 group, the Mn used was 2.77 x 10-4M. To check the reliability of the concentration typically final values of 1/T the 1/T1P values for the trans- and lP' cis-NCH3 carbons were measured at two concentrations at 2 34.5°C and the values obtained at 2.77 x 10- M Mn++ were divided by 100 for comparison with the values obtained 4 in 2.77 x 10- M Mn++ solutions (Table 36). The agreement was within experimental error, as shown in Table 36, but the values used in later calculations were those obtained 4 from the 2.77 x 10- MMn++ solutions. The temperature variation of the 1/T1P values for the carbons of the trans- NCH3, gingCH3 and Q_= 0 groups were also determined and are shown in Figures 72-74. Likewise.the temperature de- pendence of l/T2P and of AvP for all three carbons was measured over the same temperature range and these results are given in Table 37 and Figures 75 and 76. Only the value of l/T for the 9.: 0 group is measured, since the 2P uncertainties in the linewidth measurements of the carbons of the trans- and cis-NCH3 groups lead to a wide variation in the values of l/T2P for those carbons. 316 Table 35. Temperature dependence of the 13C spin-lattice relaxation times of the three carbons of DMF in a 2.77 x 10’4M solution of MnCl in N,N-dimethyl- formamide.a 2 T(°C) trans-N-methyl cis-N-methyl T(°C) §_= o T (sec) T (sec) T (sec) 1 1 1 -59.0 1.63:0.093 2.358:0.115 -55.65 0.360:0.006 -4l.95 2.855:0.l49 3.642:0.086 -31.0 0.933:0.043 -29.2 3.317:0.059 4.523i0.065 -23.35 1.275:0.065 -17.9 4.013:0.081 6.242:O.178 - 9.6 2.220:0.085 11.95 7.129io.32o -1o.222:o.224 5.05 2.501:0.146 35.0 9.432:o.131 13.033:o.202 20.1 3.346:0.118 54.2 11.964:0.281 15.263io.358 35.0 6.005:0.278 70.5 16.793:0.664 17.297:0.693 50.5 7.850:0.386 68.45 6.824:0.547 188.3 12.222:l.l6 112.9 10.893:0.554 aN,N-dimethylformamide was purified and the sample degassed and sealed in the sample tube. 317 .ooH so nooausaon ++sz 2 nos x ss.m one sou oae\a do nosao> use osaoa>ao so a euoa x ss.~ u _+~sz_ op oouaassuos outdo o x o " zuuoa as m H+Ns21o .Zauoa x ss.~ u H+mszls moo.ouoe~o.o omH.onme.m Hoo.oH~mo.o omH.onom.~ o loommoz Hoo.oHamo.o Hoo.oHsm~o.o Hoo.oummmo.o Hoo.oHoso.o o lovmmoz Hoo.oH-o.o OHH.oHomm.m moo.ouoso.o oaa.oHoom.N o Auvmmoz moo.ouomo.o Noo.ouomo.e moo.ouoso.o Hoo.oHooa.o o AuVMmUz moo.onHH.o moo.onHH.o Hoo.oneo.o moo.oHsoH.o o o n o Hlme Hlowm Hlowm Hlowm U AUONHHMEHOGV #Gmflfiflfimflfim m o. mas\a mae\a MB\H o Hs\a .Oom.vm um ++sz mo mcoHDDHOm opfifiofiu0uamnumefionz.z as use mo mcooumo may now moves coflummeoH ooauumchflmm OmH Housofiflnomxm .mm canoe .szn as macs: s e-oa x ss.~ on: soapsfloo one .ocasmsuomaagvoswvuz.z ca macaw nm021mmmMH.osv no sconce on» new anode opus soaaaxmaou Hopsosauooxe one no :oavmuna> caspauonsop on» no van nopsnsoo .Nm ouswum o mmuaoo nuaz— am uzwwupwm nbw0‘2—xatommzowmuuu / A x v OH N H.\H 3.2. mama...— .. utozunwu .ouaupzaouzu wfuuucuoz HI 0 m ardoh. HIUZ hezx eeeeeeeeeeeeeeeeeo .eeeeo OZU xm-u.-m-q--m--.-m----m----m----m----m----m----m----m---um----m----m-auom--s-m--1-mu---m11--m----m---u: o m . x I o . 1: x _. o 1 c e x . o . e. a x .1 . o u _.. o . x x O 1 _1. u _v a . u 11 11 8 . own 1 1 o . AHI V 3 r u w “H 1 o 1 .H\.H 1". 1 1 1 .. O . 4 w W . I n nm-uu-m----m---um---um-a1am----m----m----m----m--a-mas-1m1-11m11uum1111m--anm--cumuntump m m I W J n v. .- 25:3. 2 Eonsmxomoa m..w1w1..fl....m..§ ”1.1.3.31...“ “may: £53“ finwymwum a mum“ . .. . .. .. . 1: . a . . o I > . u a x m 4 ~ > gnaw. . 53%...“an . tweets smashes: . ......e. 2...“. .N..._.._.«..s.a......assesses. 13169 .sso ca «Hose 2 -oa x ss.~ use soapsaon one .ocfismshohahcposwcuz.z :« Asowm mfioZuMflw on» no sconce on» son AH9\H opus soapmxmaou Hopsoswuonxo one Ho sofipmwum> osspmsonsow on» no paw sevensoo .mu osswfim A -sOV moH x 9\4 AWm-ella.-m-'-lr--I-m-"-m'-l-m'-nuCm---‘m-l--m----m----m----mIII'mIIIImIMMw“muwwm-muwm-"u”muuuumuuuumnuum W..... 02“ fi u o1 u o . G 1 . . 1 I . I s a . 1 x r w v . “w I . 2 u o . i a . 00m 1. 1 1:- 5 “3.. 11 a} r I . I M . _ .fi- v m ' _quIImOOIOmIIoomlotanIoImlnllmOIonmIIOImltoImIllaMlllomlloIMIIOImIloImIOIImOIIlmJOIImOIIIMIIIIMIIIl_ 4 4 Mast.as. a. ..aoa.zmn.omomu W..” wszmu.mz a» a .mauoluwau mm“ uswouwzmnu u«»uwu~uwnu a“ muuwu n manuomn. n azux-cuz_..oauou.. a xobpoc u:» be u:o<>.oo. .o_. a no r» be u: > . a we .~.x o a > eoqtmeu. - hzuzmom2_.~o1uomo. u bro—c uze so u:o<>.~ouue_m. n sumo wrw »« undead.._muw>x.mocm_.~...mumucmvmuwc 320 .ocasmsnomahsposficnz.z aw macaw ahsonumo one we sconce on» new .szo ea «Hose 2 a-oH s ss.~ use soapsaoa HTI one mas opus sowpmxmaop awesoswsonxo on» we sowpmwpm> assessonsop on» «o pan nopsnaoo .35 ouswam v w‘- ,7 ww-uv v—v - . _ -m at. . pzmx-o z_._ou-oso. p oeqwnmm. . _zmxusmzw.~o-uomo. a exo_a m2» >4 u: _m11--m----m-..-m1111m----m----m----m---.m---umn-n-m-u--m---am-a--mau--m1111mnotcm----m1111muouamunno 6 x n-441m----m---am----m----m----mu---m----m----m----m----m----m----m----m1111m1111munsnm1111m---amuoan . AH-sov nos s 9\4 OIU A02! II.Ieeeeeeeeeeeeee;eoeeI ozu I I I; I OK 0! KO 1 an..aa. a. ._aoa.zmnnomoma W..»1wazwaawz u" uwswxuolawau mmfimuswanwsmuu I tarpon m1» (#2 I :ssesmss.namasarsessssasexsa. uoomv AH AH a\4 (>2 I Gwalw 1‘ m2« 8 I a an 3‘ m2. 8 K awawwanwo 321 Table 37. Temperature dependence of Au and l/T for the three carbons of DMF in a soiution ofzfdnC12 in N,N-dimethylformamide which is 2.77 x 10-4M in Mn2+. T AVP (Hz) T 1/T2P (°C) Ngh3(t)a Ngh3(c)a g,= 0 (°C) _;0 (sec—1) -56.0 0.1 0.1 0.1 -54.5 7.838 -46.1 0.1 0.2 0.3 -39.6 22.422 -35.3 0.2 0.3 1.9 -20.8 30.63 -17.0 0.1 0.0 1.8 2.7 19.635 2.2 0.3 0.1 1.0 18.0 16.808 12.5 -0.1 0.0 1.5 34.2 6.519 23.4 -0.2 -0.1 0.8 51.2 5.765 36.3 0.3 0.0 0.8 58.0 4.000 44.6 -0.1 -0.2 - ' 65.5 2.199 57.1 0.1 0.2 1.0 72.3 0.0 0.0 0.9 89.5 0.1 0.2 0.7 at and 0 Indicate groups that are trans or cis relative to the C = 0 group. 322 OH x mm.m mm: Coapzaom .sso ca maoss 2 a- Awe open one .06asmshomaznposaouz.z CH Genome Hhsooumo on» pom H1 cofivmxmaop HvaoEAMooxo on» mo soapmwpm> ouspmthEop 0:» mo paw 90959500 .mn chewam A s .v mos s e\4 . n NPQ GNU was—.14....sCl. .>Lhu.1N..l..4a... .~ mo. 3 coxcteeeeoeoeoeootw: .ooo: .....u. .maaunmstatuaoooununouuuncrnutam111umuntnunsa1uunouuncncrauunm---:-oou-wcr---uuunu 1-1u11110111141111. .u so 1 m t m J n 0 mt . _ m h . 2 oh u a - o 1 s _ _ s. u u .5 _ a _ a a * t . r w . n . n U U 1 o W a A — "Afllom v w m r s _ mm u a w B\.H F o w . ~ 1 1 c _ s w a v 1 1 s a w x w 1 s a M a .. . ~V---‘W'---“ ..... U ----“4'60“----f688'AU6860c----:u----“0-6-! ..... I ..... U--"J||"U'-"J0I--..II---“-"-UI---m » «page s: a crown maam 11» s_ was rr_rt .-ruo. 1. a 11~3.1_1uc.u .e aroma prhPCJa v— C—fuJ ....wll Cum: ..~ u >4; 1... b. T. 1 ....»c. :.CIQL u I.....ml . 0...,pr1 .u»_.n!>JhC-1—dd fir m1 .3) III c:.u¢oc. u prmznou.. ~..o. oxn. u :c»»:: m1» pa 123-».x1.n.... n p -. pa ... . .. 1 .1.u.. a» ou.up:. {Olhdfne N P2u31.d.. meA.ulu]uJo u PIC». air ou szu.ow I to h “a“ h . . . no o. . a ... «no.~n t— c..1 \ 323 . CE «5.2 +N 5.. S 5. RH .8338 a 5 535581555752 Mo 93980 05. mo . m><.3m.3m wompcoo amazon—H.393 05. mo “3.3.0.39, chafing—oases .2. enema ‘I nos s Amway a} es 9: m5 is 9n a...” 2n Tn in Ta ed Cm ] u d a a 1]]Ilul u a . s m m 111 Q can: xoz _U . 10111111.. 1 0.0 . 