L (\l‘I‘l |,|\Drl\(rw\x ‘r\(‘ 1W1'1.HI.(:JI«U..JJ~IAI‘ .mA 1\‘\ x i .1: h‘wkjlmwniqh I.- . . _—, 6.1.17 )1 V‘ r wwwflw .__ _ . i, , #JMMWHVM fir w r 1% PHINE PHOS LUORO; m _ m. VI. H“ H M ’METHYLDIF J LIBRARY Michigan State University This is to certify that the thesis entitled , STUDIES OF THE MICROWAVE SPECTRA 0F .3 METHYLDI FLUOROPHOSPHINE BORANE, N—METHYLFORMAMI DE , AND N ,N-DIMETHYLFORMAMI DE presented by Ribhi Abdelqader Elzar‘o has been accepted towards fulfillment of the requirements for Ph.D. degree in Chemistry ,/”'3 4 7 ,, Major professor Date l/[é .//773 0-7639 r y ABSTRACT STUDIES OF THE MICROWAVE SPECTRA OF METHYLDIFLUOROPHOSPHINE BORANE, NfMETHYLFORMAMIDE, AND N,N-DIMETHYLFORMAMIDE BY Ribhi Abdelqader Elzaro A brief account of the historical development, theoret- ical treatment, and experimental aspects of microwave rota- tional spectrOSCOpy is given. Results of investigations of methyldifluorophosphine borane, N-methylformamide, and N,N— dimethylformamide are presented. The microwave spectra of CH3PF211BH3 and CH3PF211BD3 have been investigated in the region 18000 to 40000 MHz. The ground state rotational transitions have been assigned for both species. No splittings due to boron quadrupole or internal rotation were observed. The dipole moment was determined to be 3.95 i 0.05 D. A structural analysis was performed and bond distances and bond angles for a reason- able structure are proposed. The microwave spectrum of N—methylformamide was studied, and the ground state rotational transitions were assigned for the species in which the methyl group is gig to the carbonyl oxygen. From an analysis of splittings in the ground state rotational transitions the height of the bar- rier to internal rotation of the methyl group has been Ribhi Abdelqader Elzaro determined to be V3 = 200 i 10 cal/mole. The dipole moment is 3.86 i 0.02 D and the quadrupole coupling constants are = 2.72 MHz, = 1.57 MHz, and ch = -4.29 MHZ. In Xbb spite of considerable effort no spectrum could be assigned Xaa to a species in which the methyl group is trans to the car— bonyl oxygen. The rotational spectra of N,N-dimethylformamide (CH3)2NCHO, (CD3)(CH3)NCHO (g_i_§_) and (trans), and (CD3)2NCDO have been studied and ground state rotational transitions have been assigned for each of the isotopic Species. The rotational constants are consistent with a planar skeleton for the compound. The barrier to internal rotation for the methyl group gig to the carbonyl oxygen has been determined to be V3 = 1079 i 10 cal/mole from a study of the CD3 species with the CH3 group gig to the oxygen. The ground state rotational transitions in the CD3 species with the CH8 group trans to the oxygen showed no internal rotation splittings which predicts a barrier to internal rotation greater than 2000 cal/mole for the methyl group trans to the carbonyl oxygen. No splittings due to nitrogen quadrupole were resolved for any of the Species, and the dipole moment was determined to be 3.85 i 0.02 D. STUDIES OF THE MICROWAVE SPECTRA OF METHYLDIFLUOROPHOSPHINE BORANE, N-METHYLFORMAMIDE, AND N,N-DIMETHYLFORMAMIDE BY Ribhi Abdelqader Elzaro A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1973 To My Wife Najla ii ACKNOWLE DGME NT S The author would like to express sincere appreciation to Professor R. H. Schwendeman for his assistance, encourage— ment, and guidance during the course of this study and prep— aration of this thesis. Financial aid in the form of Fellowships from UNESCO and Jordan University are gratefully acknowledged. iii TABLE OF CONTENTS I. INTRODUCTION . . . . . . . . . . II. THEORETICAL TREATMENT . . . . . 2.1 2.2 2.3 2.4 2.5 2.6 III. EXPERIMENTAL . . . . . . . 3.1 3.2 3.3 3.4 Introduction . . . . . Moments of Inertia . . Rigid Rotor Hamiltonian Stark Effect . . . . . Internal Rotation . . . Planarity in Amines and Introduction . . . . . Stark Modulation . . . Frequency Measurements Amides Complete Spectrometer Systems . IV. METHYLDIFLUOROPHOSPHINE BORANE . 4.1 4.2 4.3 4.4 4.5 Introduction . . . . . Spectrum . . . . . . . Molecular Structure . . Dipole Moment . . . . . Discussion . . . . . . iv Page 11 14 20 27 27 29 32 32 34 34 35 45 48 51 TABLE OF CONTENTS (continued) Page V. N-METHYLFORMAMIDE . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . 54 5.2 Spectrum . . . . . . . . . . 5.3 Barrier to Internal Rotation . . . . 65 5.4 Nuclear Quadrupole Coupling Constants 67 5.5 Dipole Moment . . . . . . . . . . 5.6 Discussion . . . . . . . . . VI. DIMETHYLFORMAMIDE . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . 78 6.2 Spectrum . . . . . . . . . . . . . 6.3 Barrier to Internal Rotation . . . . 92 6.4 Dipole Moment . . . . . . . . . . . . 93 6.5 Discussion . . . . . . . . . . . . REFERENCES . . . . . . . . . . . . . . . . . . 101 APPENDIX I . . . . . . . . . . . . . . . . . . 106 LIST OF TABLES TABLE Page 1. Notation for treatment of internal rotation . 17 2. Assumed structural parameters and rotational parameters of CH3PF2113H3, and CH3PF211BD3 . . 36 3. Observed and calculated frequencies of ground state rotational transitions for CH3PF211BH3 . 40 4. Observed and calculated frequencies of ground state rotational transitions for CH3PF211BD3 . 41 5. Observed and calculated Qébranch frequencies of ground state rotational transitions for CH3 PF2 11BH3 o o o o o o o o o o o o o o o o . 42 6. Observed and calculated Qébranch frequencies of ground state rotational transitions for CH3 PF2 1 1BD3 0 o o o o o o o o o o o o o o o o 43 7. Ground state rotational arameters of CH3PF211BH3 and CH3PF21 393 . . . . . . . . . 44 8. Ground state rotational, and centrifugal dis— tortion parameters for CH3PF211BH3 and CH3 PF211BD3 o o o o o o o o o o o o o o o o o 45 9. Comparison between the structural parameters of CH3PF211BH3 for both tilted and symmetric borane groups . . . . . . . . . . . . . . . . 47 10. Cartesian coordinates for CH3PF211BH3 in the principal axis system . . . . . . . . . . . . 49 11. Stark coefficients and dipole moments of CH3PF211BH3 and CH3PF211BD3 ,. . . . . . . . . 50 12. Comparison of the dipole moments for some di- fluorOphosphine derivatives and phosphorus— boron adducts . . . . . . . . . . . . . . . . 51 13. Assumed structural and rotational parameters of cis N-methylformamide . . . . . . . . . . . . 57 vi LIST OF TABLES (Continued) TABLE Page 14. Cartesian coordinates for cis N—methylformamide in the principal axis system . . . . . . . . . 58 15. Experimental hypothetical unsplit frequencies for cis N-methylformamide (A species) . . . . 61 16. Ground state rotational parameters for cis N- methylformamide (A species). . . . . . . . . . 62 17. Observed and calculated ground state rotational transitions for cis N-methylformamide (A species) . . . . . . . . . . . . . . .-. . . . 63 18. Ground state rotationaLand centrifugal distor- tion parameters for cis N-methylformamide (A SpeCieS) O O O O O O O C O O O O O O O O O 64 19. Comparison of observed and calculated transition frequencies for cis N-methylformamide . . . . 68 20. Rotational constants, and internal rotation parameters for cis N-methylformamide . . . . . 69 21. Frequencies of transitions used in the deter— mination of the nuclear quadrupole coupling constants for cis N-methylformamide . . . . . 71 22. Stark coefficients and dipole moment of cis N-methylformamide . . . . . . . . . . . . . . 73 23. Assumed structural and rotational parameters of DMF and its isotOpic species . . . . . . . 82 24. Cartesian coordinates of the atoms of DMF in the principal axis system . . . . . . . . . . 83 25. Observed rotational frequencies and internal rotation splittings for trans DMF-d3 . . . . . 86 26. Observed rotational frequencies and internal rotation splittings for DMF. . . . . . . . . . 87 27. Comparison of observed and calculated frequen- cies for cis DMF-d3 . . . . . . . . . . . . . 88 28. Comparison of Observed and calculated frequen- CieS for DMF-dr, o o o o o o o o o o o o o O o 89 LIST OF TABLES (Continued) TABLE 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. Page Ground state rotational parameters for DMF and its isotopic species . . . . . . . . . . . . . 90 Internal rotation parameters for the ground torsional states of DMF and DMF—d3 (trans) . . 94 Quadratic Stark coefficients and dipole moment of N,N-dimethylformamide . . . . . . . . . . . 95 Comparison of dipole moments of some related amides . . . . . . . . . . . . . . . . . . . . 97 Frequencies of A-level transitions for the v = 1 torsional motion of CH3 (trans to the oxygen) of DMF . . . . . . . . . . . . . . . . 106 Frequencies of A and E-level transitions for the v = 1 torsional motion of the CH3 group of CiS DMF‘da o . o o o o o o o o . o o o o o o o 107 Frequencies of A and E-level transitions for the v = 1 torsional motion of the CD3 group of Cis DMF -d3 0 O O O O O O O O Q C O O C O O O O 108 Frequencies of A and E—level transitions for the v= 1 torsional motion of CD3 (cis to the oxygen) Of DMF-d7 o o o o o o o o o o o o o o 109 Frequencies of A—level transitions for the v = 1 torsional motion of CD3 (trans to the Oxygen) Of DMF _d7 . . O . . 0 ‘ O O C . . C 0 . 110 Rotational parameters of the first excited torsional states for DMF and its isotopic species . . . . . . . . . . . . . . . . . . . 111 viii LI ST OF F IGURES FIGURE Page I. Model 8460A MRR spectrometer block diagram . 31 II. Projection of CH3PF2BH3 onto the molecular symmetry plane._ The orientation of the dipole moment vector, ut, is also shown . . . . . . 37 III. Projection of N-methylformamide onto the molecular symmetry plane. The probable orienta- tion of the dipole moment vector, at, is also shown . . . . . . . . . . . . . . . . . . . . 56 IV. Plots of (A - C)/2 XE K for cis N-methyl— formamide . . . . . . . . . . . . . . . . . . 60 V. Staggered and eclipsed conformations of cis N-methylformamide . . . . . . . . . . . . . . 77 VI. Projection of dimethylformamide onto the molecular symmetry plane. The probable orienta— tion of the dipole moment vector, fit, is also shown . . . . . . . . . . . . . . . . . . . . 79 VII. Projection of DMF—d3 cis and trans onto their symmetry planes . . . . . . . . . . . . . . . 81 ix I. INTRODUCTION Gas—phase microwave spectroscopy, as a method for the study of free polar molecules, has been a mature field for more than a decade. In microwave spectroscopy the electo— magnetic radiation includes wavelengths ranging from milli— meters to a few centimeters -- that is, frequencies of from perhaps 5000 to several hundred thousand megahertz (1-5). The region to higher frequency is often referred to as the submillimeter region; to still higher frequency is the far infrared region where optical rather than electronic techniques become more suitable. Microwave spectroscopy had its start in 1934 with the historic experiment of Cleeton and Williams (6) on the in- version spectrum of ammonia; no further papers on micro— wave spectroscopy appeared in the literature until 1946. The concentrated research on microwave radar during World War II provided the necessary instruments and the stimulus for the rapid develOpment of the field which immediately followed the war period. Microwave spectroscopy rapidly proved to be a powerful tool for both physical and chemical research. The method has several unique features which have proved valuable in a variety of chemical problems. 