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This is to certify that the C'3NNR STUDIES OF‘¥H€"€?§“E“?§%NS EFFECT ON HEMES Part 1 REGIOSELECTIVE ACTIVATION OF HYDROCARBONS BY HEMES Part II NUCLEAR MAGNETIC RELAXATION STUDIES OF SOME ALIPHATIC KETONWEE AND ALICYCLIC ETHERS Part III Ming-Shang Kuo has been accepted towards fulfillment of the requirements for Ph.D. degreein Chemistry 7/{Zflfib 4AM anim- professor Date 11-12-81 MS U i: an Affirmative Action/Equal Opportunity Institution 0-12771 C13 NMR STUDIES OF THE CIS & TRANS EFFECT ON HEMES Part I By Ming-Shang Kuo A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1981 II! .,,,/ /// ” Cal/v I ABSTRACT C13 NMR Studies of the Cis & Trans Effect of Hemes The following questions were addressed in the research described here: how do the porphyrin peripheral functional groups (the so-called "cis effect") and the axial ligand basicity (the so-called "trans effect") affect the electron density at the central metal? To answer this question, we used heme-ligated 13CO as a probe to measure the electron density at the central metal. The chemical shifts were recorded as we changed the electron density via different axial ligands or modification of peripheral functional groups. The results can be summarized as follows: (1) For cis effect, the dominant electron delocalization pathway is through n-overlapping as evidenced by the paramagnetic contribution to the screening tensor. (2) For trans effect, the major interaction between pyridine and CO is o-interaction as evidenced by the diamagnetic shielding. (3) For N-Me imidazole, n-bonding seems to be involved by some degree. Regioselective Activation of Hydrocarbons by Hemes The quest for the active oxene complex in cytochrome p-450 is one of the most intensely studied subjects in contemporary bioorganic and bioinorganic chemistry. We now have documented, for the first time, that such species can be obtained in model systems. Iron (III) porphy- rins reacted with 2-iodoso-m-xylene at room temperature to form a green intermediate which is capable of hydroxylating alkanes as well as the porphyrin ring itself. The fact that the green intermediate has an absorption spectrum very similar to that of Compound I of catalase suggests that the electron configurations of these active species may be the same. Magnetic susceptibility and Massbauer data support a Fe(IV)-O- structure with one electron delocalized from the d5 Fe(III) to the 6-electron oxygen atom. Using a "strapped" porphyrin, we were able to obtain the hydroxylated product, the site of hydroxylation was identi- fied unambiguously by 1H NMR spectroscopy. Nuclear Magnetic Relaxation Studies of Some Aliphatic Ketones and Alicyclic Ethers The use of NMR relaxation as a means of investigating molecu- lar dynamics in liquids has been well established. In the process of nuclear spin relaxation, molecular rotation is coupled to the nuclear spins by a number of mechanisms and, therefore, by measuring the dynami- cal behavior of the spins, it is sometimes possible to draw conclusions about molecular rotation. In general, any mechanism which gives rise to fluctuating magnetic fields at a nucleus is a possible relaxation mechanism. A number of different physical interactions have been found to be important in coupling the nuclei to the lattice and hence provid- ing a link through which energy between these two systems can be exchanged. The major objectives of this research were to investigate how . . . . l3 molecular motions affect the nuclear magnetic relaxation times of C and 170 nuclei of ketones and cyclic ethers and to gain some information about local motions and charge distributions for those molecules. In the case of carbon-l3 nuclei, the dominant mechanism usu- ally is intramolecular magnetic dipole-dipole interaction which can be separated from other mechanisms by measuring the nuclear Overhauser enhancement factor. On the other hand, oxygen-l7 nuclei are relaxed efficiently through coupling of the electric quadrupolar moment to the electric field gradients and since it is entirely an intramolecular interaction, a measurement of the relaxation time provides an excellent means of measuring the molecular correlation time, if the quadrupole coupling constant can be determined independently.~ Or, if the correla- tion time is known, T1 measurement can provide an estimate of the nuclear quadrupole coupling constant for molecules in the liquid state. We have measured spin-lattice relaxation times using the inversion- recovery method and nuclear Overhauser effect factors using the gated- decoupling method for 13C nuclei. We also measured 170 relaxation times using the progressive saturation pulse technique and line-shape analysis. Some information regarding molecular motion, such as corre- lation times, activation energies of rotation, segmental motion and ring puckering motion, were derived from the data. Nuclear quadrupole coupling constants of 170 nuclei were also estimated for some ali- phatic ketones and cyclic ethers in the liquid phase. To My Parents and My Wife. ii ACKNOWLEDGEMENT The author would like to express his appreciation to Professor Rogers and Professor Chang for their guidance and for allow- ing him the freedom to pursue two different research problems. The author also wishes to acknowledge the financial support of the Department of Chemistry, National Science Foundation and GE scholarship foundation throughout his years as a Graduate Student. iii 13 TABLE OF CONTENTS C NMR STUDIES OF THE CIS & TRANS EFFECT ON HEMES. . . . . I. A. B. II. A. B. C. D. III. A. B. C. D. IntrmuctionI I I I I I I I I I I I I I I I I I I I I Cis Effect. I I I I I I I I I I I I I I I I I I I I Trans EffeCtI I I I I I I I I I I I I I I I I I I I Experimental . . . . . . . . . . . . . . . . . . . . Preparation of 2,4-Disubstituted Porphyrin Dimethyl ESterSo I I I I I I I I I I I I I I I I I I I I I I Preparation of Iron Porphyrins. . . . . . . . . . . Preparation of 13CO-Heme Complex. . . . . . . . . . Carbon-l3 NMR Experiments . . . . . . . . . . . . . Results and Discussion. . . . . . . . . . . . . . . Results . . . . . . . . . . . . . . . . . . . . . . Theoretical Background. . . . . . . . . . . . . . . Cis Effect. . . . . . . . . . . . . . . . . . . . . Trans Effect I I I I I I I I I I I I I I I I I I I I REGIOSELECTIVE ACTIVATION OF HYDROCARBON BY HEMES . . . . . I. A. B. C. D. II. A. B. III. Introduction. I I I I I I I I I I I I I I I I I I I I Biological Oxygen Fixation Enzymes. . . . . . . . . Historical Aspects of p-450 . . . . . . . . . . . . Reaction Mechanisms and the Nature of Active Oxygen The Purpose and Approaches of this Work . . . . . . Experimental and Results . . . . . . . . . . . . . . Synthesis of Strapped Porphyrin . . . . . . . . . . Reactions Between Iodosoxylene and Iron Porphyrins; Characterization of Intermediates and Hydroxylated PrOdUCt I I I I I I I I I I I I I I I I I I I I I I DisCUSSiOnI I I I I I I I I I I I I I I I I I I I I NUCLEAR MAGNETIC RELAXATION STUDIES OF SOME ALIPHATIC KETONES AND ALICYCLIC ETHERS. . . . . . . . . . . . . . . . I. Introduction. . . . . . . . . . . . . . . . . . . . . iv 12 13 15 15 15 25 27 34 34 34 37 39 42 45 45 50 54 S9 59 TABLE OF CONTENTS (Continued) THE ORY I I I I I I I I I I I I I I I I I I I I I I I I I I. The Bloch Equations . . . . . . . . . . . . . . . II. Molecular Motions in the Liquid Phase and Time Correlation Functions. . . . . . . . . . . . . . III. NMR Relaxation Mechanisms . . . . . . . . . . . A. Dipole-Dipole Relaxation and Nuclear Overhauser B. Quadrupolar Relaxation. . . . . . . . . . . . . C. Spin-Rotation Relaxation. . . . . . . . . . . . D. Scalar Relaxation . . . . . . . . . . . . . . . B. Chemical Shift Anisotropy . . . . . . . . . . . Effect. IV. Models of Molecular Motion and Molecular Dynamics. . . . A. Diffusion Model . . . . . . . . . . . . . . . . B. Non-Diffusional Models. . . . . . . . . . . . . V. Relaxation and Fourier Transform NMR Spectroscopy A. Inversion Recovery. . . . . . . . . . . . . . . B. Progressive Saturation. . . . . . . . . . . . . C. Saturation Recovery . . . . . . . . . . . . . . EXPERIMENTAL. . . . . . . . . . . . . . . . . . . . . . I. 13C NMR Experiments . . . . . . . . . . . . . . . A. Instrumental. . . . . . . . . . . . . . . . . . B. ’I'1 Determination. . . . . . . . . . . . . . . . C. Nuclear Overhauser Effect Measurement . . . . . D. Temperature Variation . . . . . . . . . . . . . E. Sample Preparation. . . . . . . . . . . . . . . II. 170 NMR Experiments. . . . . . . . . . . . . . . A. Instrumental. . . . . . . . . . . . . . . . . . B. Lineshape Measurement . . . . . . . . . . . . . C. Sample Preparation. . . . . . . . . . . . . . . RESULTS AND DISCUSSION. . . . . . . . . . . . . . . . . I. Relaxation Studies of Carbonyls . . . . . . . . . A. Introduction. . . . . . . . . . . . . . . . . . B. Results and Discussion. . . . . . . . . . . . . II. 170 Relaxation and Nuclear Quadrupole Coupling Constants of Some Dialkyl Ketones. . . . . . . . Page 62 62 65 69 70 78 79 81 82 84 84 89 89 94 96 96 98 98 98 100 101 101 101 104 104 106 108 108 108 108 111 139 TABLE OF CONTENTS (continued) Page III. Nuclear Quadrupole Coupling Constants and the Molecular Dynamics of Ethylene Oxide, Trimethylene Oxide and Tetrahydrofuran . . . . . . . . . . . . . . . . . lSO AI IntrOductiono I I I I I I I I I I I I I I I I I I I I I I I 150 BI Resu1ts I I I I I I I I I I I I I I I I I VI I I I I I I I I 152 CI DiSCUSSiOnI I I I I I I I I I I I I I I I I I I I I I I I I 152 vi Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table Table 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. LIST OF TABLES 13C Chemical shift of CO in Heme-CO. . . . . . . Diamagnetic and paramagnetic parts of the chemical shift components. . . . . . . . . . . . Physical constants of some ketones and ethers. . 17O Linewidth (full width at half-height, error estimated to be within 5%) . . . . . . . . 13 . . . . C Spin-lattice relaxation time and nuclear Overhauser effect of carbonyl carbons. . . . . . Apparent dipolar and other relaxation rates of carbonyl carbons. . . . . . . . . . . . . . . Comparison of minimum relaxation rate temperatures for a number of ketones. . . . . . . . . . . . . Activation energies of reorientatiOn of C-H vectors, dipole moments and viscosities of dialkyl ketones. . Effective correlation times (psec) of carbons of dialkyl ketones at 30°C. . . . . . . . . . . . . Correlation times T(l,2) characterizing internal rotation of terminal methyl in n—alkanes . . . . T(l,2) Values for 3-pentanone, 4-heptanone, S’DODanone, 6‘Undecanone o o o o o o o o o a o 0 Methyl internal rotational barriers calculated from 13C dipolar relaxation rates. . . . . . . . Microviscosity factors of dialkyl ketones. . . . Spin-rotation correlation times and maximum angles of rotation of acetone. . . . . . . . . . Reduced reorientational and angular momentum correlation times for acetone. . . . . . . . . . Test of diffusion limit by the Hubbard equation. Activation energies of reorientation of some ketones Quadrupole coupling constants calculated from relaxation time studies. . . . . . . . . . . . . 170 Quadrupole coupling constants for a number 0 f C mpound S I I I I I I I I I I I I I I I I I I 3C Spin-lattice relaxation times and NOE factors for some cyclic ethers . . . . . . . . . . . . . 17O Linewidths for some cyclic ethers. . . . . . Activation energies, viscosities and dipole moments for some cyclic ethers . . . . . . . . . vii 24 102 112 113 114 116 122 124 127 127 128 130 135 136 138 141 146 148 153 153 154 LIST OF TABLES (continued) Page Table 23. Principal moments of inertia of ethylene oxide, trimethylene oxide and tetrahydrofuran . . . . . . . . . 155 Table 24. Effective correlation times of ring carbons in ethylene oxide, trimethylene oxide and tetrahydrofuran . 156 Table 25. Quadrupole coupling constants of 17O in ethylene oxide, trimethylene oxide and THE. . . . . . . . . . . . 165 viii Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 5. 6. 7. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. LIST OF FIGURES Protoporphyrin IX . . . . . . . . . . . . . . . . . Chloroprotoporphyrin IX iron (III). . . . . . . . . Trans and cis variations of electronic properties of heme complexes . . . . . . . . . .'. . . . . . . C-13 spectrum of 3-cyanopyridine-2,4-diacetyl deuteroheme dimethyl ester C-13 (90%) carbonyl. . . 3do-Orbitals. . . . . . . . . . . . . . . . . . . . 3dw-Orbitals. . . . . . . . . . . . . . . . . . . . Bonding scheme of metal-CO complex. . . . . . . . . Plot of chemical shift of 13CO vs Hammatte OR and (GI + 0R) values (cis variations) . . . . . . . Effect of substituted pyridines on trans orbitals . Plot of chemical shift of 13CO vs Hammatte OI value (trans variations). . . . . . . . . . . . . . The catalytic cycle of cytochrome p-4SO . . . . . . 'H NMR spectrum of strapped porphyrin (III) . . . . C-l3 NMR spectrum of strapped porphyrin (XVI) . . . 'H NMR spectrum of strapped porphyrin (XVI) with "a" protons decoupled . . . . . . . . . . . . . . . A: Vis. spectrum of reaction intermediate between iodosoxylene and OEP. . . . . . . . . . B: Vis. spectrum of compound I . . . . . . . . . . 'H NMR spectrum of reaction product of iodosoxylene and s trapped heme I I I I I I I I I I I I I I I I I Energy level diagram and transition probabilities for a two-spin system without J coupling. . . . . . (a) Nuclear spin magnetization in the rotating frame . . . . . . . . . . . . . . . . . . . . . (b) Flip angle a du to H1. . . . . . . . . . . . . (c) A 90° flip. . . . . . . . . . . . . . . . . . . (d) Signal in time domain (on resonance). . . . . . (e) Signal in time domain (off resonance) . . . . . Inversion-recovery method for spin-lattice relaxation times. . . . . . . . . . . . . . . . . . Spin-echo method for spin-lattice relaxation times. Nuclear Overhauser enhancement of the coupled spectra by the gating technique . . . . . . . . . . ix 14 17 17 18 26 29 31 40 47 48 49 51 51 53 72 91 91 91 91 91 95 97 103 LIST OF FIGURES (continued) Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. Design of NMR tubes for measurement of relaxation times. . . . . . . . . . . . . . . . . . Magnetization as function of time . . . . . . . . . PlOt of ln RDD’ Plot of ln ' , 1n Rt and In Av vs l/T for 3-pentanone . . . . ln Rt and ln Av vs l/T for acetone. vs l/T vs l/T vs l/T Plot of ln R , 1n Rt and In (Av) for 4-heptan0ne o o o o o o o o 0 Plot of In RD , ln R and ln (Av) D for S-nonanonEo o o o o o o o o 0 Plot of In R , In R and In (Av) D3 t for 6-Undecan n8. 0 o o o o o o 0 1/2 1/2 1/2 * k . Plot of 26 versus rj for the extended difquion made 1 I I I I I I I I I I I I I I I I I I I I I I I Plot of In R and In Av vs l/T for oxirane, oxetane and 98F . . . . . . . . . . . . . . . . . . Plot of T1 vs‘TA as a function of TC0 . . . . . . . Page 103 107 117 118 119 120 121 137 161 163 C13 NMR STUDIES OF THE CIS & TRANS EFFECT OF HEMES I. Introduction Iron porphyrins serve as prosthetic groups for an important class of proteins and enzymes known collectively as heme proteins or hemoproteins. These proteins can exhibit distinctly different func- tions which include reversible oxygen binding for transport (hemo- globins) or storage (myoglobins) of oxygen, oxygen reduction to the level of water (cytochrome C oxidase), oxygen activation (cytochrome p-450), electron transfer (cytochrome b and c), and hydrogen peroxide utilization (catalase and peroxidase). The prefixes hemes and hemo are derived from iron (II) porphyrin and hemin for iron (III) porphyrin. There are three particularly important hemes which may be called heme a, heme b, and heme c since they are associated with the a, b, and c type cytochromes, respectively. Among them, heme b is the most extensively studied natural heme, whose structure (Figure 1) has been known for more than 30 years. It is readily isolated from the hemoglobin of mammalian blood, and is also present in other heme pro- teins including myoglobins, cytochrome p-4SO, catalases, peroxidases as well as b-type cytochromes. The porphyrin ligand of heme b is Dr0toporphyrin IX; heme b is thus frequently called protoporphyrin IX iron (II), protoheme, or simply "heme". Similarly, the oxidized or iron (III) form is called hemin or protohemin and, with a chloride counter ion. hemin chloride, protohemin chloride or Chloroprotoporphyrin IX iron (III) (Figure 2)- ItII=n:II2 |"ll‘, II ,I: VII-’4‘”: "JC CII. ""2 “UUCCIM (ll-.ICUUH Figure l. Protoporphyrin IX <9 CH=CH1 CH3 .1 CH CH=CH2 C19 CH CH3 H; i H2 H2 (EH2 L COZH COzH .. Figure 2. Chloroprotoporphyrin IX iron (III) The "IX" refers to the specific arrangement of substituent groups on the porphyrin ring. A. Cis Effect Natural hemes have been modified at the carboxylic acid (e.g., by esterification) and at other groups on the porphyrin ring as well as by removal of iron to give metal-free porphyrins or by metal substitu- tion.1 Such modifications have been useful in structure elucidation, in altering solubility and aggregation characteristics, and in general studies of structure-function relationships. The availability of these materials has permitted a more systematic evaluation of substituent effects than would be possible if studies were restricted to the limited number of natural porphyrins. Differences in substituents on the periphery of the prophyrin ring of the type found among natural porphyrins have been shown to cause significant changes in the properties of iron and other metal porphyrins. ’3 The electron-withdrawing Or electron-donating character of a substituent is effectively transmitted across the porphyrin to influence the basicity of the central nitrOgens which in turn affects the properties of the metal and exerts a cis effect upon axial ligands. The basicity of the central nitrogens can be evaluated with metal-free porphyrins in terms of equilibria for protonation of the imine-type nitrogen of the neutral species to form the "acid salt". The determination cf thermodynamically significant intrinsic equilibrium constants for the successive protonation steps (K3 and K4) for a series of differently substituted porphyrins has been complicated by aggregation, limited solubility, and field effects in aqueous media. However, consistent relative basicities have been observed in acetic acid, in chloroform, and in aqueous detergent solution.4 The more- effectivity electron-withdrawing the substituents, the smaller is the pK3 value. For example, the basicity of the pyrrole nitrogen in 2,4- disubstitued deuteroporphyrin dimethyl esters was measured by pK3 values of 5.8 to 3.3 in going from mesoporphyrin (2,4-diethyl) to 2,4- diacetyldeuteroporphyrin, with corresponding N-H frequency shifts from 3316.8 to 3310.7 cm'l. One of the classical methods of probing the electronic environment of heme in hemoproteins is by the study of the formation of complexes of small ligands such as carbon monoxide, molecular oxygen, or nitrous oxide. In 1925, Hill reported evidence that pyridine hemo- chromogens contain two pyridine ligands and that one pyridine ligand can be reversibly replaced with one CO ligand; the relative amount of bispyridino and carbonyl species in a given solution are dependent on the relative concentrations of pyridine and CO. The extent of conver- sion to the carbonyl complex in pyridine-benzene solutions was readily followed via visible spectra.6 Carbon monoxide was bound less effec- tively, as the electron-withdrawing character of the 2,4-substituents of pyridine increased as evidenced by the vCO values: 1973.0 (2,4- diethydeteroheme), 1975.1 (deuteroheme), 1976.6 (protoheme) and 1978.7 <3!!!“1 (2,4-diacetyldeuteroheme) in bromofonm solution. In principle, C'-0 stretching frequencies in CO complexes can be expected to demonstrate the relative degree of triple-bond character in the C-0 bond; the larger v the greater the triple-bond character. As the CO’ triple-bond character of CO increases, a concomitant weakening of the metal-carbon bond can be expected. 13C NMR has provided another method for probing the electronic environment of CO-heme. This method, for example, has shown difference among the heme environments of several heme protein-CO complexes, including sperm whale myoglobin8 and the a and 8 chain of various species of hemoglobin.9 Recently, chemical shift of carbonyl complexes of modified heme in reconstituted hemoglobin and myoglobin have been re- ported.10 However, due to steric perturbations induced by the globin allosteric behavior,11 the results cannot be correlated directly with electron sharing tendencies of different substituents at the periphery of the porphyrin ring. Clearly, a 13C NMR study of modified hemes without globin can provide a better picture of the electronic effect caused by the alternation of functional grOups on the ring.‘ B. Trans Effect As mentioned in previous section, the structure of the por- phyrin can influence the axial ligation. It is also true that the axial ligand can affect the properties of hemes and the stability of other axial ligands. This mutual interaction between the two coordination sites on Opposite sides of the metal, known as the "trans effect" is of particular importance for heme proteins. In fact the binding of dioxygen to the pentacoordinate species A_or B, an essential step in biological oxygen transport and consumption, is kinetically and thermo- CIYnamically influenced by the trans ligand,12 which in most hemoproteins is a histidine or a sulfur moiety. proIeIn protein N I / -—-‘ / I . F .