111w}, D ) D 110310111... It: Lfiw )QII III 6 1|.llIIIIillfiflll C 3.2: oz 0 U U . O m e e as. 2 O . . . ... one 0 324 D. The Dominant Mechanisms of Relaxation To establish the relative importance of the dif- ferent mechanisms discussed in Section A (above) which can influence the relaxation of the 13C nuclei in the primary solvation sphere, a best fit of the l/T l/T2P and AvP 1P’ data to Equations (164)-(174) was made by use of the KINFIT program. The results are shown in Figures 72-75. The dipolar mechanism (Equation (166)) is dominant for l/T1M but both dipolar and scalar mechanism contribute to l/T (Equation (167)). The procedure used here depends 2M on the reasonable assumption that in the exchange process the N,N-dimethylformamide molecules exchange as a whole in and out of the first coordination sphere of the M’n2+ ions and the assumption is strongly supported by the good agree- ment between calculated and observed curves in Figure 76. II. RESULTS AND DISCUSSION 0 A. Determination of the Coordination Number, Er' Tr and the Structure of the Solvation Complex The coordination number was determined by varying the value of g from 4 to 12, and it was found that when g was equal to eight, the best fit of the calculated curves to the experimental data for all three carbons could be obtained and that the number of iterations for the calcula- tion to converge was less than fifteen. However, with other choices of coordination number, the fit of the experimental data for all three carbons only converged after 60 iterations, 325 and the deviation of the experimental data from the best fit curve was usually much greater than that obtained using coordination number eight. Thus, an assumed coordination number eight was accepted for later calculations. From the parameters obtained by the fitting of the T-; data to the calculated curves for all three carbons, values of Er and T3 were calculated and the effective dis- tances between Mn2+ and all three carbons obtained. These are shown in Table 38. The calculated Er values for the carbons of the trans: and gingCH3 groups are lower than that for the C = 0 group as a result of the internal rota- tion of the N-methyl groups. The Er value for the g_= 0 group (4.0 kcal/mole) is about the same as that for free DMF determined before (4.1 kcal/mole), since the overall molecular tumbling axis of DMF in Mn2+ apparently along the Mn2+...0 = C direction which includes solution is still the carbon of the trans-N-CH3 group. However, the Tr value at 308°K for the DMF-Mn++ system is one order of magnitude larger than T (= Tc) for free DMF, since the r solvation effect, which reduces the frequency factor, makes it more difficult for a DMF molecule to rotate in the Mn2+- DMF system. The calculated r values for all three carbons are also shown in Table 38. They indicate that the distance be- tween Mn+2 and the trans-NCH3 carbon is shorter than that between Mn2+ and the carbon of the 9.: 0 group. To explain this result, the structure shown in Figure 77 for the 2+ solvation complex of Mn in DMF is suggested. 326 .UIHH GOfluUmm ~#qu 0wmfl IIIII. III- .AmIHH cofluomm .pme on» Oman mwmv msoum o n u may on m>flumamu mcmuu paw mac masonm mumowpsH u new 0 m Halos x ms.m omm .Amomomvu p snoa x an.H am e > o s e m ..l H mH.m maos\amox m mauoa x ea c omm In mozv op as a omw .>p OH x «m.o omm .Ao.mmmze up an 0 ma- 0 com a w .< as x om.o omm .10 ".mV up n . ma- 0 mnoa x o~.m omm .Asommmvzp qo.oH«¢.m 4 .Au.mmmzv u oo.~Hsm.o~ om .«ma om.qu~.w < .Ao.mmwzv H oo.ofiso.ma Hosxamox ..ma om.ou~m.m « .Ao u me H II .I .H .l ~H.¢+Ha.m Hos\Hmox .Au.mmoze m «ca x o.¢ a um m.fixuc moz_ An\¢v NH.oHOm.N Hoaxamox .Ao.mmmzvum «as x o.m n we m.flxovmmwz_ xs\av mo.ouoo.e Hosxflmox .Ao u.wv um med x Ho.m mm ..o u we Ag\ kumgmhnmm GSHMN/ . HmHmEMHmm .mzo ca ++cz new mump uwfism uomucoo pow coflummewH Hmucmfifinmmxm may Scum pmumanoamo mumumfimnmm .mm manna 327 .souoonuupmv 05 no .3500 Moss... one 5.. «:25 .353 5.50.“ a you moss: . .ocfisaspomahspoeHvuz.z ca +~cs no sodasoo scavm>dom on» mo unsposuvm . R «BEE 328 A tetrahedral structure for the ion-solvent com- plex is suggested, with two N,N-dimethylformamides (as a dimer, (DMF)2) at each corner. From the distances found between Mn2+ and the EEEBETNC 3 carbon and between Mn++ and the C = 0 carbon, the distance between the two DMF planes in the dimer (DMF)2 may be estimated to be about 3.0 A, which is approximately equal to the sum of the van der Waals radii of oxygen (1.40A) and nitrogen (1.50A). The distance between the Mn2+ ion and the gingCH3 carbon, 6.2 A, is also within experimental error of the value ex- pected on the basis of the structure suggested Figure 77. The distance between Mn2+ and the oxygen of the C = 0 group is estimated to be about 2.60 A, which is a little bit larger than the sum of the van der waals radii of oxygen (1.40A) and Mn2+ (0.80A), indicating that the Mn-O "bond" is very weak. Also, this solvation complex is only stable at low temperatures (below -35°C) as seen from Figure 76. This is quite different from the case of Mn2+-histidine where the ion-solvent complex is stable even at +15°C9. The reason that the distance between an+ and carbonyl oxygen is so large in DMF may be that the (DMF)2 dimers are rather bulky. Also, the interaction of the paramagnetic ion and the oxygen of the C = 0 grouplsl'183 may be weak as was found for Mn++ in pyruvate carboxylase and in histidine. 329 B. Determination of the Coupling Constants between Mn2+ and Carbon At high temperatures (T )-2 >> (T )-2 and (Aw )—2 ' M 2M M so Equation (174) can be reduced to Amp = quwM (177) which, according to Equation (173), should follow the Curie law of temperature dependence. Figure 76 shows that the 13 C Av curves for all three carbons in DMF are given by P Equation (177) over all of the experimental temperature range except at low temperatures. Using Equation (177), the coupling constants (hyperfine interaction constants) for all three carbons have been determined from the AvP data in the high temperature range, as shown in Table 38. All three electron-13C hyperfine coupling constants, which correspond to isotropic contact shifts,tend toward lower field as the temperature increase and thus are positive. However, the temperature variations of the ex- perimental Av for trans- and cis-NCH carbons are of the P 3 same magnitude as the uncertainty in the measurements (:0.2Hz) so only the estimated values of A/h are presented. In the low temperature range of Figure 76 T ~ TZM’ which in- M validates the approximations leading to Equation (177) and the curvatures should therefore be described by Equation (174). 330 Grant et al.183 have found that the coupling con- stants for carbons forming n bonds are somewhat higher than those of the corresponding carbons forming only 0 bonds, indicating a relatively smaller delocalization of the para- magnetic electrons. The measured electron-lBC coupling constant for C = 0 carbon is about the same order of 181-183 magnitude as that in other complexes but the A/h values for trans- and cis-NCH3 carbons are about one order of magnitude smaller than those found for the singly 2 182 +-ATP complex. This may be 2+ bonded carbons of the Mn due to very weak "bonding" between Mn and oxygen in 2 the Mn +-DMF solvation complexes. C. Determination of AH*, AS*, Ev' EQQ_TM To obtain these values, a least-squares fit of the experimental l/T2P data to Equations (165), (167), (168), (169), (170), and (172) was made. In order to obtain the best fit of the 1/T2P data, a value of Ev = 3.16 kcal/mole is used, which is in the range 2.5-4.3 kcal/mole found for EV in the case of the Mn2+(H20)6 complex. The calculated values of AH*, AS*, Ev' and TM are shown in Table 38. The value AH* = 12.67 kcal/mole ob- tained in this way is comparable in magnitude to the AH* 2+-PHP203 2 values of about 14 kcal/mole found for the Mn complex and about 11 kcal/mole found for the Mn +-histidine 183 complex. However, the value obtained for TM(298°K), 331 8.2 x 10.9 sec, is about two orders of magnitude smaller 2+ with AMP, ATP, than that obtained in the complexes of Mn and histidine. This is due to the instability Of the solvent complex of Mn2+ in pure DMF and to the very weak "bonding" between Mn2+ and oxygen, as reflected in the long distance between Mn2+ and Q|= C obtained in this work. The large value of AS*, about 20.97 eu, is attributed to the solvation effect. Using the parameters from the best fit of the