2 The high specificity of the microwave spectrum makes it well—suited for qualitative analysis. The main require— ments are that the substances to be analyzed have suffici— ent vapor pressure (1-10 u Hg) and possess a permanent electric dipole moment. Detection sensitivities approach- ing 1 ppm are possible in the most favorable cases with present instrumentation. A very large number of substances can be detected at a level of one percent and in microgram amounts. Analyses of microwave spectra provide accurate values for bond distances and angles, dipole moments, bond preper— ties, barriers to internal rotation, nuclear quadrupole coupling constants, nuclear masses, molecular magnetic moments, low lying vibrational frequencies, stereochemical conformations, and energy differences of rotational isomers. New applications are continually being developed, as ex- emplified by recent studies of ring puckering in four— and five—membered rings (7), polarizability anisotropy (8), magnetic susceptibilities and molecular quadrupole moments (9), and rotational energy transfer (10). These advances have naturally occurred through simultaneous refinements in the experimental, theoretical and computational methods. It is clear that microwave spectroscopy has provided a considerable quantity of reliable data, often very detailed, on various molecular properties. These data are being built into the structure of chemistry and are also important for testing existing theories and stimulating new theoretical 3 developments. Although the technique is limited at present to polar molecules (oxygen is an exception) which are not very large and which have some observable vapor pressure, ”a large number of compounds and probably many new properties and effects remain to be studied. Furthermore, the possi- bilities of using microwave spectroscopy as an analytical tool have been very little explored (11). The work reported in this thesis was carried out to study some of the molecular properties and to determine dipole moments, barriers to internal rotation, and struc— tural parameters of the molecules N,N-dimethylformamide, N-methylformamide, and methyldifluorOphosphine borane. The first part of this thesis is a discussion of the theoretical and experimental aSpects of microwave spectros- c0py which are of particular importance in the present investigation. The Spectra of the molecules are discussed in Chapters IV, V, and VI. II. THEORETICAL TREATMENT 2.1 Introduction It is well known that the energy of an isolated mole— cule can, to a good approximation, be separated into elec— tronic, vibrational, and rotational parts. In a given electronic and vibrational state most polar molecules in the gas—phase absorb electromagnetic radiation in the microwave region. This absorption increases the rotational energy of the molecules and arises from an interaction of the molecular electric dipole moment with the electric field of the radiation. Rotational energies are quantized and the rotation itself is governed by well—known quantum mechanical formulas (1—5). To a first and very good approx— imation, a rigid rotating body (12) with three principal mechanical moments of inertia serves as an adequate molecular model for many of the observations. The most important effects of non-rigidity serve only to slightly alter the effective moments of inertia. Since the rotational behavior of a rigid body is deter- mined by its moments of inertia, which in turn are functions of the geometry and the mass distribution, the microwave spectrum is determined primarily by the geometric structure of the molecule. 2.2 Moments of Inertia The moments of inertia depend on the positions of the molecular masses with respect to the rotational axes. For a rigid molecule, the moment of inertia about any axis passing through the center of mass is defined by r 2 I = A mdr. (2-1) i where ri is the normal distance of the ith atom from the axis and m1 is the mass of the ith atom. . .t If xi, yi, zi are the coordinates of the 1 h atom and mi is its mass, then the moments of inertia and the products of inertia are respectively (2,12,13), = .. 2 2 2-2 IXX i mi : : —‘ , , 2—3 Ixy Iyx i inyl ( ) where equations (2-2) and (2-3) are cyclical in x, y, z and the sums are over all the atoms in the molecule. The moments and products of inertia are the elements of the moment-of—inertia tensor, a second—rank symmetric tensor I. xx xy xz (2—4) (H H H H I YX YY YZ zx zy zz . 6 The inertia tensor I, can be diagonalized by means of a similarity transformatiOn which is equivalent to a rota— tion of the inertial axes. The eigenvalues are called the principal moments of inertia, and the eigen-axis system is called the principal axis system. The three principal moments of inertia are designated as Ia’ Ib’ IC. Since the trace of the inertial tensor remains the same under a rotation of axes or by the diagonalization procedure, IXX + Iyy + Izz : Ia + 1b + IC . (2-5) In case the original coordinate system does not have its origin at the center of mass of the molecule it can be translated to the center of mass. A computer program which calculates the rotational parameters from bond lengths and bond angles has been written by Schwendeman (14). The pro— gram accepts as input the Spherical polar coordinates of each atom, computes the Cartesian coordinates, and subsequently calculates the rotational constants and interatomic dis— tances and angles. 2.3 Rigid Rotor Hamiltonian In the rigid rotor approximation the energy levels are the eigenvalues of a rotational Hamiltonian which is com- pletely specified by the three principal moments of inertia. The eigenvalue equation is HT 2 ET (2-6) where H is the rotational Hamiltonian operator, T is a 7 rotational wave function, and E is an eigenvalue. The rigid rotor Hamiltonian (2) for an asymmetric rotor can be expressed in terms of the rotational constants A, B, and C. m 4W2 2 2 2 H - h (APa + pr + cpc) (2-7) where A = ——§——-, B = ——h——-, and c = —-§——- with the 8V Ia SVZIb 8W IC usual convention that A :.B :.C. In Equation (2—7) Pa’ Pb’ and PC are the components of the total angular mo— mentum P along the principal axes a, b, and c respec— tively. Matrix elements of Pa, Pb, and PC may be derived from the commutation relationships for angular momentum operators in a rotating Cartesian coordinate system with its origin at the center of mass which are (15), [PX, Py] = -i h PZ [Py, P2] = -i h PX (2—8) [P2, PX] = -1 h Py . A solution of these equations is —i (§)[J(J+1> - K(K+1)]1/2 h K (2-9) = (§—)[J(J+1) - K2] - ll (23)[{J(J+1) — K(K+1)) X{J(J+1)-(K+1)(K+2) )11/2(2-10) ==-h2K2 B = C) and oblate symmetric top (A = B > C) types respectively. For a symmetric top the Hamiltonian matrix is diagonal and the energy levels can be expressed by a simple closed formula. For a prolate symmetric top the energy level formula is written as E = hBJ(J+1) + h(A—B)K2 , (2—12) while for an oblate top E : hBJ(J+1) + h(c—B)K2 . (2-13) For an asymmetric rotor J is still a good quantum number, but K is not. A convenient way of labeling the energy levels is by using the pseudoquantum numbers K_1, K1. Thus an asymmetric rotor level is identified uniquely if we specify J and both K_1, the quantum number with which it connects in the prolate limit, and K1, the quantum number at the oblate limit. The energy levels of an asymmetric rotor cannot be ex— pressed by a simple closed formula. In general, a secular equation must be solved to obtain the energy. This is readily done With a high-speed computer. A computer pro— gram, EIGVALS, written by Hand and Schwendeman for calculat— ing and fitting the rotational spectrum has been in use at this laboratory for several years. Furthermore, several tables of asymmetric rotor energy levels have been published (1,15). It proves convenient to write the energy levels as NIH E = (A + c)J(J + 1) + %(A - C)E(K) (2-14) where E(K) is a reduced (dimensionless) energy expressed in terms of the asymmetry parameter K. The chief value of using K is apparent from the relation, proved by Ray (17), EJ (K) = -EJT(-K) (2-15) which gives the energies for positive K from the energies for negative K, and T = K_1 ‘ K1- 10 The transition selection rules for an asymmetric rotor were given by Dennison (18) in terms of a + - notation, and later by Cross, Hainer, and King (19) in terms of K__1 and K+1. Since the energy matrices are diagonal with respect to J, the selection rules for J for the asym— metric rotor are the same as for the symmetric rotor. Thus, AJ = 0, +1, and -1, corresponding to Q, R, and P branch transitions, reSpectively. The rules for K_1 and K1 can be obtained very easily by means of group theory (19). They depend upon the orientation of the permanent electric dipole moment with respect to the principal axes. Transitions of the a, b, and c types are said to result from the three possible dipole components ua, ub, and uC, reSpectively. These selection rules may be described by giving the allowed changes in parity of the K_1 and K1 indices. If we designate a level with K_1 even and K1 odd as an eo level, then the allowed transitions are: a—type: ee <—> eo and 00 <—> oe b-type: ee <—> co and eo <~> oe c—type: ee <—> oe and co <—> eo . It is, of course, apparent that asymmetric rotors have richer and more complex spectra than linear molecules and symmetric rotors. The intensity of a rotational transi- tion may, in principle, be evaluated by the application of quantum theory, which shows that the intensity of a g-type , u n u 2 . tranSItion lS proportional to ug where “g 18 the 11 component of the total dipole moment along the molecular fixed 9 axis (g = a, b, c). 2.4 Stark Effect When a static homogeneous electric field is applied to a molecule having a permanent electric dipole moment, a torque is exerted on the rotating molecule which perturbs its rotational energy. The extent of perturbation of the rotational energy depends on the orientation of the rota— tional motion with respect to the field as well as the magnitude of the dipole moment. The orientational energy of the permanent dipole moment is given by (1,2), H = -u~e = -ugcos 6 (2—16) where E and E are the electric dipole moment and elec- tric field vectors, respectively, and 6 is the angle be— tween these two vectors. If the electric field is assumed to be along the space-fixed z direction, the angular momentum J can assume 2J+1 orientations with reSpect to 2, corresponding to integral values of MJ from -J to +J. The above perturbation term He can be added to the rigid rotor Hamiltonian, and the resulting eigen value problem can be solved by applying conventional perturbation theory. First—order and second—order perturbation theory yield expressions for the energy which vary with the first and second poWers of the electric field, reSpectively. 12 A first—order Stark effect can be observed for symmetric top molecules, and for the symmetric-top-like energy levels of asymmetric top molecules,both of which have degenerate or near—degenerate rotational energy levels. The first- order energy for a symmetric top is given by, (1) = (0) (0) EJ ILEKM - J(J+1) ‘ (2‘17) 1) Since E( in equation (2—17) depends on the first power of the quantum number M, each energy level for a given J is split into 2J+1 components. The above first—order Stark effect was derived on the assumption that the dipole moment is independent of the electric field. Actually the field perturbs the rotational motion, giving rise to an additional component of dipole moment proportional to the electric field and the inter— action produces a second—order Stark effect. The second- order Stark effect is much smaller than the first-order Stark effect and can be calculated by using second—order perturbation techniques. Golden and Wilson (20) have calcu— lated the Stark effect of rigid asymmetric rotors by second— order perturbation theory. ./ (0) (o) (0) KO)‘ [\Yi IHEIYJ > After evaluation of the perturbation sum, Equation (2-18) 13 is usually written as, (2) . 2 E . = _ 2 ' 2 _ 1 Z (Alg + M Blghlg s (2 19) 9 where g = a, b, or c, and A. and B. are called 19 1g "Stark coefficients". Since EAZ) depends on M2, each energy level is split into J+1 components; where J is the lower energy level involved in the transition. The selection rules for rotational transitions depend on the orientation of the applied electric field with respect to the microwave electric field. When the two fields are parallel, the selection rules are AM = 0, AJ = 0, i1. Therefore the rotational frequencies in the presence of the field are given by, v = v0 -t vs 2-20 where v0 is the zero-field frequency and 2 a = ‘2 "1 + 2 AB J. h 2—21 )5 s ; (AAg M g)lg/ Here AA and AB are the differences in Aig and Big for the energy levels involved in the transition. These quantities depend on the rotational constants of the mole— cule and on the rotational states involved in the transitions. Once the rotational constants (A,B,C) are known and the transitions assigned, the quantities AAg and ABg can be evaluated by means of the EIGVALS computer program. Then the plot of VM ygosz yields a slope which is a func— tion of the uz. This means that the frequencies of the 9 14 Stark components must be measured as functions of 52 to yield the three independent relations necessary to solve for uz, 2 and uz. For some transitions Av a l a Lib’ c D4 m y on y depend upon one or two of the ug and therefore evaluation of the dipole moment is simplified. For transitions involving non-degenerate levels the relative intensities of the Stark components are given by, 0) d.M2 (2—22) I(AJ il) a (J+1)2 - M2 (2—23) I(AJ where J is the lower level involved in the transition. It should be mentioned that the rotational Stark effect has proved to be excellent technique for obtaining molecular dipole moment, and also for assigning rotational transitions of low J which are often characterized by certain Stark patterns. 