437
J. Phys. Chem. 1992, 96, 431-446 This provides additional evidence that the value -1 f 2 kcal mol-' reported by W a l ~ is h too ~ ~ low.
C , / R = a,
+ a2T + a3P+ a4T3+ a5T'
-H- - u , + - +a2T -
a,TZ
a , P a6 + -a4T3 ++ -T 4 5
Appendix The supplementary material data are as follows: Table VI11 presents the Z matricesu for each of the molecular species obtained from the HF/6-3 l G * geometry optimization calculations. Molecular geometries can be obtained from these matrices. Table IX gives the moments of inertia in atomic units (amu bohr2), and Table X lists the scaled vibrational frequencies obtained at the same level of theory. Table XI presents the electronic energies resulting from the various perturbation-theory calculations using the 6-31G** basis set. The projected UHF (PUHF) and projected UMP2 (PUMP2) energiesZEare given for reference, although they are not used in the derivation of the BACs. Table XI1 gives the coefficients for polynomial fits to C , H, and S as a function of temperature (300 K IT I2500 KP for the species considered in this paper. These fits are used with the CHEMKIN software p a ~ k a g eand ~ ~ are , ~ defined ~ by
Registry No. H3SiCH3,992-94-9; H2Si(CH3)2,11 11-74-6; HSi(CH&, 993-07-7; Si(CH&, 75-76-3; H2SiCHp,51220-22-5; HSi(CH3)2, 24669-76-9; Si(CH3)3, 16571-41-8; HSiCH3, 55544-30-4; Si(CH3)2, 6376-86-9; SiCH3,88867-57-6; H3SiCH2,24669-75-8; H2Si(CH3)CH2, 137626-39-2; HSi(CH,)2CH2, 34377-79-2; Si(CH3)$H2, 19469-02-4; H2Si=CH2,5 1067-84-6; H(CH3)Si=CH2,38063-40-0; (CH3)2Si=CH2, 41 12-23-6; HSiCH2, 137626-40-5; SiCH2, 65632-07-7; H3SiCH, 66605-30-9; H2SiCH, 137626-41-6; SiCH, 68034-44-6; H,SiC, 117768-71-5; H2SiC, 74694-33-0; HSiC, 68034-43-5; H,SiC=CH, 1066-27-9; H2SiC=CH, 51286-34-1; H S i m H , 99278-14-5; Si=H, 116854-52-5; H2C=CHSiH3,7291-09-0; H2C=CHSiH2,11797860-6; H2C%HSiH, 78442-50-9; H2C%HSi, 137626-42-7; CH3SiH2SiH2CH3,870-26-8; H2, 1333-74-0; C, 7440-44-0; Si, 7440-21-3.
(64) Clark, T. A. Handbook of Computational Chemistry: A Practical Guide to Chemical Structure and Energy Calculations; Wiley: New York, 1985.
Supplementary Material Available: Tables as described in the Appendix (26 pages). Ordering information is given on any current masthead page.
RT
S
2
3 a3 2
- = a , In T + a2T + - p R
a4 as + -T3 + -P + a7 3 4
Vibrational Circular Dichroism and Infrared Spectra of 2-Methyloxirane and frans-2,3-Dimethyloxirane: Ab Initio Vibronic Coupling Theory with the 6-3 1G* (Om3) Basis Set Arvi R a d * and Danya Yang Department of Chemistry, The University of Calgary, Calgary, AB, Canada T2N IN4 (Received: January 25, 1991; In Final Form: July 26, 1991)
The ab initio vibronic coupling theory (VCT) of Nafie and Freedman using a modified 6-31Ga basis set (VCT/6-31G*(0,3) with and without electron correlation in the calculation of the magnetic dipole transition moments is applied to calculate IR and VCD intensities for (S)-2-methyloxirane and (R,R)-2,3-dimethyloxirane.The theoretical values are found to be in very good agreement with values obtained from published experimental IR and VCD spectra in the mid-IR region. Incorporation of electron correlation is found to have very little effect. The relative intensities of absorption and circular dichroism in the C-H stretching region of the IR spectrum are not as well reproduced using VCT/6-31G*(0.3),according to test results on a number of small model systems. Geometries obtained by complete optimization using the 6-31 *(0.3) basis set are in better agreement with experimental geometries than those obtained with the conventional 6-31G* basis set. The circular dichroism in the mid-IR region of the two related systems is discussed in terms of the ab initio normal modes. Comparison of the two systems suggests almost complete correspondence of the signs of the Cotton effects of equivalent normal modes in this region of the spectrum. The computed VCD results suggest a revision of the assignments of two of the normal modes of the (R,R)-2,3-dimethyloxirane.
Introduction The vibonic coupling theory (VCT) formalism for infrared (IR) and vibrational circular dichroism (VCD) intensities developed by Nafie and Freedman] has recently been implemented at the a b initio level2 and the complete IR and VCD spectra of (S,S)-2,3-dideuteriooxiraneand the other deuterated i~otopomers,~ of ethanol and a-deuterioethanol$ and of a series of small model molecules, including hydrazine and hydrogen p e r o ~ i d e ,have ~ appeared. VCT provides an alternative to the VCD formalism of Stephens: which has seen widespread application in the recent literat~re.~-'~ Extensive testing by both Stephens and co-workers and Rauk and cc-workers has established that very extensive basis sets are required to achieve reliable converged results with the ab initio implementations of either theory. The formalism of VCT
* Author to whom correspondence should be addressed. 0022-3654/92/2096-437$03.00/0
(vide infra) requires a summation over excited states for the description of the magnetic dipole transition moment. In the (1) (2) (3) (4)
Nafie, L. A.; Freedman, T. B. J. Chem. Phys. 1983, 78, 7108. Dutler, R. Ph. D. Dissertation, The University of Calgary, 1988. Dutler, R.; Rauk, A. J. Am. Chem. SOC.,1989, 111, 6957-6966. Shaw, R. A.; Wieser, H.; Dutler, R.; Rauk, A. J. Am. Chem. Soc.,
1990, 112, 5401. (5) Rauk, A.; Dutler, R.; Yang, D. Can. J. Chem. 1990, 68, 258. (6) Stephens, P. J. J. Phys. Chem. 1985, 89, 748-752.
(7) Kawiecki, R. W.; Devlin, F.; Stephens, P. J.; Amos, R. D.; Handy, N. C. Chem. Phvs. Lett. 1988. 145.411-417. (8) Lowe,-M. A.; Stephens, P. J.; Segal, G. A. Chem. Phys. Lett. 1986,
123, 108-1 16. (9) Lowe, M. A.; Segal, G. A.; Stephens, P. J. J . Am. Chem. SOC.1986, 108. 248-256. (10) (a) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J. Am. Chem. SOC.1988, 110,2012-2013. (b) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N. C. J. Am. Chem. SOC.1988, 110, 5598.
