Large intramolecular energy flow in vibrational overtone spectra of

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J. Phys. Chem. 1993,97, 6134-6141

6134

Large Intramolecular Energy Flow in Vibrational Overtone Spectra of Cyclohexene-3,3,6,6dd L. Lespade,' S. R d i and D. Cavagnat Laboratoire de Spectroscopie Molbculaire et Cristalline, URA 124, CNRS Universitb de Bordeaux 1, 351 crs de la Libbration. 33405 Talence Cedex, France

S. Abbate Dipartimento di Chimica, Universith della Basilicata, via Nazario Sauro 85, 85100 Potenza, Italy Received: December 15, 1992; In Final Form: March 2, I993

The vibrational structure of CH stretching states in gas-phase cyclohexene-3,3,6,6-d4 was studied using FTIR spectroscopy in the range 1200-1 1500 cm-1 and intracavity dye laser photoacoustic spectrometry in the range 12900-16000 cm-l. The structure was modeled using an effective vibrational Hamiltonian which describes the Fermi resonance couplings of the C H stretching states with suitable low-frequency vibrations. Some conclusions are made on the possible ways of intramolecular vibrational redistribution of the energy (IVR) on the two methylenic groups for wavenumbers below 11 000 cm-I in connection with the existence of near-infrared circular dichroism in monoterpenes.

1. Introduction The knowledge of possible pathways in the intramolecular vibrational energy redistribution of large polyatomic molecules is a question of fundamental interest in unimolecular reactions and laser-induced chemistry. The problem, in general, is very complex due to the large number of possible channels. At very high energies, the XH bond stretching overtones of smallmolecules exhibit a local mode behavior' which has allowed the performance of very exciting experimentslike the selective dissociation of the OH bond in HOD.Z In molecules of slightly greater size, a large number of experimentaland theoretical investigations have shown that one of the most rapid ways of redistribution of the CH bond stretchingovertone energy consistsof the contamination of the states by coupling with combination transitions involving HCH or HCX bending vibrations.sl0 The study of the kinetics of the isomerization of cyclobutene has shown that the energy flow was rapid enough-at least on the nanosecond time scale of the reaction-for the RRKM theory to be valid." In large molecules, the density of combination states is very high, and it gives rise, in benzene, to broad unresolved experimental line shapes in the absorption spectra.l2 In this paper, we focus our attention on a large molecule which has an even higher number of degrees of freedom for vibrations than benzene: the cyclohexene molecule. The cyclohexene ring is present in many natural compounds such as terpenes and steroids. One of the aims of our work is to get a more precise insight into the high vibrational energy flow in such molecules in order to understand more thoroughly the near-infrared circular dichroism spectra of 1im0nene.l~Indeed, the existence of a circular dichroism signal in the CH stretching overtones seems to be in contradiction with the notion of local modes, which predominates the high-energy spectra of small molecules since it has been pointed out, both for electronic14and vibrational15 transitions, that strong circular dichroism signals are to be expected for transitions involving rather delocalized molecular wave functions of an extended chiral chromophore. Actually, two ways of delocalization of the molecular wave function of high-energy vibrational transitions are possible: Fermi resonance couplings with combination states and couplings with large-amplitude motions. None of these ways can be excluded in monoterpenes like limonenes. Cyclohexene has a largeamplitude motion1618 between two equivalent half-chair conformations,but the characteristic time of the inversion is too slow for the motion to be efficiently coupled with the high-energy states. On this basis, it can be stated that CH stretchingvibrations take place on a rigid frame, or else, they are fully separated from 0022-3654/93/2097-6134$04.00/0

large-amplitude torsions. Thus, only the first way of delocalization of b e energy may exist in that molecule. Inthis study of the high-energy states of cyclohexene, we have focused our attention on all the possible couplings between the CH "local modes" and the molecular vibrations whose fundamental frequencies range from 1200to 145Ocm-land tried tomodel thevibrationalstructure of the CH stretching bands. To simplify the analysisof the data, we have started our study on the partially deuterated species, cyclohexene-3,3,6,6-d4. The structure of the present paper will be as follows: in the section 2, we will present the experimental overtone spectra of cyclohexene-3,3,6,6-d,. Section 3 will be devoted to a theoretical reconstructionof the spectra. The results will be discussed in the section 4. 2. Experimental Results

