J . Phys. Chem. 1990, 94, 125-133
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Vibrational Circular Dichroism Spectrum of 2-Methyloxetane R. Anthony Shaw, Nan Ibrahim, and Hal Wieser* Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1 N4 (Received: March 3, 1989) The mid-infrared vibrational circular dichroism (VCD) spectrum of 2-methyloxetane is reported. Theoretical spectra are calculated for a nearly planar (3-21G optimized) structure and two distinct puckered (axial and equatorial) ring conformations with the fixed partial charge (FPC) and atomic polar tensor (APT) models. The FPC calculation at the planar geometry reproduces the observed VCD sign in the majority of cases, but the VCD intensitiesare not well predicted and the ring stretching infrared absorption intensities are severely underestimated. Inclusion of a single charge flow parameter to supplement the FPC predictions brings all calculated infrared absorption intensities into very good qualitative agreement with experiment and also improves considerably the VCD intensities calculated for the ring stretching modes. The APT calculation, although generally successful in predicting the absorption intensities, is less accurate than the FPC model for the VCD spectrum. A comparison between dipole moment derivatives calculated for the two models is proposed as a means for identifying those modes which are most suited for FPC calculation. Among them the 0-CH, wag in particular is predicted to be sensitive to the ring conformation, and the observed VCD band is suggested to indicate a preference for the equatorial conformer. The methyne out-of-plane and the methyl symmetric deformations are identified as configurational markers for the 0C*H(CH3)-CH, group.
Introduction Vibrational circular dichroism (VCD) is a relatively new spectroscopic technique which measures the differential absorption by chiral molecules of right vs left circularly polarized light in the infrared region.' The VCD spectrum complements the conventional infrared absorption spectrum, each absorption corresponding in principle to either a positive or negative band. The distinguishing feature of VCD is the unique sensitivity to molecular configuration and conformation, and the present challenge is how to extract the structural information latent in the measured spectrum. Despite formidable experimental and theoretical obstacles, progress has been achieved both by empirically correlating VCD features common to structurally related molecules and through model calculations.' The study of small chiral molecules has become particularly important as a means of developing the empirical and fundamental understanding required for interpreting the spectra of larger molecules. In this paper we present the infrared absorption and VCD spectra for 2-methyloxetane (2-MO, see Figure 1) and report the results of calculations testing the accuracy of two models and exploring the sensitivity of the predicted mid-infrared VCD spectrum to changes in the ring conformation. Two dominant factors have hindered the development of routine theoretical procedures for interpreting VCD spectra. First, the evaluation of electronic contributions to the VCD intensity is not straightforward. Although the formal difficulties have been overcome r e ~ e n t l y and ~ . ~ comparisons between experimental and (1) For recent reviews see: (a) Freedman, T. B.; Nafie, L. A. In Topics in Stereochemistry; Eliel, E. L., Wilen, S., U s . ; Wiley: New York, 1987; Vol. 17, pp 1 1 7-206. (b) Stephens, P. J.; Lowe, M. A. Annu. Reu. Phys. Chem. 1985, 36, 21 3-241. (c) Nafie, L. A. In Advances in Infrared and Raman Spectroscopy; Clark, R. J. M., Hester, R. E., Eds.; Wiley-Hayden: ChiChester, 1984; Vol. 11, pp 49-93. (2) (a) Nafie, L. A.; Freedman, T. B. J. Chem. Phys. 1983,78,7108-7116. (b) Nafie, L. A. J . Chem. Phys. 1983, 79, 4950-4957. (c) Nafie, L. A.; Freedman, T. B. Chem. Phys. Lett. 1987,134,225-232. (d) Freedman, T. B.; Nafie, L. A. J. Chem. Phys. 1988,89, 374-384. (3) (a) Stephens, P. J. J . Phys. Chem. 1985,89, 748-752. (b) Lowe, M. A.; Segal, G. A.; Stephens, P. J. J . Am. Chem. Soc. 1986,108,248-256. (c) Lowe, M. A.; Stephens, P. J.; Segal, G. A. Chem. Phys. Lett. 1986, 123, 108-1 16. (d) Amos, R. D.; Handy, N. C.; Jalkanen, K.J.; Stephens, P. J. Chem. Phys. Lett. 1987, 133, 21-26. (e) Lazzeretti, P.; Zanasi, R.; Stephens, P. J. J. Phys. Chem. 1986,90,6761-6763. (f) Stephens, P. J. J. Phys. Chem. 1987, 91, 1712-1715. (g) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J . Am. Chem. SOC.1987, 109, 7193-7194. (h) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N . C. Chem. Phys. Lett. 1987, 142, 153-158. (i) Stephens. P. J.; Amos, R. D.; Handy, N. C. J. Phys. Chem. 1988, 92, 1781-1785. 6)Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J . Am. Chem. SOC.1988,110, 2012-2013. (k) Kawiecki, R. W.; Devlin, F.; Stephens, P. J.; Amos, R. D.; Handy, N. C. Chem. Phys. Lett. 1988,145, 41 1-417. (i) Dutler, R.; Rauk, A. J . Am. Chem. SOC.,submitted for publication.
0022-3654/90/2094-0125$02.50/0
theoretical spectra evaluated with such exact expressions for the rotatory strength have been generally fa~orable,~~,g*'-~ the basis set requirements are so demanding that calculations can be contemplated presently only for the smallest of chiral molecules. Second, as for infrared absorption intensities, an accurate harmonic force field is an essential prerequisite. The derivation of force fields of sufficient accuracy is particularly difficult for molecules amenable to VCD measurement due to the absence of symmetry. Ab initio methods4 have proven very u s e f ~ l ,although ~.~ in our experience reliable assignments can be achieved only by systematic scaling of the force fields.' The electronic contributions to the VCD intensity can be approximated by several models. The simplest among these is the fixed partial charge (FPC) method,* which treats the molecule as a collection of point charges with the electrons serving only to screen the nuclei. The additional influence of vibrationally induced charge flow along bonds is described by two equivalent charge flow model^.^^'^ The localized molecular orbital (LMO) modelL1was the first to treat the electronic contributions explicitly, by considering the displacements of localized orbital centroids induced by nuclear deformations. The method of atomic polar tensors (APT)'* was introduced as an approximation to the LMO model whereby the displacement of any individual nucleus is assumed to perturb only the local electronic environment. Two additional conceptually simple mechanisms, described by coupled ~ s c i l l a t o r s and ' ~ ring ~ u r r e n t s , have ~ ~ . ~been ~ found useful for
(4) For reviews see: (a) Fogarasi, G.; Pulay, P. Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: Amsterdam, 1984; Vol. 14, pp 125-219. (b) Fogarasi, G.; Pulay, P. Annu. Rev. Phys. Chem. 1984, 35, 191-243. ( 5 ) Lowe, M. A.;Alper, J. S.;Kawiecki, R.; Stephens, P. J. J. Phys. Chem. 1986, 90, 41-50. (6) Polavarapu, P. L.; Hess, B. A., Jr.; Schaad, L. J.; Henderson, D. 0.;
Fontana, L. P.; Smith, H. E.; Nafie, L. A,; Freedman, T. B.; Zuk, W. M. J . Chem. Phys. 1987, 86, 1140-1 146. (7) Shaw, R. A.; Ursenbach, C.; Rauk, A,; Wieser, H. Can. J. Chem. 1988, 66, 1318-1332. (8) (a) Schellman, J. A. J. Chem. Phys. 1973, 58, 2882-2886. (b) Schellman, J. A. J. Chem. Phys. 1974, 60, 343. (9) Abbate, S.; Laux, L.; Overend, J.; Moscowitz, A. J . Chem. Phys. 1981, 75, 3161-3164. Erratum: J. Chem. Phys. 1983, 78, 609. (10) Moscovits, M.; Gohin, A. J . Phys. Chem. 1982, 86, 3947-3950. (1 1) (a) Nafie, L. A.; Walnut, T. H. Chem. Phys. Lett. 1977,49,441-446. (b) Walnut, T. H.; Nafie, L. A. J. Chem. Phys. 1977, 67, 1491-1500. (c) Walnut, T. H.; Nafie, L. A. J. Chem. Phys. 1977, 67, 1501-1510. (12) (a) Freedman, T. B.; Nafie, L. A. J. Chem. Phys. 1983, 78, 27-31. (b) Freedman, T. B.; Nafie, L. A. J. Phys. Chem. 1984,88, 496-500. (13) Holzwarth, G.; Chabay, I. J . Chem. Phys. 1972, 57, 1632-1635.
