G . A. HEATH, L. F. THOMAS, E . I . SHERRARD AND J . SHERIDAN 43 INFORMATION PERTAINING TO MOLECULAR STRUCTURE, AS OBTAINED FROM THE MIICRO- WAVE SPECTRA OF MOLECULES OF THE ASYM- METRIC ROTOR TYPE BY WILLIAM D. GW~NN Dept. of Chemistry and Chemical Engineering, University of California, Berkeley 4, California, U.S.A. Received 4th February, 1955 For some time microwave spectra have been used to obtain the three moments of inertia of molecules of the asymmetric rotor type. These data have been utilized to obtain structural information about the molecule. In a number of examples this method has been very successful in determining not only the positions of the heavy atoms with high accuracy, but also the positions of the hydrogens in complex molecules. In later work the microwave spectrum has been employed to determine the potential barriers to internal rotation with high precision, and the Stark effect and statistical weights of levels have been useful in deciding such questions as the planarity of rings where double minimum vibrations are possible.The above problems will be discussed, along with their difficulties and limitations. In 1950 Prof. E. Bright Wilson, Jr., presented a review gaper 1 at the meeting of the Faraday Society. In that paper he discussed the methods of determining molecular structure with microwave spcctroscopy. He also presented certain examples which had been studied prior to that time. The purpose of my paper is to discuss certain of the more recent applications of this method and to illustrate how some of these methods work out in practice.I will limit my remarks prin- cipally to the work we have done with molecules of the asymmetric rotor type. Probably the most important information concerning molecular structure derived from microwave spectroscopy is the average position of the atoms in the molecule. The data from microwave spectra serve to determine the moments of inertia of the molecule, and the structure of the molecule is calculated from the moments of inertia. One characteristic of asymmetric top molecules is that they possess three different moments of inertia and the microwave spectrum is44 ASYMMETRIC ROTOR dependent upon all three, whereas the microwave spectrum of a symmetric top or linear molecule is dependent upon only one moment of inertia.Thus three structural parameters are determined for each isotopic species of an asymmetric top, as compared to one for each isotopic species of a symmetric top or linear molecule. The moments of inertia and structural parameters are the effective or average values for the vibrating molecule in its ground vibrational state. Since the structure of most asymmetric tops cannot be determined by only three structual parameters, it is necessary to combine data from several isotopic species in order to determine the structure of the molecule. Since the different isotopic species of the molecule will have different zero-point vibrations, the effective structural parameters will differ slightly for the various isotopic species. At present the only practical method for determining the structure is to ignore this difference and to assume that all bond lengths and angles are invariant with isotopic substitution.An alternate approach to the problem of vibration-rotation interaction might be to observe the spectrum of the molecule in several successive excited states of each vibrational mode and then to extrapolate back to the hypothetical non- vibrating state of the molecule. This method is not practical at present. The molecule has too many vibrational modes and, moreover, the population of molecules in upper vibrational levels for high frequency vibrations such as carbon- hydrogen stretching motions, would be far too small to be observed with present equipment. Still another approach would be to calculate the correction arising from vibration-rotation interaction. Although this calculation cannot be carried out in practice because the anharmonicity of the force fields of the atoms are not known, the principles of this calculation are well known.The vibration-rotation interaction may be divided into two principal parts, the first being the interaction if the vibrations were harmonic and the second being a result of the anharmonicity of the vibrations. The effect of the harmonic contribution would be to make the molecule appear small since the average reciprocal of the moments of inertia are measured. The anharmonicity usually makes the molecule appear larger. For diatomic molecules the anharmonic term usually dominates, but for more complex molecules the vibration-rotation interaction may be of either sign.As a result it is not possible to predict whether the vibration-rotation interaction contributed by a high frequency vibration will be larger or smaller than that contributed by a low frequency vibration. Since there seems to be no other course, we have neglected vibration-rotation interaction. We have instead studied as many isotopic species as possible in order to determine the inconsistencies involved in neglecting this interaction. For example, in the work on ethylene oxide,Z we have studied five different isotopic species, From the fifteen moments of inertia we need to determine only five bond distances and angles to determine the structure of the molecule. Also in the work on methylene chloride,3 we have TABLE 1 .