0 1992 American Chemical Society
438
The Journal of Physical Chemistry, Vol. 96, No. I , 1992
implementation to date, electron correlation was not taken into account in either the ground state or the summation over excited states. Dutler and Rauk have ascertained that the “completeness” requirements of the summation may be satisfied with the inclusion of all nonredundant derivatives (with respect to nuclear displacements) of the usual basis functions in the basis set.2 Applications to (S,S)-2,3-dideuterimxirane3 and a-deuterioethanol$ where direct comparison with expeimental VCD spectra was possible, suggest that the basis set designated as 6-31G” (obtained by adding all nonredundant derivatives to the 6-31G basis set) provides IR and VCD i n t e n ~ i t i e swhich ~ , ~ compare very well in sign and absolute magnitude with available experimental quantities. However, the size of the 6-31G“ basis set effectively precludes application of VCT to molecules containing more than three heavy atoms. Furthermore, it was not clear which features of the (transition) charge density were being corrected by the addition of the derivatives. In other words, could a simpler basis set be devised to accomplish the same end and therefore permit extension of the theory to larger molecules? Furthermore, the results without electron correlation are in very good agreement with experiment. Use of correlated wave functions even to the level of single and double CI would again render unfeasible application of the procedure to any but the smallest molecules, while inclusion of all single CI in the summation over states may be implemented without prohibitive penalty; could significant improvements be reasonably expected by using such partially electron-correlated excited states in the summation? Experimentation with various modifications of conventional basis sets, using 6-3 1G” results as a reference, has revealed that a rather trivial modification to one of the conventional Gaussian basis sets yields results which are in substantial agreement with VCT/6-3 1G“ results and with experimental measurements on larger molecules without incorporation of electron correlation. We report herein the results of experiments which establish the 631G*(0.3)basis set as a reliable vehicle for ab initio VCT studies. We also demonstrate that very little additional improvement is obtained by use of electron correlated excited states (at the level of all single CI). The reliability of the VCT/6-31G*(O”) method is established by direct comparison of calculated versus measured IR and VCD spectra of (S)-2-methyloxirane (1) and (R,R)2,3-dimethyloxirane (2).
Theory The following is an abbreviated derivation of the vibronic coupling theory of Nafie and Freedman1 which has been implemented at the a b initio level by Dutler and R a ~ k . The ~ , ~dipole strength, Dg,e,and rotational strength, Rg,e,are given by Dg,e
= b)g,e(p)e.g =
( ( @ g l p e l l @ e ) (@elped@g))
R , e = (p)g,e(m)e,g = Im
((@glPe11@e) (@ebmagI@g))
(1) (2)
Rauk and Yang
where pL,,”,p,:, k gn,and pma; denote the nuclear and electronic contributions of the electric and magnetic dipole transition moment operators, respectively. [k is the charge of particle k with mass mk which is located at a point rk relative to the origin of coordinates and moving with linear momentum p k . The wave functions and agmay be represented as (Po” and are expanded in terms of adiabatic Born-Oppenheimer functions (*:(r,Q)&”(Q)):
The variable J is either 0 or 1, denoting the vibrational ground or first excited state. The perturbation operator TN is taken as that part of the nuclear kinetic energy operator which involves only first derivatives with respect to nuclear coordinates (normal modes) Q,acting separately on the electronic and nuclear parts of wave function, namely
The normal mode dependence of qoa is expressed as a Taylor expansion about the equilibrium geometry, keeping only the first-order terms and using the identity 1 = Eel*,“) (*:I
Use of eqs 3-7, the approximation that the separation between vibrational levels of different electronic states is approximately equal to the difference between Born-Oppenheimer surfaces a t the ground-state equilibrium geometry, namely 1 Eev
=-
- EOI
1
E,O - E:
(8)
and the expansion of the normal modes in terms of internal coordinates Rn (9)
allows one to obtain, after some algrebra, expressions for the electric and magnetic dipole transition moments used in eqs 1 and 2. Specifically, for the j t h normal mode, one obtains’
where 0,and are the total molecular wave functions of the ground state, g, and a vibrationally excited state, e. The operators pel and pmag, the electric and magnetic dipole operators, respectively, are given by
(1 l),Annamalai, A.; Jalkanen, K. J.; Narayanan, U.; Tissot, M.-C.; Keiderling, T. A.; Stephens, P. J. J . Phys. Chem. 1990, 94, 194-199. (12) Jalkanen, K. J.; Stephens, P. J.; Lazzeretti, P.; Zanasi, R. J . Chem. Phys. 1989, 90, 3204-3213. (13) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N . C. Chem. Phvs. Lett. 1987. 142. 153-158. ‘(14) Jalkanen; K. J.; Stephens, P. J.; Amos, R. D.; Handy, N . C. J . Phys. Chem. 1988. 92. 1781. (15) Jalkanen, K. J.; Stephens, P. J.; Amos, R. D.; Handy, N . C. J . Am. Chem. SOC.1987, 109, 7193-7194. (16) Dothe, H.; Lowe, M. A.; Alper, J. S. J . Phys. Chem. 1988, 92, 6246-6249. (17) Amos, R. D.; Handy, N. C.; Drake, A. F.; Palmieri, P. J . Chem. Phys. 1988, 89, 7287-7297. (18) Dothe, H.; Lowe, M. A,; Alper, J . S. J . Phys. Chem. 1989, 93, 6632-6631.
(10.2)
and
The superscript VC denotes that these expressions describe a
The Journal of Physical Chemistry, Vol. 96, No. 1 , 1992 439
VCD and IR Spectra of Oxiranes
TABLE I: Comparison of Calculated Dipole Strengthsa for Hydrazine by VCT md MFP Methods
1
a
2 3 4 5 6 7 8 9
a
10 11 12
b a
b a
b a
b a a
b
4 01 855 988 1081 1268 1304 1635 1644 3265 3276 3372 3379
259.2 625.4 915.1 43.9 14.2 10.3 30.2 27.5 7.7 0.2
1 .o 5.1
208.1 515.3 730.1 47.2 15.6 9.4 33.3 26.3 1.9 0.2 9.4 11.4
198.5 495.8 705.6 45.9 15.9 10.5 32.0 24.2 1.8 0.3 9.6 11.2
449.3 364.2 67 1.6 26.1 25.2 19.8 32.7 32.0 17.5 0.6 0.1 1.6
337.8 324.8 579.7 31.6 21.4 17.4 31.5 21.4 4.2 0.3 2.0 5.4
373.6 278.7 584.8 34.3 25.3 20.7 35.5 30.7 5.4 0.1 1.7 6.2
cm-l, scaled by 0.9. cMagnetic field perturbation theory, extracted from Table VI11 of ref 28, 3-21G geometry, 'In units of 10- esu2 cm2. and force field. "Vibronic coupling theory (=APT), present results. 'Similar to 6 - 3 1 G basis set. 'Close to Hartree-Fock limit, BReference 2.