0 1990 American Chemical Society
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The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 7
Figure 1. (R)-(-)-2-Methyloxetane, giving also the atom numbering used for defining structural parameters (Table I) and local symmetry coordinates (Table IV in ref 26).
interpreting a number of VCD spectra. The approximations invoked in developing these models reflect well-defined physical assumptions which are valid only for certain classes of molecules and/or types of molecular vibrations. Although each of these models is necessarily limited in scope, the extent to which they reproduce the measured spectrum then indicates the degree to which the assumed VCD mechanism (FPC, APT, LMO) dominates. One theme common to much of the published VCD work is to identify those cases which are best suited for each of the various empirical and semiempirical models. While a number of C-H stretching VCD spectra have been the latter's predicted at least qualitatively with the FPC usefulness for interpreting mid-infrared spectra remains largely unexplored. Two molecules for which comparisons are available are trans- 1,2-dideuteriocycIobutane(DDCB) and trans- 1,2-dideuteriocyclopropane (DDCP). For the former a very good agreement has been demonstrated between the VCD spectrum observed in the mid-infrared region and that calculated with FPCZ3 For the latter, the VCD spectrum calculated with Stephens' formalismgbis in excellent agreement with the observed spectrum measured recently in the region of 925-3 100 cm-1.24 In the present context it is of particular interest to note that for all 15 bands above 925 cm-I the FPC model3balso reproduces in sign both the experimental and the more sophisticated a b initio results. These reports indicate that the FPC model incorporates a genuine source of VCD intensity and that the agreement with experiment then reflects the degree to which this mechanism dominates. The success of the FPC model has been suggested to arise from the absence of readily delocalized electron density in DDCB.laq22*23The same argument applies also to DDCP. (14) (a) Nafie, L. A.; O b d i , M. R.;Freedman, T. B. J . Am. Chem. Soc. 1983, 105, 7450-7452. (b) Oboodi, M. R.; Lal, B. B.; Young, D. A,; Freedman, T. B.; Nafie, L. A. J. Am. Chem. Soc. 1985,107, 1547-1556. (c) Freedman, T. B.; Balukjian, G. A.; Nafie, L. A. J. Am. Chem. Soc. 1985,107, 6213-6222. (d) Young, D. A.; Lipp, E. D.; Nafie, L. A. J. Am. Chem. SOC. 1985, 107, 6205-6213. (e) Nafie, L. A.; Freedman, T. B. J. Phys. Chem. 1986, 90,763-767. (0 Paterlini, M. G.; Freedman, T. B.; Nafie, L. A. J. Am. Chem. Soc. 1986,108. 1389-1397. (g) Young, D. A,; Freedman, T. B.; Lipp, E. D.; Nafie, L. A. J. Am. Chem. Soc. 1986,108,7255-7263. (h) Freedman, T. B.; Young, D. A.; Oboodi, M. R.; Nafie, L. A. J . Am. Chem. SOC.1987, 109, 1551-1559. (15) Keiderling, T. A.; Stephens, P. J. J . Am. Chem. SOC.1979, 101, 1396-14OO. (16) Polavarapu, P. L.; Nafie, L. A. J. Chem. Phys. 1980,73, 1567-1575. ( I 7) Singh, R. D.; Keiderling, T. A. J . Chem. Phys. 1981, 74, 5347-5356. (18) Marcott, C.; Scanlon, K.; Overend, J.; Moscowitz, A. J . Am. Chem. SOC.1981, 103, 483-485. (19) Singh, R. D.; Keiderling, T. A. J . Am. Chem. SOC.1981, / 0 3 , 2387-2394. (20) Polavarapu, P. L.; Nafie, L. A.; Benner, S.A,; Morton, T. H. J . Am. Chem. SOC.1981, 103, 5349-5354. (21) Lal, 9. B.; Diem, M.; Polavarapu, P. L.; Oboodi, M.; Freedman, T. B.; Nafie. L. A. J . Am. Chem. SOC.1982, 104, 3336-3342. (22) Annamalai, A.; Keiderling, T. A.; Chickos, J. S. J. Am. Chem. SOC. 1984, 106, 6254-6262. (23) Annamalai, A.; Keiderling, T. A.; Chickos, J. S.J. Am. Chem. SOC. 1985, 107, 2285-2291. (24) Cianciosi, S. J.; Spencer, K. M.; Freedman, T. B.; Nafie, L. A,; Baldwin, J. E. J . Am. Chem. SOC.1989, 111, 1913-1915.
Shaw et al. Systematic comparison of FPC with a wider variety of experimental VCD spectra should therefore identify those cases for which the model is adequate and serve as a guide for a realistic assessment of other plausible mechanisms that might augment the FPC contributions. For example, the ring current model was originally introduced to explain the discrepancy between observed and FPC calculated spectra for alanine and other amino and has since been invoked to rationalize measured VCD bias in the C-H stretching region for a number of other 2-Methyloxetane possesses two characteristics which distinguish it from both DDCP and DDCB. First, there is some degree of conformational mobility. Interpretation of the far-infrared puckering transitions suggested that both the axial and equatorial orientations of the methyl group are stable, with the two conformers separated by an inversion barrier of about 110 The measured VCD spectrum must then reflect a balance among the contributions from different conformers. Second, the presence of the heteroatom gives rise to spectral features that the FPC model cannot possibly account for, as for example the very high ring stretching absorption intensities. We have previously completed a scaled 3-21G force field for 2 - m e t h ~ l o x e t a n e . ~In~the present paper we report the mid-infrared VCD spectrum of the ( R ) - ( - ) enantiomer and corresponding FPC, APT, and charge flow calculations. This study is intended to identify and rationalize the strengths of the FPC and APT models as applied to 2-methyloxetane, rather than to provide a full and detailed interpretation for all experimental features. This is accomplished by comparing the model predictions both with experimental results and with one another. It will be suggested on this basis, and supported also by the DDCP and DDCB results referred to above, that the C H bending modes, Le., the deformations involving C*-H, CH2, and CH3, and particularly those localized at a position remote from the oxygen atom, are best suited for the FPC model. Major discrepancies between the observed and calculated ring stretching infrared absorption as well as VCD intensities are then rationalized in terms of charge flow along the C-0 bond in response to stretching of that bond. Finally, calculations for separate axial and equatorial conformers are presented. The VCD signal is predicted to be insensitive to ring inversion for many modes but changes dramatically for others. Among the latter, two modes are suggested to be particularly well suited for probing the conformational behavior within the present theoretical framework.