A. Apparatus. Cyclohexene-3,3,6,6-d, was purchased from MSD Isotopes Corp., kept out of air contamination, and used without purification. Its isotopicpurity is 98.2% deuteriumatoms. The vapor-phase Raman spectrum was obtained with a multipass cell and a Z 24 Dilor Raman spectrometer quipped with a Spectra Physics 171 Ar+ laser. The 514.5-nm line was used at a power of approximately 7 W. The spectral slit width was 1 cm-1. The IR spectra corresponding to the region Au = 1-3 were recorded on an FTIR Nicolet 740 spectrometer with different path length cells (from 10 cm to 21 m) and CaFz windows. For the fundamental region spectra, the gas pressure in the cell was a few Torrs, but for the overtone regions, the cell was filled until the vapor pressure of cyclohexene was attained. The Au = 4 region was recorded on a BOMEM A03 FTIR spectrometer of the Aerospatial Industry equipped with a quartz source, a quartz beam splitter, and a Si detector. Use was made of the 21-m path length Wilks cell. All the overtone spectra resolutions were 2 cm-1. The vapor-phase spectra of the higher overtones corresponding to the region Au = 5 and 6 were measured with our intracavity dye laser photoacoustic ~pectrometer.'~ A Coherent Innova 70 Ar+ laser was used to pump a Coherent 599-01 dye laser with the following dyes: 2-pyridine (12900-14000 cm-') and DCM (14500-16000 cm-1). A stainless steel photoacoustic cell was placed inside the dye laser cavity. A Compact microcomputer tuned the dye laser wavelength by incrementing the position of the three-plate birefringent filter via a micrometer and a stepper motor. The dye laser bandwidth was 1cm-1, and the micrometer 0 1993 American Chemical Society

The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 6135

Spectra of Cyclohexene-3,3,6,6-d4 pseudo-axial

H

7

s

4

pseudo-equatorial rseudo-equatorial

Figure 1. Cyclohexene ring interconversion motion: the two equivalent

half-chair conformations.

W a o T n e r la41

Figure 3. Gas-phase FTIR spectrum of cyclohexene-3,3,6,6-d4in the AVCH=Zregion(P=9OTorr,pathlength = 10cm). Onlythefrequencies and relative intensities of the calculated transitions are reprtsented. Figure 2. Gas-phase cyclohexene-3,3,6,6-d4spectra in the AVCH= 1 region. (a) The experimental Raman spectrum is measured at room temperature (P= 90 Torr). The calculated spectrum (broken lines) is obtained with Lorentzian band shapes (HWHM = 3 cm-I). (b) The FTIR spectrum is recorded at room temperature (P = 10 Torr, path length = 10 cm). Only the frequencies and relative intensities of the

calculated transitions are represented.

step was approximately 0.7 cm-1. Each point record was accumulated 800 times. At each wavelength, the microcomputer collected the photoacoustic signal via a Model 5209 lock-in amplifier (EG&G) referenced on the pump laser modulator, and the light power signal was measured by a photodiode on the reflection of one of the cell windows. The absorbance is proportional to the photoacousticsignal divided by the intracavity light power. The output beam of the dye laser was sent into a PHO spectrometer to check the wavelength every 500 points. The wavenumber accuracy was verified to be better than f2 cm-1. B. Results. As already pointed out, the most stable conformations of cyclohexene are the two equivalent half-chair conformations of Figure 1 which interconvert with each other with an average lifetime of le9s at 20 0C.16-i8 Rivera-Gaines et al. have performed recent far-infrared experiments on five isotopomers of cyclohexeneand have shown that other conformers are formed during the interconversion but their probabilities are too low, with respect to the half-chair one, for these conformers to be detected by high-energyvibrational spectroscopy. The energy of the bent conformation is 10 kcal above the minimum, and the planar conformation corresponds to a maximum of the twodimensional surface of the potential energy which lies 13 kcal above the stable conformation.'*