-DISTANCE (IN A) OF THE studied seven different isotopic species, giving HYDROGENS FROM THE PLANE OF THE twenty-one moments of inertia from which to C-0-c RING IN ETHYLENE OXDE calculate only four structural parameters. In order to see how this works out in C2C13H40 0.9202 practice, a part of the experimental data for CHDCHDO (cis) 0-9213 ethylene oxide and methylene chloride is CMDCHDO (trans) 0.9215 presented.For ethylene oxide the three CZD40 0.9217 moments of inertia of a single isotopic species may be combined to give the dis- tance of the hydrogens above or below the plane of the three-membered ring. These are given in table 1. Another combination of the moments of inertia of a single isotopic species gives a function of two other bond projections. A third relation gives another function of the remaining two structural parameters. 0.9203 C2H40WILLIAM D .GWINN 45 These equations may be solved simultaneously in pairs to determine the bond projections, or they may be solved graphically. We prefer the graphical method because one can look at the data from all of the isotopic species at once and can better see the small inconsistencies which result from the neglected vibration- rotation interaction. Fig. 1 shows the values of one bond projection for each isotopic species plotted against the corresponding value of the other bond projec- tion, which gives the correct moments of inertia. The second set of two structural parameters gives a plot very similar to fig. 1. Inspection of table 1 and fig. 1 shows that the inconsistencies which result from the neglected vibration-rotation interaction are only of the order of 0.001 A.FIG. 1.-Plot of the values of ZH and Zo for ethylene oxide which are consistent with the determined moments of inertia. The intersection of the various lines gives the struc- tural parameters for ethylene oxide. ZH and 20 are projections of the CH and CQ bond, respectively, upon a line perpendicular to the CC bond and through the oxygen. A, C2H40; C, CHDCXPIDO (cis) ; D, CHDCHDO (trans); E, C2D4O. B, C2C13H40; 1 I 1 1.231 1.233 1.23 2 0 Another interesting observation is that the effect of substituting C13 for C12 in ethylene oxide is comparatively valueless in determining the structure of ethylene oxide. The lines in fig. 1 corresponding to C212H4O and C1C13H40 are very nearly parallel and coincident so that very small vibration-rotation interactions would cause a relatively large discrepancy in the bond distances. TABLE 2.-THE PROJECTIONS OF THE c-cl AND C-H BONDS PERPENDICULAR TO THE SYMMETRY AXIS IN METHYLENE CHLORIDE 1.4675 1 -4674 1.4673 1.4675 1.4673 1.4677 1.4676 0.8794 0.8801 0*881 0.888 0.887 0.891 0.891 The data for methylene chloride are presented in table 2 and fig.2. The data are very similar to the data for ethyleme oxide except for one feature. The distance YH in table 2 is obtained as the small difference between large moments of inertia, and it is somewhat sensitive to the vibration-rotation interactions.0 0.0 I A-- 0 and C 46 ASYMMETRIC ROTOR Even so, the greatest variation in this parameter is only 0-012A and this variation results in only an O-OOSA variation in the C-€3 distance and a 20’ variation in the H-C-H angle.It is also interesting to notice that making an isotopic substitution for chlorine alone is of little value in the determination of molecular structure. The lines corresponding to changes in the chlorine isotope alone are again nearly parallel and coincident. The data for ethylene sulphide are very similar to the data for ethylene oxide, giving discrepancies of about 0.001 A. Likewise, changing the sulphur isotope alone results in nearly parallel and coincident lines, In view of these and other similar data, we have tentatively come to the conclusion that, although the hydrogen-deuterium substitution may (but does not necessarily) affect the vibration-ro tation iiiteractions more than FIG.2.