Experimental and Computational Details The (S)-(+) and (I?)-(-) enantiomers of 2-methyloxetane and the (S)-(+) enantiomer of the 4,4-d2 isotopomer were synthesized from the corresponding (S)-(+)- and (R)-(-)-1,3-butanediol (Aldrich) and (S)-(+)-1,3-butanediol-l,l-d2,respectively, according to Searles et The dideuteriated diol was obtained from Baker's yeast reduction of ethyl acetoacetate2" followed by reaction of the resulting hydroxy ester with LiA1H4. Treatment of the 1,3-diols with acetyl chloride29 followed by cyclization2' gave the desired oxetanes in 16-30% yield. Purification (>98%) was achieved by preparative G C on a Carbowax column. Chiral complexation chromatography, using an Mn-R-Cam column purchased from CC&CC, FRG, showed an enantiomeric excess of 79.8, 80.4, and 79.8% for the three enantiomers, respectively. Infrared absorption and VCD spectra were recorded at a resolution of 4 cm-' with a Nicolet 8000 FT-IR interferometer. Additional components needed for the VCD measurements included a KRS-5 linear polarizer (Cambridge Instruments), a ZnSe photoelastic modulator (Hinds International) operating at a modulation frequency of 37 kHz, a lock-in amplifier (Ithaco Model (25) Duckett, J. A.; Smithson, T. L.; Wieser, H. J . Mol. Struct. 1979, 56, 157-174. (26) Shaw, R. A.; Ibrahim, N.; Wieser, H. J . Phys. Chem. 1989, 93, 3920-3928. (27) Searles, S.; Pollart, K. A.; Block, F. J . Am. Chem. SOC.1957, 79, 9 52-956. (28) Deol, B. S.; Ridley, D. D.; Simpson, G. W. Ausr. J. Chem. 1976, 29, 2459-2468. (29) Meltzer, R. I.; King, J. A . J . Am. Chem. SOC.1953, 75, 1355-1359.
The Journal of Physical Chemistry, Vol. 94, No. 1 1990 127
VCD of 2-Methyloxetane
"1
16
5:,
I 2
"J 0
:1
i WAVENUMBERS
Figure 2. Vibrational circular dichroism (Ac) and molar absorptivity (e) spectra of (R)-(-)-2-methyloxetane in CCI4 solution. Region of 1100-800 cm-I: c = 3.4 M, 0.01-mm path length; 1360-1 100 em-': c = 3.4 M, 0.1-mm path length; 1500-1360 cm-I: c = 1.0 M, 0.1-mm path length. Plotted spectrum is the difference between the spectra of the (R)-(-) and (S)-(+) enantiomers, with 20000 scans accumulated for each. Uppermost trace represents an estimate of the spectral reproducibility.
391A) operating at the minimum time constant of 0.125 ms, and an optical filter (OCLI), following the design published by Nafie and Diem,Mwith the final focusing mirror replaced by anf/l ZnSe lens as recommended by Malon and Keiderling.3' The VCD spectrum of (R)-(-)-2-MO, corrected for the enantiomeric excess of 8075, is displayed in Figure 2. This spectrum differs in minor details from that included in an earlier preliminary communication,32errors in the measured intensities also having been corrected. For the (I?)-(-) enantiomer of 4,4-d2 only three bands could be clearly distinguished from the noise level. These are found at 1378 cm-' (positive band), 1353 cm-' (positive), and 1227 cm-l (negative) and appear with approximately the same relative intensities as those observed for the corresponding modes of 2-MO, namely, u13 (CH, symmetric deformation), u14 (C*-H out-of-plane bend), and u,, (/3-CH2 wag), respectively. The spectrum is not included here. VCD model calculations were carried out for three conformations of 2-MO. One was the previously reported optimized 3-2 1 G geometry,26which represents the only energy minimum on the 3-21G ab initio potential surface. This structure is referred to as "planar" in spite of a small dihedral angle of about 1.8' favoring the axial orientatioh. In addition, optimized structures were determined for the axial and equatorial orientations of the methyl group with a fixed ring dihedral angle of 15' in each case (Table I). Reoptimization of the geometry using the 6-31G* basis set, with the refined (planar) 3-21G parameters as the starting point, changes the ring dihedral angle to 6.8', with the methyl group in the equatorial position. The vibrational force field for the "planar" structure is the optimized scaled 3-21G force field determined previously.26 The 3-21G force constants were re(30) Nafie, L. A,; Diem, M. Appl. Spectrosc. 1979, 33, 130-135. (31) Malon, P.; Keiderling, T. A. Appl. Spectrosc. 1988, 42, 32-38. (32) Shaw, R. A.; Ibrahim, N.; Nafie, L. A.; Rauk, A.; Wieser, H. In
Proceedings of the 1985 Conference on Fourier and computerized Infrared Specfroscopy;Grasselli, J. G., Cameron, D. G., Eds.; SPIE Bellingham, WA, 1985; pp 433-434.
TABLE I: ODtimized Structural Parameters for 2-Methvloxetane conformation parameter equatorial" planarb axial" 1.4811 1.4807 1.4822 c-0 (1-2) 1.4747 1.4761 C-0 (1-4) 1.4757 1.5579 1.5567 1.5579 C-C (3-2) 1.5565 1.5551 1.5557 c-c (3-4) 1.5142 1.5126 1.5151 C-C (2-5) 1.0831 1.0834 1.0826 C-H (5-1 1) 1.0834 1.0836 1.0833 C-H (5-12) 1.0846 1.0847 1.0845 C-H (5-13) 1.0783 1.0776 1.0787 C-H (4-9) 1.0781 1.0776 1.0790 C-H (4-10) 1.0796 1.0799 1.0802 C-H (3-7) 1.0799 1.0796 1.0794 C-H (3-8) 11 1.67 111.74 11 1.90 0-C-H ( 1-4-9) 11 1.74 111.90 111.54 0-C-H (1-4-10) 114.30 116.77 1 15.22 C-C-H (3-4-9) 116.35 115.18 113.85 C-C-H (3-4-10) 110.70 110.64 H-C-H (9-4-10) 110.83 116.79 115.14 113.17 C-C-H (4-3-7) 112.74 116.39 1 14.44 C-C-H (4-3-8) 1 14.40 1 16.04 1 12.49 C-C-H (2-3-7) 114.70 116.57 113.10 C-C-H (2-3-8) 110.25 110.47 110.49 H-C-H (7-3-8) 110.78 1 10.77 0-C-H (1-2-6) 110.60 115.61 1 14.42 1 12.90 C-C-H (3-2-6) 110.66 110.63 111.18 0-C-C (1-2-5) 115.35 116.22 117.73 C-C-C (3-2-5) 109.85 109.61 1 10.20 C-C-H (2-5-1 1) 110.14 110.08 C-C-H (2-5-12) 110.22 110.63 110.56 C-C-H (2-5-13) 110.66 108.29 108.24 H-C-H (11-5-12) 108.35 109.09 108.89 H-C-H ( I 1-5-1 3) 109.22 108.79 108.82 H-C-H (1 2-5-1 3) 108.74 90.66 90.1 1 90.20 0-C-C (1 -2-3) 86.23 85.84 C-C-C (2-3-4) 85.85 90.94 90.46 90.42 C-C-0 (3-4-1) 92.15 91.52 91.61 C-0-C (4-1-2) 1.8 15.0 15.0 8C E(3-21G)d+ 229.66 -0.00539162 -0.00628421 -0.00564596
"For the axial (ax) and equatorial (eq) orientations of the methyl group, and dihedral angle was held fixed at 15' and all other degrees of freedom were optimized. Completely optimized structure. The dihedral angle of 1.8O favors the axial orientation of the methyl group; we refer to this structure as planar for convenience. CRingdihedral angle. dEnergy in hartrees.