----F___fe———a---- III-I-I-F——-Fc S l __s- F __—— ——— —_ I3 ——-———F: c— l' I. L: C0, N0, 02, CH3CN, CH3NC Since the axial ligands are o-bonded with the metal dZZ orbital and the ligand n-electrons interact with the dx2 and dyz orbitals. It is not surprising that the binding of small ligands are very sensitive to the trans ligand. Thus, a mixed hemochrome in which one ligand is a base-like pyridine and the other ligand a w-acceptor is much more stable than the complex in which the fifth and sixth ligands are identical.13 Furthermore, a more basic pyridine in the fifth position increases the affinity of heme for CO over that of H20- ligated heme by an order of manitude.14 In hemoglobin, the fifth ligand which is trans to O2 is part of the polypeptide chain. The only proteins whose fifth ligand may not be an imidazole ring are two gene- tically abnormal hemoglobins M Iwate and MHyde Park, in both cases histidines of the a and B chains are replaced by less basic tyrosines, respectively. The abnormal subunits do not reversibly bind oxygen and are oxidized instead. However, these effects cannot be completely attributed to the trans effect, since the replacement of histine by the bulkier tyrosine will influence the structure of the protein. Caughey7 and coworkers have studied the effect of basicity of the pyridine on C0 stretching frequencies of 4-substituted pyridine- 2,4-diacetyl deuteroheme dimethylester-carbonyl complexes. Changing the 4-substituent from cayno to amino group and thus increasing.the basicity l to 1971.1 cm-1. The decrease of pyridine decreased vCO from 1988.5 cm- in ”CO and the increase in affinity with the more basic trans ligand were interpreted in terms of the partial double bond character of the bond between iron and the carbon. I - I x / \N-Fe-C‘z'o :.x/ N-FO‘GO _ — X = CN, H, NHZ The formation of the double bond involves the overlap of electrons from the dx2 and dyz orbitals with n orbitals of the sixth ligand. The streng- thening of Fe-C bond weakens the C-0 bond thereby lowering v Trans co,’ effect on C-O stretching frequencies have also been observed in some Ru 15,16 porphyrins. For example, changing pyridine to t-butyl pyridine in Ru(TPP)CO(py) increased C-O stretching frequency from 1943 cm-1 to 1965 cm-1, a result which cannot be explained on the sole basis of n-overlapping between metal and ligand. In view of these seemingly contradictory results of infrared studies and the fact that the C-0 stretching frequency does not always reflect bond order, a 13C NMR study of trans effect on the carbonyl heme complex could perhaps elucidate the electronic environment around the heme. II. Experimental The general approach of this work was to systhesize modified heme (cis variations) which then were complexed with C-l3 enriched CO using various bases as the axial ligand (trans variations). Figure 3 illustrates the approach. X T RANS VAR, CIS VAR/'7 ERIK-u . MK '“,9§: 1’ I", 0 ( CIIJ—Cf’j?c= =-==C.‘l-—.§jc>c\c,42-'CH{\C=0 aim—C /C O‘CH5?C\IC/ CHZ‘CN CH, C CH, 2‘C'0 (D ‘itu Figure 3. Trans and dis variations of electronic properties of heme complexes 13C NMR spectrum was taken for each heme with different bases.‘ A. Preparation of 2,4-Disubstituted Porphyrin Dimethyl Esters (l) Protoporphyrin Dimethyl Ester crust", Clla II I“. tuna"; CII3 "gr gunner": ITII2I‘nIIt , ’5 Twenty grams Hemin (Sigma) was dissolved in a mixture of 50 ml pyridine and 200 ml chloroform by stirring at room temperature for 30 minutes. Eight hundred ml chloroform, 160 grams anhydrous ferrous sulfate, and 1.1 liters of methanol, were then added and HCl gas was rapidly passed thrOugh the solution until iron removal was complete. After completion of the reaction, the solution was extracted three times with 3 liters of water, twice with 2 liters 3% NH OH, and three 4 more times with 2 liters water. The chloroform solution was then dried over anhydrous sodium sulfate, filtered and evaporated to dryness. The dry residue was dissolved in minimal chloroform and applied to a 450 gram alumina column. The column was rapidly eluted with chloroform. The fractions containing protoporphyrin dimethyl ester were combined, taken to dryness and crystallized from chloroform-methanol. Yield: 10 grams. Visible Spectrum: Amax (nm) 407 505 541 575 603 630 5 171 1422 116 75 2.0 5.4 (2) Deuteroporphyrin Dimethyl Ester l'_|l2 CII‘ IIJ" (Ill i I'm : :- H'com‘rll: Lllgc‘Im (III, Five grams of hemin and 15 grams of resorcinol were mixed together and placed in a 250 ml round bottom flask. The flask was kept under an air condenser in an oil bath at 140°-lSO°C for 45 minutes. After cooling to room temperature, the mixture was triturated with ether and the solid was filtered off and washed with ether until colorless. 10 The crude hemin was air dried. The procedures of removal of iron and esterification are same as those protohemin (see (1)). The dimethyl ester was then purified through silica gel column eluted by chloroform. The elute fraction at boiling point was treated with hot methanol and cooled to give crystals. Yield: 3 grams. Visible Spectrum: kmax (nm) 399.5 497 530 566 593 621 a 175 13.4 10.1 8.2 2.2 4.9 (3) 2,4-Diacetyldeuteroporphyrin Dimethyl Ester coon} L‘llJ II:,I‘. CI“ CH3 "'JC cu: ”'2 ”we": tug... «In, Two grams crude deuterohemin was dissolved in 400 ml acetic anhydride in a 1 liter round bottom flask equipped with magnetic stir- ring bar. The temperature of the solution was brought to 0°C using an ice-water bath. Twenty—eight ml of anhydrous SnCl4 were then carefully added with stirring and the reaction was allowed to proceed for 7 minutes with the flask immersed in the ice-water bath. At the end of the reaction time the solution was slowly and carefully poured into 400 m1 of an ice-0.1 N HCl solution. The solution was allowed to stir for 2 hours to destroy the acetic anhydride. The crude diacetyl deuterohemin was isolated by suction filtration. The method of purifi- cation is same as protOporphyrin, i.e., iron removal, esterification and column chromatography. 11 Yield: 1.5 grams diacetylporphyrin dimethyl ester and 0.5 gram of mixture of 2- and 4-monoacetyl deuteroporphyrin dimethyl ester. Visible Spectrum:_ Amax (nm) 424.5 517 552 587 640 5 144 13.3 7.3 6.1 (3.3 (4) MeSOporphyrin Dimethyl Ester “mg I. ll . II .I: (l-I‘U'i3 (ill , ll'J'f ml. "'2 . Rfmuwu: £"y3w.p, Wet palladium oxide (0.7 gram) and protohemin chloride (4 grams) in 902 formic acid (0.3 liter) were maintained at 94-98°C for about 1 hour while hydrOgen was passed through the mixture. The cata- lyst was recovered by filtration and the filtrate added to 3% aqueous ammonium acetate (1.2 liters). The precipitate was collected, washed with water, and dissolved in 22 aqueous ammonia (170 m1) followed by the addition of 32 aqueous disodium tartarate (30 ml). The precipitate was dissolved in 400 ml of methanol-chloroform (1:1) and solution saturated with dry HCl for 30 minutes, followed by successive extrac- tions with water (300 ml, 3 times), with 10% aqueous ammonia (300 ml, twice), and with water (300 m1, twice). The residue from evaporation of the washed chloroform solution was chromatographed on alumina with 1,2-dichloroethane. Crystallization from l,2-dichloroethane—methanol gave 2.8 grams. Visible Spectrum: xmax (nm) 400 499 533 567 594 621 e 166 13.6 9.6 6.5 1.7 4.9 12 B. Preparation of Iron Porphyrins In a pear shaped flask equipped with a gas inlet tube 0.1 m mole of the purified porphyrin dimethyl ester were dissolved in 1 ml of pyridine and diluted with 20 ml of glacial acetic acid. A stream of argon was passed into the solution from the center tube while the mix- ture was placed in an oil bath preheated to 80°C, 1 m1 of a saturated aqueous solution of ferrous sulfate was added to the mixture using a pipet, through the gas outlet side arm. The temperature of the bath was raised to 90°C and the reaction was kept at this temperature for 10 minutes. The bubbling of gas was continued throughout the reaction. The flask was then removed from the heating bath, the argon bubbling stopped, and the mixture cooled to ambient temperature. A stream of air was passed into the solution briefly to allow autooxidation of the unstable iron (II) porphyrin. The mixture was partitioned between 60 m1 of H20 and 60 ml of chloroform in a separatory funnel. The organic phase was separated and washed first with 60 m1 of 0.2 N HCl and then with water. The chloroform layer was separated and dried by filtering through a small filter paper. Yield: Quantitative. C. Preparation of 13CO-Heme Complex All heme-CO complex were prepared directly in NMR tubes equipped with septum joint at the top. The solution of 0.005 M hemin in 2 ml CDCl3 (1% TMB) was transferred into NMR tubes, a few milli- grams of N-methylimidazole (or other pyridine derivatives) was then added into the solution. The NMR tube was then capped with silicone rubber septum and degassed thoroughly by bubbling dry argon gas. The hemin solution was reduced to heme by injecting degassed and aqueous 13 Na25204 (in phosphate buffer pH W7) through silicone septum. The reduc- tion was completed after vigorous shaking of the NMR tube and was con- firmed by typical hemechrome spectra in visible range. The 90% enriched 13CO (Stohler Isotope Chemicals, Mass.) was then transferred into the NMR tube by gas-tight syringe. The aqueous layer was then removed by syringe. The formation of CO-heme-base complex was again confirmed by absorption spectra. The conversion was essentially quantitative. D. Carbon-13 NMR Experiments 13C NMR spectra were taken on Varian Associates CFT-ZO spectrometers, operated at 20 MHz. Temperatures were regulated by the heater-sensor and V-4360 variable temperature controller and the temper- ature reading was measured by a capper-constantan thermocouple. All 3C spectra were taken at -15°C with internal deuterium lock. 8K computer memory was used to cover 4500 Hz spectrum width with no trans- mitter offset. Pulse angle was set at 4 usec (~15 degrees tip angle). About 20,000 transients were collected with total sampling time of 6 hours. The free induction decay was then exponentially weighted and fourier transformed. Chemical shift values were referenced to TMS both in Hz and PPM with digital printout. Figure 4 shows one of the typical spectra obtained under conditions stated above. 14 3 8 :3 o o 9 8 u- MMM MM’MMWLAJNNMWi‘I‘mew’mmwwmw[M 1 ‘ L l J i ' . L J 2100 PPM l 100 O C-13 Spectrum of 3-cyanopyridine-2,4-diacetyl Figure 4. deuteroheme dimethyl ester C-13 (90%) carbonyl 15 III. Results and Discussion A. Results 13C chemical shifts of carbonyl-heme complex are tabulated below. Table l. 13C Chemical shift of CO in Heme-CO <\\\\E:2f Modi- . ication Ethyl Vinyl H Acetyl x <1me °R -0.1 -0.01 0 +0.15 4-NH2 -.65 4110.0 4100.0 4100.5 4088.0 3-NH2 -.14 4118.5 4108.0 4107.5 4091.5 H - 0 4121.0 4109.0 4109.0 4092.5 4-CN +.55 4129.5 4115.0 4116.5 4097.0 3-CN +.64 4131.0 4116.0 4117.5 4098.5 N-Me Imidaz. 4113.0 4100.5 4095.5 4081.0 (All values are in Hz downfield from internal TMS.Variation: 30.5 Hz.Field strength: 20 MHz) Reading across the table gives the result Of cis effect, reading down gives the result of trans effect. B. Theoretical Background (1) Metal-Ligand Bonding in Iron-Porphyrins Porphyrins can be regarded as tetracoordination ligands which impose a near square-planar configuration on their metal chelates. In the iron chelates, two further ligands are readily coordinated to metal in the z-direction (perpendicular to the xy porphyrin plane), giving 16 essentially octahedral complexes such as the pyridine hemochromes or distorted octahedral such as oxy- or carboxy-iron hemes. Overlap of metal hybrid orbitals with ligand orbitals may thus give rise to six coordinate o-bonds, four in the plane of the porphyrin and two in a direction perpendicular to it. A The five orbitals of the 3d sub-shell are used in this way: the 3dz2 and 3dx2-y2 orbitals (symmetry type eg) are incorporated in metal hybrids which are involved in the metal-ligand-n-bonds, (Figure 5). The 3dxy orbitals of the 3d sub-shell is occupied but, by virtue of its symmetry, does not take part in bonding, while the d?! orbitals (3dxy and 3dyz) are of the correct symmetry to combine with pfl-orbitals of porphyrin nitrOgen atoms and with the w-orbitals of perpendicular ligands as well (Figure 6). The latter are available, for example, in ligands like pyridine, imidazole, carbon monoxide, or molecular oxygen. In such a case the n-systems of the ligands and the porphyrin become linked via the 3dxz and 3dyz orbitals of the metal. Metal-ligand bonding of this type is expected to be most important when the dxz and dyz orbitals of the free metal ion are filled: it leads to a flow of electron density from the metal if one of the axial ligands is a good W-acceptor like CO. The bonding between CO and transition metal at low oxidation state is believed to involve a o-bond resulting from donation of the lone pair electron on carbon to the metal and aTr-bond due to the back-donation of electrons from the filled non-bonding d orbitals on the metal to the n antibonding orbitals of CO. This is illustrated in Figure 7. Figure 5. 3do-Orbitals Figure 6. 3dn-0rbitals 18 I. ©M® + _.CsO;———> MWC= O ‘49 Q 9 Q. CEO. ——>4M IM\ 6 E (:7 Figure 7. Bonding scheme of metal-CO complex The n-bond not only has the effect of furnishing an additional bond but also increases the electron density on carbon, which then strengthens itsci-bond formation. This in turn increases the electron density on the metal and strengthens its n-bond formation. The net effect of this mutual reinforcement, or synergistic interactions between the two types of bonding, probably accounts for the major part of the M-C bond strength. Thus, n-backbonding mechanism decreases the electron population along the C0 axis and increases the electron population per- pendicular to this axis. The degree of'n-backbonding depends on the availability of electrons on the metal which can be affected by func- tional groups on the periphery of porphyrin ring and the nature of the other axial ligand. The bonding between metal and nitrogen bases (pyridine, imidazole, etc.) can be best understood by the donor/acceptor (of lone pair electrons) concept. In modern usage, a Lewis acid is defined as any substance capable of accepting electron density and a Lewis base as any substance capable of donating electron density. A Lewis acid-base interaction requires coordination of the two so that the bonding electron density 19 is shared (via electrostatic and covalent mechanism) by both the acid (acceptor) and the base (donor). In the past, it was commonly assumed that the factors governing the binding of a proton to the ligand were the same as those governing formation of the metal-ligand -bond. If the result were not parallel to the pK values, -backbonding usually b were used to explain the discrepancies. To quantify the ligands acid- base strength, Drago proposed17 a double—scale equation to correlate enthalpies of adduct formation: -AH = EAEB + CACB (1) The subscripts A and B indicate acceptor and donor, respec- tively, while E and C are two empirically derived parameters assigned to each. The merit of this double-scale proposal is to expand our ideas of acid-base interaction to allow for at leaSt two properties of each acid and base that are important in determining the affinity of each for a species of opposite type. Whatever these two properties are, the combination of acid and base that achieves the best mutual matching of those properties will be the combination yielding the strongest adduct. Both Klopman and Pearson18 have pointed out, "hard- ness" and "softness" are related to the C/E ratios. So, for our purpose, C/E scale will be used to indicate the ability of bases to interact with metals. (2) Theories of Chemical Shift of 13CO If we consider a molecule with a fixed nuclear configuration and apply a uniform magnetic field H in any direction, the secondary field H' due to the induced currents is not necessarily parallel to H at any nucleus. In other words, the relation between H' and H should be written:19 20 H’ = «IE (2) Where 3 is a second-rank tensor characteristic of the position of the nucleus in the molecule. In general, only when the applied field is along one of the principle axes of this tensor will the secondary field be in the same direction. In practice, however, the position of the nuclear resonance signal in liquids is determined by the mean com- ponent of H' along the direction ofIH averaged over many rotations; for molecules having rapid rotation (compared with any signal width due to anisotropy of the screening tensor). If we carry out this averaging, the tensor 3 can be replaced by a scalar o which is the mean of the three principal components: 1 o = 3-(0 + o + o ) (3) Although it is not directly measured in a liquid spectrum, it will be seen later that significant anisotropy of o‘is expected on theoretical grounds for a number of molecules. The chemical shift of 13C in CS2 is an example. The chemical shift tensor 0 is usually represented20 as the p . . d . . sum of a diamagnetic part 0 and a paramagnetic part 0 , i.e., o=0d+op <4) The diamagnetic term Cd is contribution to the secondary magnetic field at nucleus due to the diamagnetic Langevin-type currents.21’22 21 2 2 2 2 d _ e fix +y _ e ‘l_ 2 2 022 — 2 f 3 pdt- 2<0 It 3(xi'iy'1)|0> 2mc r 2mc 1 ri (5) 2 2 2 2 + 0 d=--(E-— fu— Ddt = e <0 |2L(x.2+z.2)| 0> yy 2 3 2 . 3 1 l 2mc r 2mc i ri (For molecule posses axial symmetry, Oxx = ny, assuming 2 axis is the axial axis.) Where p is the electron density at a distance r from the nucleus. For an atom in a molecule the induced currents cannot circu- late freely because of the hindering effects of the electric field due to the other atoms. Consequently, the secondary magnetic field is reduced by a paramagnetic (negative) contribution described by Up. This term gives the reduction in shielding due to the mixing of the ground state with the excited states. The mathematical expression for P o is complicated. By using average excitation theory, Pople23 obtained the following equation: 2 2 P _ _ e«fi -l -3 2 (ON )zz - ZmZCZ AB 2p (QNN)zz + B¢N (QNB)zz . (6) where ( ) -2-2(P (°)P -1) (P (°)P -1) +2P (O) QNN zz — xN XN yN yN xNyN (o) (0) (0) (0) (QNB)zz = ‘ ZPXNXE PyNYB + ZPXNYB PYNXB Pxx, Pyy, ny are the elements of the charge density and the bond order matrix in the molecular orbital theory of the unperturbed orbital. AB is the average electronic excitation energy. 22 As pointed out by Karplus and Pople,23 a dependence of the shift on the local electron density is manifested in the factor.2p and in the terms in PxPx, PyPy, PxPy, etc. Both the factor2p and the term (QNN) depend primarily on the local electron density at zz atom N. As the total electronic charge on the atom N increases, the orbital expand and.2p decreases. The terms involving QNB with N ¢ B represent the multiple- bond contribution. Pople23 predicted that this multiple-bond term plays an important role in determining the general pattern of carbon chemical shifts. Variations in the n-bond order terms alone have been utilized by Maciel24 to explain changes in shielding observed for carbonyl shifts of organic ketones and aldehydes. Gansow25 used this term to explain the downfield shift of carbonyl resonance in changing x from CN to alkyl for complex (us-CSH5)Fe (C0)2x. The linear correlation observed between the 13C chemical shift and carbonyl stretching force constants was taken to be strong support for the contention that vari- ations in'n backbonding causes the observed change in 6C0' A recent analysis of the 13C chemical shift tensor in CO, Ni(CO)4, and Fe(CO)S reported by Mahnke,26 Sheline, and Spiess seems to have produced clear and consistent evidence concerning the origin of carbonyl chemical shifts. Using theoretical estimates, they have calculated values, collected in Table 2, for the diamagnetic screening of C0, Ni(CO)4, Fe(CO)S and determined that the small changes in screening between CO, Ni(CO)4 could be explained by this term. . . . . l3 . However, u31ng spin-rotation constants determined from C relaxation- studies, the paramagnetic screening term was calculated for Fe(CO)5, 23 and only its increased size, due to M-CO bonding, can explain the observed deshielded 5 shift of that molecule. Furthermore, it is C0 observed that the screening tensor can be considered axial so that l . . Gav =.§ (q. + 201). It was found op (the paramagnetic screening com- ponent parallel to the axial axis) varied little, (Up of free C0 is zero by virtue of commutation between angular momentum operator and Hamiltonian), but that sizable changes in up were found for Fe(C0)5. For the purpose of this study, chemical shift theory of CO can be summarized as below: (a) In liquids, screening tensor can be separated into 3 scalar quantities: oxx’ Oyy’ 022: If axial symmetry exists, Oxx = Oyy = Cl, 022 = q‘. (z is the axis of axial symmetry.) (b) Each of the component of screening tensor can be viewed as a sum of diamagnetic and paramagnetic contribution, inherently, they have opposite signs. (See Equation 5 and Equation 6) (c) For diamagnetic screening, electron density should cause shielding, hence, high field shift. For paramagnetic screening, the opposite is true. In the case of n-backbonding, the downfield shift seemed to be caused by the increased paramagnetic screening in perpen- dicular direction and the synergistic decreased shielding in the parallel direction. 24 .Am.ommvovm.mqmv pom newumw>wonnm cm mw mfine .oo :o mtOwumasoamo mom scum nonwmuno who: mmmonuuwomo cw mwaam>m m.s~- q.kH- H.mMI o.ou m.e neaagwwo nAq.~mMI.msm-V 22m.msmI.e.mmm-v nAe.HomI.m.mmm-v BAH.~mm-.k.m~mIV m.m~m- Henna a6 Am.m~mv efla.emm.m.w4mv nAH.mNm.~.mev nae.emm.~.mamv BAH.e~m.e.kaV N «.mmm Heaag>mo m.eeHI «.mma- m.HmH- k.emfl- m.o~H- mega“ 6 oflm.e~m-.mflm-v nAe.mHm-.a.GOm-v nfim.mmm-.m.~NmIv nak.mmsa.m.mwsIv m.squ manages NAs.~mmv afim.mmm.m.msmv nAm.mmm.m.mqu nfim.mmm.m.mqmv nAm.6mm.m.mqu m.amm manages NAm.Nk~v m.mm~ o.wm~ ~.wm~ m.km~ e.km~ meaag 6 o a o a o a o a o manages NAm.-~v m.wm~ e.mm~ ~.mm~ m.em~ 6.5mm manages new: Hmououmsam Hmox< snoovmz oo mfioovmm mucwconeoo umwnm HmowEoco 65» mo momma owuocmmempmn new owumcmmsdwo .N wanna 25 C. Cis Effect Table 1 shows clearly that 5 decreases as the peripheral C0 functional group changed from ethyl (electron donating group) to acetyl ' (electron with drawing group) in all six experiments with different bases. The explanation of this change is based on the following scheme. (9%) FY The dxz orbital of Fe overlaps with CO and porphyrin n orbitals. As the porphinato ligand becomes more basic, electron density of the metal ion will be higher and more n-electrons of the metal will flow to the n-acceptor ligand CO. Since the alternation of electron density happens mainly on the x-y plane, and the observed change is downfield shift, the components affected most for the screen- ing tensor should be op. 26 If the above indicated pathway for electron density is correct, it can be predicted that those peripheral functional groups capable of conjugating with porphyrin orbitals will exert maximum effect. In other words, it is a resonance effect. Indeed, when 6C0 are plotted vs. UR (Hammatte value for resonance), a linear correlation is obtained (Figure 8). 