-Plot for methylene chloride similar to fig. 1. ZH and Zcl are distances along the two-fold symmetry axis. The curves for the isotopic species containing different chlorine isotopes alone are superimposed for CD2C12 and are closely parallel for CDHC12 and CH2C12. A, CH2C1235; B, CH~C135C137 ; C, CH2C1237; D, CDHC1235; F, CD2C1235; G, CD2CPsCP7. E, CDHCPC137 ; a heavy atom substitution, studying the various deuterated species of a molecule is much more fruitful than studying the species of the molecule with the heavy atoms substituted. Probably the main reason for this is that the hydrogens are usually near the periphery of the molecule and a substitution there creates a much larger change in the moments of inertia than does a substitution of the heavier atoms which are usually located near the centre of gravity of the molecule.We also conclude that interatomic &stances, including distances involving hydrogens, can often be given which are self-consistent to a few thousandths of an hgstrom. If these distances deviated from the actual average distances in the molecule, we believe that it would show up in the self-consistency of the data. At present there is no other method by which to compare these dis- tances. Electron diffraction technique allows the determination of the distances between the heavy atoms of a molecule, but only to within a few hundredths of an hgstrom. In general, there has been excellent agreement between distances determined by the use of electron diffraction and those determined by the use of microwaves.There have been a few discrepancies but they have usually been with early electroil diffraction work and most of them have been removed by more recent work. Electron diffraction technique is improving rapidly, and it will be very interesting when we can compare the methods to a few thousandths of an Angstrom.WILLIAM D. GWINN 47 It should be emphasized that it is not always possible to determine with high precision the structure of simple asymmetric tops. In some, the moments of inertia are simply not sufficiently sensitive to certain bond distances. An example is nitromethane, which is to be discussed later with respect to internal rotation. In this particular molecule, the microwave spectrum is determined primarily by the potential barrier to internal rotation and by two moments of inertia.The axial moment of inertia of the methyl group would be determined only if the barrier to internal rotation were very high. Of the two moments of inertia which are determined, one gives directly the 0-0 distance and the other could be used to determine the other four distances and angles in nitromethane. Thus we have the problem found so often in the more complex symmetric tops and linear molecules, the four distances must be derived froin four equations (each from a separate isotopic species) in four unknowns. The equations are rather similar and small vibration-rotation interactions seriously limit the accuracy of the solution. Partially deuterated species would make the axial moment of inertia show up in the microwave spectrum, but still not sufficiently to allow its deter- mination.It was estimated that we could not determine the C-H distance to better than 0.1 A. Therefore, since the experiments and calculations were very difficult, we decided that it was not worthwhile to attempt to determine the structiire of nitromethane by studying other isotopic species. The value of knowing bond distances and angles to a higher precision needs no elaboration. The hydrogen distances and angles are especially interesting since there were no previous values available for more than a few of the simplest of the asymmetric tops. In ethylene oxide and ethylene sulphide we were inter- ested in systems with bent bonds. We were also interested in the H-C-H angle and C-C distance in order to compare them with ethylene.The H-C-H angle turns out to be 116" 41' (ethylene oxide) and 116" 0' (ethylene sulphide), just intermediate between the extremes of 120" (as ethylene) and 109" 28' (the more conventional tetrahedral value). In methylene chloride we were interested again in the possibility of bent bonds. The C1-C-Cl angle was known to be about 112" & 2" (electron diffraction). If the bonds were not b e t , then the H-C-H angle would be less than tetrahedral. Experimentally, both angles are greater than tetrahedral (Cl-C-Cl angle = 11 1" 47' and H-C-H angle = 112" 0'). We regarded this as good evidence for the presence of bent bonds in methylene chloride. INTERNAL ROTATION There are two general methods of microwave spectroscopy for studying the barrier to internal rotation.The first is most applicable where the barrier is high and the motion of internal rotation approximates to torsional oscillation for the first few energy levels. In this case small satellite lines arising from the excited torsional vibrational state appear near the corresponding line of the un- excited molecule. The method consists of measuring the intensities of these lines and calculating by Boltzmann's statistics the energy of the excited levels. This method is straightforward but is subject to the disadvantage that the inten- sities of microwave lines still cannot be measured with high precision. The second method is to measure the frequency of lines involving a combination of internal rotation and