calculated for both the axial and equatorial conformers and scaled by using the same scaling factors as for the planar structure. The only residual Cartesian forces that resulted from this procedure and that exceeded the default optimization criterion of GAUSSIAN 82 (0.00045 hartree/bohr, or 0.0037 mdyn) amounted to 0.025 mdyn acting upon each of the four ring atoms and oriented such that the ring would flatten with relaxation of the structure. These forces were neglected in the transformation4 from Cartesian to local symmetry force constants, since they would affect appreciably only the puckering force constant and frequency which were of no direct interest in the present study. The calculated vibrational frequencies for all three force fields are compared in Table 11. Atomic polar tensors (3-21G) were evaluated for all three conformations and are available from the authors upon request. The STO-3G3*and 3-21G Mulliken charges used for the FPC calculations are listed in Table 111. Theoretical infrared and VCD spectra were then calculated for each of the three conformers by using the FPC and APT models. The calculated values for the dipole and rotatory strengths are summarized in Tables IV and V, respectively, and the corresponding theoretical spectra are plotted in Figures 3 and 4. Details of the charge flow calculations for each conformer are given separately below. Results Infrared Absorption Intensities. In published applications of the FPC model the selection of a charge set has not been subject to any rigorous guidelines. We have explored two alternatives,
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
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FIXED PARTIAL CHARGE
Shaw et al. ATOMIC POLAR TENSOR
CHARGE FLOW
Figure 3. Calculated molar absorptivity spectra for 2-methyloxetane,plotted for the axial (lower trace), optimized "planar" (middle trace), and equatorial (upper trace) conformations(see Table I and text), and using fixed partial charge (left, STO-3G charges of Table III), charge flow (middle, including only the parameter a[co/dRco in addition to the STO-3G charges, see text), and atomic polar tensor (right) models. Spectra are plotted on a common of 10 cm-l. The calculated integrated absorption intensities are intensity scale assuming Lorentzian bandshapes and a bandwidth (fwhh), approximated by e,,,A~q,~. FIXED PARTIAL CHARGE
CHARGE FLOW
ATOMIC POLAR TENSOR
hI
5
5
10 V l
F,
,
753
7
SCS
1050 13OC WRVENUMBERS
135G
1500
750
U
13
Y
900
1050 1200 WRVENUMBERS
1350
1500
750
900
1050 1200 WRVENUMBERS
I350
lkC3
Figure 4. Calculated VCD spectra for (R)-(-)-2-methyloxetane,plotted as in Figure 3
with the STO-3G Mulliken charges emerging clearly as the favored choice over the corresponding 3-21G parameters. This selection was based upon preliminary calculations which revealed that while the former generally predicted absorption intensities of the correct order of magnitude for those bending modes for which the FPC method should be most successful (see below), the latter overestimated the same intensities by an order of magnitude. It is worth noting that the relative infrared absorption and VCD intensities agree very closely for the two charge sets, with VCD sign reversal occurring for only two very weak bands (uZ3 and u 2 * ) . All subsequent calculations discussed here were
based upon the STO-3G charges. The FPC model is reasonably successful in the 1500-1000-cm-1 region. In particular, the five most prominent absorptions u I I , u I z , u I 3 . v I 7 , and uz2 are predicted and observed as the strongest features (1451, 1441, 1378, 1228, and 1061 cm-I, respectively; see Figures 2 and 3, peaks 18-16, 12, and 7, respectively, and column "FPC/pl" in Table IV). More subtle variations are not reproduced, although these discrepancies are minor in the overall context. For example, the relative intensities predicted for the four weak absorptions between 1200 and 1 100 cm-' do not correspond well with those observed ( u I 8to uZ1).and u I 5(1322 cm-I)
VCD of 2-Methyloxetane TABLE 11: Observed and Calculated Vibrational Frequencies (in em-') for 2-Methvloxetane' calcdb Y obsd planar A(ax) A(eq) approximate description' 1 2999 2997.4 0.9 1.2 8-CH2asym stretch 2 2980 2984.4 -0.3 3.0 CH, asym stretch 3 2973 2975.1 0.9 -0.1 CH, asym stretch 4 2949 2948.9 1.1 -0.2 @CH2 sym stretch 5 2938 2936.9 2.6 1.3 a-CH2 asym stretch 6 2932 2920.0 1.2 0.8 CH, sym stretch 6.3 -8.7 C*H stretch 7 (2900) 2904.2 8 2891 2892.1 0.6 -3.2 a-CH2 sym stretch 9 1482 1484.8 -1.7 -1.8 a-CH, scissor IO 1452 1453.1 -1.1 0.4 0.5 CH, asym def + 0.4 8-CH, scissor 1 1 1451 1446.0 1.3 -1.6 0.5 (3-CH2scissor + 0.3 CH, asym def 12 1441 1439.8 0.5 -1.4 CH, asym def 13 1378 1376.1 1.4 0.2 CH, sym def 4.5 C*H bend (o/p) 14 1352 1353.3 -2.3 15 1322 1325.7 -1.9 -3.0 a-CH2 wag 16 1260 1258.4 -2.5 0.6 0.6 C*H bend (i/p) + 0.3 a-CH, wag 17 1228 1223.3 6.9 4.4 P-CH, wag 18 1195 1195.9 -1.3 -9.0 @-CHItwist 19 1167 1185.1 -3.3 -1.1 0.3 a-CH2 twist + 0.2 &CH2 rock 20 1 140 1120.3 -1 1.2 20.0 0.2 H,C-C stretch + 0.2 CH,C-C stretch 21 1105 1105.9 0.2 -0.4 0.4 a-CH2 twist + 0.3 a-CH2 rock 22 1061 1063.1 -2.0 0.1 0.3 CH, rock + 0.3 CH,C-0 stretch 23 984 989.1 -4.1 1.6 H2C-0 stretch -1.3 24 953 964.4 -4.8 H2C-Cstretch 25 934 924.0 -4.6 -0.3 0.3 D-CH, twist + 0.3 CH3 rock 9.7 26 880 871.8 -1.0 CH,C-C stretch 27 856 843.8 3.7 -4.3 CH,C-Ostretch 4.1 28 795 770.7 22.9 0.5 B-CH, rock + 0.3 a-CH, rock 29 718 716.4 0.9 -54.1 ring def 30 432 430.2 -4.1 12.3 CHI bend (o/p) -0.5 -8.5 CHI bend (i/p) 31 332 329.6 4.2 -13.0 CH, torsion 32 225.0 33 90.5 39.9 24.2 ring pucker 5.5d 5.0d 6.7d "See ref 25 for derivation of the force field for the planar structure. bFor explanations of "planar", "ax", and 'eq", see footnotes a and b in Table I. A = planar - axial (equatorial). CAbbreviations "i/p" and "o/p" specify bending motions as in-plane or out-of-plane relative to the four-membered ring. Skeletal stretches are distinguished by specifying the atoms involved. dAverage error (in cm-I).
TABLE 111: Mulliken Charges for 2-Methyloxetane charge' atom charge' atom no. STO-3G 3-21G no. STO-3G 3-21G 1 -0.248953 -0.614417 8 0.064208 0.229207 2 0.076412 0.078893 9 0.056791 0.208576 3 -0.128 100 -0.531 222 10 0.057809 0.210203 4 -0.002 703 -0.067 545 11 0.063 836 0.21 1433 5 -0.188612 -0.586501 12 0.068413 0.224343 6 0.052717 0.217533 13 0.063184 0.194576 7 0.064098 0.225908 (I
In units of electronic charge.