vibronic coupling mechanism for IR and VCD intensities. The subscript (00,Ol) signifies that the transition is between the Y = 0 and Y = 1 vibrational levels of the ground electronic state of the molecule. The electronic ground state is approximated by the Hartree-Fock (SCF) determinantal wave function, and the excited states involved in the summation in eqs 10.1 and 11 are either approximated as singlet spin adapted singly excited configurations derived from the Hartree-Fock wave function (uncorrelated) or derived by all-single CI calculation (SCI correlated). Electric dipole strengths derived from eq 10 are formally equivalent to the atomic polar tensor (APT) theory. Stephens circumvents the summation over excited states in eq 11 by invoking the magnetic field dependence of the wave function, a procedure which requires solution of the perturbed Hartree-Fock equations in the presence of a magnetic field: This theory will be referred to as the magnetic field perturbation (MFP) method.6 At the limit of linear response to the magnetic field, magnetic dipole transition moments in VCT are equivalent to those obtained by the MFP approach.19 However, in actual implementation, the two methods are not equivalent, and, as shown in the Appendix, only the MFP method converges to the correct HF-limiting values by expansion of the basis set. VCT is an approximation to MFP in its neglect of higher order excitations in the summation over states. However, it requires little computational effort beyond that required for the calculation of frequencies, which must be carried out in any case unless an empirical forcefield is used, and so has the advantage of efficiency particularly for large basis sets. Furthermore, comparison of the results of the two results of the two methods against experimental results suggests that the additional approximation in the present implementation of VCT is not serious. Which method is superior in practice may even depend on the molecule under investigation or on the particular normal mode involved. A complicating factor is the choice of gauge, common origin (CO) or distributed origin (DO).20,21The computed results will depend on the choice of gauge. Additionally, the rotatory strengths are origin dependent if the CO gauge is used. A choice of origin central to the molecule is logically expected to yield results less sensitive to the quality of the basis set. The molecular center of mass is a well-defined origin for the evaluation of transition moment integrals. The question of the choice of gauge is discussed further below.
Computational Details The geometries were determined by complete optimization at the restricted Hartree-Fock level of theory using the analytical procedures of the GAUSSIAN 8222 or GAUSSIAN 8 d 3 systems of (19) See the Appendix for a discussion of the relationship between the VCT and MFP formulations of VCD theories. (20) Stephens, P. J. J . Phys. Chem. 1987, 91. 1712-1715. (21) Stephens, P. J. Jalkanen, K. J.; Amos, R. D.; Lazzeretti, P.; Zanasi, R. J . Phys. Chem. 1990, 94, 181 1 . (22) (a) Binkley, J. S.; Frisch, M. J.; Defrees, D. J.; Raghavachari, K.; Whitesides, R. A,; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. Department of Chemistry, Carnegie-Mellon University, Pittsburgh, PA. (b) Rauk, A.; Dutler, R. J . Compur. Chem. 1987, 8, 324.
programs and the internal 6-31G* basis set24as is or modified by changing the d-orbital exponent from 0.8 to 0.3 (and other values for the purpose of testing). We distinguish the original and modified 6-31G* basis sets by indicating explicitly the value of the d exponent, e.g., 6-31G*(Os. Thus 6-31G*(O.*)is equivalent to the original 6-31G* basis set. Normal coordinate analysis at the 6-3 lG* or 6-3 1*(0.3)equilibrium geometry was carried out by analytical second differentiation of the Born-Oppenheimer RHF energy.25 Harmonic frequencies for isotopically substituted species, as well as IR and VCD intensities, were accomplished by the program system F r ~ 8 5 which , ~ implements the vibronic coupling theory of Nafic and Freedman' at the ab initio level. For improved agreement with experiment, frequencies were uniformly scaled by O.gUz6 The intensity evaluations were accomplished by using the 6-31G*(O.n basis set. The origin of coordinates in all intensity calculations was the molecular center of mass. Simulated IR and VCD spectra were obtained by assuming a Lorentzian line shape of half-width 10 cm-I and using uniformly scaled frequencies (X0.9). In summary, all results are internally consistent. The equilibrium geometry, ab initio quantum mechanical force field, Cartesian displacement vectors for the normal modes, and all transition moments integrals are evaluated with the same basis set. Results and Discussion Geometries obtained using the 6-3 lG*(O") basis set for all species discussed are shown in Figure 1. Assessment of the 6-31G*(0,3) Basis Set for IR and VCD Intensities. For reasons described below, it was decided that the presence of diffuse functions of high angular momentum would contribute most to correction of deficiencies in the values of rotatory strengths calculated by VC theory. Tests were carried out on the small chiral molecules H202 and NzH4using 6-31G" values as reference. Calculations using various subsets of the 6-31G" basis set proved that satisfactory results could be obtained by addition of the derivatives with respect to nuclear displacements of the outer 1s Gaussian function of the hydrogen atoms or the outer 2p orbitals of the 0 or N, but nor both. The quality of both the dipole and rotatory strengths proved to be quite sensitive to the value of the d-orbital exponent, optimum results being obtained for a d = 0.3. Results were relatively insensitive to the type of (23) Frisch, M. J.; Binkley, J. S.; Schlegel, H. B.; Raghavachari, K.; Melius, C. F.; Martin, L. R.; Stewart, J. J. P.; Bobrowicz, F. W.; Rohlfing, C. M.; Kahn, L. R.; De Frees, D. J.; Seeger, R.; Whiteside, R. A.; Fox, D. J.; Fleuder, E. M.; Pople, J. A. GAUSSIAN 86, Carnegie-Mellon Publishing Unit: Pittsburgh, PA, 1984. (24) (a) Hehre, W. J.; Ditchfield, R.; Pople, J. A. J . Chem. Phys. 1972, 56, 2257. (b) Francl, M. M.; Pietro, W. J.; Hehre, W. J.; Binkley, J. S.; Gordon, M. S.; Defrees, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (25) Pulay, P. In Modern Theoretical Chemistry Vol 3. Methods of Electronic Structure Theory; Schaefer, H. F. 111, Ed.; Plenum: New York, 1977. (26) Pople, J. A.; Schlegel, H. B.; Krishnan, R.; DeFrees, D. J.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. A.; Hout, R. F.; Hehre, W. J. Inr. J . Quantum Chem. Symp. 1981, 15, 269.