413° 1- ‘ r 0 Hz 4100 ' a 4080 ' 6 ' 3 L .5 A" ' Py CN C),I :Ily D . : PYNH2 Figure 8. Plot of chemical shift of 13CO vs. Hammatte OR and (CI + 0R) values (cis variations) The open circles, (O , D , A) are the points would be if (oRsoI) were used instead of OR (UI is Hammatte value for inductive effect). As it can be seen in Figure 7 that o correlates poorly with C0 (OR+OI), indicating that the inductive mechanism is not the primary pathway. This resonance effect seems to be able to explain that the replacement of an ethyl by an acetyl causes a marked decrease in fre- quencies of absorption maxima whereas the replacement of ethyl by 27 bromo results in a comparable change in basicity but only slight shift of wavelengths of absorption maxima27 (bromo has much less w-inter- action with heme than that of acetyl). Similarly, introduction of nitro groups at the 2 and 4 positions of deuteroporphyrins result in a much less basic porphyrin but only small wavelength shift.28 Another interesting feature of Figure 7 is that the 3-cyano pyridine set gives the steepest slope, probably as a result of that 3-cyano pyridine is the least basic ligand among substituted pyridines and the depletion of electron density from the metal causes the CO to be very sensitive to other variations. D. Trans Effect Reading down the Table 1 from 4-aminopyridine to 3-cyano- pyridine, it is found that the 6 increases (downfield shifted) as CO the basicities of substituted pyridines decrease. This result obviously cannot be explained on the ground of n-overlapping alone as that will predict an opposite trend for OCO. There are two existing theories to explain the kinetic behavior of ligands to a trans activating group: the electrostatic theory of Grinberg, and the fl-bonding theory of Chatt and Orgel. Both theories can be rationalized by M.0. theory; the n-bonding theory can be restated in the context of the M.0. theory and referred to as the 1T-trans effect, while the electrostatic theory can be referred to as the G-trans effect. It should be remembered that the trans effect is defined as an influence on the rate of reaction. Since reaction rates are related to differences in activation energies between reactants and activated complexes, it follows that both must be conSidered in theories of the trans effect. The Grinberg's theory stresses the 28 importance of the ground state contribution to the rates of reaction, whereas the fl-bonding theory is primarily concerned with the transition state, a phenomenon not related to our NMR studies. We will therefore use electrostatic or o-trans effect to explain the results. According to M.O. theory, if the two trans ligands share the same orbital (px or py on square planar, and dZZ in octahedral com- plexes), it follows that a strong o-bonding ligand will take the larger share of the bonding M.O., leaving a much smaller share for the trans ligand. Another way to look at it is that a good U-covalent ligand will put a great deal of negative charge in the d22 orbital of the metal. This in turn will repel the U electrons of any ligand in the trans position which must also use the same orbital. In other words, the ligand trans to a good O-donor will find a lot of electron density around itself. In our cases, the carbonyl trans to 4—aminopyridine (most basic) will have the highest electron density in O orbitals. Figure 9 pictorically depicts the situation. 29 :02 1:1 ,9 O. A <3 O o ~ :0 In I'I u; ( N l dQ \ x . edonohng e“ withdrawing Figure 9. Effect of substituted pyridines on trans orbitals 30 Since the paramagnetic component along the parallel direction of the axially symmetric carbonyl complexes vanishes, the altered electron density along o-bond of CO will primarily affect the screening tensor of chemical shift through diamagnetic current. As a result, more (less) shielding will cause upfield shift (downfield shift). For C-l3 chemical shift, paramagnetic contribution usually dominates over diamagnetic contribution.20 This is a very rare case where diamagnetic current dominates. The fact that 6C0 correlates linearly with Hammatte a para- meters (Figure 10) provides another evidence for 0 interaction. It is commonly believed that cyano group withdraw electron density primarily through induction and amino group through resonance. If they could cause different degree of w-overlapping between pyridine and the metal, the correlation would not be linear, furthermore, the linear relation- ship exists for meta- and para- substituted pyridines, a fact can only be explained by the o-basicities of pyridine. Another consequence of the o-electron repelling interaction is that 6C0 of the heme complexes with richer electron density will be more sensitive to the variations of basicities of pyridines. Indeed, for mesoheme complex, 6 changes 21 Hz on going from a-amino to 3- CO cyano-pyridine; while 6 of 2,4-diacetylheme complex changed only CO 10 Hz. In order to interpret the result of N-methyl imidazole-heme- CO complex, we have to use some sort of scale to indicate the basicity difference between imidazole and pyridine. As mentioned before, Drago's C/E scale probably is the most reflective index of basicities. Using that system, N-Me imidazole has a scale of 9.59 as opposed to 31 TRANS EFFECT Hz, 4120 \ 410.. -..T o S O A ‘CHZCH3 o = Pl a -.cocn3 Figure 10. Plot of chemical shift of 13CO vs. Hammatte value . . I (trans variations). 32 5.49 of pyridine. To give some idea of this scale system, some other . . 2 nitrogen base's C/E value are listed below. 9 Compound C/E < N 18.75 Me3N 14.28 Et3N 11.19 EtZNH 10.20 <’ l 9.59 I Me < NH 9.23 H3C O N 6.88 <0}! 5.49 MeNH2 4.52 NH3 2.54 As it is readily seen, N-Me imidazole is considered much more basic than piperidine, while pyridine is somewhat better than methylamine. Unfortunately, the C/E ratio is not available for 4- aminopyridine which has very close 6CO values as those of N-Me imidazole. No matter what scale is used, 6 of N-Me imidazole cannot CO be fitted linearly with pyridine. As shown in Table l, for mesoheme complex, 6 (N-Me imidazole) is larger than 6 0 (a-aminopyridine) CO C but is smaller in acetylheme complex. Since the linear relationship was taken as evidence of O-bonding interaction, this non-linear 33 behavior of N—Me imidazole probably indicates this ligand's fl-inter- action ability which has been used to explain many anomalous kinetic and thermodynamic phenomena.3O Careful examination of Table 1 reveals that for N-Me imidazole system, w-electron transfers most into CO in mesoheme and least in acetylheme. Since electron donating group usually raises the energy level, so the mesoheme overlaps best with the low-lying orbital of w-donor. In conclusion, the results have been interpreted in terms of chemical shift theory and bonding between ligands and the metal. For cis effect, the dominant electron delocalization pathway is through n-overlapping as evidenced by the paramagnetic contribution to the screening tensor. For trans effect, the major interaction between pyridine and CO is o-interacts as evidenced by the diamagnetic shielding. For N-Me imidazole, n-bonding seems to be involved by some degree. REGIOSELECTIVE ACTIVATION OF HYDROCARBON BY HEMES Part II By Ming-Shang Kuo A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY 1981 REGIOSELECTIVE ACTIVATION OF HYDROCARBON BY HEMES I. Introduction A. Biological Oxygen Fixation Enzymes Oxygen, one of the most abundant elements on earth and being directly or indirectly essential for all forms of life, has been the subject of intensive studies by chemists, biochemists and physiologists ever since Lavoiser initiated the study of biological oxidation pro- cesses some 200 years ago. Since then, the mechanisms by which various nutrients are oxidized by living organisms have remained among the most important and interesting problems in biological science. As early as 1896, Bertrand observed that living organisms contain a number of enzymes which catalyze the oxidation of various biological compounds, and these were designated "oxydases". The early workers generally assumed that oxygen was affected and modified by "oxydases" in such a way that stable oxygen molecules were activated then bound to sub- strates. The nature of the so—called activated oxygen, however, was unknown for many years, although organic peroxides and ozonides were postulated as active forms by a number of investigators. The role of oxygen molecules per se in biological oxidation process was vigorously challenged and questioned following the discovery by Schardinger of an enzyme in milk which catalyzed the conversion of aldehydes to acids in the total absence of oxygen. This finding promoted Wieland to investigate the nature of biological oxidation processes and eventually to propose a generalized mechanism which is known as dehydrogenation theory.31 In the occasional case when oxygen molecules serve as the immediate electron acceptor, the enzymes have been called "oxidases". According to the present knowledge, classic oxidases can be divided 34 35 into three categories. In the first category, the enzyme catalyzes the transfer of one electron to one molecule of oxygen forming super- oxide anion. Superoxide is usually disposed by dismutases. In the second group, two electrons are transferred to one molecule of oxygen to produce hydrogen peroxide as a product. The utilization and dis- posal of peroxide are done by peroxidases and catalyses, a matter will be discussed later on. The third category catalyzes the transfer of four electrons to a molecule of oxygen producing water as a product. In 1950,32 during a study of tryptophan metabolism, an enzyme was isolated from cells of a pseudomonad which catalyzed oxida- tive ring cleavage of the benzene ring of catechol forming cis, cis- muconic acid as the reaction product. It was demonstrated later by heavy oxygen isotope method that the two oxygen atoms incorporated into the product were derived exclusively from molecular oxygen.33 Mason and his collaborators, using the same isotOpe, found that during the oxidation of 3,4-dimethylphenol to 4,54dimethylcatechol catalyzed by a phenolases complex, the single oxygen atom incorporated into the substrate molecule was derived exclusively from molecular oxygen.3 It was soon acknowledged that in reactions of this type, one of the atoms of molecular oxygen is incorporated into a substrate molecule and the other reduced to water in the presence of an appropriate electron donor, such as NADH, NADPH, tetrahydrofolic acid, or ascorbic acid. These two types of reactions both involved "oxygen fixation" into a substrate molecule, and they are therefore different from the classic oxidase reactions. Since they are similar to the oxygenation reactions known to occur in chemical of photochemical process, so 36 Hayaishi named them "oxygenases".3S The terms "mono" and "di" oxygen- ases are assigned, respectively, to the enzymes catalyzing these two types of reactions. The significance of bi010gical oxygen fixation in medicine, agriculture, microbiology, and also in food technology, cosmobiology, public health problems, and biochemistry in general has now been well established. Oxygenases play important roles in biosynthesis, trans- formation, and degradation of essential metabolites such as amino acids, lipids, sugars, porphyrins, vitamins, and hormones. They also play a crucial role in the metabolic disposal of foreign compounds such as drugs, insecticides, and carcinogens. Furthermore, they par- ticipate in the degradation of various nature and synthetic compounds by soil and airborne microorganisms in nature and are therefore of great significance in environmental science. Many oxygenases catalyze hydroxylation of both aromatic and aliphatic compounds. Monooxygenases also catalyze a seemingly diverse group of reactions including epoxide formation, dealkylation, decarboxylation, deamination, and N- or S- oxide formation. Although the overall reaction catalyzed by mono- oxygenases appear grossly unlike each other, the primary chemical event is identical since these processes are all initiated by the incorporation of one atom of molecular oxygen into the substrate. After the initial monooxygenation reaction the compounds become more soluble in water or become biologically more reactive in the sense that they are susceptible to the action of various dioxygenases. Among various monooxygenases, cytochrome p-QSO, the liver microsomal enzyme, plays a crucial role in the metabolism of a variety of foreign compounds, xenobiotics, including drugs, carcinogenic and 37 carcinostatic substances, antibiotics, insecticides, etc. It has been known for some time that some of the carcinogenic hydrocarbons are not independently active but become carcinOgenic when oxygenated;36-4O for example, liver microsomal enzyme converts dibenzanthracene to the corresponding epoxides, which then becomes bound to DNA or histones. The epoxides of the carcinogenic hydrocarbons, i.e., benzanthracene, dibenzanthracene, and methylcholanthrene, are more active in producing malignant transformation than the parent hydrocarbons. Other examples for the metabolic conversion of noncarcinOgenic compounds to carcino- gens are also known: for example, some aromatic amines are oxygenated to become carcinOgenic hydroxylamine or N-oxide derivatives. Bromo- benzene is metabolized to a more reactive metabolite, presumably an arene oxide which can form a covalent bond to the liver proteins and then lead to extensive necrosis. These results taken together indicate that the monooxygenation of these hydrocarbons is the prerequisite for their oncogenic activity. B. Historical Aspects of p-ASO In 1958, reports by Klingenberg and GarfinkalAI described the presence of a carbon monoxide binding pigment in mammalian liver micro- somes. In the reduced form, this pigment was found to bind CO, giving rise to a praninent absorption band at 450 nm in the difference spec- trum of the microsomes. Since the C0 complexes of known hemoproteins had Soret absorption maxima at considerably short wavelengths (about 420 nm) and since the CO difference spectrum of the reduced liver microsomes showed no peaks other than that at 450 nm, there was no immediate clue as to the chemical nature of this newly discovered pigment. 38 Evidence that the CO-binding pigment is in fact a hemoprotein was, however, presented a few years later by Omura and Sato,42 who found that, although the CO difference spectrum of the reduced pigment is atypical for a hemoprotein, the isocyanide spectrum is characteris- tic of a hemoprotein, compound. This new cytochrome was also found in the microsome fraction of the adrenal cortex. It was from the experi- ments by Ryan and Engel,43 who showed the inhibitory effect of CO on the C-21 hydroxylation.of steroids by the adrenal mitochondrial frac— tion, that the catalytic role of cytochrome p-450 in the monooxygenation process was demonstrated. The enzymatic function of cytochrome p-ASO was then more firmly established by Estabrook44 and co-workers. Since then, this type of enzyme has been found in microsomes from tissues of liver, kidney, lung, intestinal mucosa, testis, adrenal gland, and pancreas of various mammals. The presence of similar types of pigments in insects, plants, and microorganisms has also been established. The isolation and purification of microsomal cytochrome p-ASO proved difficult since the enzyme was tightly bound to membrane. Early attempts at preparing cytochrome p-ASO from membranes were thwarted by the loss of the 450 nm absorption peak and the appearance in its place of a 420 nm peak. This cytochrome p-AZO pigment has no enzymatic activity. However, recent advance in isolation techniques have result- ed in preparations of liver microsomal cytochrome p-ASO that has purity approaching that of the soluble, crystalline cytochrome p-450 from Pseudomonas putida. In 1968, Gunsalus45 reported that a cytochrome p-450 type of enzyme was inducible in a strain of P. putida by growth on d-camphor 39 as the sole carbon source. The enzyme catalyzes the hydroxylation step in the camphor metabolism: NADH: NAD O OH + H20 This cytochrome is soluble and is therefore obtainable in a pure state. The individual steps of the catalytic cycle of this system have been characterized and often used as reference to describe the enzymatic reactions of the more complicated membranerbound mammalian systems. C. Reaction Mechanisms and the Nature of Active Oxygen One of the most intriguing and challenging problems in the field of oxygenases has been the mechanism of the catalytic reaction of p-450. In recent years, a general picture of the mechanism of the cytochrome p-ASO enzymatic action has become available. The results obtained from the adrenal mitochondrial steroid hydroxylating systems and the P. putida system suggest a unified catalytic sequence independent of the source of the cytochrome. In all instances, including microsomes, it now appears well established that the initial reaction of the process consists of the rapid binding of substrate to the oxidized from of p-QSO, with the transition of the latter from the low spin to the high spin form.46 This complex formation involves a stoichiometric binding of one mole- cule of substrate to a site near the iron atom of the hemeprotein and is accompanied by a conformational change. Once the oxidized form of p-450 has been bound to substrate, it can undergo rapid reduction by way of cytochrome p-450 reductase. The reduction of cytochrome- substrate complex by the reductase presumably proceeds by way of one 40 electron transfer. The next step is considered to consist of an inter- action of the reduced cytochrome-substrate complex with molecular oxygen, giving rise to a ternary reduced cytochrome-substrate-oxygen complex; -49 or with CO, giving the characteristic 450 nm absorption in visible range. The ternary complex (cytochrome-substrate-Oz) subse- quently accepts a second electron with the formation of yet unidentified active oxygen-cytochrome-substrate complex. After transfer within this complex of one oxygen atom of the substrate and uptake of two protons, the complex dissociated into oxidized cytochrome, H20, and product. A hypothetic reaction sequence, quoted from Chang50 and Dolphin, is shown in Figure 11. :E;'/J%WRH)\\3§\ 30 R FgImfl R-OH 02 y ‘ [Ff (RH), fiez'(RH) O ‘34?’ F-‘e’IRHflI HZO - u 2_ . e- H' (& (Brackets indicate presumed transition states.) Figure 11. The catalytic cycle of cytochrome p-ASO 41 The last step of the catalytic cycle (step 4) is the most intriguing, yet least understood. The problems concerning the last step are at least 3-fold: determination of the true structural iden- tity of the oxygen derivative that attacks the substrate, the mechanism by which this active form of O2 is generated, and the mode by which the oxygen atom is incorporated into the substrate. Among the three problems, the identity of active species really is the key to the solu- tion of other two problems. Since the direct investigation of the transition state is not yet possible, many of the speculations concern- ing the 02 activation are based on model hydroxylation studies promoted by simple metal ions. They include singlet oxygen, superoxide, pero- xide and hydroxyl radical.50 In 1964, Hamilton51 noted that many of the reactions cata- lyzed by monooxygenase were very closely analogous to reaction of carbenes and nitrenes. Carbenes and nitrenes are species which have only six electrons around the carbon or nitrogen and are very reactive intermediates in many organic reactions. Carbenes, for example, insert into the carbon-hydrogen bonds of saturated hydrocarbons to give methyl derivatives, insert into C-H bonds of aromatic compounds to give toluenes, and add to olefins to give cyclopropanes. Those reactions are very similar to the hydroxylation of aliphatic and aromatic com- pounds, and the epoxidation of olefins, catalyzed by p-450. Thus the implication is that the oxidizing agent in the enzymatic reactions is an oxygen species which reacts like carbenes and nitrenes. An oxygen species analogous to a free carbene or nitrene would be the oxygen atom. However, it is unlikely that a free oxygen atom would be formed in the biochemical systems because insufficient 42 energy would be available to generate this from 02. It is known that many reactions typical of carbenes occur when the carbene is not free but is merely transferred from the reagent to the substrate in the transition state. Such reactions are called carbenoid reactions. Therefore, Hamilton suggested that the oxidizing agent is a species which is capable of transferring an oxygen atom to the substrate. This has been called the "Oxene mechanism" or "Oxenoid mechanism".52 Recent work in both model and enzymatic systems has tended to substantiate this suggestion. For example, the discovery of NIH shift53-54 (Equation 7) seems to necessitate an arene oxide as intermediate. x H x x OH ? 4-Oa,-——» .