l/T 7 2P curve, the calculated values of T3 and A are about 10- sec and 800 G, respectively, which are higher than those 2 2 obtained for the Mn +-ATP, Mn +-AMP and Mn2+-histidine complexes. However, the values T3 and T (298°K) obtained M in this system are comparable to those obtained for the Mn2+-RNA system,191 2.3 x 10.7 sec and 2.1 x 10'9 sec, respectively. Using the values of TV calculated from Equation (169) and the TV, Ev values in Table 38 in Equation (168), it is seen that l/TS E 0. Then l/Te z l/TM for Equation (165). This indicates that the ZFS factor does not make an important contribution to the scalar relaxation term. 111. CONCLUSION This study shows the feasibility of using T1 re- 13C nuclei in the Mn2+-DMF system to laxation times of achieve information about the solvation structure. To a relatively high degree of accuracy, the paramagnetic 332 relaxation rate depends only on r"6 and not on the angle between the interatomic vector and a coordinate system fixed in the molecule. This makes the method simpler to employ and, therefore, more-versatile than structural determination from the pseudo-contact shifts caused by lanthanide shift reagents. This study has also shown that the contribution from the unpaired electrons of the Mn2+ ions to the T2 re- laxation time of the carbon of the C = 0 group is primarily due to a large scalar coupling term which, however, cannot be related to the structure in any simple way. in} 333 SUMMARY A variety of nuclear magnetic resonance (NMR) techniques has been used to investigate various physical properties of a series of amides, N-substituted amides, and both symmetrically and unsymmetrically N,N-disub- stituted amides. Measurements have been made of 13 C spin— lattice relaxation times, nuclear Overhauser enhancement (NOE) factors and chemical shifts for all the carbons in these compounds. In several cases 14N, 15N and 170 chemical shifts and relaxation times have also been measured and several linear correlations among the various chemical shifts have been obtained. The results have been used to investigate various details of the electronic and geometrical structures of these amides, to obtain informa- tion concerning their conformations, to study their molecular motions in the liquid phase and to elucidate the nature of the complexes formed with solvent molecules or added paramagnetic ions. PART II THEORETICAL STUDIES OF AMIDES INTRODUCTION The electronic and molecular structures of amides, and particularly the barrier to internal rotation about the central C-N bond, has been the subject of numerous experimental and theoretical investigations during the past twenty years. Experimental determination of these barriers has been carried out by nuclear magnetic resonance methods, since they are at present the only techniques available 129-138 for this purpose. Theoretical estimates of the energy barriers have been made using various quantum mechanical methods.209-211 In this part of the thesis I report calculations of the energies of some selected amides in various con- formations. The charge distributions, charge variations in going from ground state equilibrium geometry to the excited state geometry, energies for internal rotation and electron configurations will be presented. The molecules which have been studied are formamide, N,N-dimethylformamide, N,N-dimethylacetamide, N,N-dimethyltrifluoroacetamide, N-methylformamide, N-ethylformamide, N-methylacetamide, N-ethylacetamide, N-methyl-N-ethylformamide, and N-methyl- N-ethylacetamide. Calculations have been reported in the literature using extended Hfickel theory (EHT) and the 334 335 complete neglect of differential overlap approximation (CNDO/Z). In this work, the intermediate neglect of dif- ferential overlap approximation (INDO) has been employed and properties calculated by these different methods com- pared. THEORETICAL I. GENERAL SURVEY The properties of amides were first discussed in terms of resonance among valence bond structures by Pauling, who suggested that in the ground state I and II would be the principal contributing resonance structures and that the resonance energy would be about 21 kcal/mole. ;"\C _fi /R1 {9"\ C *fi/nl R/ \R R/ \ R 3 2 3 2 The large partial double-bond character predicted (about 50%) for the central C-N bond would then account for the short C-N distance observed, for the near coplanarity of the amide framework, and for the large barriers hindering rotation about the central C-N bond. The development of molecular orbital (MO) theory has provided powerful methods for studying the electronic and geometrical structures of molecules and various approximate MO methods (CNDO/Z, EHT, PPP, and ab initio) have been used to study the energy barriers90 and various 212'213 for substituted amides. 336 solvent effetts 337 During the last decade, many different experimental methods (NMR, IR, UV, X-ray diffraction, electron dif- fraction and microwave spectroscopy) have been applied to the study of the molecular and electronic structures of amides. However, a theoretical approach should provide a more powerful method for looking into the variations in energy and charge distribution on going from the ground equilibrium geometry to the transition state geometry. Formamide has been examined quite extensively by 211’217-219 and the vibra- 214-216 a number of theoretical methods tional spectra and force constants discussed. Some results of calculations of the electron distribution in formamide are shown in Table 39. N-Methylacetamide has also been studied90 as the simplest model for the poly- peptide chain and the data for the charge distribution in that molecule are shown in Table 40. In these studies the ground state geometry has been taken to be that in which the NCO fragment and all the atoms directly bonded to it form a plane. In the transition state, it has been assumed that the COR fragment is twisted out of this plane by 90°, the nitrogen atom and the three atoms bonded to it remaining in the original plane. 214-219 it was found that the In these results, calculated quantities are very sensitive to variation in geometry and in the Slater orbital exponents. The results of all the CNDO/2 calculations are in reasonable agreement .mmm mocmummmmc .ham mocmummmm5 .mam wocmummmmH .vmm wosmummmmx .mmm mocwummmmn .Nmm mocmummmma .HNN wocwummwm .mwmhamcm :ofiumHsmom «\09200 a .N.H mH E MO HMUHQHO HOHMHm OS». HON UGOGOQXQ 03H. .HNN UUGOHUHOMO .ONN OOQQHOHOm m U .m.H ma 2 mo Hmuwnuo HmumHm mnu How ucmcomxm oneo .om mocmnmwwmn .Amsoum o u U wsu on m>wumamuv mammoupmn woman was man on» mum mm was Ham 338 N. mmH.o hma.o th.o «va.o oma.o m ~ma.o moH.o vo~.o oma.o ~va.o Hm mmo.o- sso.on smo.o- mqo.on wqo.on loom ~o~.o- m-.ou vmv.ou hm~.ou mm~.o- z som.o mam.o H¢¢.o mmm.o mmm.o o wom.o- «mm.o- mem.o- mmm.o- mmm.o- o x.fl.m.mmmmmmw fl.fl.m.mmwmmmm ougmmmmmm mmmmmw mum.nmmmmmm sea.o mmm.o nmm.o am.o sm~.o mm mmH.c mmm.