Rotational—vibrational circular dichroism

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ROTATIONAL-VIBRATIONAL

CHEMICAL PHYSICS LETTERS

29 September 1989

CIRCULAR DICHROISM

P.L. POLAVARAPU Department of Chemistry,Vanderbilt University,Nashville, TN 37235, USA Received 6 June 1989; in final form 14 July 1989

Experimental rotational-vibrational circular dichmism (RVCD) spectra are presented for methyloxirane. These spectra were obtained at 1 cm-’ resolution in the FZ1500-650 cm-’ region. It is found that the circular dichmism sign associated with the Q branch is opposite to those of the P and R branches for some vibrational bands. These unusual RVCD features are explained by developing the necessary theoretical analysis. It is found that the CD associated with the central Q branches of the rotationalvibrational bands in near-symmetric top chiral molecules provides a unique source for determining the signs of electric dipole and magnetic dipole moment derivatives.

1. Introduction

2. Experimental observations

Vibrational circular dichroism (VCD) is a measure of the differential absorption of left versus right circularly polarized incident light due to the vibrational transitions of chiral molecules. VCD has been successfully measured [ 1] for chiral molecules in the solution phase and various groups [2-61 are actively involved in utilizing VCD spectroscopy for stereochemical information, Optical activity in rotationalvibrational transitions [7] and in pure rotational transitions [ S- 10 ] are two new branches that are yet to be fully explored. We measured the circular dichroism for vapor phase samples several years ago [ 111 at 4 cm- ’resolution. At this resolution, however, rotational-vibrational circular dichroism (RVCD) features were not clearly isolated. Since there are some unique applications for RVCD spectra (vide infra) we have recently assembled a new VCD spectrometer that can provide enhanced signal-to-noise level at higher resolution. The purpose of this paper is (i) to report unusual RVCD features observed for methyloxirane and (ii) to interpret these features and show that one can determine the signs of the electric dipole and magnetic dipole moment derivatives from the RVCD spectra.

The VCD spectrometer used for the present measurements was built around a FI’IR spectrometer (Mattson Instruments, CYGNUS 100). An optical filter transmitting in the x11500-600 cm-’ range, a KRS-5 polarizer, a ZnSe photoelastic modulator and a HgCdTe detector (P = 4 x 1O’O,20% cutoff at 600 cm- ’) were rhe principal components of this spectrometer. The detector signal was processed with a lock-in-amplifier as described elsewhere [ 12 1. Measurements were made for both enantiomers and the racemic mixture of methyloxirane. The baseline artifacts were suppressed either by subtracting the raw VCD spectrum of the racemic mixture from those of the individual enantiomers or by taking one-half of the difference between the raw VCD of the two enantiomers. For vapor phase studies, a 5 cm gas cell with KBr windows was used. The data acquisition time is ~4 h per sample. Some measurements were done at the room temperature vapor pressure of the sample by exposing the cell to the sample’s vapor in a vacuum manifold. In other measurements some liquid was condensed into the side-arm attached to the cell, so that the absorbance is roughly two times that found in the abovementioned set of measurements. Both sets of measurements gave identical RVCD features. We have also verified the expected mirror image CD for the two enantiomers. For liq-

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uid phase studies, the spectra were obtained at 4 cm- * resolution for dilute solutions (CS1 and CC& as solvents) using a variable path length cell with ICBr windows. The data acquisition time was x 1 h per sample. The samples of methyloxirane were obtained commercially (from Aldrich or Fluka) and were used as received. Vapor phase spectral measurements are shown in fig. 1. The interferograms collected for 1 cm-’ resolution could also be used to derive lower resolution spectra. Such spectra at 4 cm-’ resolution are also included in fig. 1. The vapor phase spectra at 4 cm-’ resolution can be compared with the same resolution spectra obtained for liquid solution samples, shown in fig. 2.