2.5 Internal Rotation The separability of the energy of an isolated molecule into electronic, vibrational and rotational parts is not exact, and interactions between the rotation and vibrational motion always occur in higher orders of approximation. The nonrigidity of the molecule produces several effects which can be observed in the microwave region. One important effect which can influence the microwave spectrum is internal rotation (21). Internal rotation or torsional motion occurs when one part of the molecule rotates about a bond 15 relative to the rest of the molecule. This motion couples with the overall rotation of a molecule and produces cer- tain effects in its rotational spectrum. Each rotational transition exhibits a fine structure, the complexity of which depends on the height of the potential barrier hinder— ing the internal rotation and on the moments of inertia of the rotating groups. When the internal rotation involves a light group such as the methyl group and is hindered by a moderately high potential barrier (1—2 kcal/mole)—as in trans DMF (d3), for example —-a doubling of most of the ground state transitions is observed in the microwave region. The amount of this splitting leads to a very ac— curate determination of the hindering potential barrier. The potential function for such a motion should be a peri- odic function of the relative angle a between the two parts of the molecule, and must be Nefold degenerate as a goes through 27, where N represents the degree of symmetry of the internal rotor. In the case where the in- ternal rotor has three—fold symmetry, as in (-CH3), (-BH3), (~SiH3), and (-CF3) groups '°° etc., a good approximation of the potential is (7(a) = 72— (1 - cos 3d) . (2-24) A useful model is one in which the internal rotor is a rigid symmetric top which is attached to a symmetric or asymmetric rigid frame. In this case the Hamiltonian may be written as (2,22), 16 H = Hr + F(P —@)2+ We) (2-25) where Hr is the rigid rotor Hamiltonian and the coeffici- ent of the second term in Equation (2-25) is the inverse of the reduced moment of inertia for internal rotation: F = ‘hZ/Zrla . (2—26) The remaining symbols are defined in Table 1. By expanding the second term in Equation (2—25) it is found that the F6’2 is quadratic in P9 and hence may be absorbed into H . The eigenvalue problem associated with the torsional r terms, V3 FP2 + —2 (1 - cos 30,) (2—27) is well known. The boundary condition which is invariance under a —o a + 2V is satisfied by two types of periodic Mathieu functions. The first type has period 2v/3 in a and transforms according to the A Species of symmetry group C3; the second type has period 2v and belongs to the E Species. Consequently, each torsional level v consists of two sublevels, a nondegenerate level, vA(o = 0), and a doubly degenerate level, vE(o = :1). This partial splitting of degeneracy may be considered to be a result of tunneling through the potential barrier. The tunneling does not directly affect the rotational levels, since the Mathieu eigenvalues are independent of rotational quantum numbers. However,the coupling term in Equation (2—25), 17 . a Table 1. Notation for treatment of internal rotation. g = x, y, 2 refers to principal axis of inertia fixed in the framework. Ig = principal moment of intertia of entire molecule. IQ = moment of inertia of internal top about its sym- metry axis. Ag z direction cosine between top axis and the princi- pal axis g. rIa = reduced moment of inertia for internal rotation, where r = 1 — Z A2 I /I 9 a 9 9 Pg = component of the total angular momentum along J,M,K the principal axis g. total angular momentum of the internal tOp along its symmetry axis. (1 = P A i 9 9/19 rotational quantum numbers. the principal torsional quantum number for the harmonic oscillator limit. an index which gives the symmetry or periodicity of the torsional eigenfunction. For threefold barrier, o = O for the A species and o - T1 for the E species. ataken from reference 22. 18 ~2FJJP, transmits an effect of the tunneling to the rota— tional spectrum, since the coupling perturbation differs for the A and E sublevels of a given torsiOnal level. The Hamiltonian given in Equation (2—25) is diagonal in J, M, and 0, but not in K or v. lThe elements off- diagonal in K arise from the asymmetry of HI and also from the terms involving Px' Py in the operator 63 and 69:3. The elements off-diagonal in v come from the per— turbation term -2FG>P. AS in the case of symmetric mole- cules, the VanVleck transformation is applied to remove the off-diagonal elements in v so that the new energy matrix assumes the diagonal block structure. The trans— formed Hamiltonian matrix may then be factored into smaller effective rotational matrices, Hvo’ one for each torsional state. _ (n) (n) _ HVG Hr +F§ wvofp . (2 28) Herschbach (22) has tabulated the barrier-dependent perturbation coefficients Wég) for n.: 4 as functions of a dimensionless parameter s, which in turn is related to the barrier height through _ 9 In the asymmetric top basis, Specified by eigenstates . (n) (n) . of Hr’ only even n terms in E WVO dD contribute to diagonal elements, and only odd n terms to the off- diagonal elements of interest for a slightly asymmetric 19 rotor. In addition, all the perturbation coefficients of odd order (odd n) vanish for A levels. Since the perturbation coefficients do not depend on the molecular asymmetry, they may be evaluated (22) in the limit of zero asymmetry, in which the molecule consists of two coaxial symmetric tops. Nielsen (23) has shown that, in the limit of zero asymmetry, the coupling between in— ternal and overall rotation can be eliminated from the Hamiltonian by transforming to an "internal axis" system. Koehler and Dennison (24) have shown that the internal energy levels may be expanded in a Fourier cosine series, NZCI) W‘ = :Iyz Wk cos B (9 — 90) (2—30) =0 where the coefficients W2 are functions of the torsional level v and the barier parameter s. As 3 —> 00 the W with E > 0 vanish very rapidly. The perturbation co— E efficients given in Equation (2-28) can be related to Equation (2-30) as, n, (2—31) and thus they can be expressed as linear combinations of the Fourier coefficients of Equation (2—30). For moderate barrier heights Equation (2—30) converges very rapidly and it is only necessary to retain the first few terms. Therefore by use of Equation (2-31) the various perturbation coefficients W32) may be approximated in 20 terms of the first few wfi‘s. The advantage of this method, the so—called "bootstrap" method is a result of the fact that the higher order Wé3)'s may be written as linear combinations of the lower order of wfi's. In an alternative method originated by Nielsen (23) and Dennison (24), and called the internal axis method or IAM, the axis about which the top executes internal rota— tion is chosen as one of the coordinate axes. The other two axes are fixed in the framework. In this coordinate system the terms which describe the interaction between the overall and internal rotation are considerably smaller than those which arise in the principal axes method (PAM). Lin and Swalen (21) have demonstrated the connection between the two methods, and have shown that the Hamiltonian func— tions can be transformed Simply from one method to another through a coordinate transformation. 2—6 Planarity in Amines and Amides Compounds containing an N-C-O linkage characteristic of amides and polypeptides are important not only Spectro— scopically, but also biologically. The pyramidal structure of amines has been thoroughly established; valence angles at the nitrogen atom generally fall in the range 102—1120. In the case of amides, however, a variety of evidence suggests that the three bonds from the nitrogen atom are more or less coplanar. Pauling (25) has represented the above bonding system as two resonating 21 forms, and has suggested also that the HzN—C group is planar. In the first microwave investigation (26) of formamide, HZN-CHO, it was concluded that this molecule is planar, but a more detailed study of the Spectrum by Costain and Dowling (27) gave evidence that the equilibrium position of the amino hydrogen atoms is actually about 0.153 out of the plane defined by the rest of the molecule. The microwave spectrum of cyanamide (28,29), HzN—CN, also suggested a nonplanar equilibrium configuration. However, there are some rather subtle points involved in the decision, on spectroscopic grounds, as to whether the equilibrium configuration of a gaseous molecule is exactly planar. The inference of nonplanarity in gaseous amides is based on the following evidence: (a) the observation of satellite lines in the pure—rotational spectrum which ap— pear to come from very low-lying excited vibrational states, much lower than would be expected from consideration of the normal vibrational frequencies of related molecules; (b) indications of rather high anharmonicity in the vibration responsible for these states; and (c) the unusual behavior, in the case of formamide, of the ground—state intertial defect when an amino hydrogen is replaced by deuterium. A. The Inertia Defect. In the principal axis system located in a rigid body of infinitesimal thickness, the following relation is well 22 established, (2—32) where Ia’ Ib are the two inplane moments of inertia and IC is the out-of—plane moment. This relationship holds only for a rigid planar molecule. Because real molecules are not rigid, this equation does not hold exactly. There— fore the inertia defect (A) for a planar molecule is de— fined in terms of effective moments of inertia as, (2—33) and is a measure of the deviation from rigid planarity. Oka and Morino (30,31) have written the contributions to the inertia defect as a sum of vibrational, centrifugal and electronic terms, (2—34) A = A + A( + A( (vib) cent) elect) ‘ They have calculated the contributions of each of these effects for some c2v triatomic molecules. Upon compari— son of the calculated and observed values of the inertia defect in the ground vibrational state, the agreement be— tween these values was quite satisfactory. For non—planar molecules the quasi—inertial defect (A') is defined as A‘ = I - I — Ib + A" (2-35) where A" is the calculated contribution from out—of—plane 23 atoms. If (A') is very close to (A) for a non—planar molecule, the molecule is presumed to have a planar skeleton. The calculation of the inertia defect for molecules other than triatomic may be quite formidable, but as pointed out by Nielsen (32) the inertia defect is not principally a function of the anharmonic part of the potential energy, but rather a function only of the geometry and of the quad— ratic force constants of the molecule. B. Anharmonic Vibrations The potential energy in the normal coordinate system is given as, >1k.Q2. + i V—V0+ ll NIH NlH iii aijk QinQk + --- (2—36) where ki is the quadratic force constant, which is har— monic in nature and relatively easy to obtain, for small molecules, by infrared spectroscopy. On the other hand, aijk’ the cubic force constant is very difficult to obtain. It seems highly probable (27,29) that the low-lying excited vibrational states of amides are associated with the out—of—plane bending vibration of the NH2 group with reSpect to the molecular framework. If this bending vibra- tion were described by a parabolic potential function with its minimum at the planar configuration of the molecule, a series of evenly—spaced vibrational levels, designated by a quantum number v, would result. If the system is per— turbed by adding a small symmetric potential hump centered 24 about the planar configuration, it is well known that the levels of even v will move up in energy relative to those of odd v. Thus the levels v = 0 and v = 1 approach each other, as do v = 2 and v = 3, and so on; in the limit where the potential hump is very large the successive pairs become degenerate, yielding the so—called inversion degeneracy of a non—planar molecule (33). A pyramidal model for formamide (27) was proved to have two equilibrium con- figurations separated by a potential barrier. By fitting the experimental data to a Manning (34) double minimum potential, a