° mom.o hm.o mm~.o Hm mmo.o- sma.o ~ma.o pa.o «Ho.o love mov.o- mqa.o- mms.ou mm.ou Nam.o- z omq.o mm~.o mm~.o mm.o oqo.a o mmm.ou mmq.o- hem.ou av.ou mHN.H- o a mmmmmmm soauflcs an chafing an chafing an wunmmm scum mAmuflcs owsouuomam Gav mpHEmEHom How mcowusnwuumflp mmumno pmumasoamu .mm manna 339 .omm mocmumumn .mflmhamcm coflumHsmom cmxflaasz n .msoum o n O may on mmm ma msoum Hmnumalz ms» .mUHEmumomahcumEIZ Homm mm.o+ m~.o+ o~.o+ h~.o+ mH.o+ oa.o+ v~.o+ szm om.ou mm.on om.o: om.ol wm.o: ma.oa ~m.ou z mm.ot mm.o| mv.o: mv.o: mm.on mm.on m~.HI o mv.o+ mm.o+ mm.o+ mv.o+ h¢.o+ mm.o+ mo.H+ “CHOW mamflno 0cm .MMIMM mmewnom Ill cmfiaawaom acmum Iwcmaom um .flOO N\OQZU U.MN\OQZU .mamm EODG .pson mpflpmmm on» How HmeE m .Amuflcs vacouuomam :wv mpfifimumomamcumsnz ca msoflusnauumwp wmumno commasoamo .o¢ manna 340 with each other, while the charges calculated by the BET and "ab initio" methods differ from those obtained by CNDO/2. In general, the EHT method tends to exaggerate the charge separation in polar molecules, while the charge distribution obtained in the "ab initio" method is significantly dependent on the size and quality of the basis set. The calculated and experimental energy barriers of some amides are shown in Table 41. While the calculated re— sults are in reasonable agreement with the experimental values, the experimental values for a given molecule show unusually wide variations as a result of the use of approximate formulas for characterizing the lineshapes of the exchange broadened signals and the use of different solvents. Comparisons with theoretical results must be made with this in mind. II. STANDARD GEOMETRICAL MODELS Normally, the calculations involve some attempt at energy minimization with respect to molecular geometry. However, this procedure becomes impractical as the size of the molecules under consideration increases. A set of standard geometrical models for commonly occurring structural parameters in polyatomic molecules has been established by Pople and Gordon.221 The complete goemetry of molecules without closed rings can be defined by (a) the bondlengths for all bonds, (b) the bond angles specifying the 341 Table 41. Calculated energy barriers restricting rotation around the peptide bond (in kcal/mole). Compounds Barrier Barrier Barrier (EHT) _ (CNDO/2) (exptl) Formamide 15.57: 20.292 19.7:o.4d 20.66b 15.4 19.2:o.4e 25.26 . N,N-Dimethylformamide 21.13: 15.03b 20.5:o.2f 26.45b 21.6:o.3g 25.81 l9.8:0.5 N,N-Dimethylacetamide 14.61a 16.04b 16.85:0.4lh 18.93b 16.81 k 20.52 19.7:o.5 N,N-Dimethyl- 14.55: 16.6:O.li propionamide 18.63 18.9:0.4 'N,N-Dimethyl- 6.68a 11.5l pivaloylamide N,N-Dimethyl- 13.36: 16.4:O.2m isobutyramide 17.94 N-Methylformamide 25.60: 18.05: 19.0n 25.51 16.87 N-Methylacetamide 24.16: 18.80: 18.0n 21.24 18.89 Acetamide 24.01b 21.72b 16.7o Benzamide . 15.8c aReference 125. Two different set of parameters are used. dReference 231. Solvent: bReference 90. cReference 230. diethylene glycol dimethyl ether. eReference 231. Solvent: methyl propyl ketone. fReference 160. Solvent: CC14. 9Reference 125. Solvent: C2H6' hReference 232. Solvent: CC14. 1Reference 125. Solvent: cyclohexane. 3Reference 162. Solvent: CC14. kReference 233, neat. 1Reference 234. Solvent: CH2C12. nReference 235. Solvent: C2H4C12. 0Reference 242. mReference 125. Solvent: acetone. Solvent: acetone. 342 stereogeometry of the neighboring atoms bonded to each atom in the molecule, and (c) the dihedral angles specify— ing the internal rotations about appropriate bonds. The rule for using all these quantities is to use a notation xn for an atom with elemental symbol X which is bonded to nneighbors, where n is the connectivity of X. For example, the carbon atoms in ethane and ethylene will be described as C4 and C3, respectively. A. Bondlengths There are four types of bond - single, double, triple, and aromatic (for benzene rings). The standard values used for the bondlengths of the H, C, N, O, and F atoms are shown in Table 42. B. Bond Angles Five types of local atomic geometry are dis- tinguished. If the connectivity is 4, tetrahedral angles are used. For connectivity 3, the three bonds are either taken to be planar with bond angles of 120°, or pyramidal with bond angles of 109.47°. Atoms with connectivity 2 are taken as linear, or bent with a bond angle of 109.47°. The nature of the local atomic geometry is depen- dent on the presence of unsaturation in a neighboring group. The rules adopted for selecting the atomic local geometry are given in Table 43. 343 Table 42. Standard bondlengths (in Angstrom units). Bond Length Bond Length Bond Length Single bonds H-H 0.74 C4-N2 1.47 C2-02 1.36 C4-H 1.09 C4-02 1.43 C2-F1 1.30 C3-H 1.08 C4-Fl 1.36 N3-N3 1.45 C2-H 1.06 C3-C3 1.46 N3-N2 1.45 N3-H 1.01 C3-C2 1.45 N3-02 1.36 N2-H 0.99 C3-N3 1.40a N3-Fl 1.36 OZ-H 0.96 C3-N2 1.40 N2-N2 1.45 Fl-H 0.92 c3-02 1.36 N2-02 1.41 C4-C4 1.54 C3-F1 1.33 NZ-Fl 1.36 C4-C3 1.52 C2-C2 1.38 02-02 1.48 C4-C2 1.46 C2-N3 1.33 OZ-Fl 1.42 C4-N3 1.47 C2-N2 1.33 Fl-Fl 1.42 Double bonds C3-C3 1.34 C2-C2 1.28 N2-N2 1.25 C3-C2 1.31 C2-N2 1.32 N2-Ol 1.22 C3-N2 1.32 C2-01 1.16 01-01 1.21 C3-01 1.22 N3-Ol 1.24b Triple bonds Aromatic bonds C2-C2 1.20 C3-C3 1.40 C2-N1 1.16 C2-N2 1.34 Nl-Nl 1.10 N2-N2 1.35 a1.32 A used in the N - C = 0 group. bPartial double bonds in the N02 and N03 groups. 344 Table 43. Standard atomic geometries and bond angles. Atom Total excess Examples Geometry Bond angle valence cg (degrees) neighbors C4 All values CH4 Tetrahedral 109.47 C3 All values C2H4 Planar 120 C2 0,1 CH2, CH0 Bent 109.47 2,3,4 C02, HCN Linear 180 N4 All values NH4+ Tetrahedral 109.47 N3 0 NH3 Pyramidal 109.47 1,2,3,4 HzN-CHO Planar 120 N2 0,1,2 HZCHN Bent 109.47 3,4 HNC Linear 180 03 0 H30+ Pyramidal 109.47 1,2,3,4 Planar 120 02 All values 03, H20 Bent 109.47 a . . The excess valence 18 the normal valence minus the connectivity. 345 C. Dihedral Angles In open chain molecules, dihedral angles have to be specified for each bond joining atoms with connectivity greater than 1. Values mo mcoprEMoHCOU .mn CQ:Mwm 366 A 60 unnumfluaflu somcfiempmomasepm-z Ame Odin A oonmnuauuo 33536632322 3: manna . 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GWWW A HOW WMMMV A .3 .NV 3‘ M“ Na HQ a .HODESZ pooho ozom w>wpma0m hmumcm Havoe onmawc< Hmuumnwa unsposhpm mundaneoo eczema OQZH an mmofiem Hmuw>mm mo msowvmsuowsoo msoanm> new mowwnosm Haves .m: manna 369 :mHoN.H Ho.mH muumoomm.=m- on ow om H-m mmmon.a mm.o mammomoo.¢m- om on o 8.0 mmmam.a AH.o smamomoo.sm- on on o m-o oamun.a mm.o moumumoo.emu oo o o sue muomm.a mm.o mmmmmmoo.sm- on o o 6-6 mmmam.a oa.o noomoaoo.:m- om oo o m-o mmmam.a no.0 maammmoo.enu on oo o :-u mmmam.a oo.o mmmmmmoo.2m- o oo o mso :momm.a oa.o mmnoamoo.am- o on o muo mmom~.H ma.o ommmoaom.sn- o o o H-u mufismpoow Hanpmsuz mm~H~.H mo.ma mammmmma.m:- 0 cm mum Humom.a mm.ma mmmmmmma.m¢- on om H-m mmo:m.a 00.0 mmamwmoa.o¢- on o m-o memmm.a nfi.o mmammmma.o¢- oo o Nuo mommm.a oo.o mmmflomwa.oa- o o H-u munsmsnom Hanpma-z 23m 78.25865 . . an nu ma an o onouz mg» no“ hwumsm A 3 av umpssz Amono 98m winemaom hmpwcm Hmpoe A ovmamsa‘ ~930an onspgfipm 3:509:00 Acwschcaov 370 ommma.a mm.HH mammmmmo.mou o o o om H-m Homos.a mo.o mmmamm:o.no- o o o oma ~-u mcnemenom eusmm.a oo.o onmmm:¢o.nou o o o o H-o Hsnpm-z . Hsnp62-z -mo~.a mu.ma mmomommm.am- o oma oa mum mmmam.a oomwmmmm.¢mu o ona om sum mm:a~.a om.aa wmmzmmmm.smu 0 on om m-m oomom.a n:momomm.¢mu 0 ca om ~-m ::NHN.H suaammnm.:mu o o co H-m m:omm.a oo.o sandmamm.:mu o oma o mum oomnm.a No.H mmmmmmmm.an- o oma o :-o Hossm.H H:.o moaommam.:m- 0 on o m-u mmuzm.a mo.H Hmweummm.am- 0 ca 0 «no moo:m.a wfi.o eoemommm.amn o o o H-o manamsnom asapm-z onouz wgpcwtwumm A Hem.“ wwmmv A413 3‘ mm mm an c hmnasz “mono ocom 9,3233% hmuocm 13.09 A 615mg» Hmuoofinn mgpozupm mogomaoo Aumssfipsoov ‘l 371 :omaa.a mm.ma mmnmooe.anu o o o oo om Ham «unempmom ommom.a oo.o m:nmmw:.aua o o o o o H-o Henpm-z Asapme-z mmooa.a mm.ua mnwmmmao.mwu o oma 0 cm mnm ommma.a oeooouao.mou o oma o ow Sum mmnma.a o:~mnmao.mou 0 cm 0 om mum omouH.H ~moom¢ao.mo- o on o co ~-m HounH.H mm.ma wumemmao.mw- o o o om H-m mommm.a ma.o «Hmmmoeo.mw- o o ow o 0-0 mmmmm.a m:.a :mamm::o.mw- o oma o o m-o usomm.a mm.