+ (7) . g R X = tritium, halogen, alkyl groups D. The Purpose and Approaches of this Work If the hypothesis that the oxene mechanism is a general mechanism for these enzymatic reactions is accepted, there are still several questions unanswered. For example, how does the enzyme inter- act with 02 so that an oxygen atom can be transferred to the substrate? what is the mode of splitting of oxygen-oxygen bond? (Homolytically or heterolytically?) How does the enzyme system stabilize the oxygen atom to be transferred? What is the electronic structure of it? To identify the reaction intermediate in solving complicated organic reaction mechanisms, one usually use an unambiguous route to prepare the suspected intermediate. The newly prepared intermediate 43 can be compared spectroscopically with the trapped intermediate, or it can proceed to complete the reaction. The distribution of various possible reaction products usually gives a clue to the viability of the proposed mechanism. Idosobenzene is a truly unique compound in that it has a "stabilized oxygen atom" coordinated by Iodobenzene: It is known that when better coordination conditions are available, the oxygen atom can be transferred to form a new complex and release iodobenzene.SS Iron-porphyrin systems can provide the suitable coordination for the oxygen atom because of their highly aromatic nature which can lower the redox potential of Fe+3. Indeed, ferryl (Fe=O) porphyrin cation radical has been proposed to be the identity of the secondary compound (compound II) and the primary compound of the enzymatic reac- 56-58 The oxidation tions of catalase and peroxidase (compound I). state of compound I is two levels higher than that of the resting enzyme (ferric hemoprotein). In the case of catalase, compound I directly oxidizes the substrate via a two-electron step to complete the catalytic cycle. On the other hand, compound I of peroxidase reacts with a variety of hydrOgen donors, generating an organic free radical and a one-electron reduction product of the enzyme, the secondary compound, which in turn can bring about a further one-electron oxida- tion of substrate with regeneration of the resting enzyme. The elec- tronic structures of compound I and II will be discussed later. 44 When a stoichiometric amount of Z-idoso-m-xylene was added to octaethylporphinatoiron (III) chloride in chloroform or methylene chloride, the solution turned green within one minute after mixing. Upon standing at room temperature, the green color slowly faded and this process can be hastened by using a large excess of iodosoxylene. Attempts to detect hydroxylated or epoxided hydrocarbons have not been successful. It appears that under these conditions the porphyrin ring acts as a far more reactive substrate towards the active species as evidenced by the disappearance of the highly characteristic color of porphyrin solution. In order to decrease the self-oxidation tendency of the hemin and to stimulate a proximity effect commonly occurred in enzyme- substrate complexes, the following compound was proposed to react with iodosoxylene: MN" 0 O NH The green colored intermediate also provides us an opportunity to study the electronic properties of the iron-bound "oxene" species. 45 II. Experimental and Results A. Synthesis of Strapped Porphyrin Strategically, the synthesis of strapped porphyrin is similar to the synthesis of crowned porphyrin.59 Reactions were carried out according to the following scheme. (II) '1! ll propionic methyl ester pentyl I! ll (1) "Strapped" Porphyrin Two hundred mg of 2,6-bis-(2-carboxylicethyl)-l,3,S,7- tetramethyl-4,8-dipenylporphin was dissolved in dichloromethane and 100 mg oxalyl chloride was added to the solution. The solvent and excess reagent were then evaporated in vacuo. The residue was redis- solved in dichloromethane and was injected with equal molar solution of 1,8-diaminooctane along with a third solution of triethylamine 46 simultaneously to 250 ml refluxing dry dichloromethane/benzene mixture at a rate of 10 ml/hr. via a syringe pump. The resulting "strapped" porphyrin was then purified by TLC (silica/CHC13). Yield: 35%. The 180 MHZ (Bruker FI mode) 'H NMR spectrum of the strapped porphyrin is reproduced in Figure 12. The assignment of each signal was based on that methylene protons located on the bridge should (1) experience great anisotropic diamagnetic ring current produced by aromatic por- phyrin, and (2) split into pairs because of the rigidity of the hydro- carbon bridge, contrast to the relative mobil side chains. The assignments were confirmed by homonuclear decoupling experiments. Figure 12 and Figure 13 are 'H and 13C NMR spectra, respectively. Figure 14 is a typical spectrum of homonuclear decoupling experiments in which "a" protons were irradiated thus decoupled from "b" and amide protons. 47 AHHHV cwohnaooo oooomoum mo Espuooom mzz 2. .NH ouswwm <1 m1 NI r! O P N n 6 EL; [.17 . dl _ _ fl _ d _ — 3-- 3 «0,. F iii: . D a} ,,. f \f. < ./_l\\ .1/4. ..v\.tts/\xv cwhkzouoa monomwum mo enouoonm mzz mwlu .ma owsmwm 2%. ms.» 3 3. or“. com n1 . . 9.; 3.... 33 Eéxgéfii «mi... .«434._......,7a_,§§.? {$3323. a: .2...........__._.2 _ q .r ‘U__——. \ .—.. cub mm 49 {J ~—.——r ooaasoooo mcouooo :m: no“: AH>xv cwo>zaooo oooamoom mo Espuooam mzz :. ._ £3. a r u a. a _ E < < 5553 I... a}; — .— « m .. . o .u . j” .__.. a l . a .sa maawaa L m. !__ (3&1 50 B. Reactions Between Iodosoxylene and Iron Porphyrins; Characterization of Intermediates and Hydroxylated Product (1) Reactions Between Octaethylporphinatoriron (III) Chloride and Z-Iodoso-m-xylene 0.1 m mole of 2-iodoso-m-xylene was added to 0.1 m mole of GE? iron (III) chloride in dichloromethane with stirring. The solution turned green within 1 minute after mixing. When this solution was allowed to stand at room temperature, the green color slowly faded, finally into a colorless solution. The stability of the green solution can be enhanced when temperature was lowered. At -45°C, the green color solution was stable enough to permit an UV spectrum (Figure 15A) taken and to produce the typical pyridine hemochrome spectrum when added to a degassed pyridine solution of sodium dithionite. The bleached solution does not absorb visible light, indicating no porphyrin derivatives are present in the solution. No attempts were made to identify the final products. The magnetic moment of the green solution was measured by Evans method: in a 5 mm NMR tube which has a capillary melting point tube coaxially standing in the center, 0.019 m mole/ml of OEP hemin chloride in CDCl3 (12 TMS) and small excess of Z-iodoso- mexylene were added to the center tube, the space between two tubes was also filled with 12 TMS-CDCI3 solution. Because of the difference in magnetic environment between the inner and outer tube, the TMS signals exhibited a 25 Hz difference in chemical shift, the magnetic moment was then calculated to be 4.9 Bohr Magneton according to u = a¢493-, where C 1/2 -l/2 a equals to 2.522XlO-4(mole + ) ' (°K -1/2)(ml -1/2)(Hz ) at 60 MHz. T is the absolute temperature (298°K for this experiment), C is the concentration of solute in mole/ml. 51 ABSORBANCE o o 4> (D £3 h) z “I T 9 so 40 20— 1 l 1 l l l l 400 500 600 700 k (nm) Figure 15 A: Vis. Spectrum of reaction intermediate between iodosoxylene and CE? B: Vis. spectrum of compound I 52 (2) Reaction Between u-oxodimer of "Strapped" Porphyrin from (III) Chloride and 2-iodoso-mexylene Four hundred mg hemin (u-oxo dimer of IV,. obtained by passing IV through silica gel column with CHCl3 as eluent) was added to 80 ml of CHZCl2 followed by 200 mg of iodosoxylene. The mixture was stirred at room temperature for 2 hours and then treated with FeSO in hot HOAc to remove iron. The excess salt was washed with 4 water, the mixture of products was then separated on silica gel plate. The major bands on the TLC plates are unreacted starting material and a new band which has an Rf value slightly lower than that of the unreacted material. The new porphyrin has an absorption spectrum identical with that of III. When excess acetyl chloride was added to the CHZCl2 solution of the new pigment, the resulting material shows an intense IR carboxyl stretching frequency at 1740 cm"1 indicating a hydroxy group in the new pigment. Mass and NMR spectroscopy results also support this assignment. The molecular ion has a mass number 774 which is 16 mass units higher than the starting material, indicating an oxygen insertion. Other major fragments are M-lS and M-57 and M+. NMR results clearly indicate the location of the hydroxylation. (Figure 16) was at carbon d. mew; oooamoum com ozo~>x0mooow mo monoopo :owuomoo mo Eapuooam mzz m. .o~ moswwm v- m- N: T o F u m v 8%. o _ _ _ _ _ _ _ _ 54 III. Discussion The result of part 1.0. clearly suggests that an iron-bound oxygen atom can be transferred to hydrocarbons under very mild condi- tions. Since direct mixing of iodosoxylene with hydrocarbons in the absence of heme gives no reaction and the fact that pyridine hemochrome can be generated by addition of degassed pyridine solution containing sodium dithionite, it seems reasonable to assume that the green colored intermediate is the iron-bound oxygen atom which is stabilized by the porphyrin system. More significantly, the green complex has a remarkable spectral resemblance to compound I (Figure 158) of catalase,60 suggest- ing that the electronic configuration of the two may be similar. Although the present data do not allow us to distinguish the porphyrin cation radical structure from the oxygen radical i.e., P+'Fe(IV) :fi: vs. P Fe(IV) :OI, it may be speculated that two struc- tures are resonance forms of each other. In other words, the shift in electron density from porphyrin, through the iron, to oxygen is a continuous function and should be largely affected by the trans ligand as well as by environment. The observed mag. sus. seems to indicate that there are less than S unpaired electrons in the intermediate, therefore, it is entirely possible to have either the radical residing on the ring or on the oxygen (with certain degree of coupling with the high spin Fe(IV)). In view of our results, it seems that somehow the process of oxygen activation by monooxygenase may be involved with the action of catalase and peroxidase which are known to produce compound I and II during enzymatic reactions. Indeed, reactions of mixed function of 55 monooxygenase and peroxidase-oxidase have been reported.61 If peroxide is an intermediate product of 02 reduction it might be said that in many cases peroxide metabolism is involved as a part of the overall oxygen metabolism. Detailed analysis of the mechanism of O2 metabolism have revealed that three types of reaction are correlated in compli- cated way. oxidase (electron transfer) oxygenase {-9 peroxidase The recently established idea of oxyferroperoxidase structure or so-called compound III would make it easy to relate the function of peroxidase with those of electron transfer oxidase and oxygenase. 62 (1) Reaction between Compound III can be generated by three ways: peroxidase and molecular oxygen. (2) Reaction between superoxide and ferric enzyme. (3) Reaction between compound II and H202. It is most likely that compound III is the dioxygen complex of ferrous heme. Furthermore, the oxy forms of Hb, Mb, catalase, peroxidase all have similar spectra suggesting that electronic structure are very similar to each other. The following diagram shows the relationship between five redox forms of hemeprotein, all these forms could be obtained in fairly stable state under suitable experimented conditions. The arabic numbers formally indicate the effective oxidation number of the heme. 56 Ferric form (om : 4 Compound [I O o, \ R 6 ----- ?—--> 5 Compound m Compound I (oxy form) Reaction paths for peroxidase according to the number system above will be 3 + 5 + 4‘+ 3, catalase will be 3 + S + 3. It has been speculated that for p-4SO 3‘+ 2 + 6 + S + 3 is the catalytic cycle. Our results definitely support this view. We believe a detailed mechanism to explain the reaction of p-4SO, catalase and peroxidase. +3 +1 0 +2 +3 - (P-450)(P)Fe 7%(P)Pe AL) exp(-AEt/h)dt , (9) where the bar represents an ensemble average. The effect on the spin populations can be expressed as a -——-= P - P dt N8 Bo No GB , (10) if we let No = N + n and N8 = N - n, then dn n-no —=- P +P + P ‘P =‘ 1]. dt n ( a8 8o) N ( Ba as) T ’ ( ) 63 where 1 Pas + P80: 0 Pas + P80. Equation 11 shows that the net population of the spin system, and therefore the net magnetization, varies according to the first-order kinetic equation with a time constant T1, which is called the spin- lattice relaxation time. Bloch73 found that the motion of the macroscopic magnetiza- tion in the presence of an applied field could be explained in terms of phenomenological differential equations. In a magnetic field M, the rate of change of magnetization is .+ %=YMx-H ‘, (12) where Y'is the magnetogyric ratio. We can expand Equation 12 in terms of the components along three Cartesian axes and the unit vectors along these axes: + + + + I} + + + + I} -> + + A _ - 7 ((Msz-MzHy)l + (MZHX Mtz) J + (Mxify MyHQk ) . (13) In general, H consists of both the static applied field H; and the magnetic vector of the rf field Hi: the latter can be thought of as a field rotating in the xy plane at angular frequency . Thus, the com- ponents of H are H = H cos wt 2 l y = H1 Sln wt (14) H = H . z o 64 Equations 13 and 14 can be combined to give three equations for the time dependence of the components of M: dM x = . EE- Y (MyHo+MzHl Sin wt) 1“; dt = Y (MzHl cos wt - MxHo) (15) z =-y'(MzH sin wt + M H cos wt) . dt 1 y 1 Equations 15 are not yet complete, since they do not account for relaxation. It was assumed that spin-lattice and spin-spin relaxation could be treated as first-order processes with characteristic times T1 and T2, respectively. Mx and My decay back to their equilibrium value of zero, while Mz returns to its equilibrium value of MD as determined by Boltzmann's law. The final Bloch equations are, then, dM X dt dM __2. .dt ml 3?. =-y(MxH1 Sin wt+MyH1 y (MyHo-I-MZH1 Sin mt) - Mx/TZ y (MZH cos mt-MxHo) - My/T2 - (l6) 1 cosut) - (Mz-Mo) /T1 . As we have seen above, the relaxation of a spin system is caused by random time-dependent fields. The random fields may come from different sources which are brought in by thermal motions of the molecule with a suitable time scale, e.g., reorientation and diffusion in liquids, lattice vibrations in solids, collisions in gases and some torsional motions within molecules. These different sources of time- dependent random fields give rise to different relaxation mechanisms which will be discussed later after we have a full understanding of the molecule motions and the mathematical treatment of them. 65 II. Molecular Motions in the Liquid Phase and Time Correlation Functions Interest in molecular motions in the liquid phase has been increasing over the years. A wide variety of experimental methods have been applied to the study of the microdynamic behavior of mole- cules innliquids.74.78 The absorption of radio frequency, microwave, infrared and ultrasonic waves, Raman scattering and fluorescent scatter- ing of light, neutron scattering, molecular beam scattering, magnetic and microwave resonance, and double resonance experiments are all yielding detailed information on the dynamics of molecular collisions and the angular dependence of intermolecular forces which can't be detailed by traditional methods, such as viscosity and heat capacity. Therefore, spectroscopic methods are most valuable in probing the non- spherical nature of intermolecular forces. At present, the theory of molecular motion in dense phases is at a model-building level. There- fore, the treatment of any experimental measurement which is sensitive to the details of molecular motion may be divided into two parts: the determination of microscopic parameter(s) of interest from the measured macroscopic property, and the interpretation of the micrOSCOpic para- meter(s) in terms of a specific model for molecular motion. Time-dependent correlation functions (TCF) provide the most convenient mathematical form for expressing the macroscopic quantity measured experimentally as an explicit function of the microscopic molecular motion. The classical definition of a TCF for two dynamical properties A and B may be stated as CAB(t) = , (l7) 66 where the brackets indicate an equilibrium ensemble average. TCF's are particularly useful whenever one has two physical systems weakly coupled to molecular motion (TCF's appear in the equation for transi- tion states), or radiation weakly coupled to matter (the Fourier trans- form of the appropriate TCF gives the frequency spectrum in the Heisenberg picture). They provide a concise method for expressing the degree to which two dynamical properties are correlated over a period of time. In order to evaluate the effects of the weak interaction between the two systems, one only needs to know how the free motion of the separate systems affects the weak coupling between them. Thus, it is not surprising that all of the relevant information is contained in the correlation function of the coupling Hamiltonian. When A and B are different in Equation 17, CAB is called a cross-correlation function and when they are identical it is called an auto-correlation function. A correlation function tells concisely how a given dynamical property at time t correlates with its value at time t=0. If the usual assumption is made that the system is ergodic, that is, ensemble averages are the same as time averages, then one can get an average value for the function by repeating a large number of times measurement of the dynamical property p(t) at time t=O and at time t (the correla- tion is the projection of p(t) on p(0)), choosing various reference times t=O and averaging over the starting times. A TCF can be calcu- lated no matter what type of motion is occurring: however, usually the motion is random and the knowledge of its time dependence is in the form of a conditional probability function P(y2,y1/t2,t1) which gives the probability of observing the dynamical variable with value y2 at time t2 if it had a value y1 at time t Then 1. 67 f(tl) = fP(yl.t1) f(yl) dyl . (18) where y is a random function of time, f(y) is a function of y, and f(tl) is the average value of f at time t Similarly, I. f(tz) = fP(y2,t2) f(yz) dy2 . (19) Now, if we form the product f(tl) f(tz) and then perform the averaging, the result is clearly a time correlation function c = IIP(yl.tl> P=Tr{A.0(t)} . Consider a spin system embedded in a lattice formed by surrounding molecules. The total Hamiltonian can be written as H = HZ + HL + HI , (22) where Hz is the Zeeman term, HL is the lattice Hamiltonian and HI includes all of the interactions between spins and lattice. Since the lattice has many degrees of freedom, the energy levels can be regarded as continuous and can be treated classically. The coupling between the spin system and the lattice can be assumed to be very small so that the spin density operatorcr(t) can be obtained by tracing p(t) over the lattice degrees of freedom. Using these two assumptions, Redfield obtained the follow master equation of motion of the spin density matrix element:80 d d—oda'(t) = 'iIHz!O(t)]aa' ‘ BZB'RGO' 88' 0880(t) 9 (23) where R00. 88: = JaBa:B:(waB) + JGBG'B'(wG'B') (24) .. - v v 6o'8'$ JYBYanYa) 6C18 $2 Jyo 78 (m a'y) _ imt Goo'BB' = . (25) With a specific interaction Hamiltonian HI, the correlation function G can be calculated by choosing an appropriate model of molecular motion and the relaxation matrix elements (R ) can then aa'BB' be obtained. It can be shown that the above derived equation is equivalent to the famous Bloch equation when the density matrix is 69 diagonal and the population of spin states is described by the diagonal elements. III. NMR Relaxation Mechanisms As was discussed in Section I, any time-dependent fluctuating local field around the spin system will contribute to the relaxation of the spins. A number of different physical interactions have been found to be important in coupling the nuclei to the lattice and hence provid- ing a link through which energy between these two systems can be exchanged. The expression for probability per unit time of an induced transition can be written in the Heisenberg representation as 1 P -. - Wm = fl]; (V(O)V(t)> e 1(m k>t at g (27) where V are interactions and are merely the various terms in the Hamiltonian of the system which are made time dependent by molecule motions. Since the total relaxation rate is, in general, a sum of many terms of the form of Equation 27, the problem of interpreting the relaxation time comes down to the problem of deciding which terms in the Hamiltonian of the system give important contribution to R1 (total). It is possible to study R1 (total) and obtain information about each correlation function of the type defined by Equation 27. The following interactions have been found to contribute to the relaxation process under suitable conditions. They are briefly discussed below. 70 A. Dipole-Dipole Relaxation and Nuclear Overhauser Effect The prime source of spin relaxation is most diamagnetic liquids arises from the local fields produced by nuclear dipole-dipole interactions. The interactions can be either intramolecular or inter- molecular in nature. The instantaneous field produced at nucleus S by a magnetic nucleus I is given by + 4 3 cos2 913 -l Hioc = ifLI r 3 ' (28) IS where “I is the magnetic dipole moment of I, rIS is the nuclear separation, and 6 relative to the applied field. IS 13 the angle of rIS For a rigid system of intramolecular dipoles, molecular tumbling + imparts a time dependence to H through 9 S: for the internuclear loc I case, both 915 and rIS are time dependent owing to relative transla- tional as well as rotational motion. We can treat this problem quantum mechanically. Let us consider a system of two spin-l/Z nuclei and assume no J coupling. The energy level diagram for this two-spin system is shown in Figure 17. If the spins are labelled I and S, then the energy levels can be designated as follows: spin I is a. spin 5 is a, designated as (++) spin I is:;, spin 8 is 5, designated as (+-) spin I is 5, spin 8 is a, designated as (-+) spin I is 3, spin S is g, designated as (--) The W's are the transition probabilities which are: W11: the single quantum transition probability that spin I will go from a to B (or 8 too) while the state of spin S remains unchanged. 71 the single quantum transition probability for spin S when I remains unchanged. the two-quantum transition probability for the two spins to relax simultaneously in the same direction, i.e., -- to ++ or ++ to --. the zero-quantum transition probability for a mutual spin flip, i.e., +- to —+ or -+ to +-. 72 13 1I Figure l7. Energy level diagram and transition probabilities for a two-spin system without J coupling. 