29 September 1989

We will use the term RVCD for CD associated with the bands of vapor phase samples and VCD for that associated with the bands of liquid phase samples. On comparing the CD signs for vapor and liquid the following observations cafl be noted. For the 1270 cm-’ band of (R)-( + )-methyloxirane, the VCD sign is negative. However, RVCD is negative only in the P and R envelopes and is positive for the sharp Q envelope of this band. Similarly for the 1020 cm-’ band of (R)-( + )-methyloxirane, VCD sign is positive but RVCD is positive only for the P and R envelopes and is negative for the weak Q branch. The CD sign reversal in the Q branches of these two bands is the primary focus of this work. It is possible that there are similar related effects in the RVCD spec-

Hlawm 7.0

7.5

9.0

moo

6.5

l209

9.0

ll90

Wavenumber

lo.0

11.0

900

lwo

l&o

U

900

:

Fig. 1.Rotational-vibrational circulardichroism (A,C) and absorption (B,D) spectrafor ( + )-(R)-methyloxirane, obtained at 1 cm-’ resolution ( A,B) and 4 cm-’ resolution (C,D). Due to excessive absorption, the band at w 830 cm-’ is not shown. For the same reason, CD associated with the Q branch at ra1405 cm-’ in (A) may not be reliable. The 1 cm-’ absorption spectrum (B) is displayed on O1.5 absorbance scale. The 4 cm-’ absorption spectrum (D) is displayed on O-l.0 scale.

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I

II

IIll woo

CHEMICAL PHYSICS LETTERS

1 l2Qn

III

11

1111~

1100

I iow

III

29 September 1989

1 900

I

III

I

Ill3

a00

Havenumber Fig. 2. Vibrational circular dichroism (A) and absorption (B) spectra for (+ )-(R)-methyloxirane (0.5 M, C?&) obtained at 4 cm-’ resolution. Due to excessive absorbance, the bands at = 830 and 1420 cm-’ are not shown. The absorbance spectrum is displayed on O0.6 absorbance scale.

trum around * 1130 cm-‘. However, there are three different vibrational bands overlapping in this region as can be noted from the VCD spectrum. Since P, Q, R branches of these three bands strongly overlap, we will defer the analysis of this region to a later date.

3. Thecr&al

analysis

The structure of methyloxirane, showing the principal axes, is shown in tig. 3. From the ab initio optimized geometry [ 13 1, at 6-31G level, the three rotational constants A, B and C for methyloxirane are found to be 0.59, 0.22 and 0.20 cm-‘, respectively.

These values are close to the corresponding experimental values [ 14) of O-60.22 and 0.20 cm-‘. Since B and C values are nearly equal, we will consider methyloxirane as an accidental symmetric top molecule. However, due to the lack of molecular symmetry, the vibrational normal coordinates do not possess any symmetry. This would mean that even though rotational wavefunctions can be represented by the symmetric top wavefunctions, the rotationalvibrational transitions associated with any particular vibrational band of methyloxirane cannot be classified as parallel or perpendicular. This follows from the fact that -due to the lack of molecular symmetry, the vibrational transition moments do not have to be parallel to any one of the principal axes of inertia. 487

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+ b

Fig. 3. Principal axes of moment of inertia located at the centerof-mass for methyloxirane. Rotation around the a-axis has the largest, and that around the c-axis has the least, moment of inertia. The displayed coordinates obtained from a 6-31G calctdation [ 131 for C(methy1) and C*are (0.183, -0.035,1.556) and (-0.488, -0.067, 0.216), respectively, in A.

Then each vibrational band of methyloxirane can have both parallel (AK=O) and perpendicular (AK= k 1) transitions. The CD signs of the parallel transitions are determined (vide i&a) by the product (~pJ~Q,) (hz,/Cl&, where c is the principal axis of a prolate symmetric top with least moment of inertia (or largest rotational constant). For perpendicular transitions, the CD signs are governed by the sum ($daQJ (NJ@,) + GWaQd CW@J where a and b are the remaining two principal axes. Assuming that the rotational constants are independent of the vibrational state, the frequencies of the Table 1 Frequencies and relevant dipole derivatives for rotational-vibrational