~ ummmemeo.mo- o omH o o e-u mommm.a H:.H :u:mu::o.mwa o om o o mum Hmmmm.a mw.o oamnom:o.mou 0 on o o «lo mmomm.a oo.o mammou:o.nou o o o o H-o mewsmpmom asapm-z . e m m H onouz unvnmwm A 4pmmwwmmv A.s.mv u. a Q Q a nmnssz umouo.o:om m>prHmm hwpocm Hmpos onmawc< awhomnwn CQSPCSQPm mocsomsoo ACmSCHpsoov 372 The output display from the INDO program includes (a) the overlap array, (b) the Hfickel Hamiltonian, (c) the Coulomb matrix, (d) the core Hamiltonian, (e) the final Fock Hamiltonian, Cf)the final vectors, (g) the initial density matrix, (h) the final density matrix, and (i) the partial charges on each atom. Since calculations were made for many different conformations of each amide, it is possible to study the change of energy, and of partial charges on each atom, with the variations in the dihedral angles. II. DEPENDENCE OF INDO RESULTS ON CONFORMATION The results are to be presented in four sections: A. Variation of energy for rotation by angle 0 about the N-C(0) bond, B. Energy variation with respect to the dihedral angles ¢, C. Charge variation with rotation by angle 0 about the peptide bond, and D. Charge variation with respect to dihedral angles ¢. A. Variation of energy with rotation about the N—C(O) bond The variations in the energy barrier for rotation around the N-C(O) bond mainly arise from inductive, steric, and hyperconjugative interactions. However, it is still impossible to separate out the energy associated with any given type of interaction. To analyze the energy varia- tions and bond orders for different conformations of a given amide, a listing of the absolute energies, relative energies, and bond orders is given in Table 45. The 373 calculated energy barriers for rotation about the N-C(O) bond for each amide are in reasonable agreement with the experimental data and the CNDO/Z data212 shown in Table 41. In order to look into the effect of the carbonyl substituent R(C = 0) on the energy barriers in amides, some groups of amides are compared: (1) N,N-dimethyl- formamide, N,N-dimethylacetamide, and N.N-dimethyltri- 'fluoroacetamide (DMTFA); (2) N-methylformamide, N-methyl- acetamide; (3) N-ethylformamide, N-ethylacetamide; and, (4) N-methyl-N-ethylformamide, N-methyl-N-ethylacetamide. The energy barriers of the first group are shown in Figure 79. {Hueresults show that as the substituent group R(C = 0) changes from -H to -CH (or -CF3), the 3 energy barrier about the N-C(O) bond is increased. This is attributed mainly to the steric effect. This result is similar to that obtained by CNDO/Z90 but opposite to that obtained by the EHT method.9o’125 In order to compare the calculated with the experimental results, which show a decrease as the substituent group R on the carbonyl group is changed from -H, -CH3 to -C2H5 (though this tend is not unequivocally established), we must consider the solvent effect. Rabinovitz and Pines160 have found that the energy barrier for rotation about the N-C(O) bond in N,N-dimethyl- formamide decreases with increasing dilution of the amide in CCl4 and they proposed that this variation is the result of a change in amide-amide association equilibrium.. The 374 .Ehom umscman 0:9 Scum anon onouz 0:» Psonm paws» mo mawsw 0:9 m« o .Apnwfinv mowewpoomouosamaupaanpoEHuuz.z cam .Amaconev mcfismpmomasspmsnu-z.z .Apmoav munsmenomaszpwenuuz.z Cw econ. £03ng 05. ”zoom 2.8330.“ no.“ £02.30. 3998 05 .Ho somuumnsoo .ou opzwwm N d H62\aaox om.ua u a All.@ .lll m oma oma om on on o oma and oNH co co on Hoa\aaox 3H.ua u m d ‘ I I o Hoa\aaos an.na AIO m on oma and oma o d ow d a) vx o: H H H O\ +— ( tout/180x) .... N 3 375 fact that the barrier decreases with increasing dilution indicates that the barrier in the monomer is lower than 162 This solvent effect has also been studied 212 in the dimer. theoretically by Momany et al.- and experimentally by 237 In the CNDO/2 results of Momany et al., they Kamei. consider many different possible conformations of the formamide dimer and find that when hydrogen bonds are formed at the C = 0 group, the energy barrier of that amide for rotation about the N-C(O) bond is increased significantly (by about 2 kcal/mol ). This effect was also observed in the NMR studies of Kamei. Normally, the amide-amide association in neat amides increases the barrier by ca. 1 kcal/mol , while hydrogen bonding can increase the barrier by ca. 2-3 kcal/mol , compared with the barrier in a dilute solution in a nonpolar solvent.212 Using this model, with the same substituent group on nitrogen, the formation of the dimer for N,N-disubstituted acetamides will be more difficult than for N,N-disubstituted formamides since the size of -CH3 group is quite a bit larger than that of hydrogen. Another possible factor affecting association may be the geometry of the ground state, since some amides are not actually planar in the liquid phase, especially when the substituent group becomes more bulky. The assumption that all amides, even those with bulky sub- stituents, are planar will result in the calculated ground States being less stable than would be predicted for the 376 true, pyramidal ground state; the calculated energy barriers for rotation about N-C(O) would then be too low. Con- sidering these two factors, the observed energy barrier for acetamide is almost equal-to, or perhaps less than, that of formamide as seen in Table 46. This solvent effect will be described more clearly later. One very interest- ing pair of amides is N,N-dimethylacetamide and N,N-dimethyl- trifluoroacetamide (DMTFA). Both the theoretical INDO energy barrier and the experimentally determined barrier232 for DMTFA are greater than those for DMA. This difference is presumably the result of the different inductive effects of hydrogen and fluorine, since the atomic volumes for hydrogen and fluorine are similar (H: 13.1 ml/mol, F: 14.6 ml/mol), so the steric effect will not be very important. To investigate the variation of the energy barrier in amides with different nitrogen substituents (i.e., -H, -CH3 or -CH2CH3), and different substitution numbers (i.e., mono- or di- substituted), we compared the follow- ing groups of amides: (a) Those with different substituent groups but the same substitution number: (1) N,N-dimethylformamide, N-methyl-N-ethylformamide; (2) N,N-dimethylacetamide, N-methyl-N-ethylacetamide; (3) Formamide, N-methylformamide, and N-ethylformamide; (4) N-methylacetamide and N-ethylacetamide. 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The energy barriers for the first group of each set are shown in Figures 80 and 81. The results show that the barrier decreases as the substituent becomes larger or the substitution number is increased. Again, the INDO re- sults are similar to those obtained by CNDO/2 and the experimental values also show this tendency (Table 41). B. Energy variation with respect to the dihedral angle ¢ The energy for rotation about either the N-methyl group or the carbonyl methyl group in N-methylacetamide has been studied by the INDO method. .The results show that the rotational energy of either methyl group in gig— N-methylacetamide is varied slightly as the configuration of the other methyl group is changed, as shown in Figures 82-87; the variation is about 0.02 kcal/mol . Also shown in Figure 88 is the three-dimensional energy surface of gig-N-methylacetamide as a function of ¢1 and ¢2, with = 0°. The most stable configuration of ging-methyl- acetamide is with ¢1 = 60° and ¢2 = 0°. The average energy barrier restricting rotation about the N-methyl group is a little smaller than that for the carbonyl methyl group (ca. 0.03 kcal/mol). 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L. -54.6087 “5“. 6088 -5’+.6089 . Figure 88. Three-dimensional energy surface for N-methylacetamide as a function of the dihedral angles of the N-methyl (.02) and the carbonyl-methyl (01) groups. The lowest at point A withfl1 energy configuration is o - o and ”2" o = 60 386 CNDO/2 calculation, find that when the peptide bond is twisted from the configuration in ging-methylacetamide to that in trangeN-methylacetamide (where gig or trans is relative to C = O group) by an angle 0 greater than 120°, the rotational barrier of the N-methyl group rises sharply. This is highly indicative of a sharp increase in the potential due to steric repulsion. 