J . Phys. Chem. 1991, 95, 9817-9831
9817
Vibrational Circular Dichroism of Propylene Oxide R. W. KawieckiJ F. J. Devlin: P. J. Stephens,*it and R. D. Amos' Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482, and Department of Theoretical Chemistry, Cambridge University, Cambridge CB2I E W,United Kingdom (Received: June I, 1990; In Final Form: May 7, 1991)
Vibrational absorption and circular dichroism spectra of neat liquid and CS2 and CC14solutions of propylene oxide are reported. Scaled quantum-mechanical (SQM) force fields are derived from absorption frequenciestogether with ab initio SCF calculations using the STO-3G, 4-31G, 6-31G*, and 6-31G** basis sets. Absorption and VCD spectra are calculated using these force fields and ab initio SCF atomic polar and axial tensors obtained using analytical derivative methods and STO-3G, 4-31G, 6-3 1G*, 6-3 1G**, DZ/ 1P, and 6-31 1G** basis sets. Atomic axial tensors are calculated using two choices of gauge. Calculated spectra are in generally excellent agreement with experiment when basis sets of sufficient size are used for the calculation of force fields and atomic polar and axial tensors and when the distributed origin gauge is used. Agreement is less satisfactory in spectral regions where vibrational transitions are closely spaced and where Fermi resonance is substantial. The results support the conclusion that generally reliable predictions of VCD spectra can be obtained using Stephens' equation for vibrational rotational strengths together with molecular geometries, vibrational force fields, and atomic polar and axial tensors derived via ab initio SCF calculations.
Chiral molecules exhibit vibrational circular dichroism (VCD).'s2 In principle, if the VCD spectra of chiral molecules of known structure can be successfully predicted a priori, VCD spectra can be utilized to determine unknown structures of chiral molecules. Prediction of VCD spectra requires the calculation of vibrational rotational strengths. An a priori formal theory of vibrational rotational strengths has been developed by step hen^.^^^ Implementation of this theory at the ab initio self-consistent field (SCF) molecular orbital level of approximation has been accompli~hed.~-A ' ~ major goal is now the evaluation of the accuracy of this theory, implemented a t the a b initio S C F level, by comparison of its predictions to experimental VCD spectra. Definitive evaluation requires rigid molecules of known structure, whose vibrational spectra are susceptible to unambiguous analysis, and small enough to permit a b initio S C F calculations. In this paper, we present the results of theoretical and experimental studies of the VCD of propylene oxide (epoxypropane).I6 Propylene oxide is small and rigid and its vibrational spectrum has recently been analyzed in considerable detail." It closely approximates an ideal molecule for the evaluation of theoretical calculations of VCD spectra. The VCD spectrum of propylene oxide has been studied previously both e ~ p e r i m e n t a l l y ' ~ Jand ~J~ theoreti~ally.6,'~.'~,'~~ Here, we present new experimental spectra and theoretical calculations that greatly extend and improve upon these earlier studies.
Experimental Methods VCD spectra were measured using a dispersive spectrometer2'z whose lower frequency limit is currently -650 cm-' as a result of the incorporation of a C-rod source and an -10 K Si:As detector.23 In the studies reported here, the C-rod source was operated at 1.8 kW; its window was KBr or CaF2. The Spex 1500 monochromator was equipped with gratings blazed at 3.0 pm (300 grooves/") and 10.0 pm (25 and 75 grooves/") (Bausch and Lomb). Windows on entrance and exit optics were KBr or CaF,. Entrance and exit optics and monochromator were under 1 atm of Ar. A grid polarizer with a BaF2 or ZnSe substrate (PTR Optics) preceded a photoelastic modulator of either CaF2 ( 5 2 kHz) or ZnSe (37 kHz) (Hinds International). InSb (D*,,, = 1.3 X IO1') and Si:As (D*,,, = 3.3 X lolo) detectors (Santa Barbara Research Co.) mounted in a closed-cycle refrigerator (CTI) were operated at 30 K and 10 K, respectively. Detection electronics analogous to that used previously was employed. CD spectra were collected using a microcomputer and output on an x-y plotter (Hewlett-Packard 9872B). Where desired, multiple
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'University of Southern California. *Cambridge University.