is marginally overestimated in intensity relative to the two adjacent 4 vl6. In contrast, below 1000 cm-I the three features ~ 1 and dominant absorptions at 984 cm-l ( ~ 2 3 ) . 953 cm-' (~24)and 856 cm-' ( u ~ ~ )corresponding , to three ring stretching modes, are underestimated by an order of magnitude (see Figures 2 and 3, peaks 6, 5 , and 2, respectively). The APT (3-21G) method provides a much better overall prediction of the absorption intensities, particularly between 800 and IO00 cm-l where the FPC model fails. The main discrepancies in the mid-infrared region occur for the two C*-H bending modes ~ 1 and 4 +,. The force field is not likely to be the source for these errors, since both modes were readily located by comparison with the spectra of selectively deuteriated species,26and their assignments and observed frequencies are faithfully reproduced. The most plausible source of error is the atomic polar tensor for the
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 129 methyne hydrogen atom which, if indeed this is the problem, would account also for anomalies in the calculated intensities for the analogous modes of the 2,2-d2 and 3,3-dz isotopomers.26 Vibrational Circular Dichroism. Certain localized vibrational modes correspond to VCD bands at higher frequencies which are of particular interest as potential configurational probes. For example, the two prominent features at 1378 cm-I ( ~ 1 3 ,CH3 symmetric deformation) and 1352 cm-' (q4,C*-H out-of-plane bend), both positive for the (I?)-(-) enantiomer of 2-MO and also for the 4,4-d2 species, have obvious counterparts in the VCD spectrum of propylene ~ x i d e ~where " ~ they are both negative for enantiomer. These two bands evidently correlate with the (S)-(-) the configuration at the chiral carbon atom, whereas the sign of optical rotation does not. For the analogous thioethers, propylene sulfide34and 2 - m e t h ~ l t h i e t a n ethe , ~ ~VCD band for the C*-H bend retains the same sign as for propylene oxide and 2-MO, while the symmetric methyl deformation band is very weak and the sign therefore difficult to ascertain. The correlation noted here between the VCD sign of the C*-H bending mode and the absolute configuration at the asymmetric carbon of the -CH2-C*H(CH3)-X- fragment, X = 0 and S , appears to hold also for several other similar instances including 3-methyloxetane-2,2-dz (X = CDz),36several 7s-substituted deand l-aminorivatives of 5-methyl-6,8-dioxabicyclo[3.2.1]octane,37 and 1-methylindane (X = aromatic C).38 In all these cases the chiral center is part of a ring skeleton, and the vibration was identified as the "out-of-plane" deformation of the C-H bond, except for the substituted indanes where the assignment was not made in such detail. This deformation mode therefore emerges as a consistent VCD configurational marker for the -C*H(CH3)group in ring systems in general. The same utility cannot be ascribed to the symmetric deformation of the methyl group. Although the sign of this band for the 5-methyl group in the 5-methyl-6,8-dioxabicyclo[ 3.2.13octane derivatives does correlate with that observed for the same absolute configuration in 2-MO;' it is negative in 3-methyloxetane-2,2-d2 (X = CD2)36and is very weak or absent in 2-methylthietane and propylene sulfide (X = 9.34.35
The two asymmetric methyl deformations are separated in the infrared absorption spectrum at 1441 and 1451 cm-l. On the basis of earlier arguments,39 these modes would be expected to give rise to VCD features of equal intensity and opposite sign. The higher frequency mode v l l is strongly coupled with the /3-CH2 scissor (Table 11) and overlaps with ulz. While both the FPC and APT models predict a (- + -) triplet for these three modes, only a single negative feature is observed at 1451 cm-l. It thus appears that the VCD features associated with the perturbed degenerate asymmetric methyl deformations are not generally useful as a probe for molecular stereochemistry, even when the splitting of the modes is as favorable as for 2-MO. In terms of general success, the FPC model at the planar geometry and with the STO-3Gcharges reproduces the observed sign for 11 of the 12 distinct VCD bands below 1400 cm-l (peaks 2, 5-1 3, 15, and 16 of Figure 2; see also under column "FPC/pl" in Table V), although the relative intensities are not well reproduced. For two modes, ulS and Y z 6 , the VCD intensity lies below 5 VCD signal the threshold of our instrument, while for ~ 2 the apparently corresponds to a weak shoulder (peak 4) on the stronger peak at 953 cm-I. The APT model agrees with FPC in sign for (33) (a) Polavarapu, P. L.; Michalska, D. F. J . Am. Chem. Soc. 1983,105, 6190-6191. (b) Polavarapu, P. L.; Hess, B. A,, Jr.; Schaad, L. J. J . Chem. P h p . 1985, 82, 1705-1710. (34) Polavarapu, P. L.; Hess, B. A,, Jr.; Schaad, L. J.; Henderson, D. 0.; Fontana, L. P.; Smith, H. E.; Nafie, L. A.; Freedman, T. B.; Zuk, W. M. J . Chem. Phys. 1987,86, 1140-1 146. (35) Shaw, R. A.; Ibrahim, N.; Wieser, H. Unpublished results. (36) Shaw, R. A. Ph.D. Thesis, University of Calgary, 1986. (37) Shaw, R. A.; Ibrahim, N.; Wieser, H. Tetrahedron Lett. 1988, 29,
-
165-7AR .. .. . I
(38) Fontana, L. P.; Chandramouly, T.; Smith, H. E.; Polavarapu, P. L. J . Org. Chem. 1988, 53, 3379-3381. (39) Nafie, L. A.; Polavarapu, P. L.; Diem, M. J . Chem. Phys. 1980, 73, 3530-3540.
130 The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
Shaw et al.
TABLE I V Experimental a d Calculated Dipole Strengths for 2-Methyloxetane 10"Db/(esu2 cm2) Y
peak no."
1 2 3 4 5 6
I 8 9 IO 11 Ii 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
20 19 18 17 16 15 14 13 14 11 IO 9 8 7 6 5 4 3 2 1
u(obsd)/ cm-' 2999 2980 2973 2949 2938 2932 (2900) 289 1 1482 1451 1452 1441 1378 1352 1322 1260 1228 1195 1 I67 1140 1105 1061 984 953 930 880 856 795 718 432 332
1
FPCC obsd
0.0 17.2e 16.2 42.1 11.0 5.8 3.0 24.6 3.2 5.3 9.8 14.2 72.5 174.9 85.4 5.2 0.0 118.7
ax 12.8 9.2 9.8 3.8 3.1 2.3 0.9 2.7 10.3 0.1 19.0 16.8 36.0 4.9 6.8 3.6 35.1 6.4 9.3 0.4 2.2 31.0 8.3 5.3 11.1 2.3 12.6 13.2 11.1 8.7 24.9 3.1 66.7
CFd
PI
e4
13.7 8.3 9.6 3.8 3.0 2.4 1.o 2.8 10.0 0.7 22.5 13.3 34.8 5.7 7 .O 2.6 37.0 6.9 7.8 3.3 0.8 30.3 7.8 7.6 12.0 0.5 9.5 16.0 9.0 6.5 26.4 3.7 107.1
14.7 6.9 9.5 4.3 2.9 2.5 1.8 2.0 9.5 3.0 24.1 10.2 31.0 8.5 1.2 2.3 27.0 20.5 4.3 4.2 1.3 30.5 2.8 15.8 11.0 2.6 8.0 7.8 13.5 4.9 28.0 4.1 83.4
ax 12.8 9.0 9.3 3.3 3.1 2.2 1.4 1.8 6.6 0.3 13.6 16.6 37.4 6.7 1.3 11.5 37.8 7.6 9.6 1.1 6.0 140.3 135.6 82.2 21.6 6.2 154.5 15.6 14.4 10.9 27.1 3.8 67.0
Pl 14.0 7.9 9.2 3.4 3.0 2.4 1.5 1.7 6.5 1.2 16.7 13.0 36.6 7.1 1.o 8.6 43.6 6.2 7.3 1.1 1.9 151.0 170.3 53.1 19.6 24.8 123.6 16.9 11.5 8.0 29.5 4.5 101.6
APT eq 14.6 6.8 9.2 3.9 2.9 2.5 2.3 0.9 6.4 2.2 19.3 9.9 34.1 9.2 1.2 4.7 33.5 19.7 8.4 0.5 14.3 144.2 117.8 118.1 14.8 18.5 120.1 11.3 13.4 6.1 32.4 5.1 83.6
ax 39.2 31.3 37.7 27.8 38.9 17.8 34.3 88.6 2.4 2.7 23.0 16.4 47.6 41.9 4.6 33.9 24.1 17.3 13.1 4.1 10.0 99.6 171.4 97.7 15.9 1 .o 102.0 9.1 21.4 45.6 52.7 7.2 111.8
Pl 42.4 29.7 32.9 24.7 40.3 19.5 36.8 97.8 2.2 6.8 22.7 14.2 51.4 46.2 5.2 34.9 30.8 4.7 17.6 6.8 5.6 104.8 240.0 55.1 12.3 10.5 86.4 5.6 17.5 37.6 56.7 9.5 145.9
eq 47.5 23.7 28.9 27.7 37.6 19.9 54.4 84.7 1.8 12.5 20.4 11.9 65.4 40.9 5.2 29.0 31.0 13.8 13.5 3.4 16.5 76.7 180.2 123.9 8.7 5.1 93.5 3.7 19.6 35.0 61.1 10.7 125.5
Peaks numbered in Figures 2-4. FPC = fixed partial charge, CF = charge flow, APT = atomic polar tensor. "PI" refers to complete optimized structure for which the dihedral angle is 1.8'. and "ax" and "eq" refer to optimized structures for which the dihedral angle was held fixed at 15'. CUsing Mullikan net charges calculated by STO-3G; see Table 111. dUsing the same fixed charges as for FPC, but including also charge flow along the C-0 bond with displacement of the C-O stretching coordinate, parameter L&o/dRco. See text. e Unresolved bands.