238—241 had worked on the Many different groups energy barrier for rotation about the C-X bond of the CH3-XAB system, with X trigonal planar. They found that if A and B are equivalent the barrier will be sixfold, and such barriers are known to be small. When A and B are nonequivalent, a threefold component is introduced. While this will dominate the shape of the barrier its height will remain small as long as the trigonal planar configuration at X is preserved. This model can explain why most of the rotational energies for methyl groups in amides are so low. According to our INDO results, Table 46, most of the rotational energies for —CH3 in amides lie between zero and 0.5 kcal/mol, except in some special cases such as DMA, DMTFA, N-ethylformamide, and N-ethylacetamide. The rather low rotational energies calculated for methyl groups are mainly a result of our assumption that the ground state is planar, which is con- sistent with the CH -XAB system which was assumed to be 3 planar. We also measured the rotational energies for the 387 N-methyl groups in DMF and DMA by NMR Tl experiments, and found that the barrier is usually more than 1.5 kcal/mol. These large experimental values are attributed to the solvent effect and to deviations from the planar structure in liquid amides. Rotational energies of the carbonyl methyl group in DMA and DMTFA are considerably higher than those for the other methyl groups, as seen in Table 46. This is due to the presence of a trans-N-methyl group in both compounds. From the rotational energies of the carbonyl methyl group in N-methylacetamide and DMA, we find that some extra energy, ca. 5.53 kcal/mol, is needed for rotating the carbonyl methyl group in DMA over that in N-methylacetamide. This large steric interaction energy is completely con- sistent with the CNDO/2 results obtained by Momany et al. In N-methylacetamide, they found that when the N-methyl group is twisted from the gig configuration to the trans_ (relative to carbonyl oxygen), the rotational energy of the carbonyl methyl group is sharply increased. For DMTFA there is also a strong electronic interaction in addition to the steric interaction, as shown in Figure 113, where a sharp change of the eleCtronic charge distribution on the carbonyl-methyl carbon is observed as compared with DMA. The calculated rotational energy of the Carbonyl methyl group in DMTFA is 30.62 kcal/mol, which is higher than that calculated for DMA, 6.72 kcal/mol, as shown in 388 Figures 89 and 90. This strong electronic interaction energy makes the energy barrier for rotation of the -CF3 group about its threefold axis even higher than that for rotation about the N-C(O) bond in DMTFA, so we expect that the -CF3 group will stay in a fixed configuration at room temperature. Rotational energies for the N-ethyl group about the N-CIHZCHBJ bond in N-ethylformamide and N-ethylacetamide, Figures 91 and 92, are lower than calculated for the carbonyl methyl groups in DMA and DMTFA, but higher than obtained for the remainder of the methyl groups (Table 46). This is because the N-ethyl group in N-ethylacetamide considered here is gig to the C = 0 group, so the rotational energy of the N-ethyl group is mainly attributed to its greater mass. Comparing the rotational energies of the carbonyl methyl group in N-methylacetamide and N-ethylacetamide, both in the gig form, we find that they are nearly identical. That means that the rotational energies of carbonyl methyl groups are almost independent of the structure of the N- substituted group when these are trans to each other. From the rotational energies of the Eganng-methyl group in N-methylformamide (NMF) and N,N-dimethylformamide, Figures 93-95, we find that the steric effect energy due to replacing an N-H hydrogen in NMF by a gis-N-methyl group is about 0.36 kcal/mol. Comparing N-methylformamide and N-ethylformamide, we find that when one proton of the 389 “62098 ‘62099P -63'OOF -63.01, 0) ‘63002 D .p out $2 :3 “63003 P O 0H 8 P -6300“ P 6.2 - m C "4. -63005 D E G-l G-l a; “63006 P £1 [1.] '63007 b _63.08 I L l J I 0 30 6o 90 120 150 180 Figure 89. Variation of energy with rotation of the carbonyl-methyl group in N,N-dimethylacetamide: Ea = 6.72 kcal/hol. The notation G-l. G-2 refers to the configurations defined in Table 45: the values of the angle 01 corresponding to each configurations are also shown in Figure 79. 390 -140 o 02 -1L|rO-03 L. “14000“ b 1 —1L-0.05 ... ‘- -140.o6* ‘140007 ~1LI'O o 08 -140.09 Energy, in atomic units -140 0 ll 440.12 L - - L - 0 30 60 90 120 150 180 Figure 90. Energy variation for retation of the carbonyl- CF3 group in N.N-dimethyltrifluoroacetamide: Ea = 30.62 kcal/mol. 391 -5‘+-52 -54-53' -54.54' m "Sn-55’ +3 "-4 C 3 -54.56* 0 ’8 E-Z B -51+.57'E-1 3-3 A 2-1- “ EXCITED 3-5 5 L. .H -5‘+.58 S: no §-54.59[ - ‘11 .. - - - .. -54.6 G 1 G 3 G 2 c u G 5 (GROlflHD -54061- -50,62i 1 l 1 1 1 0 30 60 90 120 150 180 03 —-.- Figure 91. Energy variation for rotation of the N-ethyl group about the N-C(H2) bond in N-ethylformamide in both the ground equilibrium geometry and transition geometry: Ea(ground) = 1.05 keel/mol. 392 ~62.96 "62-97 F -62.98 - -62.99 r m ’63-00 '- .p '5 -6 .01 - g 3 B-l E-Z L3 3.1; E E '4 3 -63.02 -- EXCITED\j CU . c . '7 -63.03 L 5‘ 6 4 o ' 3-0 ' G-H ,5 10-1 0-2 6'3 \G’ji “63006 E _63.07 1 I I L l 0 30 60 90 120 150 180 03 "" Figure 92. Energy variation for rotation of the N-ethyl group about the N-C(H2) bond in N-ethylacetamide in both the ground equilibrium geometry and transition geometry: Ea(ground) = 2.88 kcal/mol. 393 -h6.09 -b6.10 ' '14’6011 I. -46012 P ““6 o 13 . EXCITED “1+6 0 1h - —u6.15 L -#6.16 r ‘Glfllflflo '“6017 b Energy. in atomic units ’“6018 _- '1’60 19 - - 6.20 ‘ 1 ' u o 30 60 90 120 dk;-i" Figure 93. Energy variation for rotation of the N-methyl group about its threefold axis by anglefi3 in N-methylformamide in the ground equilibrium geometry and in the transition geometry: Ea(ground) = 0.17 kcal/mol. 394 .msn mo zuPoEoom Esaunfiawswm cczonw .msn mo apposoow aawunwafisuo on» a“ can hupmsoow cowpamcmup unsouw on» a“ van znpoeoow on» a“ anouw mmo-z on» ma compensate an» an macaw mmo-z coflpwpou pom codpmfium> zwnocm .mm ouswam on» we zoavmpou you coapwwum> hmuocm .:¢ ouzwum .Allunnv .I «do omH oa om on oma om ow on . m x W . 4 -93? a . + _ -3 : _n,=xuso mum :-u :-o ~-o :-o "a . n "a m l 00 in m m m 1%. n- . nan. - . TIM Ntm HI#Mo+~ml We... Nlm film NI”. wmoiml Wu? 0 O m. m. ..R.%. o .. as“- o n n w. w. nonffiml Ma... 1 OWIJMI m... image- 1 Rim- Lens? 1 39%.. bmn.:n- «n.3m- 395 N-methyl group in N-methylformamide is replaced by a -CH3 group the energy for rotation about the (N-)C-R bond is in- creased by about 0.88 kcal/mol. This is the reason why the N-ethyl group rotational energy is usually greater than that for the N-methyl group. C. Charge variation upon rotation about the N-C(O) bond The computed charges on each atom for the selected amides in various conformations are shown in Figure 78 (all the charges on each atom have been multiplied by 100 in the figure). Since formamide and N-methylacetamide have been treated by a number of theoretical approaches,9o'237 we will examine these two compounds more closely and compare the results with those obtained by other methods. The charge distributions for formamide and N- methylacetamide obtained in the INDO calculations are shown in Table 47. The values are similar to those ob- tained by the CNDO/Z method.90 The sum of charges on the atoms of the peptide group (i.e., the C and O atoms of the C = 0 group, N, the carbon atoms of the carbonyl substituent and the a carbons of the nitrogen substituents) is also nega- tive, in agreement with the results of the CNDO/2 method. This produces a reasonable basis for the partial double-bond char- acter postulated in resonance theory for the central C-N bond. The variation of charges with 6, the dihedral