29 September 1989

possible transitions are summarized in table 1. For methyloxirane Aw0.6 cm-’ and Bw CwO.2 cm- ‘, which leads to the approximation A-B 2: 2B. Using this relation, one finds that some of the QP and QR transitions appearing close to v. can overlap with some of the ‘Q and “Q transitions. Since the CD sign of the former transitions is governed by that of (rYc~,/ aQI) (am,/@,) while the CD signs of the latter transitions are governed by the sign of (ap,JaQ!) (am,/ gQI) + (+&lQ,) (am,/aQ1) it is apparent that mutual cancellation of intensities can occur if the signs of these products of dipole moment derivatives are different. If such cancellation does occur, which appears to be the case (vide infra), then the QQ transitions can be considered to be predominantly responsible for the observed CD sign reversal in the Q envelopes of 1270 and 1020 cm-’ bands. It should also be noted that some of the perpendicular transitions can appear near vo, overlapping with the QQ transitions. However, such transitions are fewer in number compared to the number of possible QQ transitions at room temperature. For these reasons, we will focus on developing a theoretical expression for CD associated with the oQ transitions. The rotational strength !II associated with a rotational-vibrational transition can be written as

~(Y~~~vIL~I~,I&MKM~.

(1)

In this expression, we have assumed that the total

circular dichroism of a chhl

symmetric top

mOlede

Transition

Designation a1

Frequency ‘)

Relevant product of dipole derivatives ‘)

hko, LIB=0 &I=-LAB=0 AJ=+1,AK=o AJ=o,AK=-1 AJ=o,AK=+1 AJ=-l,AK=-1 AJ=-1,AK=+1 AJ=+1,AK=-1 AJ=+1,AK=+1

QQ Qp oR

vo

mm)

vo-2BJ vc+2B(J+l)

(akc/af2) (am&) (80Q) (8m,laO) (8kiaQ) (am,/@) (ak/aQ) (am,/@) (ak/ae)(am,i80) (ak/aQ)(am,ia&

‘Q : RP PR RR

vo+(A-B) ( 1 - ZK) v,+(A--B)(1+2K) vo-2BJ+(A-B)(l-2K) v,-2BJ+(A-B)(1+2K)

wdwh

v,+2B(J+l)+(A-B)(l-2K)

(ak/afmm,iab)

v,+2B(J+l)+(A-B)(1+2K)

(ak/aQ)

(am&%

‘) Fromref. [15]. b, For a symmetric top.Jand K are quantumnumbers for the initial state. A is the rotational constant for rotation around the c-axis. Lt iS assumed that rotational constants are independent of vibrational state. el a=a, b representing the remaining two principal axes.

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wavefimction can be written as a product of electronic-vibrational and rotational wavefunctions, which is valid in the harmonic oscillator and rigid rotor approximations. I& and @&,, are the eleo tronic-vibrational and rotational wavefunctions, respectively, of the initial state. The corresponding primed quantities are for the final state, which belongs to the same initial electronic state. It is implied that eq. ( 1) needs to be averaged over (W+ 1) levels degenerate in M and that wJKMrepresents the rotational wavefunction [ 15 ] of a symmetric top, with the usual meaning for J, K and M. The electric and magnetic dipole moment operators, k and mar respectively, in eq. ( 1) are in space-fixed axes (cu=x, y and z) and can be written in terms of those in molecule-fixed principal axes of inertia as .&Y = &%, + ~b&

+ !@cci

(2)

for (Y=x, y and z. A similar expression holds for m, with S,,, S, and S, representing the appropriate direction cosines for transformation between the space-fixed and molecule-fixed axes. It may be noted that the c-axis represents the principal axis with the least moment of inertia for methyloxirane. Since we arc interested in the QQ transitions, the rotational matrix elements are diagonal in J and K. Then only the terms involving S, in eq. ( 2 ) are relevant [ 161 because S, and Sk are pertinent for AK= f 1 transitions. With these considerations and expanding pa in terms of the normal coordinates Q, and m, in terms [ 17 ] of & and noting that special attention should be given to the evaluation of the electronic part of the magnetic dipole transition moment [ 2,171, eq. ( 1) within the harmonic approximation becomes

where 9l,( QQ) represents the rotational strength associated with the individual QQ transitions of the hh fundamental vibrational transition. Similar expressions for the remaining transitions have also been derived and will be discussed in a future article. According to eq. (3), the CD sign associated with the QQ transitions is determined by that of the product ( apJaQI) (am,/@,). We have mentioned that the observed CD in the Q envelope can be consid-