22 of the total of 33 modes and for 13 of 18 modes between 1500 and 800 cm-I, including v9 to ~27. However, the overall agreement with experimental VCD signs is significantly worse for APT than for FPC. For the single mode below 1400 cm-' where the FPC model fails to reproduce the observed VCD sign, namely, the P-CH, wag at 1228 cm-l (vI7). the APT model is also in error.
Discussion Infrared and VCD Intensities and Charge Flow for the Planar Structure. The mid-infrared vibrational modes can be broadly classified as C-H deformations and ring stretches. For saturated hydrocarbons such as DDCB and DDCP, the dipole moment derivatives, ap/aRi, are very much smaller for C-C stretches than for the majority of CH deformations. Those absorptions that show appreciable infrared intensity must therefore involve some significant amount of CH bending. The success of the FPC model for these molecules in particular suggests that for these modes both the magnitude and direction for the dipole moment derivatives are approximated adequately by assuming fixed charges in the sense of C--H+. For 2-MO the generally good reproduction of experimental intensities for the bending modes between 1100 and 1500 cm-I also suggests a genuine validity of the FPC model, specifically implying that the dipole moment derivatives ap/aQi are calculated with the correct order of magnitude. A successful calculation of the rotatory strength depends upon the knowledge of not only the magnitude of &/aQi but also the correct orientation. As a means of testing the FPC method in this regard, we have compared the values of &/aRi for all local symmetry coordinates, Ri, as calculated for both the FPC and APT models. This comparison, summarized in Table VI, identifies coordinates that are most "FPC-like" according to two criteria. First, the calculated absolute magnitudes should be comparable, except for the C*-H bends
for the reason discussed earlier. Second, and equally important for VCD, is that the FPC model provides the correct orientation for ap/aRi. A comparison of the relative orientations as calculated for the APT and FPC models may be interpreted to identify those coordinates for which the latter is completely adequate, i.e., ap/aRi agree both in direction and in magnitude, as well as to suggest means of resolving certain discrepancies between the calculated intensities of the two. The larger the angle between the parameters, the more important charge flow becomes as a possible factor contributing to the calculated infrared absorption intensities and, implicitly, also the VCD intensities. Most relevant to this discussion is the comparison of the relative orientations for the bending modes as calculated by the two methods. Assuming an angle of 30' as a reasonable criterion for distinguishing between modes which should be amenable to FPC prediction and those which are not, we find that all but seven cases fall into the former category. Six of these seven modes involve deformations centered on one of the carbons adjacent to the oxygen atom, viz., C*-H, C-CH,, and a-CH2 bends, suggesting that the deformations involving the methyl and P-CH, groups are likely better described by the FPC model than are those localized at the a-position. The only exception is the &CH2 twist which in any case has virtually zero intensity according to both models. Of the other three P-CH, deformation coordinates, the rocking and scissoring fundamentals are unsuitable as stereochemical probes, the former lying below the 800-cm-I cutoff for VCD measurement and the latter being strongly coupled with the two asymmetric methyl deformations. The j3-CH2 wag appears to be the best suited for FPC treatment according to three criteria, namely, the electric dipole moment derivative is correctly modeled, the mode corresponds to an essentially pure wagging motion, and it exhibits significant intensity in both the infrared and VCD spectra.
The Journal of Physical Chemistry, Vol. 94, No. 1 , 1990 131
VCD of 2-Methyloxetane
TABLE V: Experimental and Calculated Rotatory Strengths for (R)-(-)-2-Methyloxetane 104SRb/(es~2 cm2) V
peak no.'
1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33
20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
u(obsd)/ cm-I 2999 2980 2973 2949 2938 2932 (2900) 2891 1482 1451 1452 1441 1378 1352 1322 1260 1228 1195 1167 1140 1105 1061 984 953 930 880 856 795 718 432 332
1
FPCc obsd
f (-48)'
f
89 42
f
14 -53 49 -40 38 -3 5 -145 106 183
(+I
f
-1 30
ax -1.3 4.8 -1.3 -1 1.0 6.4 1.8 -0.5 0.7 0.3 0.1 28.0 -45.9 5.9 16.5 -18.2 11.2 71.4 -27.9 -45.5 -3.1 15.1 -11.1 4.7 21.2 -4.3 -1.2 -33.7 1.5 40.2 -18.3 -5.6 2.1 -6.7
-'See Table IV. /No measurable intensity; A t
CFd
PI -1.8 -0.6 0.0 -0.2 0.8 0.9 -0.9 1.4 -2.6 -16.8 31.6 -29.1 4.6 20.5 -23.3 17.8 15.8 9.3 -34.7 25.0 -2.9 -16.3 1.4 19.9 1.3 9.0 -32.9 1.4 17.2 -12.0 -6.7 2.1 -2.9
< 5 X IO4 M-'
eq 0.8 -7.6 0.5 11.6 -5.9 0.1 -1.8 2.1 -6.0 -25.4 29.8 -12.7 2.6 22.2 -27.7 29.2 -57.3 17.0 17.9 36.1 6.6 -3 1.8 -4.8 13.7 11.4 27.2 -24.7 -18.5 -0.1 -4.5 -5.8 -0.2 3.1
Idp/aR,lb/ 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26-33
@-CH2rock C - 0 stretch CHI rock C*-H bend (i/p) a-CH2wag a-CH2twist CH, bend (o/p) @-CHItwist a-CH2 scissor methyl C-C stretch C*-H bend (o/p) C-H stretches
LAPT/FPC' 1.1 2.2 3.2 4.2 7.9 8.2 8.7 9.1 9.6 11.0 16.7 18.0 19.5 21.4 25.8 26.6 28.2 48.7 57.8 65.5 86.1 101.2 117.1 154.3 168.3 154-173
FPC
APT
12 6 7 7 6 4 6 6 8 6 7 8
16 1 12 15 8 23 7 5 8 6 14 7 2 75 3 61 5 3 6 1 10
1 21 5 18 6 6 8 1 7 0 5 0 4 5-7
PI -0.0 -4.0 0.9 -0.2 1.1 1.2 -2.4 2.7 1.6 -21.3 31.3 -28.2 6.1 55.9 -1.9 0.2 18.2 6.0 -34.0 -14.6 23.7 -62.4 6.3 58.5 -3.3 15.8 -85.9 15.2 27.7 -1 1.0 -6.2 2.0 -2.6
APT eq 2.2 -10.3 1.4 11.4 -7.0 0.3 -3.2 4.7 1.o -28.6 27.8 -13.1 6.6 55.0 -20.1 13.8 59.6 9.8 20.4 5.9 57.0 -87.8 -29.0 64.1 4.1 27.0 -4.2 -55.5 9.6 -2.8 -5.0 -0.5 2.0
ax -12.7 15.3 -22.6 -19.1 57.3 -8.6 -14.7 17.3 9.3 -32.6 53.5 -46.2 18.4 14.9 -0.6 -50.3 37.0 -35.3 -17.6 11.0 5.6 -18.7 50.4 34.3 -36.8 -5.1 -57.1 37.2 31.5 14.2 -16.1 7.5 -18.1
PI -19.9 -10.9 -1 1.3 28.0 16.7 -15.2 -27.1 41.4 6.2 -66.0 69.3 -25.3 13.2 16.7 -4.3 -53.8 15.0 -6.3 -8.2 -0.2 12.7 -23.7 33.5 48.1 -37.7 12.4 -45.1 17.0 24.0 14.5 -12.8 6.8 -10.9
eq -5.7 -41.4 -0.3 75.9 -33.4 -18.0 -51.5 74.4 -0.5 -76.3 71.0 -6.5 2.7 14.7 -8.6 -52.7 -7.9 17.6 10.7 -3.9 6.4 -15.4 -7.8 44.3 -1.7 10.7 0.8 -21.3 16.6 15.3 -11.1 1.5 -3.8
cm-I.