0022-3654/91/2095-9817$02.50/0
scans were averaged. Calibration was carried out using A1203 or CdSe (Cleveland Crystals Inc.) birefringent plates and a second grid polarizer. VCD spectra were measured at slit widths providing an optimum compromise of signal-tenoise ratio and spectral resolution. Resolution was always is the wavefunction of G at Ro when a perturbation
1? denotes
7f' = -(&&H,q
is applied. iizl and
are the electronic contributions to
(6) and
jimag,respectively. Mk@ is origin dependent. Its origin dependence is given by4
(7) where p i s the vector from 0 to 0'. In the common origin (CO) gauge, (Mk@)'is evaluated using eq 5 for all h4k6 tensors. In the distributed origin (DO) gauge, with origins a t nuclei, (M$O_is %valuated using eq 7 with 0' for each M b tensor placed a t Yis then the vector from 0 to the equilibrium position of nucleus
e,;
A.
In the common origin gauge, the equation for rotational strengths4 is
where A and AA are absorbance and differential absorbance (AL
- AR),respectively, C and 1 are concentration (M) and path length (cm), and
[
J(r) = -
yi2
*Ti (B - $2
+ 712
]
L " / i ( p ) de = 1
(2)
The contributions of neighboring transitions, reflectance, and drift were allowed for by subtracting a linear background function prior to the fitting.
Theoretical Methods Dipole and rotational strengths of the ith fundamental vibrational transition of energy hwi are given by the equation^',^ D(O+1)i = I(OIcZcII1 )i12 R(*l)i = Im [(OlcZc,ll)r(lIcZmagl0)il (3) where pel and pmagare electric and magnetic dipole moment operators, and
( o l ( ~ m a g ) @ l )l i
= -(Zh
3wi)"2cM~$Aa,i Aa
(4)
and hfk@ are atomic polar and axial tensors: respectively, and are given by (24) Kumata, Y., Furukawa, J., Fueno, T. Bull. Chem. Soc. Jpn. 1970,
43, 3920.
(25) Schellman, J. A. Chem. Reu. 1975, 75, 323.
e,
(lGi)Do = + ( 1 1) (hft@)' is the atomic axial tensor of atom A, calculated with the origin at-thz equilibrium =@on of nucleus A. The contributions h2Im [P;@,]and h2I~JIJP;L.~] to [R(O+l)i] in eq IO are referred to as the " P . W and 'P.L" terms, respectively. Dipole strengths are gauge independent and given by
The equilibrium geometry of propylene oxide is predicted at the S C F level of approximation using GAUSSIAN82 (CRAY XMP
The Journal of Physical Chemistry, Vol. 95, No. 24, 1991 9819
Vibrational Circular Dichroism of Propylene Oxide
/””“ r24
YB7
Figure I . S-(-)-propylene oxide: structure, atom labeling, and internal coordinates.