barrier of 370 i 50 cm;1 hindering the "inver— sion—wagging" type of motion was determined. C. IsotOpic Substitution In 1953 Kraitchman (35) formulated the problem of structure determination in terms of the changes in the moments of intertia between isotopically substituted mole- cules. For a non-planar asymmetric top Kraitchman"s formu- lation can be summarized as follows: c2 =<(fi)(Pg-PC>[1+(Pg-Pa)/(Pa-PC)][1+(Pg—Pb)/(Pb-PC)1> ' ' ‘ (2—37) where — = [(M + AM)/MAM (2—38) and Pa = 2 miazi = are + 1b - Ia] . (2—39) i . Here I , Ib’ I are the principal moments of inertia, the a c P's are the second moments, defined by Equation (2—39), M is the total mass of the "parent" molecule, and AM is the 25 mass change on isotOpic substitution. In Equation (2—37) the primed quantities refer to the isotopically subSti— tuted molecule and the unprimed quantities to the parent molecule; Equations (2-37) and (2-39) are cyclical in a, b, and c. The quantities a, b, and c are the coordinates of the substituted atom in the principal axis system of the parent molecule. Costain and Dowling (27) have investi- gated ten isotopic species of formamide by microwave spec— troscopy. The inertia defect was found to decrease when— ever a heavier isotOpe was substituted for any atom in the HZN group, and in fact was negative for four of the species studied. It was concluded that the molecule is non—planar with the HZN-C group forming a shallow pyramid. The most probable structure of formamide was given, and the double— bond character of the C-0 bond and N-C bond was esti- mated by using an empirical formula proposed by Pauling (25). The double—bond character in formamide turned out to be 86 percent for the C—0 bond, and 25 percent for the N-C bond. Another parameter, the bond order, may be used to char— acterize the interaction, if a molecular orbital scheme is considered in which the four Pz or n-bond electrons are mobile over the N—C—O linkage. On the basis of a HUckel molecular orbital (HMO), Kumer and Murty (36) have deter— mined the charges on oxygen, carbon, and nitrogen atoms and have determined also the bond orders of C-0 and C-N bonds in several primary, secondary, and tertiary amides. 26 The result showed that the C-0 and C-N bond orders in (DMF) are 1.932 and 1.259 reSpectively. The electronic structure of amides is characterized by resonance stabilization, due to the delocalization of the carbonyl, v- and nitrogen lone pair electrons, result— ing in an increased double-bond character of the C-N bond and a tendency towards a planar structure. Formamide (27) has been shown by microwave Spectroscopy to have a slightly pyramidal conformation about the nitrogen atom in the gas phase while N,N-dimethylformamide is es- sentially planar (this work). III. EXPERIMENTAL 3.1 Introduction Spectroscopy is essentially a determination of energy levels of molecules, atoms, and nuclei. The experimental methods employed to do this consist, fundamentally, of measurements of frequency, because the energy difference between the two levels involved in a transition determines the frequency of radiation which is emitted or absorbed by the particular molecule, atom or nucleus being investigated. The problem of the experimental spectrosc0pist is thus to measure the frequency of the emitted or absorbed radiation as accurately as possible. As in other types of absorption Spectroscopy, the es— sential components of a microwave Spectrometer or molecular rotational resonance (MRR) Spectrometer are the radiation source, absorption cell, and detector. The source is nor— mally a vacuum tube oscillator; reflex klystron oscillators have received the greatest use, with backward wave oscilla- tors (BWO) next in importance. The output of such tubes is highly monochromatic, but the frequency band width is not perfectly sharp because of environmental fluctuations (elec— trical, mechanical, and thermal). The output frequency of a klystron may be scanned continuously by a combination of 27 28 mechanical and electronic control, while in a BWO the fre— quency control is entirely electronic. Microwave radiation is normally transmitted through a waveguide. This is a metal pipe, usually of rectangular cross section, whose dimensions are comparable to the wave— length of the radiation. Waveguides of different sizes are required to cover the full microwave spectrum. The absorp- tionUZmDOm~E _l._ mmhmISO> _l| 3029.:qu —l r «CUES ll :2: 5&on «02582 «95335 oz< ill :20; 2. «023002 «95:82 9 $2: 2%.. Boss .H OHDWflh lllullll\\fi _ $5.1m messiah”... fl # «OhUmEo 4 _. T _ T h JJ Ir H H. jmu F h K_1 + 1, J -> J, with the lines of a given band having the same value of K_1. In each band the spacing between successive transitions decreases as the frequency increases; this gives rise to a characteristic clustering of lines at the high frequency edge, or band head. 36 Table 2. Assumed structural parameters and rotational parameters of CH3PE211BH3, and CH3PF211BD3. r(PF) 1.552 R < (FPF) 100? r(PB) 1.832 < (FPB) 115.470 r(PC) 1.834 < (FPC) 101.450 r(BHS) 1.20 < (BPC) 1209 r(BHa) 1.226 < (HaBHa) 112.690 r(CH) 1.093 < (HCH) 109.190 Rotational constants (MHz) and moments of inertia (amu.gz). CHBPFZBH3 CH3PF2BD3 A 4185.7 4024.1 B 3630.3 3251.1 C 3482.2 3119.1 Ia 120.7 125.5 Ib 139.2 155.4 1C 145.1 162.0 K —0.578 -0.708 37 .CBOEm omaw we .um .H0000> DSTEOE maomflo may m0 coflumucmfluo one .mcmHm Anumfismm Hmasomaoe 0L0 ouco mmmmmmmmu m0 coauomflonm P —..O—_..._ MW0 .HH onsmam 38 The K___l quantum numbers of the bands are easily determined from the positions of the band heads which are not much affected by rotational asymmetry. The spacing between successive band heads is almost constant throughout the recorded region (18 — 40 GHz) for the two species. This Spacing, which is about twice the value of (A - (B + C)/2), was found to be 1240 MHz for methyldifluoro- phosphine- 11BH3, and 1700 MHz for CHéPlelBD3. These values were very sensitive to the structural parameters, which were varied until they could be reproduced for both species. The rotational constants obtained from the struc- ture are the ones Shown in Table 2; they were used to calcu- late rotational energy levels and transition frequencies. These calculations were done by means of the computer pro— gram EIGVALS (48). The required input data for the EIGVALS program are the rotational constants, quadrupole coupling constants and dipole moments. The program calculates the rotational energy levels, quadrupole coupling energies, transition frequencies, line strengths, Stark effect coef- ficients, and Stark shifts for a rigid asymmetric rotor. The intensity and Stark effect for any rotational transi— tion are extremely important for spectral assignments. Transition intensities are calculated from line strength (49,50), while Stark effects are calculated from Stark co— efficients which are calculated by second—order perturbation theory from the line strengths and energy levels. 39 A search of spectral regions predicted by EIGVALS dis— closed groups of transitions which were approximately separated by (B + C) as expected for a-type transitions. Both a— and b—type transitions were observed. The ob— served and calculated frequencies of the assigned transi— tions for the two Species are compared in Tables 3 - 6, while the rotational parameters from the rigid rotor fits are presented in Table 7. The assignment of the transi- tions in the two species were verified by the Stark effect, relative intensities, frequency fit, and expected isotope shift. The spectrum of the 10B Species in natural abundance was predicted to lie in very rich regions and unfortunately a—type transitions could not be identified for either IOB species. The high J —> J, Qébranch transitions were fit for both species by using the computer program CDFIT which was written by R. H. Schwendeman. This program fits the observed assigned transitions by the method of least squares. It uses a model Hamiltonian including rigid rotor and quartic centrifugal distortion terms. It was observed that a good fit (standard deviation = 0.28 MHz) was obtained when fit— ting any one of the Q-branches with the low J Rébranch transitions. However, the standard deviation increased to 1.92 MHz when a fit including two Q—branches was attempted. This suggests that sextic distortion parameters are import— ant. The eight adjusted molecular parameters, three rota— tional constants and five centrifugal~distortion parameters, are given in Table 8. 40 Observed and calculated frequenciesa of ground Table 3. state rotational transitions for CH3PF2118H3. Transition v v Avb obs calc 211 — 312 21708.13 21708.91 -0.78 303 - 404 28429.50 28429.40 0.10 313 - 414 28315.10 28314.82 0.28 404 - 515 35517.30 35517.57 -0.27 413 - 514 36056.32 36056.31 0.01 414 — 515 35359.37 35359.26 0.10 404 — 505 35435.04 35435.0 0.04 423 — 524 35771.50 35771.66 —0.16 432 — 533 35901.09 35901.17 —0.08 431 - 532 35965.69 35965.80 —O.11 4,,2 - 523 36168.38 36168.16 0.21 aIn MHz; estimated uncertainty in observed transitions Rigid rotator parameters used to calculate frequencies are in Table 7. i0.05 MHZ. .- V o calc Table 4. Observed and calculated frequencies 41 a of ground state rotational transitions for CH3PFZIIBD3. Transition Vobs vealc Avb 202 — 303 19139.0 19138.31 0.68 313 - 414 25312.0 25312.37 —0.37 322 — 423 25580.65 25581.04 —0.39 303 — 4O4 25459.72 25459.31 <0.41 312 — 413 25814.37 25814.56 —0.19 431 - 542 37911.80 37911.88 —0.08 523 ~ 624 38697.89 38697.34 0.54 533 — 634 38440.92 38441.49 -0.57 524 - 625 38324.65 38324.47 0.17 515 — 616 37917.80 37917.61 0.18 514 — 615 38627.44 38626.85 0.58 551 — 652 38423.70 38423.91 -0.21 550- 651 38423.70 38423.95 —0.25 505 - 606 38012.90 38013.11 -0.21 505 — 616 38169.80 38169.75 0.04 36970.60 36970.80 —0.20 524 _ 615 a In MHz; estimated uncertainty in observed i0.05 MHz. Rigid rotor parameters used to calculate frequencies are in Table 7. Table 5. Observed and calculated Qébranch frequencies of ground state rotational transitions for CH3PF211BH3. Transition vaSa Vcalcb Ave 2015 6 2016’5 18725.90 18725.83 0.07 2215'8 - 2216,7 18674.96 18674.85 0.10 2415,10 2416'9 18607.85 18608.15 —0.30 2615,12 2616,11 18522.45 18522.45 0.00 2815 14 2816'13 18414.08 18413.90 0.17 3015 16 3016,15 18277.90 18277.86 0.03 2216 7 2217’6 19917.03 19916.37 0.65 2416 9 2417’s 19860.11 19860.29 -0.18 2616,11 1617,10 19788.30 19788.45 -0.15 2816,13 1817,12 19697.85 19697.84 0.00 3016,15 3017,14 19584.34 19584.94 —0.60 3216,17 3217,16 19445.94 19445.57 0.36 aIn MHz; estimated experimental uncertainty 10.05 MHz. bCalculated from rotational parameters given in Table 8. C _ Av - v obs -V calc' 43 Table 6. Observed and calculated Q—branch frequencies of ground state rotational transitions for CH3PF211BD3. Transition Vobsa Vcalcb AVG 1311,3 — 1312’, 19418.30 19418.40 -0.10 1511’5 - 1512,4 19395.70 19395.53 0.16 171,,7 - 1712,6 19362.87 19362.82 0.04 1911’9 - 1912’8 19317.55 19317.53 0.01 2111,11 - 2112,10 19256.28 19256.47 -0.19 2311,13 - 2312,12 19175.92 19175.86 0.05 1512,4 - 1513,3 21098.94 21098.76 0.18 1612,5 — 1613'4 21086.71 21086.58 0.12 1712,6 - 1713’5 21072.70 21072.23 0.46 1912,8 — 1913,7 21035.86 21035.93 -0.07 2112,10 — 2113,9 20986.85 20987.45 -0.60 231,,12 — 2313,11 20924.21 20924.04 0.16 aIn MHz; estimated experimental uncertainty i0.05 MHz. bCalculated from rotational parameters given in Table 8. C _ - 0 AV - Vobs Vcalc 44 Table 7. Ground state rotational parametersa of CH3PE211BH3 and CH3PF211BD3. A Parameter CH3PE211BH3 CH3PF211BD3 b A 4194.60 4044.75 B 3659.57 3262.54 0 3507.23 3135.47 1: 120.4825 124.9459 1b 138.0969 154.9026 IC 144.0952 161.1801 P d 80.8548 95.5684 aa 65.6117 Pbb 63.2404 P 57.2420 59.3342 CC K —0.55674 -0.72051 aObtained from rigid rotator frequency fit. bIn MHz; uncertainty in the rotational constants is 10.05 MHz. c . 22 In u.82 ; converS1on factor: 505376 MHZLL . dIn n.32 - p = (I + I — I )/2, etc. ' ’ aa b c a 45 Table 8. Ground state r0 ational, and centrifugal distor- tion parameters for CH3PF211BH3 and CH3PF211BD3. Parameter CH3PF211BH3 CH3PF211BD3 A 4194.42 4044.68 B 3659.47 3262.55 0 3507.10 3135.50 DJ —0.00288 0.00034 D —0.01099 0.00306 JK DK 0.13447 —0.12395 D 0.01446 -0.00174 WJ 0 —0.13736 0.11726 WK aIn MHz; obtained from CDFIT program. 