TABLE VI: Comparison of Molecular Dipole Moment Derivatives with Respect to Local Symmetry Coordinates As Calculated for the FPC and APT Models coordinate (R,) pucker a-CH2 rock ring def ring C-C stretch CHI asym def CH, bend (i/p) CH, asym def CH, rock P-CH2 wag P-CH, scissor ring C-C stretch CH3 sym def CH, torsion C - 0 stretch
ax 0.3 1.8 -1.3 -10.2 7.3 2.5 -1.7 0.5 3.2 -3.9 26.7 -44.1 6.6 55.4 10.5 -11.9 75.6 -30.0 -45.0 13.7 -25.2 -55.9 16.1 48.8 4.3 -10.9 -94.2 35.6 48.3 -18.1 -5.4 2.3 -5.6
1
1 10 3 13-20
'Angle between ap/aR, for APT and FPC (in degrees). b p in units of electronic charge (e) X A; R in A (stretches) or radians (bends).
The ring stretches are also of interest when viewed in this context. For each of the four modes u22 to uZ4 and ~ 2 (peaks 7 7-5
and 2 of Figures 2 and 3), the infrared absorption intensities are severely underestimated by the FPC model. The corresponding VCD intensities are similarly underestimated, although they are reproduced in sign. For these modes the APT model is distinctly more accurate in both the infrared and VCD. The success of the FPC model in matching the experimental VCD signs may be rationalized by noting that for each of the four ring stretching coordinates the FPC and APT values for ap/aRi lie within 26' of one another at worst. The dipole moment derivatives thus follow closely the direction predicted on the basis of fixed partial charges in the sense C+-O-, even though the magnitudes predicted by FPC for d p / a R , are too low. This comparison suggested that the FPC model could be improved significantly by including a charge flow parameter, d4co/aRco (see ref 9 for notation and sign conventions), which transfers negative charge from carbon to oxygen as the (2-0 bond is stretched. In this manner the magnitude of the dipole moment derivative, ap/dRco, would be increased, with the direction predicted by the FPC and APT calculations retained. The variable dtw/aRw was adjusted to best reproduce the infrared absorption intensities measured for ~ 2 and 3 u2, (HzC-O and CH3C-0 stretch, coordinate numbers 16 and 14, respectively). The optimal value of 0.35 e/A then reproduced the observed absorption intensities 3 vZ7and also brought v24 into much better agreement for ~ 2 and with experiment (see Figure 4, peaks 6, 2, and 5, respectively). Simultaneously, u22 which was formerly too weak by a factor of 2 is now too intense by the same factor. The calculated dipole strengths for other modes are not affected substantially by the inclusion of this charge flow parameter, except for u26 which is now predicted with moderate intensity. The computed FPCfcharge flow spectrum is in excellent qualitative agreement with that observed (Figure 3), with the largest discrepancies in the FPC spectrum uniformly reduced. Perhaps more relevant as a test for this approach being physically sound is that the corresponding VCD intensities for u22 to u24 and v2, are all
132 The Journal of Physical Chemistry, Vol. 94, No. I , 1990
brought into much better accord with the experimental values (see Table V and Figure 4, peaks 7-5 and 2, respectively), although for u2, there remains a discrepancy of an order of magnitude (peak 6). Finally, it is evident that including only the charge flow term d[co/dRco affects the VCD not only for those modes which are predominantly ring stretches, namely, u22 to u24 and ~ 2 7 ,but also for certain higher frequency bending modes, notably, u20. u Z I ,and (peaks 9, 8, and 13, respectively), with the bands for the first two inverted relative to the FPC and experimental results. Although the FPC model does not properly account for the measured VCD intensities, it is our interpretation that the agreement in sign for most measurable bands, combined with the good reproduction of the observed C-H bending intensities (1 100-1500 cm-I) and the DDCP and DDCB evidence cited earlier, implies that the model reflects a genuine first-order contribution to the observed spectra. In addition, the improvements noted for the ring stretches by including only the single parameter dEco/dRco are sufficient to suggest that the charge flow model has the capacity to reproduce both the infrared and VCD spectra in a consistent manner and that genuine mechanisms contributing to the observed intensities are reflected by this parameter as well as others which may arise. A complete derivation of all such parameters is beyond the scope of the present study, although it is clear that reasonable values for the neglected charge flow terms may be anticipated to dramatically affect the appearance of the calculated spectra. The discrepancies noted above for certain higher frequency bending modes are then attributed to the neglect of such terms in the model calculation and are not interpreted to suggest a deficiency of the model itself. Symmetric Methyl Deformation. We have suggested previo ~ s l that y ~ the ~ VCD intensity of the CH, symmetric deformation band ( u 1 3 , peak 16) may arise by a mechanism analogous to the ring current model developed by Freedman and Nafie.I4 The observed dissymmetry factor (At/t) of about 8 X lo-' exceeds the calculated value by an order of magnitude, while the observed infrared absorption intensity is reproduced to within 25-30% by both the FPC and APT predictions. The absence of this band in the spectra of 2 - m e t h ~ l t h i e t a n eand ~ ~ propylene sulfide34 suggests some distinct electronic contribution to the intensity of the observed bands in both 2-methyloxetane and propylene oxide.), One way of accounting for the observed VCD and infrared absorption intensities simultaneously would involve augmenting the FPC calculation by including a charge flow parameter which transfers positive charge from C(2) to C(5) as the angles LC(2)C(5)H increase in the course of the deformation. This parameter would then raise the contribution to the transition moment originating with the concerted motion of the three positively charged hydrogens and could be optimized to reproduce the measured dipole strength. This charge flow is equivalent to an injection of negative charge into the ring at C(2). According to predictive rules advanced by Freedman, Nafie, and wworkers,lGlk this influx of charge would then flow preferentially toward the oxygen atom, resulting in a net ring current of positive charge around the ring in a counterclockwise direction as viewed from the face to which the methyl group is attached and thereby providing a contribution to the magnetic dipole transition moment which is perpendicular to the ring. The right-hand rule then predicts that this contribution will form an angle of less than 90' with the direction of the electric dipole transition moment, the latter lying essentially along the C(2)-C(5) bond, and therefore enhance the positive intensity predicted for the symmetric deformation mode. Effects of Conformational Flexibility. While the experimental evidence cited earlier25 clearly suggests that stable axial and equatorial conformers can exist at room temperature and that they are separated by a potential barrier to ring inversion of about 110 cm-l, the ab initio structures at both the 6-31G* and 3-21G levels indicate only single minima on the potential surface. We interpret these differences as indicating a very flat potential with at best a low barrier separating the two conformers. A range of ring conformations characterized by varying dihedral angles should
Shaw et al. therefore be possible, and even in the absence of a barrier one orientation would be favored over the other. For this reason it was of interest to reexamine the VCD spectrum with the aim of identifying features that either indicate the presence of separate equatorial and axial conformers or suggest a preferred conformation. The model calculations were repeated for both the axial and equatorial conformers, using optimized structures and force fields evaluated at an assumed dihedral angle of 15' in each case. Each of the force fields was then scaled by using the factors previously optimized for the planar structure.26 The observed positions are reproduced well for both conformers (Table 11), with an inordinately large frequency shift observed for only one mode in the experimental range of interest, namely, v2,, (peak 9), and for two others ( u Z 8 and u29) between 700 and 800 cm-l. The overall fit improved only marginally if the scaling factors were reoptimized for the new structures. More importantly, the VCD signs and relative intensities were largely insensitive to further refinements. The AFT absorption intensities show some interesting variations as the reference structure is changed (Table IV). For some cases the dipole strength either increases or decreases regularly as the ring is inverted, while for others it is altered in the same sense relative to the planar