angle for rotation about the peptide bond, in DMF, Table 47. Charge distributions in formamide and N-methyl- acetamide (in electronic units) calculated by the INDO method. Formamide N-methylacetamideb Atom' Charge Atom Charge (electrons) (electrons) O -0.397 0 -0.418 C(O) 0.455 C(O) 0.429 N -0.232 N —0.202 H(C) -0.083 H(N) -.103 H1(N)a 0.140 H2(N)a 0.116 aHl and H2 are hydrogen atoms gig and trans to the C = 0 group, respectively. bFor cis-N-methylacetamide, where the N-methyl group is cis to the C = 0 group. This is the same conformation as that in Reference 90, but designated there as the trans form. 397 formamide, DMA, DMTFA, and N-methyl-N-ethylformamide is shown in Figures 96-100. The variation of the charges is sharpest for the nitrogen and oxygen atoms of the peptide bond when the amides are twisted from the equilib- rium geometry to that of the transition state. For symmetrically N,N-disubstituted amides, Figures 96-99, the partial charges on the atoms of the amido group are identical at 0 = 0° and 0 = 180°, while for unsymmetrically N,N-disubstituted amides, e.g., N-methyl-N-ethylformamide, the partial charges on the amido group atoms are different at 6 = 0° and 0 = 180° (but the difference is negligible). For the remaining atoms, excluding those of the amido group, in symmetrically and unsymmetrically substituted amides, the variation of the partial charges is unsymmetrical since the electronic environment is completely different when 0 = 0° and e = 180°. For the symmetrically N,N-disubstituted amides, the gig and trans atoms are exchanged, while for unsymmetrically substituted amides there is no relation- ship between the two forms. As the peptide bond is twisted from the planar arrangement (0 = 0° or 180°) to the transition state (0 = 90°), we find that the charges on the carbonyl oxygen and carbon atoms are decreased, while the charge on nitrOgen is increased. These results are consistent with the charges predicted on the basis of the resonance 208 structures I and II suggested by Pauling (discussed in 398 0.52 0.48 t f C 0.40 .. H Iflz 2: 0.1-Ll, 1 a. 3 0.10 - 2 1 '3 a 2: 3 ‘5 3 -0.08 8 H3 ‘5 -O.12 O m “H. H “p. 0 ”0.20 - g "4 \I -0.24 . m N o E.” b '2 -0.28 O H "‘3 ”0032 1‘} at? -0036 -O.I+O- -o.tm+ 1 1 1. L ‘ 30 60 90 120 150 180 C>-—-)> Figure 96. Variation with 6 of the partial charges on the atoms of formamide. The numbering of the atoms corresponds to that in Figure 79. 399 0.52 0.48 0.44 -0.04 -0.08 "o o 12 -0,. 16 ”0020 Partial Charges ( in electronic units ) -0.24 r- I -0.34 C) “0038 b 1 l J_ l I -0.42 30 60 90 120 150 180 (3 ---)> ‘92::0P; Q%3::(r’ Figure 9?. Variation with-9 of the partial charges on the atoms of N,N-dimethylformamide. Partial Charges ( in electronic units ) 400 0.48 0.44 ‘h‘ C2 r/ \ 0.40 t d: 2:; 0.20 . ___ y N .1: 15 0.06 . 0.02 .- —o.od. / any :5 “P -0.16 r -0.20 r- N “002“)- :r fiE -0.36 . -0.40 .. ° "Oouh’ l J l J J 0 30 60 90 120 150 180 G-l E-l G-l 0 —-> Figure 98. Variation with e of the partial charges on the atoms of N.N-dimethylacetamide. 401 C2 m 0.187 \ f. C 5 0 l4r- c7 3 .3 a; 5 u 13 0.0 :4_ H8— : 0.00 — H .. .5 W V -0.04r- :IO H5--- 8 +4.: : :: ff -0.12- . H9 - (U :5 H -0.16*- N (U ..4 I: m -0.20r p. -0.24 -0.28 -0032 -O.36 0 30 60 90 . 120 150 180 C) -——)> Figure 99. Variation with e of the partial charges on the atoms of the peptide bond in N,N-dimethyl- trifluoroacetamide. 402 0.48 A X 0.44/ 0.24 A 0-16 1- \C?’ :2 APE a; “H 0.05 no 5 y “3 0.01 I- H ’ 2 segues-fer: ___ -~-- wa *’ H """""" H4 .............. Hu--_ ....... . r8": -0 . O3F‘w"“fig-9".77771'5"???.71'2;.:..'.:°'?"?‘2‘:‘.‘o'.‘?rI' 1'5: ~ 1 ”9L .5 -0.07.. H5”- N) E 5 -0.15 Tu :3 -0.19 5.. a“! ~0.23 . "fi 1: -0.33 I- -O. 37 )- o -O.l+l | I l l | 0 30 60 90 120 150 180 (D --d>~ Figure 100. Variation with e of the partial charges on the atoms of the peptide bond of N-methyl-N-ethyl- formamide. 403 the Theoretical section of this part of the thesis). In resonance theory it is predicted that in the ground state geometry structures I and II contribute about equally, while in the transition state geometry any contribution of structure II is impossible since the fragment RC0 is perpendicular to the fragment NR Therefore, compared 2. with the ground state, the charges on oxygen and carbon will be decreased in the transition state while the charge on nitrogen will be increased. Assuming that a hydrogen bond is to be formed, we will find that a departure of angle 0 from 0° or 180° to- ward 90° will lead to a weaker hydrogen bond. Expressed in another way, we will find that a hydrogen bond will stabilize the energy of the ground state more than that of the transition state, since there is more charge on oxygen in the ground state. Hence the energy for rotation about the N-C(O) bond will be increased as the hydrogen bond is formed. D. Variation of charges with respect to the dihedral angles ¢ The variation of the partial charges with respect to o, the dihedral angle for rotation of the methyl about the bond to the methyl carbon (or the ethyl group about the N-CH2 bond), in DMF, DMA, DMTFA, N-methylformamide, N-methylacetamide, N-ethylformamide, and N-ethylacetamide is shown in Figures 101-115. The variation of the partial 404 0.50 0.46 b ‘2 r~ 0.42 ' :E :5 := g 0.20 r C o L, '2 0 16 ~ C9 0 :3 4+: #- 8 0.06 - H G c 0.02 _ «a V “4— I! a -0.0? JD..— W E "11""12'" O -0.06 " H7& H8 '3 '3 -0.10 ,.. H4 $4 (0 De ‘Oolu' F I! —0.18 b s; a: -0.38 ’ C) -0.42 0-1 1 014 1 G-l 0 30 60 90 120 “’3" ’ 0=0°7 ¢2=O° Figure 101. Variation with 03 of the partial charges on the atoms of the N-CH3 group of N,N-dimethyl- formamide. The notations G-l. G-4 given at the bottom of the figure refer to choices of dihedral angles listed in Table 45. 405 0.50 0.46 - C2 A 0.42 P '0 8 1:: 33 020 § ' c5 0 1 «g 0.16 - t9 3 ‘rL’ :1: +3 3 0.06 - H 0) ,5 0.02 - t. "73‘": 3 ‘0'”me 00 5 "° '— 0 -0.06 )- H,"& H12 H .3 010 H 1’. ' 4 (0 On -0.141- -0.18- N 45 :1: —o.38_ o 0-3 0-2 0- -O.l|v2 41 I I 0 30 60 90 120 ¢3—> 0: 0o 3 ‘92: 60° Figure 102. Variation with 05 of the partial charges on the atoms of the N-methyl group of N,N-dimethylformamide. 406 0.50 0.46 4 __ £2... 0.42 - m 5: A: 3:} 0.20 ~ 5 L . o - .2 0.16 4:9 3 a: (F *5 0.06 O H 0 0.02 ~ 5. H,5 1 w “0'02 FE_1n___..:=n=====nn===::£§§%:: °’ ”' H &H "' a) ll 12 Ifizfrh‘ ,2 -0.06 b O H “4 ,3 -o.10 - 4..) u A? u. -0. r- N -0.18 - 1: -..; . G-B -o.42 IE1 ' I l ' 6-1 ' 30 60 90 120 “’2 —" (D==OP';<93==(f’ Figure 103. Variation withfl2 of the partial charges on the atoms of the N-methyl group of N.N-dimethylformamide. 407 0.50 00’46 - C2 0.42 _ ’K 0 20 4’ a? m ' P 0.16 . o . ‘9 g at :5 .p o .9: 0 02 0 ° 7 .' .5 ° V -0.02 g HIo . g "7&H8'" an -0.06 - H"&HI4 i5 7‘, —0.10 P H4 ..4 ‘fi ‘6 -O.l4 t. D‘ II -0018 - -..: . -0.42 F4 1 G-lz 1 G; 0 30 60 90 120 (D24 (3==1)° ; ¢ky=mbop Figure 104. Variation with 02 of the partial charges on the atoms of the N-methyl group of N.Nedimethylformamide. 408 0.50 0014'6 '- C: 0.42 - £5 a: m 0.18 C; . f. s: 3 0.14 - 0 H "3‘ o 10 5 u ' " *3 a. :3 0.02 G) c: .H H V -0.02 H g “6 a) -0.06 P a E! E5 IL__V '3 -O.10 '- w. T: 23 I: m -0018 - a. II -0.22 r- T -0o38 r o G-l G-3 G-2 0:3 G-l -0.42 ' ' 0 30 60 90 120 03—” Figure 105. Variation with 03 of the partial charges on the atoms of the N-methyl group of N-methylformamide. -.. - 409 0.48 0.44 - C2 0.40 r- t 4r ,4 0.20 . c9, :0 2: 0 l6 5 e .3 g 0.12 " Ha I... .p 3 0.08 b H O ‘3 0.04 - :1 I "7 3 0.00 - 6 ’30 _ ___ H" g -0 04 gm: :2: U ' 1 H --.... 4 r; 12 or) “0008 b E. 4' 4' -0.18 b "0022 N -0.l+0 ‘ o T -1 032 013 03-2 G-ll ”0"” '0 30 60 90 I20 q’I""' 9: 0° ;¢2=O° Figure 106. Variation withfll of the partial charges on the atoms of the carbonyl-methyl group of N-methylacetamide. 410 0.48 0.44... C2 Partial Charges ( in electronic units ) C) -o.44r . 