4.3 Molecular Structure Two isotOpic Species were studied for methyldifluoro- phOSphine borane. The molecular structure of the compound was found to be especially sensitive to the value of (A - (B + C)/2), and great effort was expended to obtain a reasonable structure which gives the experimental value of (A - (B + C)/2) for both species. To obtain a molecular structure reasonable assumptions had to be made concerning some of the molecular parameters. The geometry of the methyl group was assumed to include 46 r(CH) = 1.093 R and < PCH = 109.750. The borane group was assumed either tilted (45) away from the fluorine atoms or symmetric (46) with reSpect to the PB bond. Then, if the PF bond length is assumed, the remaining molecular parame- ters, r(PC), r(PB), < (FPF), < (FPC), < (FPB), and < (BPC), may be determined by-a fit of the rotational parameters 1 and Ic for both Species. a’ Ib' The fitting was done by means of the computer program STRFIT written by Dr. R. H. Schwendeman. Table 9 shows a comparison between the calculated fitting parameters of the compound for both a tilted and a symmetric borane group. It was found that the calculated PC bond length and the FPF and BPC angles are quite sensitive to the assumed PF bond length. The FPF and BPC angles were found to be unreasonable for a PF distance greater than 1.55 A or less than 1.54 8. With the above PF bond distances and fixed methyl group geometry the structural parameters of the compound were tested for several symmetric borane groups. A series of calculations were carried out by assuming the BH bond distance equal to 1.19 A, 1.20 A, 1.21 R, 1.22 R, and 1.23 A. The result of these calculations Showed that the PC, PB bond lengths, and BPC angle are very sensitive to the BH bond distance. This appears to be a result of the proximity of the P atom to the center of mass. The most reasonable results are shown in Table 9, where the PF bond distance is assumed to be 1.55 A and 1.54 A for both tilted and symmetric borane groups. The PC and PB bond 47 Table 9. Comparison between the structural parameters of CH3PF2BH3 for both tilted and symmetric borane groups. Bond Angles and Bond Tilted BH3 Symmetric BH3 Distances P—F 1.542 1.552 1.542 1.552 P-c 1.799 1.779 1.669 1.649 P—B 1.863 1.863 1.993 1.995 < FPF 100.860 99.970 100.860 99.970 < ch 117.250 118.390 118.560 119.520 < ch 102.210 102.670 108.400 108.830 < FPB 115.920 115.290 109.570 108.950 'B-Ha 1.2262 1.2262 1.202 1.202 B-Hs 1.20 1.20 1.20 1.20 < HaBHa 112.530 112.530 116.340 116.340 C—H 1.0932 1.0932 1.0932 1.0932 < HCH 109.190 109.190 109.190 109.190 48 distances obtained from the assumed symmetric borane group seem to be unsatisfactory, and consequently it is highly probable that the molecular structure has a tilted borane group although the tilt may not be quite that assumed. The Cartesian coordinates in the principal axis system for the structure with PF = 1.558 and the tilted borane group are given in Table 10. 4.4 Dipole Moment The shifts in the frequencies of the Stark components of transitions in CH3PF2BH3, and CH3PF2BD3 were measured as a function of electric field (E) in a Stark cell which was calibrated by measuring the Stark shifts in the J = 1-2 transition in OCS (”0C8 = 0.7152D) (51). The resulting slopes for both species, dAv/dEZ, were used with Eq. (2—21) to calculate the dipole moment components, ”a and ubl (uc = O by symmetry). The observed and calculated slopes for the two species along with the resulting dipole moments are given in Table 11. The data in Table 11 give values for CH3PF2BH3 of Iuas = 3.52 D, = 1.765D, and \ut\ ‘Ubi = 3.95 i 0.05 D, and for CHSPFZBDa values of ‘u al 3.50 D, = 1.95 D, and ‘u = 4.00 D. For CH3PF2BH3 iubt ti the angle between the a—axis and the dipole moment vector is 26.060, while for CH3PF2BD3 the angle is 29.130. These angles require that the dipole moment vector be oriented as shown in Figure II. A comparison of the reported dipole moments for some difluorOphosphine derivatives and phosphoruséboron adducts is given in Table 12. 49 Table 10. Cartesian coordinates gor CH3PF211BH3 in the principal axis system. Atom a b 0 P1 0.1096 —0.0541 0.0000 F2 -0.4328 0.7819 1.1871 F3 -0.4328 0.7819 —1.1871 B4 1.9521 —0.3354 0.0000 H5 2.5263 0.7182 0.0000 H6 2.0625 —1.0072 1.0195 H7 2.0625 —1.0072 -1.0195 C8 -0.9632 -1.4740 0.0000 H9 —2.0066 -1.1485 0.0000 H10 -0.7755 -2.0787 0.8908 H11 -0.7755 —2.0787 —0.8908 aThe coordinates shown here were calculated from the struc- tural par meters given in Table 9; tilted borane group and PF = 1.55%. 50 Table 11. Stark coefficients and dipole moments of CH3PF211BH3 and CH3PF211BD3. Transition M dv/dE2(obsd)a'b Calcd CH3PF211BH3 404 - 505 11 15.50 15.47 12 87.0 87.25 13 207.0 206.89 414 — 515 11 18.65 18.47 12 97.50 97.55 13 228.0 229.20 0 = 3.52 1 0.05 D 0b = 1.765 1 0.005 D u = 0.0 D ut = 3.95 i 0.05 D CH3PF211BD3 303 ‘ 404 0 ‘19000 ~19.00 11 64.40 64.40 11 = 3.50 i 0.05 D “b = 1.95 i 0.01 D 4.00 + 0.05 D 1;. l! a 2 ' = . 2 . In MHz/(kv/cm) , assuming “0C8 0 715 D bUncertainty in observed slopes is 10.5%. 51 Table 12. Comparison of the dipole moments for some difluoro— phosphine derivatives and phosphorus-boron adducts. Compound HT Ref. HPF2 1.32 43 CH3PF2 2.056 42 CH3PH2BH3 4.66 44 (CH3)3PBH3 4.99 44 F3PBH3 1.64 46 HFZPBH3 2.5 45 CH3PF2BH3 3.95 This Study aIn Debyes. 4.5 Discussion Several results of the study of CH3PF2BH3 are worth comparing to results of studies of related phosphorus4boron adducts. These are the effect of the coordination on bond distances and bond angles, the relative stability towards dissociation, and the large dipole moment. .Methyldifluorophosphine borane is related to several phosphoruseboron adducts as well as to difluorophOSphine derivatives. If the structural parameters of CH3PF2 (42) are compared to those of the coordinated species, CfiaéFzBfia, the P-F bond length is smaller, while the FPF and FPC 52 angles are larger in the coordinated species. A similar effect is also evident upon comparison of the structural parameters of HFZP with HFZPBfls (45) and HFZPO, which is isoelectronic with HFZPBHQ. I In general, the data reported by Kuczkowski (43-46) reflect these two trends, namely bond lengths to phosphorus decrease and bond angles about phosphmus increase as more electronegative groups are attached. These trends can be rationalized by several semi-empirical models such as: 1) electron—pair repulsion (52), 2) hybridization changes, (53), 3) d orbital participation (54). Each of the pre— ceding models incorporates the concept of electronegativity differences in order to rationalize systematic changes in structural parameters. The H3B-X distance in different H3B-X adducts has also been discussed in terms of orbital following and hyperconjugation in borane adducts (55). And, Percell (55) has applied the hybrid orbital force field (HOFF) of Mills (56) to these same trends. The CH3PF2BH3 addition compound is very stable at room temperature. It gave almost the same spectrum after being stored at room temperature for about two months. After three months or so a portion of the gaseous sample turned into liquid drops of very low vapor pressure. The short P-B bond is consistent with the stability of CH3PF2BH3 towards dissociation to its component donor and acceptor molecules. Chemically, the stability of the compound is not surprising in View of the fact that CH3PF2 is considered a strong Lewis base. 53 The dipole moment of CH3PF2BH3 (3.95 D) is considerably larger than that in HFZPBH3 (2.5 D).. Similarly, a big dif— ference in the dipole moment was reported for CH3PF2 (2.05 D) and PFZH (1.32 D). Since the primary electronic effects of CH3 and D are usually considered to be comparable, this is evidence of some unusual electronic effect in both CH3PF2BH3 and CH3PF2. Kuczkowski (43-46) has pointed out that coordination compounds tend, in general, to have rather large dipole moments, and CH3PF2BH3 is no exception to this rule. The large moments are usually attributed to the appreciable bond-moment associated with the dative bond. The reported (44) P-BH3 bond moment is approximately 3.4—4.0 D. V . N -METHYLFORMAMI DE 5.1 Introduction Compounds containing an N-C-O linkage characteristic of amides and polypeptides are important not only spectro— scopically, but also biologically. Pauling (25) described the N-C-O bonding system in terms of two resonating forms, and suggested that the HzN‘C group is planar. This pic— ture, in which the C-N bond has an appreciable partial double—bond character, has been supported by work in a number of fields (57—60); In the first microwave investigation (26) of formamide, the simplest member of the above class of compounds, it was concluded that formamide is indeed planar in the gas phase. However, a more detailed study of the Spectrum by Costain and Dowling (27) gave evidence that the molecule is non- planar with the HzN—C group forming a shallow pyramid. A proton NMR study of N-monosubstituted aliphatic amides in solution showed that the configuration,in which the alkyl substituent is cis to the carbonyl oxygen, is predominant (61), and that the percentage of the trans con— former increases slightly as the nitrogen substituent be~_ comes more bulky. The percent SEE. conformer decreases from 92% for N-methylformamide to 88% for N—ethylformamide 54 55 and N-isoprOpylformamide (62). Studies of vibrational spectra of geometrical isomers in amides (63) have also shown that the majority of the N-monosubstituted amides exist predominantly in the gig form. A microwave study of N-methylformamide,CH3NHCHO, was undertaken in response to the current interest in the struc— tural and bonding aspects of substituted amides. The pre— ferred configuration has been shown to be the one in which the N-methyl group is gig to the carbonyl oxygen as in Figure III. Unfortunately, it was not possible to assign a spectrum to the trans species. This is consistent with the results of the nmr and ir studies mentioned above. The barrier to internal rotation, the nuclear quadrupole coupling constants, and the dipole moment were determined for the gig species. The rotational spectrum was observed at both room and dry ice temperature. 5.2 Spectrum The preliminary structural parameters of N-methyl~ formamide were transferred from formamide (27). The rota— tional constants were calculated with the STRUCT computer program. The molecular parameters, atomic coordinates, and moments of inertia for gi§_N-methylformamide are given in Tables 13 and 14. The molecule is predicted to have an a4b inertial plane of symmetry. Therefore, only a and b—type transitions should be observed. 56 .cBonm no managonm QLB 2 mo :oauomnoum .HHH musmfim OmHm mH .um .Houoo> quEoE mHomHU 030 m0 coaumusmfl .mamHm mHuoEEmm HmHSUmHOE mzu ouco moHEmEHomahgumE: , mI/ MI P Nu m . as: r o0 m 00 NI 3 57 Table 13. Assumed structural and rotational parameters of cis N-methylformamide. ‘A—‘_ r(NC2) 1.376 2 < NCO 124.00 r(NC6) 1.470 { NCH 113.00 r(NH5) 1.0 { CNH 119.0O r(CH) 1.093 { OCH 123.00 r(C20) 1.193 { CNC 122.70 Rotational constants (MHz) and moments of inertia (u.22) cis N-Methylformamide A 19851.39 B 6125.00 C 4824.19 Ia 25.45 Ib 82.51 I 104.75 K -0.82 58 Table 14. Cartesian coordinates for cis N-methylformamide in the principal axis system.a Atom a b c N1 0.5769 —0.6342 0.0000 C2 —0.7905 —0.4814 0.0000 H3 -1.3267 »1.4339 0.0000 04 —1.3438 0.5754 0.0000 H5 0.9503 —1.5618 0.0000 C6 1.5034 0.5070 0.0000 H7 0.9335 1.4396 0.0000 H8 2.1333 0.4655 0.8922 H9 2.1333 0.4655 —0.8922 aThe coordinates shown above were calculated from the assumed structural parameters given in Table 13. ordinates are in The co- 59 The spectrum calculated by the EIGVALS computer program from the assumed parameters served as a guide in the initial search for an assignment. An assignment was made by ob- serving the characteristic Stark effect of several low J R—branch a and b-type transitions. Transitions in the Qébranch series J - J o,J 1,J—1’ their resolvable Stark effect and quadrupole hyperfine split— were also identified by tings. A Q—branch plot for both series is shown in Figure IV. The graphical values of (A-C)/2 and (K) agree well with those obtained by numerical fitting of the rotational frequencies. After it was realized that the transitions in N-methylformamide were widely split by internal rotation of the methyl group, these transitions were assigned to the levels of A symmetry of the internal rotations. The ob— served assigned A-level transitions, corrected for quadrupole hyperfine splittings, are compared with calculated values in Table 15. The comparison shows considerable deviation from the rigid—rotor frequencies which is attributed to the in— ternal rotation of the methyl group. The corresponding ef— fective rotational parameters of the A—level transitions are given in Table 16. A good fit for A—level transitions was obtained by using the CDFIT computer program including centrifugal dis— tortion parameters. The result of this fitting and the adjusted eight molecular parameters are given in Tables 17 and 18, respectively. The parameters of Table 16 give a very small out-of—plane second moment of inertia Pcc' The 60 7800-1- 4” Po,“ 0“3 / t) 65 SC) N/ “oil/evfl. 7 30% L'- 7541.2 675‘6 (A—C) 24 2 7400-1- ““8008 1 1 11 l l 1 I 1 T I _.73 —-79 K —-80 -81 --82 Figure IV. Plots of (A - C)/2 233 K for gi§_N-methyl- formamide 61 Table 15. Experimental hypothetical unsplit frequencies for gi§_N-methylformamide (A Species). A a 7‘ 7 7157 Transition Vexp Vcalc Deviation MHz MHZ MHZ 000-> 111 24888.80 24888.43 0.36 110-—> 211 24116.43 24116.45 -0.02 101-—> 212 34694.67 34694.67 -0.00 111-—> 212 21112.71 21113.80 -1.09 212 —> 303 21259.79 21259.31 0.47 202 —> 303 33455.90 33456.57 —0.67 211-—> 312 36097.17 36097.99 -0.82 313-—> 4O4 33755.03 33753.80 1.23 303 —e 312 19343.51 19342.65 0.85 404 —> 413 23228.42 23227.62 0.79 505 —> 514 28566.61 28566.24 0.36 606-—> 615 35466.23 35467.08 -0.85 aCorrected from observed frequencies by using parameters in Table 21. the quadrupole b . . . Calculated by using the rotational constants given in Table 16. 