geometry, whether the ring is folded axially or equatorially. While these calculations might be expected to reveal some preference for one conformer over the other, the differences are generally small, particularly in view of the overall accuracy of the calculated intensities. The ring stretching modes provide the clearest evidence for some degree of puckering, with the intensities calculated for v22, u2,, v24, and v2,, for both conformers all brought into better agreement with experimental values relative to those calculated for the planar structure. This is best demonstrated for u2, where the intensity at the planar geometry exceeds that observed by 33% but agrees to within 5% for each of the two puckered species. The VCD spectrum must reflect a balance among contributions from a range of dihedral angles, and even with a nearly planar structure on average one of the two species must be energetically favored over the other. If this is the case, then the preferred orientation might be deduced from the spectrum by identifying those normal modes for which VCD shows a clear conformational dependence. Assuming that only two distinct conformers are present, the VCD bands corresponding to such a mode may appear either as separate features for each species or, if the frequency is unaltered upon inversion, as a single feature reflecting the sum of the contributions from both conformer. The three sets of model calculations all indicate that the VCD sign changes for several of the modes in the 800-1400-~m-~ range as the ring is inverted (see Table V). Among those modes predicted to be sensitive to inversion, the @-CH2wag (u,,, peak 12) is most striking. The FPC value for the equatorial conformer mirrors the experimental VCD sign and intensity, whereas the planar and axial conformations should lead to a sign opposite to that observed. Only a very small frequency shift of about 2.5 cm-' upon inversion of the ring is predicted for this mode by the force field calculation, indicating that the observed band likely represents a superposition of contributions from both conformers. If our earlier analysis is correct, and the FPC model is particularly well suited for the @-CHIdeformations, then this evidence clearly suggests a predominance of the equatorial species in solution. The sign changes predicted for u18 and u20 (peaks 11 and 9) support the same conclusion. An exception to the trend is uI9, where the observed VCD sign is reproduced only for the planar and axial structures. In this case the larger rotatory strengths predicted for the axial species might dominate the observed signal even with a predominance of the equatorial structure. In the case of the H2C-0 stretch, u23rit would appear that the three calculations also favor the axial orientation. Although the intensities are underestimated, the FPC model at the planar structure does reproduce the observed sign for this and the other three ring stretching modes. The earlier discussion suggests that this observation is not fortuitous. The VCD feature corresponding to the most intense infrared absorption consists of a positive band,
VCD of 2-Methyloxetane as indicated in Table V, superimposed over a higher frequency negative band for which only a shoulder is evident. This assignment is consistent with the force field calculation, which indicates the equatorial band to lie about 6 cm-' above the axial, and also with the FPC-VCD calculations predicting negative and positive features for the equatorial and axial conformers, respectively (Table v). Finally, we note that in the majority of cases where the FPC model predicts a change in sign for an observed VCD band upon inversion of the ring, both the C F and APT models predict the same behavior. Although it is premature to speculate on the significance, it is encouraging to find that such agreement among the calculated spectra does exist, thereby supporting the conclusions suggested on the basis of the FPC spectra.
Conclusion The VCD spectrum is reported for 2-methyloxetane in the region 800-1 500 cm-l. Based upon the optimized 3-21 G geometry and scaled harmonic force field, the theoretical spectra are reported for the fixed partial charge (FPC) and atomic polar tensor (APT) models. With regard to the former, the most encouraging observations are a generally good qualitative agreement with experimental absorption intensities over the 1100-1 500-cm-' range and the reproduction of the measured sign for 11 of the 12 VCD bands observed between 800 and 1400 cm-I. Major deficiencies of the model include a severe underestimation of the ring stretching absorption intensities and generally poor agreement with observed VCD intensities. The APT model, while reproducing the infrared spectra more reliably, estimates the VCD characteristics even less accurately than FPC. The major discrepancies between the FPC calculated and experimental absorption spectra result primarily from an underestimation of the dipole moment derivative a p / a R for the C - 0 stretching coordinates. By augmenting the FPC calculation with a single charge flow parameter which transfers negative charge from C to 0 as the C-0 bond is stretched, the differences were reduced significantly, improving uniformly also the calculated VCD intensities for the four ring stretching modes. A comparison of the dipole moment derivatives a p / d R i calcharge flow culated for the two models suggested the d&-,/dR, parameter as the principal correction term and proved useful as a means of identifying those modes for which the FPC model might be best suited. Based upon this latter and other additional criteria, the @CH2 wag was identified as one of the "FPC-like" coordinates, apparently contradicting the observation that for the same mode the FPC calculation at the optimized 3-21G structure does not reproduce the experimental VCD sign. Subsequent model calculations for fixed axial and equatorial structures were then
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 133 interpreted to suggest a predominance of the equatorial conformer, with the observed VCD band for the P-CH2 wag then being reproduced in sign and the majority of other modes whose sign also showed a conformational dependence supporting the same conclusion. While this runs counter to the 3-21G ab initio structure, it is in accord with the 6-31G* optimized geometry, which predicts an equatorial conformer with a ring dihedral angle of 6.8O. On an empirical level, this study extends the scope of the C*-H out-of-plane deformation as a configurational marker for the 0-C*H(CH3)-CH2 group and further suggests that the CH, symmetric deformation may also prove useful in the same capacity. The C H 3 asymmetric deformations, although well separated in the absorption spectrum, did not give rise to the bisignate VCD signature which might be anticipated for perturbed degenerate modes,39and no stereochemical information could be inferred from the single negative feature observed between 1400 and 1500 cm-I. Finally, a distinction emerged between those modes whose VCD bands can serve as configurational markers and those which reflect conformation. The methyne and symmetric methyl deformations appear to be insensitive to conformational variations, while the P-CH2 wag and a ring stretching mode indicate a preponderance of the equatorial conformer of 2-methyloxetane. The VCD spectrum of 2-methylthietane is particularly interesting in this regard, as both axial and equatorial species are undoubtedly stable and nearly equal in energy. The spectrum and analysis will be reported in a forthcoming publication.
Acknowledgment. This work was supported by an Operating Grant (to H.W.) from the Natural Sciences and Engineering Research Council of Canada (NSERCC). The very first VCD measurements on 2-methyloxetane were attempted (by R.A.S.) in the laboratory of Dr. L. A. Nafie at the Department of Chemistry of Syracuse University, Syracuse, NY, in 1984. We most gratefully acknowledge the help and encouragement that Dr. Nafie has given us to facilitate our entry into the field of vibrational circular dichroism. We are indebted also to Drs. A. Rauk and R. Dutler of this department for making available GAUSSIAN 82 and for many productive discussions and to Dr. R. S. Roche of the Department of Biological Sciences at this University for kindly lending us the lock-in amplifier which was used throughout most of the initial phase. This amplifier has since been replaced be a new one purchased with an Equipment Grant from NSERCC for which we express our gratitude on this occasion. R.A.S. acknowledges the award of a Postdoctoral Fellowship from the University of Calgary. We also thank the Academic Computing Services of the University for access to the Honeywell/Multics and Cyber 205 Supercomputer systems. Registry No. 2-Methyloxetane, 21 67-39-7.