over-all rotation.This method is extremely time- consuming but yields a precise value for the barrier height. The disadvantage of this method is that the investigator starting such a piece of research can, at present, give no prognosis for the outcome of the investigation. It may be that the spectrum is too complicated to be interpreted or that the lines critical for the barrier determination do not lie in the region of his spectrograph. Several mole- cules have been successfully studied. Dennison 4D 5 ~ 6 and co-workers have determined the barrier in methyl alcohol as being 1070 cal/mole, thus clearing up a long-standing problem in chemistry. Very recently Shimoda, Nishikawa48 ASYMMETRIC ROTOR and Itoh 7 have determined the barrier in methyl amine to be 1950 cal/mole.We have studied nitromethane and deuteronitromethane,S and this work will be discussed. The barrier to internal rotation in nitromethane had been investigated pre- viously 9 9 10 by thermodynamic methods and had been found to be something between 0 and 1100 cal, probably about 800 cal. If each oxygen interacted with the methyl group with a barrier which could be represented by a three-fold cosine function, then the barrier in nitromethane would be zero. The measurement of the actual barrier in nitromethane was measured by us in order to test the validity of assuming cosine functions to represent the barrier to internal rotation, Con- sidering the interaction of a single oxygen with the methyl group, the barrier to internal rotation could be given as (1) E3 E6 V = -cos 3$ + -cos 693 + $cos 993, 2 2 where the terms in &, Eg, E12, etc., represent the deviations from a simple cosine barrier.When the interactions of both oxygens are added together, the barrier for nitromethane would become (2) Y = E6 cos 64 -t El2 cos 1256 + &8 cos 18$, (3) V = - v6 cos 65b + F c o s 124 + y c o s 185b. 2 or The barrier V6 in nitromethane would represent the deviations from a simple cosine barrier for the interaction of a methyl group with a single oxygen, and V12 would represent the deviations from a simple cosine barrier in nitromethane. The interpretation of the spectrum followed the usual technique of microwave spectroscopy. The Stark effects were resolved where possible, lines with low J quantum numbers were selected, and trial assignments were made until every- thing was in agreement.The energy levels could have been calculated from the theory of Burkhart and Dennison,s but not easily. Our work was greatly facilitated by a theory worked out by Myers,ll in which the matrix elements are obtained as a solution of the matrix commutation rules. The resulting energy matrix was obtained in a form much more convenient for determining energy levels for molecules with low potential barriers. The theory of the Stark effect was also extremely important, because various types of transitions have different and very characteristic Stark effects. Most of the lines studied were rather inseiisitive to the height of the barrier. There were, however, four lines which, in the case of a free rotor, arose from two sets of doubly degenerate levels.These corresponded to the set K = + 1, k = + 3, a n d K = - l , k = - 3 ; andthesetIC=-l,k=+3,andK=+l,k=-3, where K corresponds approximately to the angular momentum of the whole molecule about the axis of internal rotation, and k corresponds approximately to the angular momentum of the methyl group about the same axis. Some of the terms involving the barrier v6 in the energy matrix connect these degenerate levels. As a result, the barrier splits the degeneracy of the levels, and the frequencies of the corresponding lines are very sensitive to, and approximately linear in, the height of the barrier. The splitting of these lines was approximately 1800 Mc/s and this corresponded to a barrier height v6 of 6-00 f 0.03 cal/mole (2.10 cm-l/ mole).In the same way, the splitting of the K = 0, k = f6 lines could be used to determine the V12 component in the barrier. Experimentally the k = k 6 lines were not split, so there is no evidence for any V12 term. From the resolution of the spectrograph and the sensitivity of the method, the upper limit to V12 can be set as 0.03 cal/mole. It is difficult to estimate the magnitude of the interaction of a single oxygen with a methyl group, but it must be in the order of magnitude of 1-2 kcal. SinceWILLIAM D. G W I N N 49 the barrier in nitromethane is much smaller than this, and since the V12 term is so much smaller than the v6 term, we conclude that the series given by eqn, (1) converges rapidly and that a simple cosine barrier is an excellent approximation to the barrier in nitromethane.Deuteronitromethane has also been studied, and the barrier in this molecule was found to be 5.17 f 0.03 cal. At first this 12 % decrease from nitromethane seems a bit large, but it does not appear unreasonable when