62 Table 16. Ground state rotational parameters for cis N-methylformamide (A Species). Parameter V = 0 A (MHz) 19985.315 B 6404.443 c 4903.119 1a (n.22) 25.2873 1b 78.9102 1C 103.0723 a 2 Paa (u.g ) 78.3475 Pbb 24.7247 P 0.5626 CC K -0.8009 63 Table 17. Observed and calculated ground state rotational tran51tions for cis N-methylformamide (A Species). Transition Vobsa Vcalcb AVC 000-> 111 24888.73 24888.20 -0.47 111 —> 212 21112.49 21112.35 0.13 101-—> 202 22497.38 22497.28 0.09 110 —> 211 24116.33 24116.20 0.12 101 —> 212 34694.50 34694.00 0.50 211-—> 312 36097.21 36097.31 -0.10 221 -9 322 33917.80 33917.88 —0.08 202 —> 303 33455.83 33456.11 —0.28 212-—> 313 31597.60 31597.76 -O.16 303 —> 312 19343.86 19343.79 0.06 313 —> 404 33755.09 33754.92 0.17 413 —¢ 422 37428.39 37428.42 -0.03 404 —> 413 23228.82 23228.32 0.49 505 —> 514 28565.32 28565.95 -0.63 606-—> 615 35464.92 35464.70 0.21 615 —e 624 35714.0 35713.99 0.00 716«—> 725 36481.94 36481.88 0.05 817-—> 826 38728.93 38728.96 —0.03 In MHz; estimated experimental uncertainty 10.05 MHz. bCalculated from rotational parameters given in Table 18. AV = Vobs - Vcalc' 64 Table 18. Ground state rotational, and centrifugal dis— tortion parametersa for cis N-methylformamide (A Species). Parameter v = 0 A 19987.553 B 6405.127 C 4902.444 . 04 DJ 0 0 2 .04 DJK 0 00 — . 14 DK ‘ 5 3 9 DWJ 0.1422 6.0625 DWK aIn MHz; Obtained from CDFIT program. 65 expected value (1.6 u.Rz) is much larger than the value in Table 16 (0.562 u.g2). The departure of the spectrum from a rigid—rotor fit, and small PCC value indicated an effect of a low frequency vibration (64). On the assumption that the anomalous value for PCC was caused by the internal rotation of the methyl group, the value of the potential barrier which would correct PCC to the expected value was calculated (as— suming that the molecule possesses a planar skeleton). 5.3 Barrier to Internal Rotation A low barrier hindering the internal rotation of the methyl group in gig N—methylformamide produced very large splittings between A and E levels. To account for these splittings the matrix ch was calculated from Eq. (2-28) including perturbation coefficients to fourth order. _ 4 (n) 10’ HVG - Hr + Fnél WVO 0° (2-28) The matrix obtained from the above equation factors into blocks of dimension 2J + 1 for each J. The matrix was diagonalized and the eigenvalues were calculated by means of the computer program INROT. The barfier to internal rotation was predicted to be so low that the validity of the perturbation method used by the INROT program was in doubt. Therefore, the calcula- tion was repeated with the FREEROT computer program which uses a lowébarrier approximation in which free-rotor wave 66 functions form the basis set for the torsion of the methyl group (65). The required input data for the FREEROT pro- gram are the three-fold barrier height (V3), the moment of inertia of the internal rotor about its symmetry axis (Iy), ( . the angle between the symmetry axis of the internal rotor and the principal axis (0), and the rigid rotor rotational constants A0, B0, and CO. For N—methylformamide 21’ _. 2 (2) 1:! _ 2 (2) : A0 — AA 0' FWOA , B0 - BA 6 FWOA , Co CA. A preliminary calculation was carried out with the effective second moments of inertia obtained from the A-level fre— quency fit and by using the above relations an approximate barrier height, V3 = 190 cal/mole, was obtained. With this barrier height and calculated values of the other five rotational parameters the FREEROT program was used to pre— dict the frequencies of the E transitions. The E—level transitions were then found and finally assigned through their characteristic first order Stark effect. Final values of the internal rotation parameters were determined from a least-squares fit of 12 measured frequencies, six A-level and six E-level. The molecule was assumed to have a plane of symmetry such that the direction cosine, A between the methyl group axis and the out-of—plane C axis was zero. It was further assumed that the A—E splittings would vary linearly with the various parameters Pi' 67 BAv 0Av = Z ( )0P. . i SPi 1 The derivatives (BAv/BPi) were obtained numerically by varying each parameter individually and noting the effect on the Av's. The results of the calculation are given in Tables 19 and 20. In tables 19 and 20 the results of two calculations are Shown. In one calculation the methyl group moment of inertia was alloWed to vary and finally settled at the rather small value of 3.04 u.22. In the second calculation Ia was fixed at the more reasonable value of 3.16 u.82. The results show that the values of the barrier height are so close that it can be reported as V3 3 200 i 10 cal/mole. 5.4 Euclear Quadrupole Coupling Constants The majority of molecules have no electronic angular momentum. If any hyperfine structure of rotational transi— tions is observed, it is therefore usually (66) due to the interaction between a nuclear quadrupole moment and the gradient of the electrical field produced at this nuclear position by the remaining molecular charges. The interac— tion of the quadrupole moment of the 14N nucleus of the N—methylformamide with the electrical field gradient pro— duces a hyperfine structure in certain transitions. This interaction causes the respective nuclear spin I and the molecular rotation J to couple to a resultant F. The analysis of the rotational spectrum in the microwave region 68 Table 19. Comparison of Observed and calculated transition frequencies for cis N-methylfomrmamide. . . a b C TranSition Vobs (VobS-Vcalc) (VObS-Vcalc) A Species 211 —> 312 36097.21 2.85 "2.45 101-—> 202 22497.38 —3.30 —6.55 221'—> 322 33917.80 -2.60 ~6.86 313-—> 404 33755.09 2.24 1.65 220-—> 321 34384.25 0.63 —3.47 E Species 211-—> 312 34636.67 ~7.97 —0.24 111 —> 212 22423.50 8.63 10.83 313-—> 404 34210.93 -2.53 —2.22 220~—> 321 33798.85 4.00 16.27 aIn MHz; observed frequencies. b . . . . Obtained by u81ng parameters in Table 20 With I” = 3.04 u.82. CObtained by using parameters in Table 20 with I = 3.16 u.32. (Y. 69 Table 20. Rotational constants, and internal rotation parameters for cis N-methylformamide. Effective Rotational Constants A = 19.98531 GHz B = 6.40444 GHz C = 4.90311 GHz Internal Rotation Parameters IQ = 3.16 u.22a IQ = 3.04 n.22b A0 = 19.4755 0H2 A0 = 19.4843 GHz B0 = 6.3289 GHz B0 = 6.3301 GHz 00 = 4.9053 GHz 00 = 4.9048 GHz a = 0.078149 a = 0.075244 6 = 0.030350 6 = 0.029276 F = 172.60297 GHZ F = 178.59683 GHz v3 = 199.50 cal/mole v3 = 204.95 cal/mole 9 = 50.070 0 = 50.130 s = 5.387 s = 5.349 —__ a Parameters obtained from least squares fit with I fixed at 3.16 u.gz. a Parameters obtained from least squares fit with I varied. n 70 including the hfs yields besides the rotational constants of the molecule the nuclear quadrupole coupling parameters. The hyperfine splittings in 14N are of the order of one to two MHz; therefore, a first-order correction to the rigid- rotor Hamiltonian Should be quite adequate. H = Hr + HQ (5—1) where HQ that appears above is the correction term. For the frequency of any transition this correction may be written as AVquad : A0‘Xaa + AB F‘ vaS Vcalc 303 —> 312 4-—> 4 19343.84 19343.83 3-—> 3 19342.43 19342.42 2 —e 2 19344.32 19344.33 404 —> 413 5 —9-5 23228.71 23228.71 4 —> 4 23227.22 23227.21 3 —> 3 23229.09 23229.09 505 —> 514 6 —> 6 28567.05 28567.02 5 —> 5 28565.32 28565.29 606-—> 615 7 —> 7 35466.71 35466.50 6.—> 6 35464.92 35464.72 ggadrupole Coupling Constants .1 C = : Xaa 2.72 MHZ Xzz 2.73 MHz Xbb = 1.57 MHz Xxx = 1.55 MHz ch = —4.29 MHz ny = -4.29 MHz = o eaz 6.34 aIn MHz. bvcalc = the hypothetical unsplit frequency plus the hyper— fine quadrupole splitting. C- Xaa eQ (bzv/Baz), etc. 72 5.5 Dipole Moment The shifts in the frequencies of seven Stark components of four transitions in N-methylformamide were measured as a function of electric field (E) in a Stark cell which was calibrated by measuring the Stark shifts in the J = 1 —e 2 transitions in OCS (DOCS = 0.7152D) (51). The Stark co- efficients for these transitions were computed by neglecting the small quadrupole interaction. The resulting seven slopes, dAv/dEz, were used with Eq. (2—21) to calculate the dipole moment components, ”a and ”b (uc = 0 by symmetry). These slopes were also fit by least-squares and the observed and calculated results along with the result- ing value of the dipole moment are given in Table 22. These data give values for N-methylformamide of (na| = 2.95 D, lubl = 2.48 D and ‘Ht‘ = 3.86 1 0.02 D. For N- methylformamide the angle between the a-axis and the dipole moment vector is (40.050). Although the Sign of the dipole moment and the Sign of the angle are not determined by these data,the most probable orientation makes an angle of 33.70 with the C—N bond and is directed as shown in Figure III. 5.6 Discussion Interpretation of the relatively low barrier to in— ternal rotation in cis N—methylformamide should take into account the following: 73 Table 22. Stark coefficients and dipole moment of cis N-methylformamide. a . Transition M (av/c132)obs (dv/dE2)ca1Ca 000-—> 111 0 332.33 326.76 101 —> 202 0 -68.50 —66.32 1 258.0 259.65 110-—> 211 0 119.0 117.54 1 —1714.0 -1717.99 1 1830.0 1831.08 pa = 2.95 1 0.02 D ab = 2.48 i 0.01 D no 2 0.0 0t = 3.86 1 0.02 D aIn MHz/(KV/cm)2, assuming MOCS = 0.7152 D. 74 (1) By comparison with the barrier height determined for methylamine (V5 = 1976 cal/mole (67)) the H3CNH fragment should give rise to a contribution to the barrier of about 1 kcal/mole favoring a configuration in which the methyl group staggers the NH bond. (2) The contribution of the H3CNC fragment to the bar— rier height is not easy to predict. The barriers to internal rotation in H3C-N'CH2 (68) and H3C-N=CH(CH3) (69) are 1970 cal/mole, and 2109 cal/mole, respectively. In neither case, however was the equilibrium configuration of the methyl group determined. The barrier to internal rotation in di— methylamine (70) is 3200 cal/mole presumably favoring a staggered configuration. Thus, in addition to not knowing whether to consider the amide NC bond as a single or double bond, we do not have sufficient information on bar— ier heights of methyl groups attached to nitrogen. (3) In the configuration in which the methyl group in gig N—methylformamide staggers the NH bond the distance be- tween one of the hydrogen atoms of the methyl group and car- bonyl oxygen is less than the sum of the van der Waals' radii (2.60 2) for the two atoms. In the eclipsed configura- tion the distance is larger (Fig. 5). It has been shown in a large number of cases that a severe effect on the barrier to internal rotation occurs when— ever atoms approach distances which are smaller than the sum Of the van der Waals' radii. The magnitude of this effect has been shown to be 1-2 kcal/mole which can either increase Or decrease the barrier height depending on whether the steric hindrance occurs when the methyl is in its low energy or high energy configuration, respectively. 