The symmetry of the half-chair conformer is Cz, and the transitions are of A and B species, all infrared and Raman active. The cyclohexene molecule is a slightly asymmetric top with the greatest inertia axis beilig perpendicular to the plane formed by the double bond and the binary axis and the medium inertia axis being parallel to C2. Thus, vibrations of species A will give bands with a PR envelope, and those of species B will give rise to hybrid bands between A and C types of an asymmetric top with a PQR envelope and a more or less pronounced Q branch. The deuteration of cyclohexene-3,3,6,6-d4 does not change the symmetry of the molecule since the deuterium atoms are symmetrically displayed respectively to the Cz axis. The spectra of the excited states of CH stretchings are displayed in Figures 2-7. The wavenumber positions of the principal peaks are indicated in Table I. The olefinic CH stretching transitions correspond to well-defined slightly asymmetric bands whose wavenumbers from Av = 2 to 6 are regularly displayed on a Birge-Sponerplot (Figure 8). Thus, these transitions correspond to pure local modes whose harmonic frequency ( w ) and anharmonicity ( x ) are given in Table 11. One can notice that the vibrational energy of the first excited state is calculated with these parameters 13-16 cm-1 below the experimental wavenumbers. This discrepancy is also observed for cyclopentene isotopomers20 and certainly reveals a coupling between this mode and a lower frequency mode combination like CCH bend plus C - C stretching. In opposition, the methylenicCH stretchingtransitions give relatively complicated spectra with too many absorptions respective to the number of inequivalent CH bonds. These extra bands must be assigned to overtones or combinations of lowfrequency vibrations strengthened by a Fermi resonance.

Lespade et al.

6136 The Journal of Physical Chemistry, Vol. 97, No. 23, 1993

'. aSao

8400

8300

6200

WFIVENUMBER Figure 4. Gas-phase FTIR spectrum of cyclohexcne-3,3,6,6-d~in the AVCH= 3 region (P = 90 Torr, path length = 21 m). The calculated spectrum (brokenlimes)is obtainedwith Lorentzianband shapes(HWHM = 15 cm-I).

M- 1

F i e 6. Gas-phase photoacoustic spectrum of cyclohexene-3,3,6,6-d4 in the AVCH= 5 region. The spectrum is measured at room temperature (P = 90 Torr). The calculated spectrum (Circle line) is obtained with Lorentzian band shapes (HWHM = 65 an-').

15.94

I

"

1iooo *

"

iotbo .

Figure 5. Gas-phase FTIR spectrum of cyclohexcne-3,3,6,6-d4 in the AVCH= 4 region (P = 90 Torr, path length = 21 m). The calculated spectrum (brokenlines)isobtainedwithhrentzianbandshapes(HWHM = 20 cur*).

The Fermi resonances are already present in the fundamental spectrum. Indeed, besides the two pairs of bands near 2945 and 2874 cm-1 which correspond to the in-phase and out-of-phase transitions of the pseudoequatorial and pseudoaxial CH bond stretchings, respectively, a relatively strong absorption of species B at 2932 cm-1 can be assigned to the out-of-phase overtone of CHzbendings which has gained intensity from the CH stretching transitions. The Fermi resonance is present in all the spectra up to the Av = 5 overtone at least. At these high energies, the resonance no longer arises with the CH2 bending combinations but with combinations of modes whose fundamental frequencies are lower like waggings and twistings. The existence of Fermi

15.71

15.47

15.24

x 10*3 CH-1 Figure 7. Gas-phase photoacoustic spectrum of cyclohexene-3,3,6,6-d4 in the Av = 6 region (P= 90 Torr). The calculated spectrum (circle line) is obtained with Lorentzian band shapes (HWHM = 70 an-').

resonances with these lower frequencies modes is more evident in the spectra of cy~lopentene-3,3,4,4-d~~m where the resonance with the CHz bending combinations vanishes at Av = 2, and the resonance with the CHI wagging combinations appears at Av = 4 only. In cyclohexene-3,3,6,6-d4, due to the greater number of methylenic groups and, thus, of low-energy modes,the rcsonance is effective for all the overtones we have measured.

3. Analysis A. Zero-Order Hamiltonian. In order to understand more thoroughly the spectra, we have tried to model the experimental results. We have built a Hamiltonian where the C H stretching vibrations are considered as weakly coupled Morse oscillators with interactions in the potential energy between the two CH2 groups.Z1 We are conscious of the great number of parameters, and we have tried to minimize the number of unknown variables.

The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 6137

Spectra of Cyclohexene-3,3,6,6-d4

AE (cm.1)

TABLE I: Experiwntrl and Calculated Frequencies (in cm-1) of the CH Stretching Overtones of

'1

cY~bx-3366e

3100

O M

polyad hv=l

IR 1234 1272 1338 1455 1 460 2 873

Raman

calcd

1234 1272 1338 1455 1460

1 234 1272 1338 1455 1 460 2 812

assignment HCC deformation HCC deformation HCC deformation HCH bending 6 HCH bending 6 out of phase

(