73 The Hamiltonian for this two spin-1/2 system (I and S) is H = HM -11YIHOIZ -fiYSHOSZ + H , (29) where HM is the Hamiltonian operator for the motion of the two nuclei I and S, which is commuted with the spin operators. The next two terms are the Zeeman energies of the spins in the constant magnetic field Ho, H' is the dipolar interaction term of nuclei I and S, which is consid- ered as a perturbation, Zy. y +-> ++ ++ n: = -(fi I S) [3 MW) (s-v) - 1'5] . (30) r From EquatiOn 29, Equation 31 can be derived: on , , -iW t = 1.. <0|H (t)|8> e as dt , (31) where‘ is the average of ”as over the statistical ensemble. The quantity <8‘H'(O)|a> is the autocorrelation function G(t) of , so that Equation 31 becomes = .fa, G(t)e-1w‘38t dt . (32) By analogy with Equation 25, the right hand side of Equation 32 is Juefi‘ae)‘ Thus the transition probability was is directly related to the spectral density at "(18' This relationship is the link between T1 and information on molecular dynamics. H'(t) can be written as a product of an operator A, acting on the variables of the system, and a random function F(t) of time. For the dipolar mechanism, the A.1 are 74 the usual spin Operators and the F(t) are random functions of the rela- tive positions of the two spins with respect to Ho, which are given by the second-order Legendre polynomials Y2 m' Equation 30 can be 9 written as , _ -3 Equation 32 can now be written as 2 — Jm(WaB)< o|A|B> , (34) where a: Y (0)Y (t) > _ on -W t _f < Z,m 2,m meae) - [a Gm(t)e (:8 dt us 6 . (35) r If r, the internuclear distance, is assumed constant and motional narrowing holds, evaluation of the matrix elements for the transition probabilities specified in Figure 17 yields W0 =‘%O kzjo (HS-WI) = 15 szC ”11 = 1370' sz1 (WI) 3 '36 kzrc Wls = 276 szl (”3) = %5 kZ-cc (36) wz = I5 RZJ2 (NEWS) = % kzrc . where k = YIYS‘fi/r3 and the subscript for each J is the change in total spin quantum number upon transition. Solomon has shown that for two-spin systems the rate of change for the Z- magnetization of the I spin is given by d I 2 dt I = - p(< Iz>-Io) - O(-So) 9 (37) 75 where p = W0 + W1C + W2 = l/T1(I) (38) a = w2 - ”o = 1/T1(IS) . (39) and IO(I) and 10(5) are the equilibrium z-magnetization values for the I and S nuclei. The second term on the right-hand side of Equation 37 is a coupling term and indicates that the relaxation of the carbon z-magnetization is affected by the proton polarization. Such coupling manifests itself experimentally in deviations from exponential recovery of 12(1) and requires analysis of data in terms of two relaxation times 1/‘53nd l/o. In practice, this coupling term is often negligible, and to a good approximation the decay of I2 is exponential with time constant pc. However, it can be shown that if 12(8) = 0, then Equation 21 can be solved under steady state condition: Hlm CO I <2) I ‘1‘“ Olo o =1+%%=1+%“I-{S} (40) Equation 40 expresses the condition that if‘n # O the steady-state magnetization of the I spin differs from the Boltzmann value by the factorlq which is known as the nuclear Overhauser enhancement (NOE) factor. In practice, 12(3) = O can be achieved simply by observing the I spin and decoupling the S spin simultaneously. By substituting the conditions 82 = O and S0 = nIO pcfis into Equation 37, the expression d dt = ‘p 4’9 (l +nI-{S})IO (41) is obtained. The differential equation can be easily solved and the result is 76 I - I = 2 I e (42) 1': where I0 is the new equilibrium magnetization and equal to (l+n)IO. Equation 42 demonstrates that under S-spin-decoupled conditions the I-spin dipolar process is governed by a single time constant T1(=l/o). In the extreme narrowing limit, i.e., (WI-MS)2 rbzqcl, the following equation can be derived easily from Equation 36 W : W : W : W = 2 z 3 : 3 : 12 (43) and Equation 40 becomes * I .9 = = .c.1§ = Iii. When other mechanisms contribute to the relaxation of I-spins, the observed NOE value is decreased, since only the dipolar mechanism contributes to W2 and W and other mechanisms contribute only to W1. 0 Substitution for the various transition probabilities from Equation 36 into the 1/TlI expression (Equation 38) yields 2 213 1.. = l..:£.:§___. {J (w -w )+3J (w )+6J (w +w )} = (45) T1(I) 20 r 6 o s I 1 I 2 I 3 Is 31 YIZYSZ’fi 1’ r156 for the relaxation of an I spin by a single S spin. Equation 45 can be modified to take into account interaction from other spins directly attached, or attached to other atoms in the molecule, if it is assumed that To is the correlation time for each such interaction. For this case the relaxation time of spin I due to the dipolar interaction, T1(DD), is given by 2 2 2 1 _1; YI Ysfi Teff (46) T (DD) - ._ 6 c ’ 1 1-1 rIS eff . . . . . . . . where To is the effective isotropic correlation time. Similarly, for NOE in the multi-S-spin system, the equation YS 2 n - =— I { all S } 2y (k I J . + 4W D1 11) (47) H'MU' can be derived where JDi is the spectral density and is a constant. * WII is the non-dipolar contribution to the relaxation rate W1. non-dipolar interaction is negligible, Equation 47 reduces to Equation If the 44. In such cases the number of protons is irrelevant. Thus, if dipolar interactions dominate the relaxation process, the same NOE Y value (23—) will be observed for all I nuclei. Otherwise, the number I of nearest S spins can lead to variations in the values of NOE. It is of intereSt to consider the spin-lattice relaxation time of the decoupled I spins. Under these conditions all S spins are saturated and d 1 2 ‘4': n dt " ' 5 k :JDi + 2Wu F Iz> ' (1+ I- s>101 (48) and l l 2 * Combining Equations 44, 47, 49, the following extremely important relationship can be derived: II (Total) - 71(obs) T1 (DD) ‘ n (max) ° (50) 78 This relationship can be used to find the degree of contribution of dipolar interaction to the relaxation processes. B. Quadrupolar Relaxation A relaxation pathway that is available to spins having a nuclear spin quantum number 521 is the quadrupolar process. The non- spherical symmetry of the nuclear charge distribution gives rise to an electric quadrupole moment that can interact with the electric field gradient tensor of the molecule. Molecular motion imparts a time dependence to the field gradient, which yields a fluctuating electric field at the resonant nucleus capable of inducing transitions between nuclear quadrupole levels. Thus, while the effect is electrical in nature it does provide a means for magnetic relaxation. The Hamiltonian for this quadrupolar interaction is H1 -- Q - G(t) . (51) where 3 is the quadrupolar coupling tensor and E is the electric field- gradient tensor. The P tensor is exactly of the form of the r functions in Equation 33, where now the 6 refers to the angle between the Zeeman field and the symmetry axis of the V tensor. In the case of cylindri- cal symmetry the 5 tensor can be expressed in terms of one parameter, Q, the nuclear quadrupole moment. In the principal-axis system, the P tensor can 3e diagonalized, i.e., the only non-zero elements are i; , ig- , -%V , where V is the electrostatic potential at the nucleus. 8x By 82 Furthermore, it can be shown that the field-gradient tensor is trace- less, i.e., 2 32V 32V av _ 7+7+—2—-o . (52) 3x ay 32 79 Thus, only two components are independent and conventionally the field- gradient tensor is expressed in terms of the two quantities _ 32V _ 32V 32V 32V q--—2- and n -(——2‘—2-)/ --2- . az 3x By 82 The second term is called the asymmetry parameter since it measures the deviation of the field-gradient tensor from axial symmetry. Pro- ceeding through the same arguments as for the case of intramolecular dipole-dipole relaxation, we obtain 2 2 1__l_3(2I+3) n egg TlQ T20 “0 12(21-1) 3 1‘ q where l/TlQ is the quadrupolar relaxation rate, I is the spin quantum number, f1is the asymmetry parameter, $99 is the_quadrupolar coupling constant (QCC) and IQ is the time constant characterizing the corre- lation function of the eigenfunctions with quantum number L=2 for the symmetric top. Apart from a normalization factor, the latter functions are identical with the matrix elements of the rotation matrix Dz’m, (3,8 ,Y ) of dimension L=2 (ch 8, y, = Euler angles describing the rotation of the rigid body constituting the molecule). If we assume that the molecule performs isotropic rotational motion, TC may be shown to be the same correlation time as occurs in Equation 25, that is, the correlation time of the spherical harmonics of order 2 for the isotropic motion of a vector. C. .Spin-Rotation Relaxation The spin-rotation interaction arises from magnetic fields generated at a nucleus by the motion of a molecular magnetic moment 80 which arises from the electron distribution in a molecule. The Hamiltonian can be expressed as Hgi-E-im (53) where 3 indicates the rotational quantum state and C is called the spin-rotation tensor. This interaction is made time dependent by . . . . S colliSions which alter J. For spherical molecules, T1 R for the case of the magnetic nucleus being at the center of symmetry is expressed by l Zkt 2 T SR 2 ImC J ' (54) 1 H where Im is the moment of inertia, C is the isotropic spin-rotation interaction constant, and T: is the angular momentum correlation time. Equation 54 assumes that the effective epicenter of rotation is the center of gravity. For a magnetic nucleus in a cylindrically symmetric environment but away from the center of gravity, Equation 54 becomes 1 _ 2m: 2 2 ’ “5r - ‘71..“u ”Cl) 1.1 ' (55) T1 3h where the parallel component of C is given by the principal vector of the rotation axis. For a nucleus along the symmetry axis of a sym- metric top, l/TlSR is given by 1 Zkt 2 2 TlsR 3:32 ( "I H Tu I J. J.) ( ) 81 . . . It may be shown that the angular momentum correlation time, TJ, which is a measure of the time a molecule spends in any given angular momen- tum state, is related to the molecular reorientation correlation time To by the equation 81 ‘t1 = J C I/6kT (57) It should be noted that Equation 57 only holds at temperatures well below the normal boiling point of a liquid. The important distinction between this relaxation mechanism and the others discussed is that :3 becomes longer as the sample temper- ature increases, whereas 7% becomes shorter. As the temperature be- comes quite high and the sample becomes a gas, collisions become more infrequent and the molecule remains in a given angular momentum state for a longer period of time. On the other hand, the higher the temper- ature the faster a molecule reorients and the shorter is 2;. The result of this is that for the spin-rotation interaction the relaxation time T1 becomes longer as the temperature decreases. D. Scalar Relaxation The multiplet structure observed in high-resolution NMR is a second-order effect originating for the most part from the Fermi hyperfine coupling of nuclei through electrons. This spin-spin coupling, distinct from nuclear dipolar coupling, is observed for magnetically nonequivalent nuclei existing in the same molecule provided (1) that there exists no rapid time-dependent processes that average the spin- coupling constant A to zero, or (2) that the inverse of A is much less than the T1 value of either coupled nucleus. Rapid chemical exchange would lead to a violation of condition (1) if the frequency of exchange is much greater than the frequency of the induced coupling. The exchange process thus gives rise to a fluctuating local field at the site of the nonexchanging nucleus. Such a relaxation mechanism is denoted by Abragam as scalar relaxation of the first kind. Violation 82 of criterion (2) may arise if nucleus j is relaxed by a fast quadrupolar process that collapses the spin coupling with nucleus i. If the local magnetic field thus produced at i fluctuates (due to flipping of spin j) at a frequency comparable to the Larmor frequency of i, relaxation can be induced. Such a process is termed scalar relaxation of the second kind and the perturbing Hamiltonian is given by H' = A I'S . (58) In scalar relaxation of the first kind the coupling constant (=2nJ) carries the time dependence, while in scalar relaxation of the second kind the time dependence originates with the coupled spin 8. Although the origin of the time dependence differs, the formulae for T13C are the same for the two kinds of scalar relaxation. In a manner similar to that shown above for the dipole-dipole interaction, it may then be shown that 2 T ._l§E' = 3%—.s(s+1) SC 2 2 , (S9) - T T1 1 + ("I us) so where the correlation time for scalar coupling 13C is the chemical exchange time 1; in one case and the quadrupolar relaxation time for the second case. E. Chemical Shift Anisotropy A relatively rare source of spin relaxation is via anisotropy in the chemical shielding tensor ;. Anisotropy in the screening of a magnetic nucleus by surrounding electrons results in 3 having direc- tional components which have a temporal dependence as the molecule tumbles relative to Ho. The modulated local magnetic field thus 83 produced can induce spin relaxation if it has appropriate frequency components. The coupling Hamiltonian is given by + -> H'=-HO'Y‘hU'I , (60) . . . SCA which results in formulation of II as 2 2 Y H l I o 2 2 2 = 0' 0' T T SCA s (012 + 23 I 31 ) c ' (61) l The ng terms represent the components of the anisotropic part of 5. This mechanism depends on the same correlation time as the dipolar interaction, but has an explicit quadratic field dependence in the region of motional narrowing. Thus, this mechanism can easily be differentiated from others by field-dependence study. If g is axially symmetric, then two of the principal values of g are equal and Equation 61 reduces to 1 SCA T1 =-21—S-YIH (a -o)2 T , (52) where on and o are the components of 0 parallel and perpendicular to ' .L the symmetry axis, respectively. 84 IV. Models of Molecular Motion and Molecular Dynamics A. Diffusion Model As was mentioned in a previous section, information on molecu- lar motion can be derived from the spin-rotational and molecular- reorientational correlation times. Because I DD can be obtained 1 directly, the reorientational correlation time is of more general . . . 1' Eff DD . . . utility. Evaluation of c from T1 data Vla Equation 46 prOVides a measure of the time required for a given I-S vector to reorient by l rad but can be considered quantitatively accurate only in the case of isotropic reorientation of a molecule. Generally, symmetry features are not such that reorientational isotropy holds. Under these condi- tions, an assumed model of molecular reorientation is required before quantitative information on molecular motion is obtainable. Specifi- cally, this situation arises because NMR relaxation depends only on the power density'J(w) of motional fluctuations at the Larmor frequency, and hence information on other frequencies is not derivable. Thus, the explicit form of the correlation function is not available for the NMR experiment and some kind of model to relate the various quantities is required. Most models of molecular reorientation assume rotational diffusion and convert correlation times to rotational diffusion con- stants via the relation Di = 1/611, where Di is the diffusion constant about the ith molecular axis. In the simplest case-isotropic reorien- T Eff mtionr c is merely equal to l/6D. 2 r Bloembergen, Purcell and Pound evaluated8 c by Debye’s application of hydrodynamics theory83 appropriate to spheres in a viscous fluid: 85 T. = 371* ' ‘63) where n is the macroscopic viscosity and a is the radius of the mole- cule. This approximation can easily lead to results which are wrong by one order of magnitude. The experimental value of Tc is usually smaller than that given by Equation 63. In the literature the case has been treated where the rotational diffusion coefficient becomes very great,84“86 i.e., the rotational friction constant becomes very small. If the friction constant is exactly zero, we would have a dynamically coherent reorientation process. There were two early attempts to correct the failure of the Debye theory for nonviscous fluids. Gierer and Wirtz87 took into account the discontinuous nature of the liquid in a simple quasi-steady-state calculation of the torques acting on a rotating molecule by its neighbors and obtained a friction constant . 3’: 81rn83 [6(a) + (1 +§>'31‘1 . (64) where b is the radius of the molecule and a is the radius of the neighbor. For b = a 3 g = Snna./5 , (65) which is 1/6 the value predicted by the Stokes-Einstein relation. Hill88 based her calculation of dielectric relaxation times on Andrade's theory of viscosity and obtained an expression for the relaxation time which depended on the mutual viscosity of the solute-solvent pair. Applying this theory to pure polar liquids she obtained 86 _ 3(3-/2) 3 Tc - -_2ETF— n a ° (66) So far the correlation thme Tc has a well-defined micro- dynamic meaning in terms of a molecular reorientation process only for isotropic rotatiOnal diffusive motion. This means that the particle has to be of essentially spherical shape and that the torques exerted by the molecular surroundings must also have essentially spherical symmetry relative to the center of the molecule on the average. If the shape of the molecules deviates greatly from a sphere, there are generally three rotational diffusion coefficients about the three molecular axes. The simplest case of an anisotropic system is that of a symmetric top molecule. Woessner and Snowden89 and Huntress90 have DD developed expressions for T1 based on orientation of a rigid ellip- soid. The Woessner and Snowden expression is 2 2 2 ‘ l _ Nfi YI YS (3 cos26 -1)2 + 3 sin2 6 cos26 ‘+ IIZD)‘ r 6 [ 241)1 SD,+D“ IS 2 2 2 3 sinae ] _ N“ YI Ys eff (67) aunt-mu”) ’ —""’5 Tc : rIs where D1, D‘lare the rotational diffusion constants perpendicular and parallel to the symmetry axis and 6 is the angle between the relaxation vector and the principal axis of the diffusion tensor. In order to show the relation between the effective correlation time in Equation 67 and the correlation time Tc in Equation 45, Shimizu computed the ratio T eff c [TC as a function of axial ratio for prolate and oblate symmetric tops. He found that for many molecules, i.e., those with axial ratio 87 less than four, anisotropic motion does not make a large difference in the calculation of relaxation times. To evaluate both diffusion constants, either the dipolar relaxation times of two carbons with different geometrical dependences (different relations to the symmetry axis) of the I-3 vectors are re- quired, or an independent source of information must be available for one of the parameters. For asymmetric top molecules, all three principal values of the rotational diffusion tensor are required to characterize the molecular dynamics. Consistent with this, at least three different IDD values for nonequivalent geometrical configurations are required to I solve the three independent simultaneous equations necessary to evaluate the diffusion constants. Again, Woessner91 has given an expression for 11”” nfivzvz c c c 1 = I s l 1 + 2 + 3 + T DD r6 4R1+R2+R3 4R2+R1+R3 4R3+R1+R2 1 I-S . c4 + C5 1 ’ 6[(R2-L2)172+R1 5[R-(R2-L2)1/2] where R = 1/3 (R1+R2+R3) and 12 = 1/3 (R1R2+R2R3+R3Rl). 31.32.33 are the respective rates about the principal axes, where the C's are geo- metrical functions. The correlation time describing the quadrupolar relaxation process, as mentioned before, equals 15 under isotropic conditions. If the nucleus under consideration lies in a group which undergoes intramolecular rotations relative to the rest of the molecule, the correlation time t as calculated from Equation 52 no longer refers to the whole molecule but is a mixture of contributions from the rotating 88 group and the whole molecule. Zeidler92 has treated the problem in question following the approach given in Woessner's paper concerning the same situation with magnetic dipole-dipole interactions. Zeidler's result is the following 2 [370(217'3x2") (QCC)2 [% (3 coszS-1)2Tc + 1 12(21-1) l .1... T (68) 1 2 2 1 1 '1 {1‘30 C05 8'1) } (7+?) c1 0 where 8 is the angle between the principal axis and the intramolecular ] . axis of rotation, the time to is the correlation time in the absence 1 of internal rotation and to is the time constant of the intramolecular jumping process between equilibrium positions. For a rotating methyl group one has 8 = l80°-109.5°=70.S° and r = 0.11 r + 0.89 (Tl + .11..)‘1 . (69) q Cl c o 1 Thus, if To << Tc , the limiting result is 1 = 0.11 . 