one considers the zero-point vibrations of some of the vibrations of the methyl group. The sym- metrical H.C.H bending mode of the methyl group would change the distance between the oxygens and the hydrogens, and the shortest distances would be most effective in determining the barrier. The barriers are in the right order, the higher barrier (nitromethane) being associated with the higher amplitude motions and the lower barrier (deuteronitromethane) being associated with lower amplitude motions, The splitting of the lines used to determine the barrier height was about 1800 Mc/s. The splitting was measured to f 0.1 Mc/s and could be measured more accurately. Since the splitting is approximately linear with the barrier, the barrier could possibly be measured to an accuracy of 1 part in 18,0QQ, or 0.0003 cal. However, effects of centrifical distortion and vibration are present and the precision is limited to 0.03 cal.INVERSION DOUBLING AND PLANARITY OF RINGS The question of planarity of rings often arises in chemistry and there are several ways of attacking this problem with the techniques of microwave spectroscopy. !C) (a) ( b) FIG. 3.-Possible potential cnergy functions and energy levels for ring puckering vibra- tions. For some rotational levels the statistical weights for -t- levels are gl, for - levels they are g2, and for & levels they are gl + g2.For other rotational levels gl and g2 are interchanged. If the complete structure of the molecule has been determined with microwave spectroscopy, then the question of planarity of rings has already been settled. There are, in addition, several techniques which allow the problem of planarity of rings to be settled without a complete determination of structure. The question of planarity of rings centres about the potential energy function and the corresponding energy levels associated with the ring puckering motion. Fig. 3 represents the various possibilities. The molecule may have a planar ring, as represented in fig. 3a, or it may have such a high central maximum that it is convenient to think of the molecule as having a rigid puckered ring, such as indicated in fig.3c, or the height of the central. maximum may be low enough so that it is convenient to think of the molecule as having inversion doubling. Probably the best way to demonstrate that a molecule does not have a planar ring or a plane of symmetry in the plane of the ring is to measure the component50 ASYMMETRIC ROTOR of the dipole moment perpendicular to the ring. From the Stark effect of several lines of an asymmetric rotor it is possible to determine the three individual com- ponents of the dipole moment along the three principal axes of the molecule. The existence of a component of the dipole moment which is perpendicular to a supposed plane of symmetry is conclusive evidence that the plane of symmetry does niat exist.The fact that the dipole moment of ethylenimine 12 makes an angle of about 30" with the plane of the ring leads to the positive, yet not surprising, conclusion that the N-H bond does not lie in the plane of the C-C-N ring. If the molecule is planar, the sum of the two small moments of inertia is approximately the third. (There is a small inertial defect as a result of the vibration- rotation interaction.) If the molecule is not planar but has a plane of symmetry with a two-fold axis (2) of rotation in that plane (& symmetry), then perhaps the best method is to make use of the different statistical weights of various rota- tional levels. These different statistical weights arise from the various hydrogen nuclear spin states.Experimentally this requires the measurement of the in- tensities, but does not demand a very precise measurement. Part of the rotational levels in an asymmetric rotor (classes A and Ba) have one statistical weight and the rest (classes Bb and Bc) have another statistical weight. If the rotational line of a molecule is in an excited vibrational level of the ring puckering motion, these statistical weights alternate with the symmetry of the vibrational level, which is indicated in fig. 3. The method of utilizing the symmetries of the ground vibrational state has been applied to pyrrole by Wilcox and Goldstein,l3 who found that pyrrole was planar. They report that the spectrum of pyrrole contains several pairs of lines in which the two members of the pair are very close to each other and have different statistical weight.Measuring these intensities to decide between a 6 or 10 statistical weight is easy and reliable. In trimethylene 0xide,l4 CH2-CH2-CH2, the statistical weights were 7 and 9 and the appropriate lines were not close to each other, so use was made of the alternating statistical weights of the vibrational levels. If the ring were planar, the intensities of the lines arising from the various vibrational levels should be in the ratio of 7 : 9 exp (- El/kT) : 7 exp (- E2/kT), etc., for some lines, and for others the ratios should be 9 : 7 exp (-El/kT) : 9 exp (- E2/kT), etc. The lines arising from the excited vibrational states appear as satellites to the lines arising from the ground state, and it is easy to measure the intensities to sufficient accuracy to know that the statistical weights are necessary and that the first two vibrational separations are about 60 cm-1.If the potential function could be changed at will and a potential function were gradually changed from that represented in fig. 3a through the case of inversion doubling (fig. 3b) to the rigid puckered molecule of fig. 3c, we would observe the satellite line of the excited vibrational levels with their statistical weights to coincide in pairs, as indicated in fig. 3c, where all lines would have equal statistical weights. Since in trimethylene oxide we find from the statistical weights that the lowest vibrational level is symmetric and the next level is antisymmetric, and the third level is symmetric, we know that the vibrational levels in trimethylene oxide are single levels.Since the levels are approximately equally spaced, we know that there is no inversion doubling and that the trimethylene oxide sing is planar. The planarity of trimethylene oxide could also have been deduced from the Stark effect. If the molecule were puckered with a high central maximum, the Stark effect would be very sensitive to the component of the dipole moment perpendicular to the ring. The Stark effect shows no contribution from such a dipole. From the accuracy of the Stark measurement, an upper limit can be set to the perpendicular component of the dipole. From this it can be estimated that the upper limit to the ring bending is only 0" 20' (dihedral angle between the !-,AWILLIAM D .GWINN 51 C-C-C plane and the C-0-C plane). Such a high barrier separating two minima only 0" 40' apart would be physically unreasonable and need not be considered as a possibility. If the central maxima were lower, the degeneracy of the two vibrational levels would be removed (as in fig. 3b) and the Stark effect would not always be so sensitive to the perpendicular component of the dipole moment. If the separation of the lowest two vibrational levels were between 0 and 2cm-1, then the upper limit of this angle might be sometimes less than 0" 20', and sometimes greater than 20' (as the separation of the vibrational levels change) but it would never be larger than 4". Any separation of the first two levels between 0 and 2 cm-1 would still require too high a barrier to have the two minima only 8" apart, and this possibility can be eliminated.If the splitting of the ground state were greater than 2cm-1, the Stark effect would be of little value but we should observe the splitting of the satellite lines (at least in the upper states). The satellite lines show no such splitting, therefore the independent conclusion is reached that trimethylene oxide is planar and that there is no inversion doubling. If a molecule had inversion doubling, there would be a possibility that combina- tion inversion doubling and rotational transitions would be present, but it would only be chance that these lines would appear in the microwave region. Thus their absence is no evidence against inversion doubling. Our interest in trimethylene oxide stems from the recent work in infra-red and Raman spectroscopy which indicates that cyclobutane has a puckered ring. In the four-membered rings the classical ring strain would tend to make the rings planar while the preferred staggered positions of the hydrogen in internal rotation would tend to make the rings puckered. Trimethylene oxide, having fewer hydrogens, would have less tendency to have a puckered ring. The ring strain is the predominating term and trimethylene oxide is planar. 1 Wilson, Faraday SOC. Discussions, 1950,9, 108. 2Cunningham, Boyd, Myers, Gwinn and LeVan, J. Chem. Physics, 1951, 19, 676. 3 Myers and Gwinn, J. Chem. Physics, 1952,20, 1420. 4 Burkhard and Dennison, Physic. Rev., 1940, 71,408. 5 Hughs, Good and Coles, Physic. Rec., 1951, 84,418. 6 Ivash and Dennison, J. Chem. Physics, 1953,21, 1804. 7Shimoda, Nishikawa and Itoh, J. Chem. Physics, 1954, 22, 1456; J. Physic. Chem. 8 Tannenbaum, Johnson, Myers and Gwinn, J. Chem. Physics, 1954, 22, 949 ; and 9 Pitzer and Gwinn, J. Amer. Chem. SOC., 1941, 63, 3313. 10 Jones and Giauque, J. Amer. Chem. SOC., 1947, 69, 983. 11 in preparation for publication by Myers, Univ. of California, Berkeley, California. 12 Johnson, Myers and Gwinn, J. Chem. Physics, 1953,21, 1425. 13 Wilcox and Goldstein, J. Chem. Physics, 1952, 20, 1656. 14in preparation for publication by J. Fernandez and Gwinn, Univ. of Calif., Smith, M.Sc. Thesis (Univ. of Calif., Berkeley, Calif., 1953). Japan, 1954,9, 974. material in preparation for publication. Berkeley, Calif.