75 The result of this discussion is that interpretation of the low barrier in gig N-methylformamide is very diffi— cult in the light of the present knowledge of barrier heights in nitrogen compounds. It is made particularly difficult by the lack of knowledge of equilibrium configuration of the methyl groups. It is possible, in principle, to deter- mine these equilibrium configurations by microwave spectros- copy by studying the Spectra of CHZD species. That this has not been widely done is due to the expense and/or dif- ficulty of preparing the isotopically-labelled compounds. In Spite of the uncertainty involved, two simple interpretations of the low barrier in N—methylformamide are especially attractive. In the first of these the low barrier is simply the result of cancellation of the nearly equal but opposite contributions to V3 from the HSCNH and HacNC fragments. That is, the methyl group faces two bonds 180O apart. Where these two bonds are equivalent, as in CH3N02 (71), for example, it is known that V3,= 0. In the present compound the non-equivalence of the NH and NC bonds leads to a net V3 of 200 cal/mole. For this interpretation the NC amide bond would have to be an es— sentially Single bond and the Ho-o-O steric effects must be ignored. In the second simple interpretation the H3CNH and H3CNC fragments give rise to a relatively high V3 contri— bution favoring an equilibrium configuration in which the methyl group staggers the NH bond. In this configuration 76 the H----0 steric effect is most severe and increases the potential energy, thereby decreasing v3. The net result is a V3 of 200 cal/mole. For this interpretation the NC bond would have to be regarded as having signifi- cant double bond character and the H°---0 steric inter— action must be Significant. Which of these two interpre— tations is closer to the truth, if either, will have to be decided after further work. 77 g! f, o a‘ 1‘5" / . ,. ’ .. .. __H O H STAGGERED C N H H ,/ O ./ / 1qu ,9 / / H ECLIPSED C N H \ H Figure V. Staggered and eclipsed conformations of Eli N-methylformamide. VI. DIMETHYLFORMAMIDE 6.1 Introduction Dimethylformamide is a member of the class of com- pounds including the amides and polypeptides in which the N-C-O linkage has a major role in determining the struc— ture and intramolecular dynamics. As mentioned before, Pauling (25) postulated that the central C-N bond in amides has an appreciable doubleebond character. As a result of this doubleébond character, amides and substituted amides should have planar or nearly planar skeletons. An electron diffraction study of DMF in the gas phase (72) showed that the compound is nearly planar. NMR studies of amides in solution (62) have shown the possibility of geometric isomerization about the C-N bond and barriers to internal rotation about this bond have been reported for several amides. Dielectric constant measurements (73) in the vapor phase at 1100 for N-methylformamide and N,N-di- methylformamide gave values of the dipole moment as 3.82 and 3.80 Debyes, respectively. Dimethylformamide (DMF), Figure VI, has been a subject of interest in this laboratory for several years. In 1968, H. B. Thompson assigned the ground state rotational Spectrum of DMF-d7, and also made a preliminary aSSigment for the parent 78 m MQO HAW .cBOLm omHm ma .ud .Houom> ncmEOE maomao mLp mo coaumusmflno HQ .H> musmflm I a oonoum 0:9 .mamHm muumaawm ansomHOE mnu ouso mUHEmEHomamnquac mo 20.0 _ 9 VI I oo 79 NE .1 80 compound. In 1969, A. H. Brittain restudied the rotational spectra for the two species and studied the Stark effects of several transitions. In the present study the ground state rotational Spectra of gig and trans DMF-d3, Figure VII, were assigned. Rota- tional spectra in excited torsional states for both tops attached to the nitrogen atom were studied in all three isotopic species. The barrier to internal rotation of the methyl top gi§_to the oxygen atom was determined from the Spectrum of trans DMF-d3. The barrier was confirmed through the fitting of A and E—levels in the ground state rotational spectrum of the parent compound. Stark measure- ments were repeated and the dipole moment was determined for the parent compound. 6.2 Spectrum The preliminary structural parameters of N,N-dimethyl— formamide were transferred from formamide (27). The rota- tional constants were calculated with the STRUCT computer program. The molecular parameters, atomic coordinates, and moments of inertia for the parent Species are given in Tables 23 and 24. The moments of inertia for the other three isotopic species are also presented in Table 23. The inertial plane of symmetry for the compound is the an plane; therefore, a and b—type transitions Should be observed. The preliminary rotational constants were used to calculate energy levels and transition frequencies. 81 H b H I c C ~ H,H N lo , a .211 C D//\D H b D C C O \N Da TRANS 2C H/( \ H,H Figure VII. Projections of DMF-d3 cis and trans onto their symmetry planes. 82 Table 23. Assumed structural and rotational parameters of DMF and its isotopic Species. Bond Distances and Bond Angles N1C2 1 .376 2 1110203 124.00 N1C5 1.470 03C2H4 123.00 czo 1 .196 N1C2H4 113 .00 C2H4 1.093 C2N1C5 120.00 C5H7 1 .093 1110511., 109 .500 N1C6 1.470 H10C6H12 109.440 Rotational Parametersa DMF gi§_DMF-d3 t£§n§_DMF-d3 DMF~d7 Ia 58.7263 70.1023 64.0689 79.3343 Ib 119.1094 123.1452 132.9158 136.9717 IC 171.4167 183.5003 187.2375 203.3131 r -0.5422 —0.3940 —0.5748 -0.3801 a . . . 2 Moments of inertia are in u.g . 83 Table 24. Cartesian coordinates of the atoms of DMF in the principal ax1s system. Atom a b c N1 —0.43198 -0.00158 0.0000 C2 0.78462 —0.64442 0.0000 03 1.83917 —0.08019 0.0000 H4 0.69219 —1.73350 0.0000 C5 —0.48710 1.46737 0.0000 C6 —1.67658 —0.78380 0.0000 H7 0.52880 1.87060 0.0000 H8 -1.01557 1.81265 0.89227 H9 —1.01557 1.81265 —0.89227 H10 —1.43724 -1.85027 0.0000 H11 -2.25961 —0.54178 -O.89227 H12 —2.25961 —0.54178 0.89227 aThe coordinates shown here were calculated from the as— sumed structural parameters given in Table 23. The co— ordinates are in . 84 These calculations were performed by the EIGVALS computer program. An initial search in the predicted spectral region re- vealed that each ground state rotational transition is accompanied at higher frequencies by several transitions of moderate intensity which exhibit a Stark effect identical to that of the main transition, as expected for Vibration- ally excited states. In this study confirmed assignments of the ground state rotational transitions for all isotOpic species are presented here, while proposed assignments for the excited states are given in Appendix I. The reasons for this separation are discussed below. A) Ground State Spectrum: Although EIGVALS calculations indicated that each spec- trume should consist of a~ and b-type transitions, only a-type Rebranch transitions were observed for all isotopic species. The assignments were substantiated by rigid—rotor fits and characteristic Stark effects. No splittings due to nitrogen quadrupole were observed, but on the other hand, measurable ground state splittings due to internal rotation were observed in both the parent and in the trans DMF—d3 Species. Both A and E—level transitions were observed in most of the ground state transitions of trans DMF—d3 and were confirmed through rigid-rotor fitting and theoretical calcu— lation of the splittings. A comparison of observed and 85 calculated frequencies for a number of transitions is given in Table 25. After the barrier was determined for the methyl top, A and E—level transitions for the normal species were confirmed in a similar manner. A comparison of the observed and calculated frequencies for a number of transitions is given in Table 26. As mentioned above, the ground state rotational transitions do not split in either the DMF—d7 or the gig DMF-d3 species. The absence of internal rotation splittings in the gi§_DMF—d3 ground state transitions predicts a bar- rier for the methyl group trans to the aldehydic oxygen greater than 2000 cal/mole. A comparison of the observed and calculated frequencies for gig DMF—d7, and DMF-d7 are given in Tables 27 and 28, respectively. The ground state effective rotational parameters for all isotopic species are shown in Table 29. B) Excited State Spectra: Dimethylformamide and its isotopic species exhibit rich spectra in both the K and R—band spectral regions. Each ground state rotational transition is accompanied at higher frequencies by several transitions. These transitions are probably the corresponding rotational transitions in low— lying excited states of the methyl torsional motions. It was noticed that these excited states for gi§_DMF—d3 occur more often in a consistent pattern. In this Species each ground state transition is followed by three pairs of 86 Table 25. Observed rotational frequenciesa and internal rotation splittings for trans DMF-d3. Tran81tion VA VE (VA ‘ VE) 321 —> 422 27281. 45 0. 04)b 27278.05 0. 09 3.40(-0.05) ) 312-—> 413 27662. 0. 20) 27659.50 0.12) 3.0 (0.08) ) ( ( 414 —> 515 29201 10 03) 19201.10(O. 64 ( ( 423 —> 524 32052. 20 0.11) 32049.85 0. 9) 2.35 -0. 01) 432-—> 533 32846. 70 -0. 08) 32843.60 -0. 07) 3.10 0. 00 ) 0. 03) ) 4.49 0 .01) ( ( ( 413 -> 514 34148.16 —0. 14) 34145.02(-0.14) 3.14(0. 04 422 ~> 523 34589.10 0. 0 ) 34584.61(0.06 ( ( 5 515 —> 616 34784. 70 0. 05) 34783.95 10 ( 50( (-0 ( ( 431-—> 532 33183. 85(-0. 06) 33180.10(—0.19) 3.75 ( ( ( 48.(0 (-0 ) (0. 35) 0.75 —0. 04) ) 35202. 48(0 50) ( ) 524-—> 625 38166. 38 13) 38164. 08 0. 05 2.30(-0.2) aIn MHz; estimated uncertainty is 10.05 MHz. Values in parentheses are observed minus calculated fre— quencies. Rotational constants are in Table 29, internal rotation parameters in Table 30. 87 Table 26. Observed rotational frequenciesa and internal rotation splittings for DMF. Transition v v (VA - v ) 202 —> 303 20690.70 0. 04)b 20689.50 0. 12 1.2 (~0.04) 220 —> 321 22320.10 0. 09) 22317.15 —0.2 2.95(—0.15) ) ) 211 —> 312 23217.10 0.08) 23214.30 .199) 2.80 —0. 2) ) OO O O 313 —> 414 25830.00 0 03) 25829.10 0.90 ( (-0 312 —> 413 30648.90 30645. 20 .7o(-0 02) —0. 21) 3. 00(—0. 03) 414 —> 515 32019.90 —0. 04) 32019.05 0.00) 0.95(-0.08) A /\ /\ /\ /\ /\ /\ /\ l O H N V -0.10) 4.60(0.04) ( ( ( ( (-0 423 —> 524 35369.20(-0. 08) 35366. 20 ( ( 322 —> 423 28506.65(0. 05) 28504.0(-0.1) 2.65(0.00) ( 331 —> 432 39039.30 —0. O7) 39036.55(0.1) 2.75(—0.05) aIn MHz; estimated uncertainty is 10.05 MHz. bValues in parentheses are observed minus calculated fre— quencies. Rotational constants are in Table 29; internal rotation parameters in Table 30. l‘illj 88 Table 27. Comparison of observed and calculated frequenciesa for cis DMF-d3. Transition Vobs Vcalc Avb 330 —> 431 28084.42 28084.59 —0.17 312 —> 413 29164.27 29164.19 0.07 321 —> 422 29444.35 29444.13 0.21 414 —> 515 30008.67 30008.45 0.21 404-—> 505 30409.54 30409.39 0.15 423-—> 524 33505.22 33505.22 0.00 413 —> 514 35617.40 35617.52 —0.12 431 —> 532 35654.20 35654.66 -0.46 515-—> 616 35656.76 35656.75 0.00 505 —> 606 35848.40 35848.27 0.12 422-—> 523 37221.82 37221.20 0.61 524 —> 625 39700.11 39700.63 -0.52 a . . . . . In MHZ; estimated uncertainty 1n observed frequenc1es is 10.05 MHz. bv obs v calc Rotational constants are in Table 29. 89 Table 28. Comparison of observed and calculated frequenciesa for DMF—d7. Transition Vobs Vcalc Avb 101 -> 202 12042.50 12042.41 0.08 110 —> 211 13475.50 13475.38 0.11 111 —> 212 11166.00 11165.93 0.06 211-—> 312 20012.45 20012.53 -0.08 220-—> 321 19501.70 19501.75 -0.05 221 —> 322 18481.15 18480.99 0.15 313-—> 414 21881.60 21881.66 -0.06 322._> 423 24421.60 24421.78 —0.18 aIn MHz; estimated uncertainty in observed frequencies is 10.05 MHz. v calc 3 AV. Rotational constants are in Table 29. 