440 The Journal of Physical Chemistry, Vol. 96, No. 1, 1992
Rauk and Yang
TABLE 11: Comparison of Calculated Optical Rotatory Strengthso for Hydrazine by V C T and MFP Methods
MFF freqb sym l 2 3 4 5 6 7 8 9 10 11 12
a a b a b a 6 a b a a b
6-31G*
6-31G*(0.3) CO' 82.9 40 1 855 -236.9 262.6 988 1081 -35.0 50.8 1268 1304 -56.9 1635 -6.2 1644 -2.4 -20.5 3265 3276 -2.4 3372 -16.8 3379 27.8
DOh 60.9 -189.2 200.7 -20.2 32.2 -34.6 -4.9 -4.1 -12.5 0.1 -9.6 29.8
VCTd*'
6-31G(EXT)/
CO' 59.1 -207.0
218.6 -25.0 46.4 -44.6 -6.8 3.2 6.0 -1.3 -39.4 34.9
VD/3P*
DOh
CO'
55.1 -207.7 209.2 -20.7 40.4 -37.8 -6.8 1.4 4.6 -0.6 -27.4 25.3
54.1 -198.1 222.2 -23.2 47.9 -49.6 -7.7 3.4 5.3 -0.9 -27.9 24.5
6-31G*
DOh no CI' 54.2 95.4 -197.3
-185.1 178.0 -25.3 88.6 -79.1 -5.8 2.1 -21.4 -2.7 4.3 11.1
220.4 -22.2 47.2 -48.9 -7.7 3.3 5.2 -0.7 -27.4 24.6
6-31C
SCIj 96.0 -184.8 176.6 -24.0 88.5 -79.6 -5.2 0.7 -25.8 -3.4 5.6 14.3
no CI' 44.3 -154.6 162.7 -17.1 67.0 -60.9 -6.3 6.6 -2.2 -0.4 -8.2 11.8
6-31(3*(0,3)
SCIj 44.3 -153.9 161.1 -15.4 65.8 -60.1 -4.7 4.1 -3.1 -0.9 -14.0 19.2
no CIi 45.3 -131.8 143.7 -21.3 71.4 -66.5 -5.5 6.2 -7.1 -1.0 -10.9 17.1
SCIj 46.4 -131.5 142.2 -19.3 70.9 -66.9 -4.6 4.4 -8.6 -1.3 -15.6 23.9
cm-', scaled by 0.9. 'Magnetic field perturbation theory, extracted from Table VI11 of ref 28, 3-21G geometry, "In units of esu2cm2. and force field. dVibronic coupling theory, present results. 'Common origin (center-of-mass) gauge. 'Similar to 6-31G basis set. gClose to Hartree-Fock limit. Distributed origin gauge. Uncorrected approximation to excited states. 'All singly excited configurations CI.
I
15W
Figure 1. Geometries by 6-31GS(0.')optimization. The parameters are listed in Table 111: a, hydrogen peroxide; b, hydrazine; c, oxirane; d, (R,R)-2. (S)-2-methyloxirane, (S)-l;e, (R,R)-2,3-dimethyloxirane,
atom, so a value of 0.3 is suitable for N and 0 and, as the results on 1 and 2 suggest, for C as well. It is not informative to produce extensive tabulations of the results of all of the tests. Only representative results on hydrazine are listed in Tables I and 11. Rather we provide a rough measure of the quality of results in the form of a triple of numbers, (s,m,n), for rotatory strengths, where the first number, s, indicates the number of errors in sign, the second, m,the number of cases where the sign is correct but the magnitude deviates from the 6-31G" value5 by more than a factor of 2, and the third, n, the number of normal modes (usually 3 N - 6). Thus, for H202,with the 6-31G*(0.3)basis set, one obtains (0,2,6). The two errors in magnitude occurred for the 0-H stretches, which were both calculated to be too large. Other tests produced {0,3,6)(631G*(O"), (0,2,6)(6-31G*(0.4)), and (0,3,6)(6-31G*(0.8)).For N2H4,5 (Table 11), one obtains: (1,4,12)(6-31G*(0.2)),{0,1,12)(6-31G*(0.3)) (1,1,12)(6-lG*(0~4)), and (1,4,12}(6-31G*(0,8))(no CI columns of Table 11). Again the largest errors in magnitude occur in the stretches of the bonds to H. The same test applied against the and for gauche-ethanol4 6-3 1 G" results for 2,3-dide~teriooxirane~ yields {1,1,15}and {3,5,21),respectively. A visual comparison of the 6-3 1G" and 6-3 1G*(0.3)results for 2,3-dideuteriooxirane are shown in Figure 2, together with a qualitative evaluation of the
1400
I
I
1500
14W
::
I
I
I
I
13w
1200
1100
1wO
900
I 1200
I
I
1300
11W 1003 v em-'
I
I
I
I
8W
7W
600
I
I
I
I
$00
8W
7W
600
Figure 2. Simulated VCT/6-31G*(o.3)IR and VCD spectra of
(S,S)2,3-dideuteriooxiranein the region 600-1 500 cm-I. The superimposed dashed VCD spectrum uses SCI correlated excited states in the summation over states. The displaced dashed spectra are VCT/6-31G". Lorentzian line shapes and a width at half-height of 10 cm-' were assumed. experimental results. The single error in sign occurs for the weak rotatory strength of the band near 750 cm-' and the error in magnitude for the weak band near 1120 cm-'. A similar assessment may be applied to dipole strengths, namely, a couple of numbers, (m,n),which have the same interpretation as above. For H202,5one obtains (2,6)(6-31G*(0,2)),{0,6}(631G*(0.3)),(0,6)(6-31G*(0.4)), and {1,6)(6-31G*(0.8)). For one obtains (3,12}(6-31G*(0,2)),{ 1,12)(6-31G*(0.3)),{2,12)(631G*(0.4)),and (2,12)(6-31G*(0.s)).With the 6-31G*(O.') basis set, the single error occurred for the weakest absorption, an N-H stretching combination calculated to have intensity 0.1 X esu2 cm2(0.4 X lo4 em2cm2 by 6-31G"). The same test applied against the 6-3 1G" results for 2,3-dideuteriooxirane3 and for gauche-ethanol4 yields {0,15)(seeFigure 2) and (2,21),respectively. In seeking a smaller basis set with which to carry out ab initio vibronic coupling theory calculations, it was clear the emphasis should be. placed on the electronic contributions to the magnetic dipole transition moment (eq 11). The magnetic dipole transition
The Journal of Physical Chemistry, Vol. 96, No. 1, 1992 441
VCD and IR Spectra of Oxiranes
TABLE III: 6-316*(O” Geometries of N2H4, H202, Oxirane, 2-Metbyloxirane, and 2,J-Dimethyloxinae H202 NzHz oxirane 2-methyloxirane C,
C,
parameter‘ a b C
d e f g h i j ab ac ad ae af ag
aIcb 1.431 0.957 0.957
102.2 102.2
exptlc 1.464 0.965 0.965
99.4 99.4
-1 12.3
-121.6
151.9 -89.1 29.7
C,
I
ex& 1.447
calP 1.464 1.079 1.079 1.079 1.079 1.4456 1.4456
107.6 107.6 111.5 111.5 108.5
bd
bg ce cf ch ci cj dg ef hi hj ij bac bae baf cag dae daf eag ach aci acj
calP 1.434 1.004 1.004 1.007 1.007
C,,!