7O 'rq Tel ( ) The dependence of quadrupole relaxation in NMR upon molecular shape was examined by Shimizu93 who derived an equation for rigid ellipsoidal molecules undergoing anisotropic rotation Brownian motion. His result ‘TEff c was similar to Equation 8 except that was replaced by 1 (~53) f (emu). where 4 2 -1 _1_ 2_2 3sin9° 65in290 f (809a) - (a) [3 (3 C05 90 1) ]+’(7;-:-§-9 + ( 5o + 1 ). (71) 89 B. Non-Diffusional Models Isotropic Brownian diffusion gives correlation times which are much too large. The calculation of correlation times for isotropic rotation in spheroidal molecules was the subject of-a series of papers by Steele and co-workers.84.86 They observed that the forces governing translational motion are quite different from those restricting free rotation in the liquid, and one should not in general expect to find any relationship between the viscosity, which depends on the transla- tional friction, and relaxation times, which usually depend on the rotational friction. The calculated time correlation functions were found to be well represented by Gaussian functions and comparisons with experimental data showed better agreement than given by the Debye model. Atkins94 has obtained Steele's result as the classical limit to a quantum mechanical calculation based on a model wherein the mole- cules rotate in the liquid as determined by their free-rotor Hamilton- ian. The intermolecular interactions enter the model as Gaussian damp- ing of the resultant time correlation functions. The effects of spin- rotational relaxation in these spheroidal molecules were not consid- ered for this inertial model until recently, when it was shown that the spin-rotational relaxation rate should increase as Tllz.95 V. Relaxation and Fourier Transform NMR Spectroscopy For the two decades following the first realization of the NMR experiment, spectra were obtained by sweeping either the excitation frequency or the field through the region of nuclear resonance fre- quancies. The inefficiency of this method becomes evident from the fact that only one line can be observed at a given point in time. This 90 is of even greater concern when nuclei with intrinsically narrow lines covering a wide absorption range are studied. It would be more advan- tageous to excite the whole band of frequencies simultaneously. A straightforward idea for realizing such an experiment leads to the multichannel spectrometer where a multitude of transmitters, each covering a band in the order of a typical line width, serve as an excitation source. Such an approach, however, turns out to be unfeasi- ble for economic reasons. An analogous experiment offering the same advantages in terms of enhanced sensitivity is provided by the pulsed NMR method. It is known that a strong pulse of radiofrequency energy covers a large band of frequencies, thus being capable of exciting all resonances of inter- est at once. At the end of the pulse period, the nuclei will process freely with their characteristic Larmor frequencies reflecting their chemical environment. The resulting macroscopic transverse magnetiza- tion induces an ac signal in the receiver coil with the amplitude de- caying exponentially. The free precession signal is therefore also denoted as free induction decay (FID). Under proper experimental conditions, the FID, which represents the time development of the magnetization M(t), contains information identical to that in the con- ventional frequency spectrum where the magnetization is observed as a function of frequency M(w). The two domains are mathematically related by a Fourier transformation. This turns out to be requisite since, except for the simplest cases, the time domain signal is not interpretable visually. The operation of Fourier transformation of an FID signal into the frequency spectrum requires a digital computer. Prior to transforming the FID, it has to be converted into digital (d) ”O no “If, c"":' ff 91 / filo-l: 0‘”: -5.“ \‘ -— A \/ 151,:oc_32%—2 /’ / Figure 18. (a) Nuclear spin magnetization in the rotating frame. (b) Flip an angle a due to H (c) A 90° flip. (d) Signal in time domain (on resonance). (e) Signal in time domain (off resonance). 92 form, which is accomplished by a device referred to as analog-to- digital converter (ADC), an integral part of the computer station. In order to benefit to the maximum from the increased sensitivity per unit time, the experiment is repeated many times, i.e., a train of equally spaced radiofrequency pulses is applied to the sample and the response of each pulse is coherently added in the memory. The motion of the macroscopic spin magnetization when sub- jected to a radiofrequency pulse is best visualized in the so-called rotating frame of reference. This is a Cartesian coordinate system with the x and y axes rotating around the z axis with a frequency equal to the Larmor frequency of the nuclei as shown in Figure 18 (a). The 2 axis of this coordinate system coincides by definition with the axis of the external field. In the absence of an rf field, the magnetiza- tion resulting from the excess population of spins pointing in the field direction is therefore collinear with the field axis. In contrast to the fixed coordinate system, the rotating frame has the advantage of simplifying the description of the motion the magnetization performs when the rf field acts on it. If trans- tions are to be induced, a circularly polarized radiofrequency field has to be applied in which the field vector rotates about the z axis with the Larmor frequency of the nuclei. In the rotating frame, however, this rf field becomes static. Since the spins themselves do not precess in this representation, the cause for the precession, the Ho field, can be thought of as being nonexistent. The only effective field the magnetization experiences is the H1 field. Figure 18 (b) mirrors this situation. The magnetization consequently is nutated around the direction of the H1 field (x' axis) with an angular 93 frequency H If the radiofrequency pulse persists for a period t, 1. then the magnetization is nutated away from its equilibrium position by an angle <1='YH t, commonly denoted as the flip angle. After the l transmitter has been turned off, the magnetization remains in the position it has reached at this instant. Turning back to the fixed coordinate system, this corresponds to a precession around the effect- ive field, which is now the Ho field. Clearly the signal induced in the receiver coil, whose axis is perpendicular to that of H0, is largest for a 90° pulse (Figure 18 (c)). This requires that the trans- mitter be turned on just long enough to rotate the magnetization into the xy plane. The signal induced in the receiver coil (usually along the y axis of the fixed reference frame) then exponentially decays to zero due to effective transverse relaxation. Figure 18 (d) displays the time domain signal obtained on the assumption that the radiofre- quency is exactly at resonance with the spins, which all have the same chemical shift. Since the detector uses a reference frequency which is in phase with the H frequency, the measured response is just an 1 exponential decay. If we assume that the transmitter frequency is applied slightly off resonance relative to the Larmor frequency of the nuclei, the latter change their relative phases at a rate which is equal to their difference frequency Aw, leading to the FID represented by Figure 18 (e). The most striking advantage of the Fourier transform NMR technique is the rapidity of data collection which has made possible the studies of nonequilibrium states of nuclear spin systems. Measure- ment of relaxation times in a spin system containing more than one closely spaced transition was very difficult before Fourier transform 94 NMR spectroscopy was deveIOped. At present, most high-resolution T1 studies are carried out by using one of the common methods generally referred to as (a) inversion recovery,96 (b) progressive saturation97 and (c) saturation recovery.98’99 A. Inversion Recovery We have seen that the macroscopic spin magnetization in thermal equilibrium is aligned along the +2 axis, i.e., the direction of the magnetic field Ho. Application of a l80"pulse nutates it onto -z, as depicted in Figure 19. In terms of spin population, this situation corresponds to an exact inversion of the equilibrium populations of the two Zeeman levels. Since return to thermal equilibrium in general is exponential with time, and the equilibrium vabue of Mz(t) is M., the process obeys the differential equation = - ________ . (72) which, after integration, yields M - M2 = Ae-t/Tl . (73) The constant A in Equation 73 depends on the initial conditions. In the case of an inversion-recovery experiment, Mz(0) = ‘Mm by definition, and thus A = 2M , which, upon insertion into Equation 73, gives M, - M2 = 2M e-t/Tl 95 At a time t (t 5 T1) after the initial perturbing pulse has elapsed, the magnetization has partially recovered. If a 90‘ observing pulse is applied and the resulting FID is collected and Fourier trans- formed in the usual manner, the relative intensities of the various lines reflect their individual relaxation times. The experiment is thus characterized by the pulse sequence (18o‘-c-9o‘-I)n . where T Z ST1 is the recovery time between successive pulse sequences. From Figure 19 it is recognized that, for an absorption mode phase setting, the line for a particular nucleus may appear to be positive or negative depending on whether the observing pulse is applied before or after the magnetization has passed through zero. In principle, two different measurements suffice in order to determine T1: one each to obtain Mz(t) and M.. However, more precise data are retrieved from a set of spectra obtained by barying t. By plotting ln(M.-M(t))/M.. against t, the time interval between the perturbing and observing pulse, ideally a straight line with slope -l/T1 should be obtained. VIZ A A [ _ 1’1:;= ,-:l: Time \ Figure 19. Inversion-recovery method for spin-lattice relaxation time 96 B. Progressive Saturation If the spin system is subjected to repetitive 90’ pulses, a dynamic equilibrium will eventually be established in which the satura- tion effect of the rf pulses and that of the relaxation balance each other. Provided that the magnetization is all transverse at the end of the pulse, and exclusively longitudinal at the moment the pulse is initiated, the spin dynamics are governed by Equation 73. The initial conditions in this case demand that MZ(O) = O and thus A = Mg, which lead to -t/T1 Ma-Mz = Mme . (74) The steady-state situation is usually reached after three to four pulses, which means that the first few FIDs should be disregarded. Apart from this, the experiment requires no other provisions and the spectra are obtained by simply varying the pulse interval. The T1 data are determined in the manner described for the inversion-recovery experiment. The progressive saturation method lends itself in particu- lar to situations where, for sensitivity reasons, a large number of transients are to be collected. The method, hawever, is restricted to Tls that are not substantially shorter than the acquisition time, which sets a lower limit to the pulse interval. Progressive saturation experiments put more stringent demands on instrumentation and are thus more susceptible to systematic errors. C. Saturation Recovery The initial complete elimination of the magnetization, not only along the z axis, but also in the xy plane, is peculiar to this technique. This is accomplished, for example, by a 90° pulse followed 97 by a field gradient pulse along the z axis, which has the effect of dispersing Mxy as illustrated in Figure 20. After a time t 5 T1, the magnetization has partially recovered and can be measured in a manner analogous to a Fourier transform of the FID following a 90° pulse. The sequence required can be written as (90° - HSP -c- 90°)n in which HSP stands for a homogeneity-spoiling pulse. HSP Figure 20. Spin-echo method for measuring spin-lattice relaxation time. 98 EXPERIMENTAL I. 13C NMR Experiments A. Instrumental A Varian CFT-ZO high resolution nuclear magnetic resonance spectrometer was used to obtain the 13C NMR spectra. The CFT-ZO spectrometer is a computer-controlled, pulsed FT NMR instrument oper- ated at a constant field of 18.7 kG. The spectrometer can be described as follows: (1) Computer The CFT-ZO utilizes a Varian 620i mini;computer which has a 12K memory and each word has 20 bits. The main functions of the com- puter are data collection and manipulation, which are achieved by entering every command and parameter through the console keyboard. The main parameters that affect data collection are spectra width (SW), transmitter offset (TD), pulse width (PW), number of scans (NS), mode of decoupling and decoupler offset. The data manipulation programs include convolution of time domain (exponential weighting), Fourier transformation and linkage to various output devices (recorder, oscillo- scope and hard-line printer). For relaxation time experiments, more parameters must be fed into the computer, e.g., the pulse width of the pumping pulse, the time delay between pulses, the time delay between scans, the pulse width of the homogeneity spoiling pulse (only for the homospoil method) and the number of experiments. (2) Transmitter Three frequencies have to be generated: (1) 20 MHz for 13C resonances, (2) 80 MHz for 1H decoupling and (3) 12 MHz for the deuterium lock. All three frequencies are derived from a master 99 oscillator (18 MHz) and are phase-locked to each other. Any instability of the master-crystal frequency is compensated by a synchronous prOpor- tionate correction on the remaining frequencies. The decoupler frequency may be applied either as a continuous wave or as a pulsed wave depending on whether single-frequency decoupling or wide-band decoupling is desired. (3) Analog-to-Digital Converter (ADC) Since the process of Fourier transformation is generally carried out on a digital computer, the FID signal has to be converted from its original analog into digital form before it is stored in the computer. This is accomplished by means of the ADC. The digitization process involves sampling of the signal at a frequency twice as high as the spectrum width. The most important criterion associated with the ADC concerns the dynamic range of the signals that are to be digitized, i.e., the accuracy with which the amplitude of the incoming signal can be digitalized. In 13C spectroscopy, this is usually not a critical problem since the S/N ratio for a single transient rarely exceeds 100:1. The CFT-ZO utilizes an ADC which gives a range of 220 = 106 . (4) Probe The probe of CFT-ZO utilizes a cross-coil arrangement. It provides better homogeneity of the rf field than a single-coil probe, a property which may become significant in relaxation studies. (5) Receiver During the free precession period following the pulse, the signal enters the receiver as a band of radio frequencies near the basic transmitter frequency. After passing the phase detector there 100 results a series of audiofrequencies, which are filtered by being fed through a low-pass filter with a band width which can be chosen inde- pendently by entering a parameter into the computer. In use the filter band width is set to equal the spectral width. Since the phase detector of the OFT-20 does not allow distinction between positive and negative frequencies, the rf carrier has to be placed so that the audiofrequencies (vi-\b) all have the same sign. In other words, the carrier frequency Vb is placed at one end of the spectrum. Otherwise, foldover of peaks may occur. B. T Determination l The methods used to determine T for this study are the l homospoil and inversion-recovery pulse sequences. It was found that the latter method provides more accuracy so the former method was abandoned at an early stage of the investigation. As described before, the inversion-recovery pulse sequence utilizes a 180° pulse to invert the magnetization, followed by an observation pulse (90’) after a suitable delay time. For most of the T1 experiments of this study fifteen different time delays were employed ranging from 1 sec to 4Tl sec. The peak heights of each signal of interest were then fed into a Nicolet 1080 computer to calculate the T using a two-parameter 1 exponential fit program and the equation M2 = M0(1-2exp (-t/T1)) , (75) where the constants M0 and T1 are optimized in an iterative manner. In Equation 75, a pre-exponential factor 2 is assumed because of the inversion of magnetization. If the inversion pulse angle is missed, then the accuracy of T will be seriously affected since the 1 101 pre-exponential factor will not be equal to 2 under those conditions. The 180° pulse of the CFT-20 spectrometer in our department was measured to be 46 usec for 13C. C. Nuclear Overhauser Effect Measurement The NOE is determined by using the NOE-suppressing procedure.100 Two spectra having different pulse sequences are recorded, one with the proton decoupler on all the time, the other with the decoupler on only during the 90° pulse and acquisition time, as shown in Figure 21. The ratio of peak heights for the two spectra was then measured. To minimize systematic error, the recovery time between pulses was set as long as possible (at least 10 times T1). D. Temperature Variation The temperature at the 10 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 temperature-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 desired 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. The exact temperature reading was measured by a copper-constantan thermocouple before and after each experiment. The variatiOns usually were within 1°C. E. Sample Preparation All chemicals except ethylene oxide and hexafluoroacetone were purchased from Aldrich Chemical Co., Milwaukee, Wis. Ethylene oxide was purchased from the Matheson Co., E. Rutherford, N.J. 102 Hexafluoroacetone was purchased from PCR Co., Gainesville, Florida. The boiling points and melting points of these compounds are listed in Table 3. Table 3. Physical constants of some ketones and ethers Compound B.p. M.p, Acetone 56 -95 3-Pentanone 100 -42 4-Heptanone 144 -34 S-Nonanone 181 -6 6-Undecanone 226 14 Diisopropyl ketone 125 18 Di-t-butyl ketone 155 -10 Hexafluoroacetone -28 -129 Ethylene oxide 135 -111 Trimethylene oxide 50 -100 THE 66 -108 All liquid chemicals were dried with molecular sieves then distilled. Ethylene oxide and hexafluoroacetone were condensed to a liquid and used directly without purification. After purification, the compounds were placed in an 8 mm NMR tube which was fitted with a vac- uum joint in advance. The samples were then connected to a vacuum line for oxygen removal by the freeze-pump-thaw method. After no further air bubbles were seen, the samples were sealed and inserted into a 10 mm NMR tube with two Teflon spacers. The 8 mm NMR tube has a restriction just above the sample volume to minimize the diffusion between gaseous and condensed phase. The whole set-up is depicted in Figure 22. 103 ->H-4- tp- 90 degree pulse -r- -:-Il : Delay Time ” ZAcquisition :Time h. T:ann:ittcr(C-13/ #0 :# on I FID E : 5. Receiver 0?? ;\\j/\K/h‘T— ; ” F‘Repetition Time —-P'§ ASM ‘51 WA}"""- AAA NM '11 Figure 21. Nuclear Overhauser enhancement of the coupled spectra by the gating technique .0 in Time pulmmum 1111 1mm H2 Trancnitter(H) L- A biKcTeflon spacer (N. 10 mm tube 8 mm tube #— Constriction b.- 5&2 Figure 22. Design of NMR tubes for measurements of relaxation times 104 II. 170 NMR Experiments A. Instrumental The 170 NMR spectra were collected using a Bruker WH-lBO spectrometer. The spectrometer consists of a superconducting solenoid magnet operating at 42.3 kG, a Nicolet 1180 computer, and the necessary accessories such as plotter, disk system and electronic hardware. This spectrometer is computer controlled, and is a pulsed FT NMR spectro- meter. The lock channel uses a 2D signal, at about 45 MHz. The 17O resonance frequencies are generated by a dial-in frequency synthesizer located in the front panel of the console. The signals are then picked up by a broad-band probe. The WH-l80 spectrometer is an ideal instrument to study low natural abundance nuclei and those giving weak NMR signals because of the following features: (1) Large Bore Magnet Because of the unusually large diameter bore of the magnet, it can accept up to 20 mm o.d. NMR sample tubes giving a factor of sixteen improvement over 5 mm tubes in terms of sample content and a factor of 256 in terms of time saving. (2) Quadrature Detector In conventional FT NMR, a single phase-sensitive detector (such as present in the OFT-20 and DA-60 spectrometers) can only determine the magnitude of the frequency difference between the signal and the rf pulse but not the sign of this difference so the rf pulse is usually set at one end of the spectral region to avoid folding back of resonance. This will give rise to two problems since (1) the power bandwidth of the rf pulse must be equal to twice the total spectral width (i.e.,y'H > 2 (sw)), and (2) noise from the unused 1 105 side of the carrier frequency is folded into the spectral region, decreasing S/N by 40%. 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 positive and negative frequencies (relative to rf carrier) can be carried. Thus, the rf pulse may be 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 ofvr2 or a time saving factor of 2. (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 brings an effective gain of a factor of four. Switching from normal to quadrature detection is performed by a signal pregram command. (3) Higher Magnetic Field Since the sensitivity is proportional to the square of the magnetic field, the advantage of using a higher field is obvious. The 170 nuclei resonate at about 25 MHz with a field of 42.3 kc. 106 Other features, including phase alternating pulse sequences (PAPS), unlimited memory size (direct link to disk), homo- and heteronuclear decoupling, provision for multiple pulses etc., are also very important for relaxation time studies. B. Lineshape Measurement The 170 nuclear resonances are characterized by very broad lines as a result of very efficient quadrupolar relaxation. Therefore, lineshape measurements have a smaller percentage error than for most nuclei and oxygen removal is not necessary. Another advantage of observing fast-relaxing nuclei is that the pulses can be applied almost continuously without any delay time between pulses and this greatly reduces running time. The disadvantage is, of course, that the resonance signals sometimes get so broad that only if there is a flat baseline can the observer determine the full-width at half- height. Another troublesome problem associated with 170 NMR is the large rf power (~55 usec for a 90"pulse) required to flip the nuclear spins. In order to minimize the pulse leakage associated with the large rf power, the receiver is delayed a few hundred microseconds before being turned on. Figure 23 illustrates the whole sequence. 