1 1 0 30 60 90 120 $1» ==o°; o,=ao° Figure 107. Variation with 01 of the partial charges on the atoms of the carbonyl-methyl group of N-methylacetamide. 411 0.48 0.44- c; 0.40 - n W :11 0020 F" c, 0.16 r 0.12 1- H8 0008 P Partial Charges ( in electronic units ) -0.04 - " '— C4 -0008 P #z 2: -0.18 - II -0022 " a? -0.40 C) - G- - G G- -0.44 7 19 C1 5 1'9 ‘j 0 30 60 90 120 ‘91—" o=o° ; ¢2=oo° Figure 108. Variation with 01 of the partial charges on the atoms of the carbonyl-methyl group of N-methylacetamide. Partial Charges ( in electronic units ) 0.44 0.40 0.20 0.16 0.12 0.08 0.04 0.00 -000“ 412 ‘m'm-“IEZI—II—m 'H - flyjé (11..---- -___1 c4 o i ‘92 _” 0=O° ; ¢1=0° Figure 109. Variation withfl2 of the partial charges on the atoms of the N-methyl group of N-methylacetamide. 413 0.48 0.41} |' C2 0040 I. :1: ’= A 0020 D c9 :2 ___— ... 0.16 L. 5 3 0 12 1 5 ' "a $4 +3 8 0.08 b H 0 .5 0.04 .. g 0.00 40 E o -000," '3 I: -0008 h a“! "0018 -0022 “Coho -0044 Figure 110. Variation with 02 of the partial charges on the atoms of the N-methyl group of N-methylacetamide. 414 0.48 0.44 - (Cg at. 11 0.00 ‘- 7-- -0. 04 ‘7'“ "1'5“ -0008 b \\ ‘I -0018 b Partial Charges ( in electronic units ) ”0022 - '0.l+0 -0.44 2 0=O°; ¢1=60° Figure 111. Variation with 02 of the partial charges on 'the atoms of the N-methyl group of N-methylacetamide. 415 0.48 0.44)- ‘2 0.40" 1: 1; Partial Charges ( in electronic units ) I .0 o w” 4 I I l l fl -0.l6" II -0.20_ -0.24" -0036P - . 0" 0 4 O G-l l GiZ—' cl G-l -0.L”+ 30 60 90 120 “’1 ""* Figure 112. Variation withfl1 of the partial charges on the atoms of the carbonyl-methyl group of N.N-dimethylacetamide. 416 0.70 0.66 A; c” at 0.36 _ aS§L____ ,4 0.32 . m .2 e .. 5 0.20 - .3 CL. c: 0.16 .. O h .p 8 H 0.12 0 fi ° 0.08 m 3; 0.04 n a! .C " 0.00 '3 ..4 ‘5 -o.04 t , "5&"6 :3 ab :: "Oelo.p II -0.14 . ' -0.24CT: ’ F ‘ F ‘0028 - '5 -0.32 . -0.36 ML: 0 30 60 90 120 ‘91 ""' Figure 113. Variation with 01 of the partial charges on the atoms of the carbonyl-CF3 group of N,N-dimethyltrifluoroacetamide. 417 0.46 0.42 - r4 )1 m 0.22 C 0.18 4L_____. 0.14 r- 0.10 0.02 -0002 -0006 -0.103E fiL ‘0018 Partial Charges ( in electronic units ) —0.22 N . T J -0,42 1 1 l l l J - o. 30 60 90 120 150 180 “’3‘" Figure 114. Variation with £53 of the partial charges on the atoms of the N-ethyl group of m-N-ethyl- formamide. 418 00u8 0.44 _. C2 0.40 t :z “5 0022 p ,1 c9 3 0018 p ”.53 o 0.14 .. «"1 § P 0.10 O 0 H 9 0.06 £2 .... D 0 2" m “0002 1: O T" -0006 ...-q , P :5 {a Q.. "0018 n -0022 I. N -0.40 I) -0.44, 1 11 1 1 .1 1 0 30 60 90 120 150 180 (D3 --- Figure 115. Variation with 03 of the partial charges on the atoms of the N-ethyl group of gig-N-ethyl- acetamide. 419 charges on the hydrogens of the methyl groups is usually very small in the ground state. Comparing Figures 101-103 for N,N-dimethylformamide, we find that when the configura- tion of the methyl group is changed from the stable one to a less stable one, the charge on oxygen is decreased and that on nitrogen is increased, although the change is small. Comparing Figures 101, 103, 104 with Figure 102, we see that the charge on H6 is less when this hydrogen is eclipsed with oxygen. In N-methylformamide, Figure 105, the change in the charges on oxygen and nitrogen shows the same tendency as was found for DMF when the N—methyl group was twisted from the stable configuration to a less stable one. In N-methyl- acetamide the reverse behavior is observed for the charges on oxygen and nitrogen when the N-methyl group goes from a stable configuration to a less stable one, Figures 106 to 109 and Table 45. The charge variation of either methyl group is also nearly independent of the configuration of the other methyl group in N-methylacetamide since the carbonyl-methyl and N-methyl groups are trans to each other- One especially interesting pair of amides is DMA and DMTFA. Comparing Figures 112 and 113, we find that the charge on C7 is very strongly dependent on the -CF3 configuration. This may account for the high rotational energy of the -CF3 group. The partial charge on C12 is also greatly decreased when the protons in the -CH3 group 420 are all replaced by fluorine, as seen in Figures 112 and 113. This reduction in charge is mainly attributed to the high electronegativity of fluorine. The variation of charges on oxygen and nitrogen shows the same trend found for N-methylacetamide, as the configuration of -CH3 or -CF3 is varied from a stable one to a less stable one. The charge variations for the atoms of N-ethylformamide and N-ethylacetamide, Figures 114 and 115, are unsymmetrical since the electronic environments are completely changed when the N-ethyl group is rotated from one configuration to the other. This effect is especially enhanced in N-ethylacetamide and there is no apparent order to the variation of the charges on oxygen and nitrogen. The information we have obtained so far from energy barriers and charges is consistent with a simple molecular orbital description of the peptide bond. In order to explain some spectral characteristics, the following qualitative description of the energy levels for the ground state and the transition state is given. Assume that the n system of a C = 0 group interacts with a lone pair on the nitrogen of a neighboring amino group. If there is no interaction, or equivalently when the amino group - NRR' is twisted 90° out of the plane of the -CR = 0 group, the orbitals of the non-interacting system are shown at the left of Figure 116. In order of increasing energy, the energy levels are: a NCO orbital 421 of the C = 0 group, which is lowest due to the large con- tribution of the electronegativity of oxygen, the lone pair of carbonyl oxygen, no; the lone pair of nitrogen, * assumed to be pure 2p; and a “CO orbital, which (in con- trast to NCO) is concentrated at the carbon atom. When there is an interaction, the C = 0 group and nN, the -NRR' group conjugate with each other. According to perturbation theory, the orbital energies and wavefunctions are modified as follows by the interaction: (l) 2 _ (o) Hnn' En _ En + .2 E - E . n #n n n (0) H602 ¢ = ¢ + 2 ¢ . n n n'#n EEOY- EA?) n Some rules govern the interaction: (1) Orbital inter- actions are pairwise additive, (2) Energy levels repel each other, (3) The interaction strength between two levels is dependent on the overlap and inversely proportional to the separation of the energy levels, and (4) The inter- action of two orbitals will result in the mixing of their wavefunctions. The lower energy level mixes with the upper one in a bonding way, while the upper one mixes with the lower one in an antibonding manner. According to these rules, we obtain the energy levels for the ground state shown at the right side of Figure 116. Again, in order of increasing energy, the 422 /' ":0 *‘s‘ “~—H—'n'+ O 0: 90° 0 = 0 Unconjugated Conjugated Figure 116. Qualitative description of the energy levels of a typical peptide bond in the conjugated and unconjugated geometries. 423 lowest energy level is 0+, which results from NCO mixing with nN stabilizing its energy in a bonding way. The second lowest one is no, which lies in the nodal plane of the n orbitals and is unaffected by the interaction. Then comes the n which is due to the interaction of n 0’ N * with NCO and NCO. The interaction strength is given by the equation, ' * nN ‘ 1To ' nN + C1 1Tco ’ C2 1Tco' where c1 and c2 are the mixing coefficients. It has been proved that the nodal plane is between C and N, implying that c2 > c1 and hence that nN is stabilized as a conse- quence of the interaction. The highest energy level is * n_, which is due to the mixing of n with n CO 4' destabiliz- ing it in an antibonding way. From the qualitative energy levels so obtained, one can explain some of the experimental results: (1) There is an energy barrier hindering rotation of the -NR2 group out of conjugation with the -CR" =