119.6 119.6 119.6 119.6 59.6 59.6 116.3 114.2 116.3 114.2
113.3
-90.2
155.46 0.0 -102.3 -102.3 -155.46 102.3 102.3
exptlC 1.470 1.085 1.085 1.085 1.085 1.434 1.434
116.3 116.3
cakb 1.465 1.080 1.507 1.080 1.082 1.448 1.448 1.090 1.091 1.089 120.0~ 122.8 119.5 116.7 59.6 59.6 116.1 114.2 116.0 116.4 110.4 110.4 110.6 114.1 112.2 108.2 108.4 108.7 154.2 -0.9 -102.15 -103.6 -156.5 102.2 101.2 144.0 -96.4 24.0
“See Figure 1 for a definition of the parameters. bThe letters denote bonds; e.g., a is the length in dihedral angle (deg). cReference 33. dReference 34. eReference 35. /Reference 31. Assumed.
moment is derived via a sum over excited states which imparts angular momentum to the ground states description in the presence of a magnetic field. The electronic dipole transition moment in VC theory (eq 10.2) is formally equivalent to that derived by atomic polar tensor theory and is reasonably well described by a polarized basis set. Since a conventionally polarized basis set (e.g., 6-31G*) yields a very poor description of the magnetic dipole transition moment, and hence the rotatory strength (at least within VC theory), it seemed reasonable that, within the constraints of keeping the basis set a t about the same size, the polarization functions should be modified to cover the regions of the molecule most poorly described by a set of Gaussian functions, namely, the region further out from the molecule. Because of the form of the operator, r X p , the low electron density far from the molecular center would contribute significantly to the magnetic dipole transition moment if it had angular motion. It should be noted that unlike the 6-31G” basis set, the 6-31*(0.3) basis set (and the 6-31G*(0.8) basis set) does not satisfy the “completeness” criterion as defined by Dutler and Rauk, namely, that eq 10.1 and 10.2 should give identical results.2 All results cited above and discussed below are derived from expression 10.2 for the evaluation of the electric dipole transition moments. Assessment of the 6-31G*(0.3)Basis Set for Geometries. The 6-3 lG*(O%ptimized geometries of hydrazine, hydrogen peroxide, 2-methyloxirane (l),tranr-2,3-dimethyloxirane(2) are shown in Figure 1 and compared with experimental geometries and with 6-31G*(0.8)and 6-31G“ geometries, where available, in Table 111. In most cases, the 6-31G*(O”) geometry is closer to the experimental geometry than obtained with other basis sets, especially with respect to bond lengths. The average deviations of all lengths
2,3-dimethyloxirane n
12
exptk‘ 1.464 1.499 1.082h 1.450 1.447 1.090h 1.090h 1.090h 122.7 119.1h
115.1 109.5h 109.5* 109.5h
cab? 1.466 1.5075 1.5075 1.083 1.083 1.450 1.450 1.090 1.091 l.08g5 123.3 123.3 116.6 116.6 59.6 59.6 115.8 116.3 115.8 116.3 110.4 110.5 110.6 112.0 112.0 108.2 108.3 108.8 -153.4
2.16 103.3 103.3 157.7, -101.1 -101.1 -145.2 95.2 -25.4
A, ab is the bond angle (deg), and abc is the
listed in Table I11 is 0.009 A, compared to 0.028 for the 6-31G** basis set. Significant improvement is seen in the geometry of the oxirane ring. The worst deviation occurs with the 0-0bond of H20z,0.033 A too short. Molecular geometry was not a consideration when choosing the basis set, so it is an additional bonus that, almost invariably, the 6-3 1G*(0,3)geometry is closer to the experimental geometry than would have been obtained with conventional basis sets.
Assessment of Excited-State Correlation for IR and VCD Intemities. Whether evaluated by expression 10.1 or 10.2, inclusion of the excited-state CI has no effect on the computed electric dipole transition moments and IR intensities are unaffected. In the case of (lO.l), energy weighting does not occur in the summation Over excited states, and, since all-single CI wave functions are derivable by a unitary transformation of the set of singly excited spinadapted single determinantal configurations, use of either set in the summation yields identical results. However, energy weighting does occur in the evaluation of the magnetic dipole transition moment (eq 1 l ) , and neglect of electron correlation even at the SCI level is expected to have an effect on the results obtained for the optical rotatory strengths. In fact, optical rotatory strengths obtained by use of SCI-correlated excited-state wave functions are not significantly different from those obtained by the simpler uncorrelated approach for the present test set of molecules (HzOZ, N2H4,oxirane-d2, and gauche-ethanol). None of the evaluations as presented above are changed except in a few instances involving stretches of bonds to hydrogen. The results for hydrazine presented in Table I1 are typical. The most significant changes due to SCI are in the N-H stretching modes, the largest being a change from 11.8 to X lod4 to 19.2 X lo-” esu2 cm2 in the rotatory strength
442
The Journal of Physical Chemistry, Vol. 96, No. 1, 1992
TABLE I V 6-31G*(0,3)Vibrational Frequencies of 2-Methyloxirane (1)
Rauk and Yang and 2,1Drmethyloxiraw (2)
2-methyloxirane (1)
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
calcb 214 387 421 821 902 976 1041 1126 1210 1255 1259 1288 1381 1512 1562 1610 1623 1655 3141 3220 3235 3242 3273 3351
freq, calcC 193 348 379 739 812 878 937 1013 1089 1130 1133 1159 1243 1361 1406 1449 1461 1490 2827 2898 2912 2918 2946 3016
cm-' obsd 200 360 419 747 829 895 950 1023 1104 1132 1146 1168 1265 1368 1407 1446 1458 1499 2935 297 1 2984 3002 3052
calc'
750 840 883 94 1 1017 1103 1132 1146 1170 1257 1374 1411 1441 1453 1501
assignment' CH3 torsion I CHI group II CH3 group asym CO str ring CC str CH2, CH, rocks + I CH ring def + C-CH, str CHI twist I CH CH2, CH3 rocks CHI wag I CH bonds d, e CH, rock I CH + CHI, CH3 rocks ring breathing + 11 CH CH, umb CHI scis, CH3 ump + I/ CH asym CH3 def asym CH, def CH2 scis CHI sym str CH3 asym str CHI asym + CHI sym str CHI sym str C H str CH2 asym str
+
+
sym la 16 2a 26 3a 36 46 4a 5a 56 6b 6a 76 7a 86 8a 90 96 loa 106 11a 116 12a 126 13a 136 14a 146 15a 156 16a 17a 166
cald 196 215 257 296 478 488 804 875 964 1049 1122 1127 1208 1238 1278 1294 1374 1468 1523 1532 1603 1610 1620 1623 1664 3140 3141 3218 3219 3233 3236 3262 3269
2,3-dimethyloxirane (2) freq, cm-I calcC obd assignment' 176 185 CH3 torsion 194 200 CH, torsion 23 1 249 I CH3 group 266 289 I/ CH3 group 430 466 II CH3 group 439 473 I CH3 group asym CO str 724 722 ring CC str 788 812 867 886 ring def + C-CH3 str CH3 rock + I CH 944 959 1010 asym C-CH, str 1015 1014 1022 I CH CH3 rock CH3 rock 1087 1110 1114 CH, rock 1110 1150 1154 I CH CHI rock 1165 1163 I CH 1237 1254 /I CH + ring breathing 1321 1335 II CH CH3 umb 1371 1381 1379 1381 CH3 umb + 11 CH asym CH3 def 1443 1426 1449 asym CH3 def 1445 1458 1452 asym CH3 def 1461 1452 asym CH3 daf ring breathing 1498 1489 2826 CH3 sym str 2827 CH3 sym str 2896 CHI asym str 2897 CH3 asym str 2910 CH3 asym str + CH str 2912 CH, asym str CH str CH str 2936 2942 CH str
+ +
+
"From computer animation of normal modes. Terminology: I = perpendicular to ce or bd plane (Figure 1); I/ = parallel to ce or bd; str = stretch; def = deformation; umb = umbrella motion; scis = scissor. *6-31G*(O.'),unscaled. c6-31G*(0.3), uniformly scaled by 0.9. dBands 4-18 from ref 7; the rest from ref 36. 'Scaled 6-31G** force field at a corrected geometry, ref 7. 'Reference 32.