107 A l . . I Magnetization I 'I II II I ' ' I] I I, I I ll 1 j_: t0 t1 t2 Time Figure 23. Magnetization as a function of time for FID acquisition in the Bruker WH-l80 NMR spectrometer. O----t0 is the pulsing time, t0 is time FID starts t0---t1 is the delay time before receiver is turned on t0---t2 is the acquisition time 107 108 As is obvious from diagram, the efficiency of data collection depends on how fast the magnetization decays. If t is set too late, 1 then S/N ratio will be severely affected (given the same amount of time). In our experiment, it was found that a delay of 400 usec was enough to remedy the power leakage yet give a reasonable S/N ratio for the least dilute sample in a reasonable amount of time. C. Sample Preparation The samples were purified as described above. All samples were placed in 15 mm o.d. NMR tubes which were inserted into 20 mm NMR tubes using Teflon spacers. A solvent for deuterium look was placed in the annular space. RESULTS AND DISCUSSION I. Relaxation Studies of Carbonyls A. Introduction In the past, a great many 13C nuclear relaxation studies were devoted to observation of hydrogen-bearing carbon atoms due to the simplicity of interpretation of the results. On the contrary, very few studies have been done on quaternary carbon atoms. Jones, Grant and Kuhlmann101 first showed that NOE data can be used for specific assignments of quaternary carbon resonances in some polynuclear aro- matic hydrocarbons. Anderson102 t 1. noticed that in acenaphthene C-ll exhibited the longest spin-lattice relaxation time followed by C-12 and then C-9,lO. This result can be understood by considering that C-ll is separated by three bonds from the nearest protons, while C-12 and C-9,10 are relaxed by geminal protons. Buchanan103 has used geminal deuterium isotope effects and spin-lattice relaxation times 109 in order to confirm assignments of quaternary carbon resonances in phenanthrene and dibenzanthracene. In a recent relaxation studyloa-106 involving relaxation measurements in molecules such as codeine, brucine and reserpine, it was demonstrated that subtle differences in the relaxation times of quaternary carbons are significant and can be utilized for specific assignments of these resonances. However, none of the above studies was concerned with molecular dynamics or any other physical constants. Among the various kinds of quaternary. carbons, carbonyl carbons are a very important class, yet very few relaxation studies have been made on them. Crossley107 used dielec- tric relaxation to study intramolecular rotation in aliphatic ketones. Most of the nuclear relaxation studies have been concerned with the spinning motions of terminal methyl groups.108 Another readily extractable piece of information from relaxation studies, other than the correlation time, is the nuclear quadrupole coupling constant of quadrupolar nuclei in molecules in the liquid phase. This parameter, in the form of the electrostatic field gradient at the nucleus under study, is of considerable interest in the theory of molecular structure. Two streams of interest are apparent. In the first, the nuclear quadrupole coupling constant is used as a sensitive test of the adequacy of a complicated self- consistent wave function for a relatively small molecule, the pre- dicted field gradients being calculated exactly from the wave function under study. In the second, the experimental nuclear quadrupole coupling constant is used to obtain the approximate electron distri- bution in the neighborhood of the nucleus in question and to correlate this information with other experimental parameters derived from 110 studies of reaction rates or UV spectroscopy, for example. The first is thus more the concern of the physicist and the second of the chemist. The nuclear quadrupole coupling constants for solid samples are usually Obtained from nuclear quadrupole resonance spectroscopy, but less frequently from NMR, ESR and Mossbauer spectroscopy. For gaseous samples, this parameter usually is obtained from pure rota- tional spectroscopy, but less frequently with molecular beam methods, which are mainly confined to diatomic molecules. For liquids, nuclear relaxation studies are the most feasible way to determine quadrupole coupling constants. 111 B. Results and Discussion The measured 170 linewidths for a number of ketones are given in Table 4 and the 13C spin-lattice relaxation times and NOE factors for the carbonyl carbons are shown in Table 5. (1) Relaxation Mechanisms of Carbons in Ketones For carbon-13 nuclei in an oxygen-free sample the possible relaxation mechanisms are dipole-dipole (13C-1H), spin-rotation, chemical shift anisotropy and scalar coupling. Since the experiments were all done at natural abundance for carbon and oxygen, the scalar coupling mechanism can be ruled out. The contribution of the magnetic dipole-dipole mechanism to the total 130 nuclear relaxation can be easily found by Equation 51: Rate (DD) = T1 (total) = “obs . Rate (total) T1 (DD) , "max In the case of the lH-BC dipolar interaction, ”max is equal to rh/Z %:= 1.988, under extreme narrowing conditions. T1 (DD) can thus be obtained unambiguously. The results of this calculation for a number of ketones are given in Table 6. 112 Table 4. 170 Line width (full width at half-height, error estimated to be 1 5%) Temp. (°K) Temp. (°K) Avl/2(Hz) Avl/ZU-Iz) Acetone ' . 3-Pentanone 203 116.5 243 337 213 90.0 245 318 223 87.5 263 221 243 66.5 273 209 259 54.0 283 175 263 53.3 293 141 275 48.0 303 119 283 43.0 318 98 293 42.1 333 87 303 36.2 340 81 323 33.0 - 5-Nonanone 4-Heptanone 297 600 284 361 316 409 290 312 346 250 313 204 357 207 326 168 367 185 337 145 385 150 347 122 392 138 357 105 323 32 6-Undecanone 300 983 314 698 Hexafluoroacetone 330 570 183 a 471 339 470 193 351 351 385 203 280 370 298 213 235 385 250 223 180 233 126 Di-isopropyl Ketone . 255 365 Di-t-butyl Ketone 275 228 300 220 295 136 305 209 300 130 320 150 315 115 340 133 356 112 370 95 113 Table 5. 13C Spin-lattice relaxation times and nuclear Overhauser factors for carbonyl carbons in some ketones. T (°K) 11 (sec) NOE T (°K) T1 (sec) NOE Acetone 3-Pentanone 187 31 1.50 235 43 1.62 203 37 1.30 255 50 1.10 213 41 1.24 280 60 0.77 235 42 0.94 294 57 0.65 257 - 34 0.60 306 52 0.50 276 31 0.49 322 46 0.39 293 28 0.40 328 42 0.33 303 22 0.26 348 32 0.19 357 28 0.16 4-Heptanone S-Nonanone 267 48 1.52 280 56 1.32 275 36 1.90 292 60 1.15 291 45 1.68 310 71 1.00 306 53 1.43 318 76 0.86 328 63 1.20 325 75 0.79 333 63 1.14 330 72 0.71 346 61 0.90 342 69 0.56 367 56 0.62 6-Undecanone 306 33 1.55 318 38 1.47 330 43 1.38 342 50 1.20 360 52 1.05 377 50 0.85 383 45 0.69 114 Table 6. Apparent dipolar and other relaxation rates of carbonyl carbons Acetone T (°K) 187 203 213 235 257 276 293 303 - Rate (total x 102 (sec-1) 3.23 2.70 2.44 2.38 2.94 3.23 3.57 3.72 Rate (DD) x 102 (sec-1) 2.43 1.76 1.51 1.12 0.88 0.79 0.71 0.64 Rate (other) x 102 (sec-1) 0.80 0.94 0.93 1.26 2.06 2.44 2.86 3.08 3-Pentanone T (°K) 235 255 280 294 306 322 328 348 357 Rate (total) x 102 (sec-1) 2.33 2.00 1.67 1.75 1.92 2.17 2.38 3.03 3.57 Rate (DD) x 102 (sec-1) .1.88 1.10 1.67 1.75 1.92 2.17 2.38 3.03 3.57 Rate (other) x 102 (sec-1) 0.45 0.90 1.03 1.18 1.44 1.75 1.99 2.72 3.28 4-Heptanone T (°K) 267 280 292 310 318 325 320 .342 Rate (total) x 102 (sec-1) 2.08 1.78 1.67 1.47 1.31 1.33 1.39 1.45 Rate (DD) x 102 (sec-1) 1.58 1.18 0.96 0.71 0.57 0.53 0.49 0.41 Rate (other) x 102 (sec-1) 0.50 0.60 0.71 0.71 0.74 0.80 0.90 0.94 S-Nonanone T (°K) 275 291 306 328 333 346 367 Rate (total) x 102 (sec-1) 2.78 2.22 1.89 1.59 1.59 1.64 1.79 Rate (DD) x 102 (sec-1) 2.64 1.87 1.35 0.95 0.90 0.74 0.55 Rate (other) x 102 (sec-1) 0.14 0.35 0.64 0.64 0.69 0.90 1.24 115 Table 6. (continued) 6-Undecanone T (°K) 307 318 330 340 360 377 383 Rate (total) x 102 (sec-l) 3.03 2.63 2.33 2.00 1.92 2.00 2.22 Rate (DD) x 102 (sec-1) 2.32 1.93 1.60 1.20 0.97 0.85 0.77 Rate (other) x 102 (sec-l) 0.71 0.70 0.73 0.80 0.95 1.15 1.45 The "other" possible mechanisms listed in Table 3 are spin- rotation and chemical shift anisotropy. The contribution of chemical shift anisotropy can be estimated by Equation 62 to be l. CSA I... 2 2 2 - rI H0 (00) To . i-i 1 U‘ Assuming a Ao value of 300 ppm, and a To value of lo-nsec, RCSA is estimated to be 1.88 x 10.5 (at 18.7 kG), which is neglible compared to the total relaxation rate (3:10-25ec). After ruling out chemical shift anisotropy, the only possible mechanism left for "other mechanisms" is the spin-rotation interaction. The temperature dependence of the spin-rotation relaxation rate is different from those of other mech- anisms, namely, the rate is higher when the temperature is raised. In the case of quaternary carbons of ketones, it can be seen clearly that the rate of "other mechanisms" increases as the temperature increases. This is taken as a strong evidence for the contribution of spin- rotation to the total relaxation rate. After establishing that the total relaxation rate is the sum of the dipolar and spin-rotation rates, the temperature dependence of 116 the total relaxation rate can be explained. At low temperatures the dipolar mechanism dominates over the spin-rotation mechanism, so the slope of the plot of the logarithm of total relaxation rate vs 1/T is positive. At high temperatures the spin-rotation mechanism becomes the dominant mechanism, which gives a negative slope as seen in Figures 24, 25, 26, 27, and 28. At certain temperatures neither mechanism is very efficient, consequently the total relaxation rate reaches its minimal value at that temperature. It is interesting to list these minimum temperatures, together with the boiling point and melting point for each ketone. Table 7. Minimum relaxation rate temperatures for a number of ketones. Compound Tmin M.p. B.p. Acetone -38 -95 56 3-Pentanone 7 ' -42 100 4-Heptanone 45 -34 144 S-Nonanone 58 -6 181 6-Undecanone 87 14 226 The logarithm of the relaxation rate (total and dipolar) is plotted versus the inverse of absolute temperature in Figures 24, 25, 26, 27, and 28 for acetone, 3-pentanone, 4-heptanone, S-nonanone and 6-undecanone, respectively. Linear relationships between R and 1/T DD are found to exist for all ketones studied. The linear relationships can be rationalized by use of the equation 1' = ‘l' e5 a/RT O 117 R x 102 (sec-1) ——l .v x 10-2 (Hz) .O' 9'0 ‘ . . 13 _I.. = Dipolar Relaxation Rate of3 C --- = Total Relaxatipn Rate of C "‘” = Linewidth of 0 I I 4 1000/1 5 Figure 24. Plot of 1n R , 1n RC and 1n4m' vs. 1/T for acetone. DD 118 ' \ / / R x 102 (sec-1) U\\Ck Ofl //D/ 1— w x 10'2 (Hz) -- f-= Dipolar Relaxation Rate of 130 "' = Total Relaxation Rate of 13C "" = Linewidth of 170 I 1 1 3 lOOOIT 4 Figure 25. Plot of 1n RDD’ 1n Rt and luau vs. 1/T for 3-pentanone. 119 R x 102 (sec-1) 1— w x 10’2 (Hz) Dipolar Relaxation Rate of 13C Total Relaxation Rate of 13C Linewidth of 170 Figure 26. Plot of 1n R , 4-heptanone. 1000/T 3.5 1n Rt and 1n (‘9) vs. 1/T for 1/2 120 -5 5 ‘ ,2/ \CK / 2 ‘flm’ R x 10 (sec-1) —— 1 /1- l / / O/ 09x 10.3 (Hz) II— . / . .0 /// ,/// - = Dipolar Relaxation Rate of 13 .25, "’ = Total Relaxation Rate of 13C . 0’ "' = Linewidth of 170 I/O 6’ I I 3 1000/T 4 Figure 27. Plot of 1n R , 1n Rt and 1n (4V) vs. l/T for S-nonanone. DD 1/2 121 -5 5- \\ Ck 2 -1 R x 10 (sec ) ////' /0' *3 . Av x 10 (Hz) — ,/O 13 j = Dipolar Relaxation Rate of C ' = Total Relaxation Rate of 13C //£9/// = Linewidth of 170 6 3 1000/T 4 Figure 28. Plot of 1n RD 6-undecanone. D’ In Rt and ln (MOI/2 vs. l/T for 122 where Ea is the activation energy. The term "activation energy" can be regarded as the change in p0tentia1 energy of the molecule associ- ated with the dynamical processes which cause the delay of the time correlation of the property under consideration. .The change in poten- tial energy occurs somewhere on the dynamical "path" of the molecule. It is not necessarily the difference in potential energy between a final and an initial state. The change in potential energy may occur repeatedly during the relevant process. For instance, for the time correlation of the canponents of a vector connecting two particles to vanish, generally very many translational steps of the molecules are necessary. Since the term "activation energy" has no clear physical meaning in the models of the microdynamic theories, its interpretation has to be based on macroscopic measurable physical prOperties such as viscosity, dipole moment and moment of inertia. The activation energies calculated from the slopes of the plots of log RDD vs 1/T, together with the viscosities and dipole moments, are listed in Table 8. Table 8. Activation energies of reorientation of C-H vectors, dipole moments and viscosities of dialkyl ketones Compound Ea(kca1/mo1e) r1(cp at 25°C) 11(Debye, 25°C) Acetone 1.26 0.316 2.74 3-Pentanone 2.47 0.496 2.82 4-Heptanone 3.26 0.857 2.70 S-Nonanone 3.38 1.282 2.69 6-Undecanone 3.39 1.932 2.68 123 Although the activation energies increase from 1.26 kcal/mole to 3.39 kcal/mole as the viscosities increase from 0.316 cp for acetone to 1.932 cp for 6-undecanone, they do not correlate at all well when the substitution becomes heavier. This is not surprising when it is considered that the process of viscous flow used in measuring the macroscopic viscosity involves both translational and rotational motion of the molecules, while dipolar relaxation is mainly caused by molecular rotation, which may, however, necessitate some displacement and, hence, translational motion of the neighboring molecules. The activation energies of heavier ketones obviously are not controlled by the viscosity of the medium. It has to be noted that the correlation time is a function only of microscopic viscosity, which does not corre- late with the macroscopic viscosity when the macroscopic viscosity is high. In addition to frictional forces, there are also inertial and electrostatic forces which are known to exert some influence or the reorientational motion of molecules. The inertial influences usually are in parallel with those of frictional forces, since the result of more alkyl substitution, in general, is the increase of the ’moment of inertia and the macroscopic viscosity. 0n the other hand, heavier alkyl substitution does not increase the dipole moments of the ketones, since the high polarities of aliphatic ketones are mainly contributed by the polarity of the carbonyl group. By means of dielectric relaxation studies, Crossley107 found that the dipole moment vectors approximately bisect the RXR angle for aliphatic ethers and ketones, where X is an oxygen or a carbonyl. If the molecular reorientations of heavier ketones are influenced by the electrostatic 124 forces, the carbonyl group will have the least mobility compared to that of the methylene groups. In other words, the carbonyl group becomes the anchoring group of the whole molecule and the rest of the molecule experiences different degrees of local motion. Indeed the measurements of T1 of carbons along the alkyl chain confirmed this assumption. The effective correlation time of each carbon can be obtained by combination of Equation 46 and Equation 50: 6 Teff _ (n l. r(c-H) c 1.98 T1 N Y 2Y 2 C H For quaternary carbons, it is assumed that there are four nearby protons with internuclear distances 2.1263. For methylene and ‘ methyl carbons, 1.092 is used for the C-H internuclear distance. The results of the calculations of effective correlation times are listed below. Table 9. Effective correlation times (psec) of carbons of dialkyl ketones at 30°C. Compound 1(C0) 1(Ca) ' 1(C8) 1(CY) 1(C6) 1(Cs) Acetone 2.72 0.16 3-Pentanone 3.24 0.54 0.51 4-Heptanone 4.93 1.37 1.01 0.74_ S'NOnanOne 9054 1096 1075 1.52 0e97 6-Undecanone 15.6 4.09 3.80 3.12 2.66 1.34 It is evident that the quaternary carbons have much longer effective correlation times than those of alkyl carbons in every ketone and that the correlation times of alkyl carbons decrease mono- tonically toward the end of the chain. The localized motion along an 125 aliphatic chain (or along any other molecular substructure) is called . 109 . 13 segmental motion. To observe segmental motion from C T1 measure- ments, the local motion must approximate or exceed the overall tumbling rate of the molecule. The multiple degrees of freedom inherent in these segmental motions generally preclude exact mathematical repre- sentation of effective correlation times. Significant information can then be derived from semiquantitative analysis of TCEff results. Lyerla110 35 31. have determined the relaxation times for the n-alkanes (n=7,10,l3,15,18,20). The alkane not only has accessible a variety of conformations but a given C-H vector may also undergo anisotropic reorientation in a particular conformation. Thus, averages of several T eff c O correlation times are contained in However, the results were interpreted based on a simple model of alkane reorientation suggested by trends in the Téeff values. First, for a particular resolved carbon the correlation time progressively increases as the chain length increases. Second, the correlation times increase from the chain ends toward the center of each alkane. Finally, the ratio of Téeff for methylenes in the interior of the hydrocarbon relative to end methyls increases monotonically from approximately 1.5 in heptane to about 7 in eicosane. These results were taken as an indication that the rota- tional motion of an internuclear C-H vector in the hydrocarbons can be analyzed in terms of (1) an overall rotation of the molecule (considered rigid) with average rotational rate 10-1, which decreases as molecular weight and viscosity increase, and (2) internal motion due to rotation about individual carbon-carbon bonds in the chain with rate 11-1, which is largest at chain ends. For molecules having segmental freedom but slow overall reorientation, (TCeff -1 3 Ti-1 ) 126 . . . -1 . For rapid overall rotation (i.e., To large), such as occurs in small eff -1 -1 . . ) z T . The expreSSion for the rate of rotational molecules T .(C o reorientation of the jth carbon in the chain is assumed to be given by (jrcefffl = (55.1)‘1 +'1 . ' <76) . The advantage of the above assumption is that the internal motion of the terminal methyl can then be found by the following equation: -1 _ -1 («(1.2>)‘1 = (IICEff) (zrceff ) (77) where (1(1,Z))-1 is the rate difference between the terminal methyl and terminal methylene carbons in a given alkane. Substituting Equation 76 into Equation 77 yields -1 1 - 2 - . (10.2)) = < ‘1) 1 -< ‘1) 1 . (78) The right-hand side of Equation 78 involves only internal correlation times since the overall correlation times of all carbons in a given alkane are equal and the terms involving To cancel. Hence, in each alkane the difference in internal rates ('r(1,2))-1 should represent the rate of methyl group rotation alone, since the methyl group motion is the result of all rotations that effect its neighbor- ing methylene, plus its own rotation about the terminal Cl-C2 bond. Therefore, T(1,2) should be independent of alkane molecular weight. The calculated values of TE(1,2) tabulated in Table 10 show that this is in fact the case. 127 Table 10. Correlation times T(l,2) characterizing internal rotation of terminal methyls in n-alkanes. (From Reference 110). n-Alkane t(1,2) C-7 7.9 psec C-10 7.0 psec C-l3 6.5 psec C-15 6.9 psec C-18 6.5 psec C-20 7.3 psec The motions of alkyl ketones are very similar to those of n-alkanes except that the segmental motion is more pronounced due to the electrostatic forces of carbonyls. The segmental motion of alkyl chains can be analyzed in a manner analogous to that of n-alkanes. The T(1,2) values calculated for 3-pentanone, 4-heptanone, S-nonanone, 6-undecanone are tabulated below. Table 11. T(1,2) Values for 3-pentanone, 4-heptanone, S-nonanone, 6-undecanone. Compound T(1 .2) ' 3-Pentanone 9.18 psec 4-Heptanone 2.77 psec S-Nonanone 2.69 psec 6-Undecanone 2.70 psec The model works fairly well for C-7, C-9 and C-11 ketones but for 3-pentanone, T(1,2) is much longer than for the others. Pre- sumably, the small size of the molecules fails to meet the requirement of constant 10' Since r(1,2) represents the time characterizing methyl group rotation, it is related to the rotational potential barrier V0 for thermally activated rotation according to Equation 79:108 128 R. = Roe.Vo/RT int . (79) where Ro can be assumed to be the rate of rotation of a methyl fragment 12 rad/sec, Vo = 0).111 Calculation of in the gas phase (R0 = 8.8 x 10 V0 using (1/2.7) psec as Rint yields a value of 1.9 kcal/mole. [As a comparison with other methyl internal rotational barriers, the V0 values for a number of molecules are listed in Table 12. 1 Table 12. Methyl internal rotational barriers calculated from 13C dipolar relaxation rates. MOlecules Vo (kcal/mole) (CH3)2$0 (CH3)2C0 (CH3)CC1 (CH3)3C01 (CH3) c0001 n-Alkanes (a; m-xylene Cis-Z-butene Trans-Z-butene Isobutene 2,3-Dimethyl-2-butene N \l n3hah4c> we NJF‘C>UDR)C>BJ HOVO‘ L‘ O‘HO‘U’IQON Segmental motion along short chains usually is less marked. Intermolecular hydrogen bonding does not slow overall molecular reori- entation enough in l-butanol112 to produce greatly different 13C T15 for the four carbons. However, in N,N-di-n-butylformamide the molecular anchor represented by the Y junction at the nitrOgen does restrict motion sufficiently so that segmental motion along the four-carbon 113 chains can be observed. Segmental motion has been monitored in long alkyl chains by 13C T1 measurements on l-decanol114 and on lecithin 129 models for biological membranes. The effective correlation time for the l-carbon of decanol is seven times longer than that of the 10- carbon. For sonicated dipalmitoyllecithin vesicles (bilayer structures) Tceff decreases by a factor of fifty along the lS-carbon aliphatic . l . . chains. 15 Segmental motion was also found to eXISt for the n-butyl- ammonium ion in various media due to the anchoring ability of ionic forces.116 Our results show that a polar compound can be an effective anchoring group for an alkyl chain as short as four carbons. The results in Table 5 also provide a chance to compare the microscopic and macroscopic viscosities. Stokes' simple formula for a rigid sphere rotating in a viscous liquid was assumed by Debye to be applicable to a spherical molecule surrounded by other molecules of similar size, i.e., 3 Tc = gig; ’ (80) in which n is the ordinary viscosity of the liquid and a is the radius of the sphere. This equation has been employed widely for many years. It was soon discovered, however, that the relaxation time does not follow the increase in viscosity for highly viscous liquids. The concept of internal or microscopic viscosity has been developed to account for this anomaly. There were many attempts to correct the failure of the Debye theory. The corrections usually are in the form of a coefficient or factor f. In the past, various values of f have been obtained empirically ranging frcm 0.008 to 1.0. Equation 80 can then be rewritten as below, where a3 is replaced by (2;) 0.74 M/p, giving 130 T: A}! 