90 Table 29. Ground state rotational parametersa for DMF and its isotopic species. Parameter DMF gfigggé D§%§da DMF-d7 A(MHz) 8927.80 8185.47 7494.36 6604.66 B 4203.77 3770.91 4061.47 3657.52 0 2964.67 2714.03 2772.34 2502.80 AA 1.91 0.51 AB 0.69 0.57 AC -0.03 -0.02 1a(u.22) 56.6069 61.7406 67.4341 76.5414 1b 120.2196 134.0195 124.4317 138.2165 1C 170.4661 186.2085 182.2919 201.9859 paa(u.22) 117.0393 129.2437 119.6447 131.8305 Pbb 53.4267 56.9648 62.6471 70.1554 Pcc 3.1802 4.7757 4.7869 6.3860 r -0.5844 -0.6136 —0.4539 -0.4369 a . . . . . Estimated uncertainty in rotational constants is 10.7 MHz for A and 10.04 MHz for B and C; AA = AA — AE, etc. 91 doublets which have almost the same magnitude of Splitting. One pair of these is relatively more intense than the other two, and seemed to be the first excited torsional state for the CD3 top which has a barrier of 1079 cal/mole. The assumed A and E-level transitions fit the rigid—rotor model and the observed splittings agree nicely with the calculated splittings obtained by the INROT computer pro— gram. One of the other two pairs also fits the rigid rotor model and the comparison between the observed and calculated frequencies for this spectrum is given in Appendix I. The origin of this second set of doublets is not clear. It cannot be the second excited state of the CD3 torsion be— cause the splittings are too small. It cannot be the first excited of the CH3 torsion because the splittings are too large. It cannot be a mixed mode because there is no more intense set of transitions to be the first excited state of the other mode. A search for excited states in the normal and DMF-d7 Species disclosed a group of transitions to higher frequen- cies of the ground state lines. Among some of these transi~ tions a similar pattern of doublets was Observed which fit the rigid-rotor model as Shown in Appendix I. The interpre— tation of these transitions is unclear. The complexity of the spectra and the incoherence of the excited state transitions with respect to the ground State rotational transitions suggests the possibility of considerable coupling between the two tops attached to the 92 nitrogen atom. Preliminary calculations of the predicted Spectra for two tops with coupled internal rotation with a computer program written by Dr. R. H. Schwendeman showed that the complexity of this problem is such as to be beyond the scope of this thesis. 6.3 Barrier to Internal Rotation The analysis of internal rotation splittings in the ground state rotational transitions of DMF was carried out by using the effective Hamiltonian for each torsional state _ 4 (n) (n) Hvo - Hr + F nil wVO 6) (2-28) The matrix elements of HVG were calculated from Eq. (2-28) including perturbation coefficients to fourth order. As mentioned above, the internal rotation splittings were observed in both DMF and DMF-d3 (trans) in which the CH3 top is gi§_to the carbonyl oxygen. The splittings were calculated by means of the INROT computer program. Assuming that v3 >> v6, only Ia, 1g, A, B, c, and V3 are variable parameters. Of these, the effective rotational constants were used from the assigned spectrum and the di— rection cosine, kg, was calculated from the assumed struc— ture. The moment of inertia of the methyl top, Ia, was taken as 3.16 u.82. The remaining adjustable parameter is V3, the three-fold barrier to internal rotation. The dif— ference between the Observed and calculated splittings for -E£3E§ DMF—d3, and DMF normal species are given in Tables 25 93 and 26, respectively. The best value of V3 is 1079 1 10 cal/mole for £322§_DMF-d3, and 1072 1 10 cal/mole for normal DMF. These values are for the methyl group gig to the oxygen atom. All internal rotation parameters used in these calculations are given in Table 30. 6.4 Dipole Moment It has been mentioned that the Stark effects provided an essential part of the evidence for assignment of DMF transitions. Most of these transitions exhibit clean and resolvable Stark Components. The observed second-order Stark displacements in the frequencies of six Stark compo nents were measured as a function of electric field (E). The Stark cell was calibrated by measuring the Stark shifts in the J = 1 —e 2 transition of OCS (“0C ‘ 0-7152D (51))- S The resulting six Slopes, dAV/dEz, were used With EQ- (2‘21) to calculate the dipole moment components: ”a and p“bl (00 = 0 if a plane of symmetry is assumed). The slopes were also fit by least-squares and the observed and calcu- lated values along with the resulting value of the dipole moment are given in Table 31. For DMF Ina) = 3.795 D, tub) = 0.625 D and Wt] = 3.845 1 0.02 D; the angle be- tween the dipole moment vector and the a axis is 9.350 and between the vector and ON internuclear line is 37.20. The latter value requires an assumption concerning the orientation of the dipole moment since only the squares 0f the components are Obtained from the Stark effect. The IIIIIIIIIIIIIIIIIIIIIIIIIr—— 94 Table 30. Internal rotation parameters for the ground torSional states of DMF and DMF-d3 (trans). Assumed DMF DMF-d3(trans) Ia 3.16 n.82 3.16 u 82 9 87.810 88.080 0.9992 0.9994 g F 164.30265 GHZ 163.84457 GHZ Determined A0 8926.57 MHz 8184.47 MHz B0 4203.76 3770.90 00 2964.67 2714.03 S 30.4134 30.6976 v3 1072 1 10 cal/mole 1079 1 10 cal/mole 95 Table 31. Quadratic Stark coefficients and dipole moment of N,N-dimethylformamide. - I a a TranSition IMI (av/6E2)Obs (av/3E2)ca1c 212._> 313 0 —16.73 -16.10 1 130.0 130.38 2 568.70 569.71 211._> 312 0 _15.30 —14.67 1 —110.66 —105.86 220-—> 321 0 96.10 94.51 (Hal : 3.795 1 0.02 D lub| = 0.625 1 0.01 D IHCI = 0.0 D l0 I = 3.845 1 0.02 D t aIn MHz/(Kvolt/cm)2 assuming HOCS = 0.7152 D. 96 orientation of the dipole moment assumed is that shown in Figure VI. Table 32 shows a comparison of reported dipole moments for several amides. 6.5 Discussion There are three important results of the investigation of dimethylformamide and its isotopic Species. A) Planarity of DMF: To test the planarity of the compound the effect of isotopic substitution on the inertial defect was applied in a manner Similar to that proposed by Laurie (75). In this treatment expressions for the out—of—plane effective second moments of inertia for the parent and three other isotopic species (Table 29) are derived on the assumption of a plane of symmetry, as follows: Pég) = a 2 a - A/Z 150%.; + Iét) P66) — mH2 — A/2 1.20:1. 1:0 Pig) = mH2 ’ 1/2 I P(d7)= ( a a ) _Q' _ A/2 where Ia and Iét) are the moments of inertia of the 97 Table 32. Comparison of dipole moments of some related amides. Compound uta Methodb Reference Formamide 3.71 M.W. 74 N-methylformamide 3.856 M.W. This Work N,N-dimethylformamide 3.845 M.W. This Work Acetamide 3.75 D.C. 73 N-methylacetamide 3.71 D.C. 73 N,N—dimethylacetamide 3.80 D.C. 73 N-methylpropionamide 3.59 D.C. 73 aThe total dipole moment in Debyes. bM.W. indicates microwave spectroscopy; D.C. indicates dielectric constant measurements in the gas phase. 98 CH3 tops cis and trans to the oxygen, respectively. The superscripts p, c, t, and d7 on PCC refer to parent, cis CD3, trans CD3 and d7 species, respectively. From the first three values of PCC it is found that A 0.0538 u.22 whereas A = 0.0466 u.22 from the last three values. This is exceptional agreement for this kind of calculation and together with the reasonableness of the numbers suggests that the molecule has a plane of symmetry or nearly so. The difference in the A's could be the result of one or more of the following effects: 1) The Ia's are not the same in CD3 tops as in CH3 tops.' 2) The A's are not the same in all Species. 3) DMF-d7 contains a deu— terium in the CH0 part, 4) The A rotational constants needed to calculate the P 'S are not as precise as de— cc sired (1 1 MHz). B) Barrier to Internal Rotation: One result of the present study of dimethylformamide is that for the methyl group gig to the oxygen atom the barrier to internal rotation (V3 = 1079 cal/mole) is approxi- mately 900 cal/mole higher than the corresponding barrier height in gig N-methylformamide (V3 = 200 cal/mole). In the discussion above of the barrier in N—methylformamide two simple interpretations were given for the rather low barrier height in that compound. Since neither of the interpretations would be expected to be altered in DMF, the higher barrier in this compound is most easily explained as 99 being the result of an interaction between the two methyl groups, perhaps a gearing effect. As pointed out above, there are evidences in the Spectra of the excited torsional states of some of the Species that a top-tOp interaction is taking place and that further analysis of this effect is in progress. It should be pointed out, however, that the micro— wave spectrum of dimethylamine has been interpreted without considering top—tOp interaction terms. Also, the higher barrier in DMF compared to N-methylformamide matches a cor— responding trend in methylamine (V3 = 1976 cal/mole (67)), dimethylamine (V3 = 3200 cal/mole (70)), and trimethyl— amine (V3 = 4400 cal/mole (76)). The relatively high barrier to internal rotation (v3 > 2 kcal/mole) for the methyl group E£a£§_to the oxygen atom in DMF may be interpreted as favoring the steric mechanism involving an O-°--H interaction for the low barrier in N—methylformamide. This is because the contributions from the H3CNH and H3CNC fragments Should be comparable for both methyl groups in DMF. The O‘°°'H interaction is absent for the methyl group trans to oxygen, however. It is re- placed by an H:---H interaction in which the two hydrogen atoms never approach distances which are smaller than the sum of the van der Waals' radii. It should be reemphasized here that these are highly speculative and tentative interpretations. 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APPENDIX I APPENDIX I The following tables of frequencies of rotational transitions in DMF and its isotopic species are given prob- able assignments as the low—lying first excited states for the CH3 and CD3 torsional motions. Table 33. Frequenciesa of A-level transitions for the v = 1 torsional motion of CH3 (trans to the oxygen) of DMF. Transition Vobs Avb 303 —> 404 26895.0 0.03 322 —> 423 28559.30 0.10 312 —> 413 30694.20 0.11 423 —> 524 35435.8 -0.07 431 —> 532 36886.20 -0.02 413 —> 514 37813.30 -0.08 aIn MHZ. bAv = v — V ; the calculated frequencies are obtained obs calc from the rotational constants given in Table 38 107 Table 34. Frequenciesa of A and E—level transitions for the v = 1 torsional motion of the CH3 group of Transition VA VE 322 —> 423 27131.80(0. O7)b 27136.30(O.40) 331 —> 432 27864.30(L7 4) 27869.10(1.16) 414 —> 515 30042.90(—0. 07) 30044.5o(o 3) 404 —> 505 30438.2o(0 .21) 30439.30(0. 43) 423 —> 524 33543.8o(o .16) 33548.40(0.1 432 —> 533 34864.50(-1. 20) 34871.08(-1. 26) 422 —> 523 37273.65(-0. 19) 37283.20(0.08) 524 —> 625 39743.08(-0. 09) 39747.52(—0.31) 515 —> 616 35697.10(-0.19) 35698.18(—0.18) aIn HMZ . bThe quantities given in the parentheses are (Vobs - Vcalc)' The calculated frequencies are obtained from the rotational constants shown in Table 38. . a Table 35. Frequenc1es of A and E—level transitions for the v = 1 torsional motion of the CD3 group of cis DMF—d3. Transition VA VE 322 —> 423 27157.80(0.02)b 27162.40(0. 32) 331 —> 432 27888.50(0.00) 27895.0 (0. 66) 404 —> 505 30468.60(—0.22) 30469.40(0. 09) 423 —> 524 33576.10(—0. 18) 33581.0 (0.4) 413 —> 514 35684.80(0 .50) 35688.90(0 04) 431 —> 532 35744.90(0 .13) 35754.40(—0 2) 422 —> 523 37308.14(— —0. 09) 37318.09(-0 07) 524 —> 625 39781.85(-0. 55) 39786.24(-0. 62) aIn MHz bThe values given in parentheses are (Vobs — Vcalc)' The calculated frequencies are obtained from the rotational constants given in Table 38. 109 Table 36. Frequenciesa of A and E-level transitions for the v = 1 torsional motion of CD3 (cis to the oxygen) of DMF-d7. Transition v v A E 321 —> 422 26613.0 (-0. 04) 26620.50(—0. 18) 422 ~> 523 33613.0 (0. 03) 33621.80(0 .14) 515 —> 616 32208.80(0. 05) 32209.80(0 23 ) C 505 -> 606 32361.50(—O. 05) 32361.50(-0. 23) 606 —> 707C 37329.0 (—0 3) 37329.0 (—0. 63) 616 —> 717C 37264.8 (0.1) 37264.8 (-0. 63) aIn MHz. bThe values given in parentheses are (vObs - vcalc). The calculated frequencies are obtained from the rotational constants given in Table 38. cUnresolved transitions. 110 Table 37. Frequenciesa of A—level transitions for the v = 1 torsional motion of CD3 (trans to the oxygen) of DMF—d7. Transition Vobs Avb 422 —> 523 33586.50 0.00 505 —> 606 32306.60 0.22 515 -> 6516 32154.80 0.06 524 -> 625 35770.50 0.00 516 —> 717 37201.00 —0.05 606 —> 707 37265.0 0.00 aIn MHz. bAv = , the calculated frequencies are obtained vobs —Vcalc _ from the rotational constants given in Table 38. 111 .0 cam m How um: so.o9 cam . < How Nmz o.HH mum mudmumsoo HMCOMDMDOH CH mwfiusflmuumucd wmpmfiflummm smme.eu mmmv.on Hfihv.ou mome.ou Newm.o1 s 00 enme.m wovm.e weew.e hamm.e msoe.m m vam.os wwmo.os mmfie.me wwme.um oewm.mm new mm mumm.HmH neme.fimfi «www.mfifi hamm.eHH wewe.mHH Aam.sv m me.momm mfl.thm mo.wssm me.mssm mm.msmm <0 He.oeem ms.memm mw.esev wm.moee 6H.wome 4m < oe.omhm mm.smho om.mwes Hs.msvs «8.6Hmm Aumzv a Amcmsuvmoo Amflovmoo «no 8mo mzo mumumsmumm seumzo menmzo who .mwflowmm camouomfl muH tam MED How mmwmum HMCOHmHou Cwufloxm umuflw 0&0 mo mnoumfimumm HMCOHumuom .wm maQMB b- W)r))))mg))(I) LIBRARIES l