of the highest frequency mode (6-31G" basis set). Comparison of the columns of Table I1 which corresponds to different basis sets reveals that the effect of SCI is similarly small for all three basis sets. The optical rotatory strengths for 2-methyloxirane were also calculated by VCT/6-31G*(0.3),with and without SCI. The results, which are listed in Table V and displayed graphically in Figure 3, confirm the observations on systems already discussed that SCI produces little change in the VCT results. These are discussed further below. The effect of incorporation of electron correlation in both the ground and excited states will be explored in future work. The Question of Gauge Revisited. The question of choice of gauge for the computed results requires further attention. Magnetic dipole transition moments in the current VCT formulation are evaluated in the CO gauge, and therefore they are dependent on the choice of origin. Origin dependence is expected to be less severe with judicious use of a distributed origin (DO) gauge and may be technically avoided if the origins (or common origin) are connected to the molecular structure as in the case of the DO (with origins at nuclei) gauge which has been proposed and implemented by Stephens.m The present VCT implementation cannot be readily reformulated to Stephens' DO gauge. In any case, the origin dependence of the rotatory strength does not per se originate in the origin dependence of the magnetic dipole transition moment, but, rather, in the necessary use of approximate electronic wave functions with concomitant lack of colinearity of length and momentum formulations of the electric dipole transition moment.*' Stephens has asserted, on the basis of extensive tabulations of test calculations on small molecules, that use of the DO (atomic centers) gauge reduces the basis set dependence of (27) Moscowitz, A. In Modern Quantum Chemistry; Sinanoglu, O., Ed.; Academic Press: New York, 1965; Vol. 3, p 31.
-0.6, I ~ W
I
1m
I
im
I
iiw
I
J
I
I
im
900
m
700
900
m
700
v m-'
14w
.1m
1200
11w loo0 v m-'
Figure 3. VCT/6-31G*(O.') IR and VCD spectra of (S)-1 in the region
700-1400 c d . The superimposed dashed VCD spectrum uses SCI correlated excited states in the summation over states. The experimental spectra were reconstructed from intensities and frequencies from ref 7 (see also Table V); Lorentzian line shapes and a width at half-height of 10 cm-' were assumed; VCD was not measured near 810 cm-I.
The Journal of Physical Chemistry, Vol. 96, No. 1, 1992 443
VCD and IR Spectra of Oxiranes TABLE V 6-31G*(0,3)Frequencies and Electric Dipole and Optical Rotatory Strengths of (S)-Z-Methyloxirane (1)
dipole strengths optical rotatory strengths freq calc‘ cal& obsc calcbid calcCJ cal& obs‘ calcdf ~~
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
-5.9 -12.7 193 10.4 348 65.6 118.6 135.8 -12.5 -9.9 379 31.6 739 37.8 65.4 28.8 -129.5 -123.2 812 227.4 303.0 236.0 -176.8 -146.7 8.3 19.2 24.6 -255.1 -216.9 878 937 65.0 76.8 101.0 477.3 487.2 -40.2 1013 24.1 67.4 26.4 -55.7 1089 28.2 32.8 37.2 52.5 62.9 2.5 20.5 25.5 -68.4 -58.3 1130 1133 16.3 18.2 2.8 185.4 153.2 4.5 4.9 18.7 43.1 31.7 1159 1243 15.7 32.6 14.0 79.6 33.8 8.6 18.3 13.3 -58.4 -53.7 1361 1406 34.3 63.7 45.0 -130.3 -127.8 1449 10.4 18.3 7.9 -20.6 -20.1 1461 14.7 20.5 12.1 47.3 39.1 1490 17.2 20.9 21.6 -35.1 -30.1 2827 24.7 -6.1 2.7 -5.0 2898 28.9 11.4 2912 3.3 -71.5 -128.5 2918 41.8 100.3 194.7 2946 38.3 -62.9 -118.1 3016 25.0 13.7 39.5
-282 -503 908 -112 152 -406 478 -53 175 -89 -208 -52
-57 38 -263 142 -16 8 110 11 72 69 -20 -125 -1 2 -2 -65
‘X0.9, cm-I. b10-40esu2 cm2. cReference 36. dReference 7, method of Stephens, 6-31G** geometry, force field, and atomic axial and polar tensors. eVCT/6-31G*(03)no CI. esuZcm2. WCT/631G*(03)all single CI (SCI).
the computed quantities and leads to more rapid convergence of these quantities.** While this is true in most cases, a study of the VCD spectrum of methylthiirane by the MFP theory using the 6-31G* basis set found that results obtained using the C O gauge with origin at the molecular center of mass gave results in better agreement with experiment than when the DO gauge was used.29 The MFP results on hydrazine, extracted from a much more extensive tabulation of Stephens and co-workersZ7and listed in Table 11, shed some light on the interdependent basis set and origin dependence of the computed results. Symmetry requires that electric and magnetic dipole transition moments of transitions of u symmetry be parallel and therefore rotatory strengths of these transitions are origin-independent even in the CO gauge. The discrepancy between the CO and DO gauge results, both origin independent, for these normal modes (Table 11) is attributable, to basis set effects and is observed to decrease systematically as the quality of the basis set increases. The results for the very large VD/3P basis set are essentially converged and may be taken as the “correctn values at the HF limit for the particular geometry and force field. Inspection of the values obtained with the smaller 6-31G* basis set reveals that, of the seven normal modes of u symmetry, three of the CO results (for modes 6, 10, and 11) are numerically closer to the “correct” results than the D O results. The same is true for three ( 5 , 7, 12) of the five normal modes of b symmetry, the CO results for which are origin-dependent but which were calculated at the center-of-mass origin. Clear superiority of the DO gauge for this molecule is only demonstrated for fewer than half (1-4,9) of the normal modes when a basis set considered adequate for many molecular properties is used. Even for the much larger 6-31G(EXT) basis set, which is comparable to our 6-31G” basis set, the CO (center-of-mass) results for two of the a modes (6, 8) and two of the b modes (3, 5 ) are closer to the correct results than the DO results, while results for four (2, 4, 7, 9) of the remaining eight modes are equally close. One should not belabor the point on the basis of such a small sample but we believe the results in Table 11, those in other (28) Jalkanen, K. J.; Kawiecki, R. W.; Stephens, P. J.; Amos, R. D. J. Phys. Chem. 1990, 94, 7040. (29) Dothe, H.; Lowe, M. A.; Alper, J. S . J . Phys. Chem. 1988,92,6246.