version K).26 Library basis sets are used. Maximum and root-mean-square forces after optimization are 4.5 X 10-4 and 3.0 X 1 O4 au, respectively. A quasi-experimental equilibrium geometry is also derived from the 4-3 l G equilibrium geometry using the approach of Blom, Slingerland, and A l t ~ n a .Bond ~ ~ lengths are corrected using the differences between experimental and 4-31G theoretical CC, CO, and CH bond lengths in ethylene oxide2*together with CC and C H correction factors recommended by Blom et-a1.27 We refer to this geometry as the corrected geometry (goRR). First and second derivatives with respect to Cartesian displacement coordinates of the energy of propylene oxide at chosen geometries are calculated at the SCF level of approximation using GAUSSIAN 82. The results are reexpressed in terms of internal coordinates using the equation of P ~ l a y . *The ~ quadratic terms constitute the harmonic force field in internal coordinates. In the case of calculations at theoretically optimized geometries, residual nonzero Cartesian first derivatives are neglected. The internal coordinates used in this work are defined in Figure 1 and Table I. The transformation of force fields from Cartesian to internal coordinates is carried out using a modified version17 of the vibrational analysis program of McIntosh and Peterson.30 Vibrational frequencies and SAujmatrices are calculated from force fields using the same program. Atomic masses employed are taken from GAUSSIAN 82 (Mc = 12.00000, Mo = 15.99491, M H = 1.00783 amu). Calculated force fields are scaled to fit experimental frequencies using the algorithm recommended by Pulay and co-workers3’
kii = q K i i
k, =
6Kij
(13)
where Kii and Kij are diagonal and off-diagonal calculated force constants, and ai are scale factors. The number of independent scale factors is limited by constraining scale factors for chemically similar internal coordinates to be identical. Scaling is carried out using a modified version of a program written by Lowe and Alper.I7 Atomic polar and axial tensors, P& and M$,are calculated using analytical derivative methods implemented in the CADPAC program, as described previ~usly.~ Library basis sets are used. In the case of basis sets developed by Pople and co-workers, these (26) Hehre, W. J., Radom, L., von R. Schleyer, P., Pople, J. A. Ab Inirio Molecular Orbital Theory; Wiley: New York, 1986. (27) Blom, C.. E.;Slingerland,P. J.; Altona, C. Mol. Phys. 1976,31, 1359. (28) Kawiech, R. W.; Jalkanen, K. J.; Stephens,P. J.; Lowe, M. A,;AImr, J. S. To be published. (29) Pulay, P. In Modern Theoretical Chemistry; Schaefer, H. F., 111, Ed.; Plenum Press: New York, 1977; Vol. 4. D 153. (30) McIntosh, D. F.; Peterson, M. R.’ QCPE 1977, 11, 342. ( 3 1 ) Benhegyi, G . ; Fogarasi, G.; Pulay, P. THEOCHEM 1982, 89, I . Fogarasi, G.; Pulay, P. Vibr. Spectra Srrucr. 1985, 14, 125.
(1/8j1/2r6,[2a2(1bd-9)- ai(&-8) - a;(10-6-8)] (1/6)’/2r6a[289(8-6-3)- plO(9-6-3) - 811(10-6-3)] (1/2)i/2r68[a1(9-6-8) - a3(10-6-8)] (1/2)”2rse[/3~~(10-6-3) - 810(9-6-3)1 ~(9-6-3-1) ~ ( 1 0 - 6 - 3 - 1 ) ] R24 = t‘68[T(8-6-3-1)
R~~= R2, = RZ2= R23 =
+
+
OSee Figure 1 for atom numbering scheme and definition of coordinates. Atom numbering differs from that in ref 17.
are identical with those used in GAUSSIAN 82,26 with the exception of 6-31 lG**, where six d functions are used in place of five. The basis set D Z / l P is the double-{ basis set of Dunning32 (9sSp contracted to 4s2p on C and 0 , 4 s contracted to 2s on H (scale factor 1.2)) augmented by one set of polarization functions (d(0.8) on C, d(0.9) on 0, and p(1.0) on H): 9sSpld/4slp contracted to 4s2pld/2slp. Mr;8 tensors are calculated using origins at the molecular center of mass and at each nucleus. Dipole strengths and rotational strengths using either the common origin gauge or the distributed origin gauge are then calculated by combining oi, SAu,i,P$, and Mkp values according to eqs 8, IO, and 12.
Results and Discussion The absorption spectra of propylene oxide at 1-cm-’ resolution as neat liquid and in solution in CC14and CS2are shown in Figure 2. Studies of the spectra at progressively lower resolutions indicate that at 1-cm-I resolution they are very close to fully resolved. Neat liquid and solution spectra are extremely similar. Peak frequencies (Table 11) vary by