0.74f pRT in which 0 is the density and M is the molecular weight. Calculation of f using known n andga values for each ketone at 25°C gives the results shown in Table 13. Table 13. Microviscosity factors for dialkyl ketones. rc( psec} o( smcm 3) n( cp) M( sin/mole) f Acetone 2.72 0.79 0.32 58 0.39 3-Pentanone 3.24 0.81 0.496 82 0.22 4-Heptanone 4.93 0.80 0.857 106 0.15 S-Nonanone 9.54 0.82 1.282 130 0.16 5.6 0.83 1.932 154 0.15 6-Undecanone 1 The increase of f from 6-undecanone to acetone can be viewed as a departure of the molecules from spherical shape, which causes or increases translational motion of the surrounding molecules and, consequently, increases the macroscopic viscosity and decreases some- what the difference between it and the microscopic viscosity. Some additional insight into the molecular motion of these systems is provided by examining the theoretical result in the inertial limit of motion. In the inertial limit, the mean periods of free rota- tion about the major axis of rotation can be determined from Equation 81, which is obtained from the equipartition principle rid = (Ii/k1)“2 . (81) 131 where I1 is the moment inertia about the ith axis. If is much T . f,i larger than 1; eff’ then the motion is diffusionally controlled. 0n 9 is much larger than T the other hand, if Ti ., then the motion is 9 ,eff f i in the inertial limit. Values of Ia’ I 40 b and IC of acetone have been calculated to be 49, 59 and 102 (x 10' gmcxfz), thus giving Tfa, values of T r fb’ fc 0.34, 0.37 and 0.49 psec, respectively. Compared to Ti eff for 9 quaternary carbons, these values are rather small, suggesting the likeli- hood of diffusionally controlled reorientation of the carbonyl group in acetone. However, the methyl group of acetone has a value very T i,eff close to the 1f i values, indicating that the rotation of methyl is . 9 intermediate between the diffusional and inertial limits of motion. For heavier ketones, the calculation of moments of inertia becomes very difficult as a result of the many possible conformations of the alkyl chains. At any rate, the changes of moment of inertia are much larger than those of T..' i,eff ketones. Consequently, If i of the carbonyl carbon becomes comparable 9 with Ti eff for the same carbon. As a result of this, the diffusional 9 on going from lighter to heavier model cannot work well on heavier ketones. Anotherimportant motional parameter obtained in this study, is the spin-rotational correlation tbme YSR' To find the spin-rota- tional correlation time, one can use Equation 54, provided that the spin-rotation moment-of-inertia product CI is known. CI is a measure of the coupling between the rotational velocity of a molecule and the nuclear spin, which results in chemical shift variations and pro- vides a spin-lattice relaxation mechanism. It is measured in units of rad erg sec. Although the symmetry axis of acetone is only a two-fold 132 axis, it is assumed that the molecule can be treated as a symmetric top, since the values of Ia and Ib are very close to each other. The . . . . . . 117 equation for the spin-rotation relaxation rate of a symmetric top is ZTDSR :SR 1/T TSR = ZkT/Bh2 [(Cnl ”)2 ‘-——— + 2(C I )2 I: ] . (82) E chj 13 If one recognizes that Iici : 1/3 j-x y z , (Ij C. J) = (IC)trace for C in many molecules. Equation 82 can then be simplified to117 l 2kTC'O xxx 1 189 0 69 MW 58 LX X -10048 X 12.37 zz S=C=0 1.32 0 MW 56 CEO 4.43 0 MW 57 X -1028 xx H/ Lx YY X 10.17 22 X -502 MW 60 Y xx D0 x -7.4 L. W x x 12.6 zz P93 x (04-4) 16.9 0.7 NQR 62 all}: ,0** 22 ’l \ X (0*) 15.6 0.9 cc P¢3 0; . 22 e O 149 character in the oxygen orbital used to form the bond. Lacking this information, detailed discussion is impossible. The difference between the QCC of acetone and that of formal- dehyde can be attributed to anisotropic rotational motion of the latter. Recall that Equation 88 is derived with the assumption of isotropic reorientation of the molecules in question. If the molecules reorient anisotropically, the field gradient experienced by the nucleus in question will be different from that predicted by Equation 88. Another way of examining the error introduced by anisotropic motion is to consider the effective correlation time f(9,a) as discussed in the section on Theory. The effect of anisotropic reorientation is always to reduce the correlation time compared to that for isotropic reorienta- tion. Consequently, the calculated QCC will be increased somewhat if anisotropic motion is taken into account. Comparing the present results with previous values obtained by other methods, it can be seen that the QCCs are very close to the microwave results for formaldehyde except for the low value obtained. for acetone. However, acetone has not yet been studied by microwave spectroscopy. It has been implied from the results of the last section that the motion of ketones becomes less anisotropic on going from acetone to 4-heptanone. Thus, the values of the QCCs of this series probably start at 12.4 MHz for formaldehyde and reach 14.1 MHz for 6-undecanone. Notice that a value of 12.37 MHz was obtained for gaseous formaldehyde and it is known that the QCC value is often about 102 higher for molecules in gas phase than in the condensed phase. Nonetheless, the 12.37 MHz is used because of the omission of 150 asymmetry parameters. Recently131 some successful NQR experiments on 17O at natural abundance have been reported and it will be of great interest to compare our results directly with results from NQR spec- troscopy. III. Nuclear Quadrupole Coupling Constants and the Molecular Dynamics of Ethylene Oxide, Trimethylene Oxide and Tetrahydrofuran A. Introduction 13C NMR offers a uniquely powerful tool for studying molecular dynamics due to the dominance of the spin relaxation by the dipolar interaction of 13C with the directly bonded protons. The measured relaxation time can,with the aid of an appropriate model, be directly used to obtain information about the motion of individual C-H bonds. The relaxation behavior of small cyclic compounds has inter- ested many investigators. Most earlier work was concerned with the isotropic motion of the whole ring132 and the spinning motion of methyls attached to the ring, although internal motions, such as ring puckering motions, were known to exist for most of the molecules studied. The lack of a good model was the main reason for the neglect. Attempts to describe the relaxation behavior in terms of internal motion have been limited to use of a free internal rotation model and to an approximation in which the different relaxation times reflect different effective correlation times for each carbon in the ring. The interpretation of internal diffusion coefficients or correlation times deduced from the application of such a model is ambiguous. For example, if the ring only alternates between conformational states, the lifetime of each conformation will be the same for all carbons in the ring, but 151 T1 differences can still be predicted due to differences in the angular factors involved. London133 recently proposed a model to deal with internal motions. His approach is based on a bistable system able to alternate between two different conformations. Such an approach leads to an evaluation of the observed relaxation times in terms of the overall diffusion rate, the lifetimes of the two states, the angle between the particular C-H vector and the effective axis about which it rotates due to the jump, and the range through which the C-H vector jumps; his approach was able to explain the different relaxation times of the ring carbons of proline. Four-membered ring molecules undergo a ring puckering vibra- tion, the nature of which depends upon the balance between ring strain, which favors planarity, and the eclipsed methylene proton interaction, . . . . . 134-136 which favors torSion and nonplanarity of the ring. Functions of the type V = a22 + 024, where Z is the distance of the ring atom from the mean plane of the ring, have been used to describe the poten- tial energy of the system. If the coefficient a is negative, a double minimum potential occurs. If the ground vibrational level is above the top of the barrier, the planar form may be taken as the equilibrium conformation. If the ground vibrational level is below the top of the barrier, the molecule must be considered as rapidly interconverting between two non- planar equilibrium conformations. In cyclobutane the height of the hump separating the two minima is about 500 cm.1 and the lowest six vibrational energy levels are below the top of this barrier to planar- 137 1 ity. In trimethylene oxide (oxetane) the barrier is only 15.5 cm- and the ground vibrational level is some 12 cm-1 above this. Thus, 152 oxetane provides an example of a molecule which has only one equilibrium conformation (planar ring) but which undergoes a large amplitude ring-puckering vibration. It will be of interest to examine the effect of this on the C-13 relaxation time. Another important physical constant extractable from the NMR relaxation studies is the QCC of the oxygen nucleus in the ring. In this regard, we obtained the 17O QCCs for ethylene oxide, oxetane, and tetrahydrofuran (THF). B. Results The 13C spin-lattice relaxation times and NOE factors for ethylene oxide, trimethylene oxide and tetrahydrofuran are given in Table 20 and the 170 linewidths in these compounds in Table 21. C. Discussion As discussed in a previous section, the relaxation rate of 13C nuclei due to dipolar interaction with 1H can be obtained by multi- plying the apparent rate byl1/l.98 and the 170 quadrupolar relaxation rate can be obtained by multiplying the linewidth by W. ’The semi- logarithmic plots of 1n RDD and ln.4V1/2 vs l/T for each cyclic ether are presented in Figure 30. A linear relationship is found in each case. The calculated activation energies, together with the viscosities and dipole moments, are listed in Table 22. 153 Table 20. 13C Spin-lattice relaxation times and NOE factors for some cyclic ethers Ethylene Oxide T (°K) 195 206 219 230 244 255 263 T1 (sec) 8.1 10.0 12.6 14.2 17.0 19.1 19.8 NOE 1.98 1.98 1.98 1.98 1.98 1.90 1.80 Trimethylene Oxide T (°K) 199 222 235 253 258 273 281 303 Car1 (sec) 6.1 10.3 12.6 18.0 18.6 21.1 22.5 27 Cgi'1 (sec) 6.5 11.9 14.1 20.5 21.0 23.9 25.0 30.3 n = 1.98 for Co and CB at all temperatures. Tetrahydrofuran T (°K) 210 222 240 250 263 308 T1 (sec) 6.0 8.3 10.5 14.2 17 26.1 NOE 1.98 1.98 1.98 1.98 1.98 1.98 T1 of Ca and C3 are identical within experimental error. Table 21. 17O Linewidths for some cyclic ethers Ethylene Oxide T (°K) 200 212 222 235 246 257 263 Avll2 (Hz) 98 76 63 53 45 40 37 Trimethylene Oxide T (°K) 210 220 236 245 254 278 300 Avll2 (Hz) 104 93 75 60 57 4O 27 Tetrahydrofuran T (°K) 225 231 240 250 263 281 291 300 320 Avll2 (Hz) 207 175 155 130 104 82 75 65 52 154 Table 22. Activation energies, viscosities and dipole moments for some cyclic ethers 17 13 , ea. 0)_1 1:2 0-1 «were no») kcal mole kcal mole Ethylene Oxide 1.61 1.48 a 1.85 Trimethylene oxide 1.86 1.74b 0.45 1.80 1.79C Tetrahydrofuran 2.05 2.30 0.55 1.75 aEthylene oxide is a gas at 25°C and atmospheric pressure. bFor Cg. CFOI‘ Cg e 155 The activation energy appears to change with viscosity and not with dipole moment. The activation energy presented here probably is the averaged value for motion about all three principal directions since the moments of inertia along these three directions do not differ much. They are listed in Table 23 for all three cyclic ethers: Table 23. Principal moments of inertia of ethylene oxide, trimethylene oxide and tetrahydrofuran Principal Moment E0 TMO ‘ THF Ia x 10“0 gmem'2 33 70 89 Ib 38 74 106 Ic 59 125 196 Using deuterium substituted THF, Hertz and Goldammer138 obtained a value of 2.5 kcal/mole for the activation energy from a deuterium lineshape study. Since the largest component of the field gradient tensor of deuterium has the same direction as the C-D bond, the activa- tion energy obtained by the deuterium study should give the same result as the 13C study which is concerned with the C-H bond. The activation energy obtained in the present 13C study is 2.3 kcal/mole in excellent agreement with their results. For ethylene oxide and trimethylene oxide, no comparison can be made. The effective correlation times can be calculated as before for the ring carbons. For N = 2 and r = 1.098, the following relation- ship is obtained: 1 eff c (psec) = 23.5/T1(DD) (sec) . 156 The effective correlation times at -lO°C obtained in this way are listed below in Table 24. Table 24. Effective correlation times of ring carbons in ethylene oxide, trimethylene oxide and tetrahydrofuran Time E0 TMO THF T1 (0) sec 21.7 18.7 17.6 T1 (3) sec 21.2 17.6 To (3) psec 1.11 1.36 Hertz st 31.138 obtained a value of 0.8 psec for the deuterium C-D correlation time in TDF at 25°C. The 13C relaxation time due to the dipole-dipole mechanism at 25°C is 29.4 sec, which gives 0.8 psec for Tceff: thus, the two methods again give excellent agreement. An interesting observation made in the 13C T1 study is the non-equivalence of Tls for Ca and C8 of oxetane. Although in some cases they do not differ more than experimental error, the fact that the T18 for Co. are consistently lower than those for C3 at each tempera- ture suggests that the observation is valid. What it implies is, then, that the two magnetically nonequivalent methylene groups have different motional behavior. This difference in motional behavior could be interpreted as molecular association or a ring puckering motion. The former hypothesis is ruled out on the ground that the difference is greater at higher temperatures where less association is expected. The ring puckering phenomenon in trimethylene oxide has been 139 R140-142 143-145 studied by microwave, I and NMR spectroscopy. To underStand the puckering motion from a dynamical point of view, we need 157 an appropriate model. Recently, London133 proposed a ring-puckering model to explain the unequal values of T1 for the proline ring carbons. His approach is based on a bistable system alternating instantaneously between two different conformations, and an isotropic overall tumbling of the molecule whose ring carbons are relaxed dominantly by directly- bonded protons. Following Wallach, the orientational autocorrelation function for the C-H vector146 is G(t) = g e-6Dot Idao(8)I 2 < eia[Y(O)-Y(t)] >. (92) In the above expression, Do is the isotropic rotational diffusion coefficient, the da°(B) are the reduced Wigner rotation matrices,147 and the summation runs from -2 to +2; 8 is the angle defined by the relaxation vector and the symmetry axis of the jump. The factor exp(iaY) is defined using the usual Euler angle‘Y: Y represents a rotation about the initial 2 axis (the internal jump axis) such that a subsequent rotation about the y axis will leave 2' along the appropriate C-H vector: i.e., Y'is chosen so that y is perpendicular to‘z and 2'. In obtaining the autocorrelation function, exp(iaY(O)) represents the initial transformation to the C-H vector and exp(ia (t)) represents the transformation at time t. Since the present model assumes that the molecule is in either conformation A or B at all times, the calcu- lated function, and hence the relaxation times, are independent of the particular path through which the C-H vector moves in going between conformations. For this reason, the choice of axes and hence the angu- lar factors 8 and y are not uniquely defined. Results are most readily interpreted by defining B in terms of a fixed molecular axis about which the C-H vector would rotate in going from conformation A to B. 158 Letting A and B represent the normalized fraction of molecules in states A and B, the time-dependent probabilities that a molecule is in either state are described in the relations dA/dt -A/rA + 8er ' (93) dB/dt MyA - B/TB . (94) where TA, TB are the lifetimes of A and B, respectively. Equations 93 and 94 have the solutions: A(t) at/r ‘f¢(1/TB+K/TB C) -T/T TC(1/TA-K/TB C) e B(t) where l/t'c = 1/1‘A + lira and K is an arbitrary constant determined by the boundary conditions. Using the above results, the conditional pro- babilities can be found. These probabilities can then be used to evaluate the averaged quantity in Equation 92, giving =< e210 O'Y) > = 1 ( (TA-+13) -1'/‘rC ] [ I 2+IB2+25ATB cos 49 + 2 TATB( 1-cos 4 6)e < e“ YO'Y) > :< e’“ Yo'Y) > = --1-—-[r 2+1 2+2: 1 cos 26 + 2 A B A B (TA+TB) -r/r ZTATB(1-cos 26)e c ] where in the above expressions the jump is assumed to change Y from +(-)e to -(+)e. The average vector in Equation 92 can then be divided into two parts, 159 §< eia(Yo-Y)> = M(a) + N(a)e-T/Tc o It is apparent then that o o , G(t) = cle'T/Te + Cze-(I/Tc + Ute)T , where _z 2 _ 1 3.4 22 C1 ‘ a I dao(8)I M(a) ‘ E":;';2'[4 Sln'B (TA +1B +ZTATB C°S 46) TA B 2 + 3 sinzg coszg (TA2+TBZ+ZTATB cos 29) + (2_22%_£;l)2 (TA+TB)2] 2 l 3 4 = Z = — ° - C2 a | dao(8)I N(a) ( +1 )2 I2 Sin 8 TATB (1 cos 49) + TA B 6 sinza coszs tATB (l-cos 26)] . (95) Finally, the relevant spectral density will be given by Fourier trans- formation of G(t): r (1/Tco+1/TC)-1 20 1 2 I 2 2 1 +‘(wrc°) 1 +( w ) ) ( 1/1 C°+1 If C . (96) If all motions are in the extreme narrowing limit and the conditions rc<>TB’ the bracket in Equation 95 approaches unity so that G(t) approaches e-6Dot . Thus the internal jump motion will produce no effect. Physi- cally, this result indicates that if the molecule spends an overwhelming portion of time in either the A or B conformation, the internal jump mechanism fails to affect the relaxation rate. To have a significant effect on the relaxation time, the lifetimes of the two conformers have to be approximately the same. The lifetimes of the two conformers of trimethylene oxide are identical. Hence Equation 96 can be reduced to 3 cos26-1)2 2 J(uD = %{ %-sin48(l+ cos 46) + 3 sinzs coszs (1+ cos 26) + ( ~21 T 0 ___TE—1z + %~[% sin“ (1- cos 49) + 3 sinzs coszg (1- cos 26)] 1+w To c 1 r c 9 1+0211 c o where 1/rc1 = UTC + 2/1:A and Ice is the correlation time in the absence of jump. It must be emphasized at this point that although the internal jump is uniquely defined by a particular dynamic model, the choice of the angles 8, 6 which describe the conformational transition is not. In the preceeding discussion 8 has been defined using the axis about which the various C-H vectors are assumed to rotate in making the con- formational jump and 6 is the half-range of the jump. The values of 6 and 6 thus obtained are therefore most readily interpreted in terms of a molecular model. However, since the model employed here assumes 161 AV x 10.1 (Hz) 5... Figure 30. Plot of 1n R - 1 1- O = 170 Linewidth D = 13C Relaxation £§i3:17”’ E0 Rate TMO ‘ _.... = THF 1 L ‘ A 1000/T 5l .< DD and lnAy vs. l/T for oxirane, oxetane and THF . 162 that the molecule is always in conformation A or B, the relaxation para- meters calculated are independent of the motional pathway between these states. In general, an infinite choice exists for the angles (3,9 ) describing the transition. -A convenient choice is B = 90°, i.e., the jump axis is chosen perpendicular to the initial and final orientations of the C-H vector. For trimethylene oxide, if B = 90° is chosen for the initial and final orientation of C-H vector, then the range of jump is approximately 26° (the dihedral angle of puckered oxetane is about 9 l3 ).14 Under extreme narrowing conditions, Equation 95 and Equation 96 then are further reduced to x...) = 0.856 rc° + 0.144 Tel (98) and NflzYczyl-IZ o l 10 o l/T1 - 6 [ 0.856 1 +0.144 r ] = 4.25 x 10 [ 0.856 T + c c c " C-H 1 0.144 Tc ] , . (99) where in Equation 97 an A value of 1.092 is assumed. C-H The first term in Equation 98 derives from the isotropic motion in the absence of internal motion and the second term derives 0 from the internal jump motion characterized by (l/tc + ZITA)-1° Since . l . o o the maximum value of Tc is To (when T >>rc ), the effect of the A puckering motion thus is always to lower the relaxation rate. For trimethylene oxide, the lowering of the relaxation rate by the puckering motion is between zero and 142 depending on the relative values of T o and TA' To illustrate this point, I is plotted against 1 in Figure 1 A 31 with different values of 10°. 163 ‘2 ‘rfxlo 0'8 -__-u<19 ...-\ " 30'- \r *— (sec) 10 l L J . 10'13 [_ 1 TA sec 10'9 10 l 1‘ Figure 31. Plot‘of T vs I for various values of T; l A 164 In order to use Equation 99 or Figure 31, we need to know either Tco of TA and solve for the other. In theory, we could estimate 0 . . . . . . Tc from the ViSCOSity and denSity or by dielectric constant studies, then obtain the value of TA. In practice, however, the value of TA is . . . . o . very senSitive to the variation of To for a given T At any rate, 1. some results can be gleaned from Figure 31. Firstly, the absolute . . . . . o . value of T1 becomes insenSitive to the variation of TA when To is greater than 2 psec. Secondly, T reaches a constant value when r is 1 A much greater or smaller than tco' Thus, Figure 31 provides us a narrow range of values of Tco' For example, with a T value of 2.7 sec, Tco u l fluctuates very narrowly around 10 psec. The difference in T1 between Ca and C8 of oxetane can be explained by the difference in 6. It is known that in a cyclic molecule the C-H vector rotations have different ranges.133 Our results suggest that the Ca-H vector has a smaller range of rotation than that of the 08-8 vector and the differences become smaller when the temperature is lowered, as reflected by the difference in T The above conclusion 1. is based on the unlikely assumption that the C-H vector does not rotate more than 45°. The nuclear quadrupole coupling constants of ethylene oxide, trimethylene oxide and THF can be calculated assuming that the field- gradient vector of oxygen and the C-H vector have the same correlation . . . . o . time, Since the effect of puckering motion on re 15 not very great. The QCCs calculated are listed in Table 25. 165 Table 25. Quadrupole coupling constants of 170 in ethylene oxide, trimethylene oxide and THF Compound QCC (25°C) QCC (-lO°C) Ethylene oxide . 10.6 Trimethylene oxide 11.3 11.4 THF 16.6 16.2 *Averaged '1'l of Ca and C a is used. The QCC can be correlated with the percentage p character of the lone pair orbitals around the oxygen nucleus. 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