published tables,27and conclusions reached by others29do not support an unambiguous superiority of the DO gauge over the C O (center-of-mass) gauge for the modest-sized basis sets that must be used for practical VCD investigations of molecules containing more than a few heavy atoms. The incorporation of the DO gauge within the VCT formulation of VCD theory is being pursued and will be reported in subsequent publications. The MFP results in Table I1 cannot be directly compared to the VCT results since the former were derived at a geometry and using an a b initio force field derived using the 3-21G basis set. Unpolarized basis sets are known to yield poor geometries for nitrogen-containing compounds.30 The VCT results are derived for geometries and force fields consistent with the particular polarized basis set. In particular, the discrepancy in sign for mode 9 awaits resolution by internally consistent MFP/VD/3P calculations. The 6-31G*(0,3) Geometries of 2-Methyloxirane (1) and fmns-2,3-Dimethyloxirane(2). Geometries of 1 and 2 optimized with the 6-31G*(0.3)basis set are shown in Figure 1 and listed in Table 111. The slight asymmetry of 0.003 A in the C-0 bonds of the oxirane ring interpreted from the microwave spectrum of 13’is not reproduced by the geometry optimization. Introduction of the methyl group results in a small expansion of all the bonds of the oxirane ring. The trend is continued with the introduction of the second methyl group. A small asymmetry is present in the methyl groups but is very similar in the two compounds. Vibrational Frequencies with the 6-31C*(0.3) Basis Set. The calculated and uniformly scaled (X0.9) harmonic frequencies of 1 and 2 are listed in Table IV together with observed frequencies. Uniform scaling corrects for systematic errors and brings the calculated spectrum into the correct range but does not affect the normal modes from which intensities are calculated. The major discrepancy in the range 700-1400 cm-’ occurs for two bands calculated to be nearly degenerate at 1130 and 1133 cm-’ but observed to be well separated at 1132 and 1146 cm-I. As much as can be judged, the assignments listed in Table IV are consistent for the most part with those of Stephens and co-workers and Polavarapu and co-workers. We propose a reversal in the assignment of the two bands at 1015 and 1022 cm-’ on the basis of the VCD calculations (vide infra). The I R and VCD spectra are discussed in some detail in subsequent sections. The IR Spectrum of 2-Methyloxirane (1). The 6-3 1*(0.3) IR spectrum and the experimental spectrum reconstructed from the published frequencies and dipole strengths’ in the range 7W-1400 cm-’ are compared in Figure 3. The calculated intensities are somewhat smaller than the observed values but in satisfactory agreement overall. The most intense band, observed at 829 cm-I, is calculated to be predominantly the stretching of the C - C bond of the ring (bond a in Figure 1). The VCD Spectrum of (S)-2-Methyloxirane (1). The VCT/6-31G*(o.3)VCD spectrum, with (dashed line) and without (solid line) SCI, and the experimental spectrum reconstructed from the published frequencies and rotatory strengths7 in the range 700-1400 cm-I are compared in Figure 3. The calculated intensities are almost a factor of 2 smaller than the observed values, but the pattern of signs and relative intensities are in very good agreement overall. Excessive IR absorbance at 829 cm-’precludes measurement of the VCD at that position. A negative Cotton effect of moderate strength is predicted by the VCT/6-3 1G*(0.3) calculation, whereas Stephens and co-workers have predicted a weak positive rotatory strength for this transition with all basis sets except 6-31G**.’ Use of SCI has little effect on the overall or relative intensities (see also Table V). The appearance of the calculated VCD spectrum does not match very well the experimental spectrum in the region 1100-1200 cm-’ but only one transition, that observed at 1168 cm-’ (mode 12, Table V), is calculated to have the wrong sign. The calculated near degeneracy (30) (a) Binkley, J. S.; Pople, J. A.; Hehre, W. J. J . Am. Chem. Soc., 1980, 102,939. (b) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. A b Initio Molecular Orbital Theory; John Wiley & Sons; New York, 1986, p 147. (31) Creswell, R. A,; Schwendeman, R. H. J . Mol. Specfrosc. 1977, 64, 295.
444
The Journal of Physical Chemistry, Vol. 96, No, 1, 1992
Rauk and Yang
TABLE VI: &31G*(@,3) Frequencies d E k M c Mpole and Optical Rotatory Strengths of (R,J?)-2,3-Dimethyloxirane(2)
\(
-I
6-31G'10
-2.
-3.k
1400
1
I
I
1300
1200
IIW
I
I
low
m
v an-1
I
I
em
7w
Figure 4. VCT/6-G*(O') IR and VCD spectra of (R,R)-2in the region 700-1400 cm-l. The experimental spectra were reconstructed from relative intensities and frequencies established by fitting Lorentzian line shapes to the published spectra in ref 32; Lorentzian line shapes and a width at half-height of 10 cm-' were assumed.
of two bands near 1130 cm-I, alluded to above, results in complete cancellation of the weaker negative CE. In actuality, the two bands are well separated. The weaker negative band is not covered up and forms the prominent feature in the experimental spectrum in this region. The VCD spectrum of (a-1is discussed more fully in comparison with that of the dimethyl system below. Using the rating schemes introduced above, the VCT/631G*(O.s IR and VCD spectra rate as (5,15)AND {1,6,12)({1,7,12) with SCI), respectively, as compared to the experimental spectra listed in Table V. The I R and VCD results of Stephens and co-workers' (Table V), obtained using the DO gauge, have a similar rating, (5,151 and {2,7,121,respectively. The IR Spectrum of trans-2J-Dimethyloxiraw (2). The 631G*(0.3)IR spectrum from 700 to 1400 cm-l is shown in Figure 4 together with an "experimental" spectrum generated by fitting Lorentzian line shapes with the correct relative areas to the experimental IR spectrum of Polavarapu and c o - ~ o r k e r s . ~The ~ simulated experimental spectrum has been adjusted to match the dipole strength of the strengest absorption a t (895 cm-I). The calculated dipole strengths and relative dipole strengths obtained by the curve fitting to the experimental spectrum are listed in Table VI. Polavarapu and c o - ~ o r k e r have s ~ ~ noted that the 6-31G** basis sets results in the prediction of erroneously large IR absorption intensities for a number of bands in the 100(t1500-~m-~ range, better values being obtained with the unpolarized 6-3 1G basis. As can be seen in Figure 4, the 6-31G*(O.nbasis set yields relative intensities which are for the most part in good agreement with the observed intensities. The two methyl rocking modes at 1087 and 1114 cm-' are calculated to have similar intensities and (32) Black, T. M.;Bose, P. K.; Polavarapu, P. L.; Barron, L.D.; Hecht, L. J. Am. Chem.Soc. 1990, 112, 1479-1480. (33) Cremer, D.; Christen, D. J . Mol. Spectrosc. 1979, 74, 480. (34) Harmony, M. D.; Laurie, V. W.; Kuczkowski, R. L.; Schwendemen, R. H.; Ramsey, D. A.; Lovas, F. L.; Lafferty, W. J.; Maki, A. G. J . Phys. Chem. ReJ Data 1979, 8, 619. (35) Hirose, C. Bull. Chem. SOC.Jpn. 1974, 17, 1311. (36) Polavarapu, P. L.; Hess, B. A,; Schaad, L. J. J. Chem. Phys. 1985, 82, 1705.