29 September 1989

ered to be predominantly due to the QQ transitions. Hence, (a@@) (am$&) is positive for the 1270 cm-’ band and negative for the 1020 cm-’ band of ( + )- (R)-methyloxirane. This constitutes the first experimental determination of the sign of the product (a&aQ!) ( flm,/a&). Furthermore, since the VCD signs (fig. 2) are determined by the sum of three products (a&,/aQJ (am,/a&), it follows that the sum (a&&$) (a%/%%) + (&if@/) (ambiaf&) is negative for the 1270 cm- l band and positive for the 1020 cm-’ band of (R)- ( + )-methyloxirane. In reaching this conclusion we have not used the observed RVCD signs of P and R branches because the transitions in these branches, when adequately resolved, can exhibit bisignate RVCD features. We have also considered other possibilities for the CD sign reversal in the Q envelopes of the 1270 and 1020 cm-’ bands. One such possibility is the Coriolis interactions [ 181 between two different vibrational modes through a molecular rotation. However, the appropriate Coriolis constants Cc, determined from the ab initio force constants [ 131 are very small for the 1270 cm- ’band. The only significant value found for Cc is that due to Coriolis interaction which a C-H stretching vibration. Due to the large frequency difference between these vibrations, it is unlikely that Coriolis interactions are responsible for the signal reversal in the Q envelope of the 1270 cm-’ band. 4. Conclusions We have measured the RVCD spectra for methyloxirane and found that the CD associated with the Q envelope has opposite sign to those of P and R branches for some rotational-vibrational bands. These observations are explained by considering methyloxirane as an accidental symmetric top. It is shown that for an accidental symmetric top chiral molecule, CD associated with the Q envelope can be used to determine the sign of the product (apJ aQ,) (am,iaa). Acknowledgment This work was supported by grants from NIH (GM29375 ) and Vanderbilt University. 489

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CHEMICAL PHYSICS LE’ITERS

References [ 1 ] G. Holzwarth, E.C. Hsu, H.S. Masher, T.R. Faulkner and A. Moscowitz, J. Am. Chem. Sot. 96 (1974) 251. [2] PJ. Stephens and M.A. Lowe-, Ann. Rev. Phys. Chem. 36 (1985) 213. [3] L.A. Nafie andT.B. Freedman, Spectroscopy 2 ( 1987) 24. [ 41 T.K. Keiderling, Appl. Spectros. Rev. 17 ( 1981) 189. (51 M. Diem, J. Am. Chem. Sot. 110 (1988) 6967. [6] R.A. Shaw, N. [brahim and H. We&r, Tetrahedron Letters 29 (1988) 745. [7] P.L. Polavarapu, in: Proceedings of the Workshop on Circularly Polarized Synchrotron Radiation, eds. F.C. Allen and C. Bustamante (Plenum Press, New York, 1985 ). [8]L.D.BarronandC.J. Johnston,J.RamanSpectry. 16 (1985) 208. [9] P.L. Polavarapu, J. Chem. Phys. 86 (1987) I 136.

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[lo] W.R. Salzman, Cltem. Phys. Letters 134 ( 1987) 622. [ 111 P.L. Polavarapu and D.F. Michalska, J. Am. Chem. Sot. 105 (1983) 6190. [ 121 P.L. Polavarapu, in: Fourier transform infrared spectroscopy, eds. L.J. Basile and J.R. Ferraro (Academic Press, New York, 1985). [ 13 ] P.L. Polavarapu, B.A. Hess Jr. and L.J. Schaad, J. Chem. Phys. 82 (1985) 1705. [ 141 J.D. Swalen and D.R. Herschbach, J. Chem. Phys 27 (1957) 100. [ 15 ] G. Herrberg, Infrared and Raman spectra of polyatomic molecules (Van Nostrand, Prince-ton, 1945). [ 161 H.W. Kroto, Molecular rotation spectra (Wiley, New York, 1975). [ 17 ] A.D. Buckingham, P.W. Fowler and P.A. Galwas, Chem. Phys. 112 (1987) 1. [IS] I.M. Mills, Pure Appl. Chem. 11 ( 1965) 325.