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
sym
calca
fw
dipole strengths calcb 'obs"'
la 16 2a 26 3a 36 46 4a 5a 56 66 6a 76 7a 86 8a 9a 96 10a 106 lla 116 12a 126 13a 136 14a 146 15a 156 16a 17a 166
176 194 231 266 430 439 724 788 867 944 1010 1014 1087 1114 1150 1165 1237 1321 1371 1379 1443 1449 1458 1461 1498 2826 2827 2896 2897 2910 2912 2936 2942
4.7 7.4 2.9 9.5 0.2 105.3 56.5 87.5 113.3 10.9 46.6 50.2 30.6 29.8 7.9 7.2 4.1 32.4 0.1 31.5 1.2 14.1 25.4 16.3 18.2 50.7 6.1 6.7 52.4 15.1 0.3 7.0 91.9
44 110 113 16 47 77 40 38 7.9 7.2 5.8 32
optical rotatory strengths calcd.' "obs"' 10.3 3.0 -10.0 -7.5 -16.0 -75.9 374.0 913.4 -502.1 106.6 -564.6 249.7 -17.0 -840.8 92.2 76.6 -102.9 -214.1 -23.9 39.5 129.0 240.7 225.8 -304.9 164.5 24.2 -12.8 127.2 -174.1 -32.3 57.9 198.7 -217.3
374 1187 -43 1 340 -655 250 -17 -841 92 77 -6 8 -7 1
X0.9, cm-I. lo-@ esu2 cm2. 'Relative magnitudes only, from Lorentzian fit to spectra of ref 32; see Figure 4. dVCT/6-3G*(o,3). io4' esu2 cm2.
separation with a variety of basis sets,32including the present. In the experimental spectrum, only a single slightly broadened band is observed at 11 10 cm-'. Apparently the uniformly scaled or unscaled a b initio force fields predict too large a separation for the in-phase and out-of-phase motions since the total intensity observed a t 1110 cm-' is consistent with the calculated sum of the intensities of the 1087- and 11 14-cm-' bands. "he VCD Spectnrm Of ( R , R ) - 2 , 3 - b t h y b W ((R,R)-2). Comparison with VCD of (S)-1. The VCT/6-31G*(0.3)VCD spectrum from 700 to 1400 cm-' is shown in Figure 4 together with an experimental spectrum generated by fitting Lorentzian lines shapes with the correct relative areas to the experimental VCD spectrum of Polavarapu and c o - w o r k e r ~ .The ~ ~ simulated experimental spectrum has been adjusted to match the rotatory strength of the positive CE at 812 cm-I. The calculated rotatory and relative rotatory strengths obtained by the curve fitting to the experimental spectrum are listed in Table VI. The similarity between the two spectra is striking, abetted by the fact that the erroneously positioned antisymmetric methyl motion at 1087 an-' is calculated to have a very weak negative CE. The prominent features of the VCD spectrum are discussed in some detail below. The numerical values of the frequencies are those associated with the experimental spectrum.32 The band at 722 cm-' with a moderate positive CE is the asymmetric C-O stretching deformation of the ring. The sign is diagnostic of the absolute configuration of the asymmetric centers since in ( 8 - 1 the sign of the CE of the corresponding mode (at 750 cm-I) is reversed. The strong positive CE at 812 cm-' is due to the stretch of the C-C bond of the three-membered ring and is largely uncoupled from other motions. The C E of the corresponding absorption in (S)-1 is obscured by the strong IR absorption but is calculated
VCD and IR Spectra of Oxiranes
The Journal of Physical Chemistry, Vol. 96, No. 1, 1992 445
The weak positive VCD feature near 1160 cm-' in (R,R)-2is attributed to symmetric and antisymmetric methine bending modes at 1163 and 1154 cm-I, respectively. Both are predicted to have weak positive rotatory strengths of similar magnitude. As discussed above, the visual agreement between the calculated and observed VCD spectra of (S)-1 in this region is not good. Three transitions occur in this region (beside the one at 1103 cm-I already described). All are complex modes involving methine bends and deformations of the CH2 group. Two are calculated to be nearly degenerate but observed to be well separated. These are readily identified by the theoretical CEs whose signs and relative magnitudes are calculated correctly. The sign of the C E observed at 1168 cm-I and calculated at 1159 cm-' is calculated incorrectly, the single clearly identifiable error in the theoretical VCT/631G*(0.3)treatment of this molecule. The symmetric and antisymmetric in-plane (of H-C*-CH3) methine bends at 1254 and 1335 cm-I, respectively, are both predicted and found to have weak negative CEs. The former is coupled to the symmetric ring breathing mode and is very similar V to the analogous mode of (S)-1 a t 1265 cm-I. The (S)-1 mode 1600 15M1 1400 1300 appears to have a larger admixture of the ring breathing comv cm-l ponent. The signs of the CEs may be dominated by the breathing Figure 5. VCT/6-31G*(o.3)VCD spectra of (S)-1 and (R,R)-2in the motion, which would be expected to be, and is found to be, sensitive region 1300-1600 cm-I. The experimental spectrum of (S)-1 was reto the chirality of the local environment. constructed from intensities and frequencies from ref 7 (VCD was not The in-phase and out-of-phase umbrella motions of the methyl measured near 1450 cm-I); Lorentzian line shapes and a width at halfgroups are predicted to have weak and oppositely signed CEs which height of 10 cm-' were assumed. almost cancel because of the near degeneracy of the vibrational frequencies. Only the antisymmetric combination is predicted to have a moderately strong negative CE, consistent with the to have any IR intensity and is assigned to the strong IR band reversed handedness a t the chiral center. observed at 1381 cm-I. The umbrella motion of the methyl group The most intense IR absorption of (R,R)-2,a complex mode in (S)-1 is found at 1368 cm-I but also mixes weakly with the which couples the symmetric ring deformation with the symmetric CH2 scissor which occurs at 1407 cm-I. Both modes are predicted C
