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
( 1. The wagging or twisting modes, labeled w for commodity,are normal modes which contain HCC bendings. To describe the high-energy spectra up to Au = 6, only three modes have to be considered, the others having a harmonic wavenumber too low to enter in resonance with the CH stretching overtones. B. Higher Order Coupling Terms. As already pointed out by Wallace25 or Sibert et a1.,Z6 the anharmonic coupling terms may be expressed according to two perspectives: the Hamiltonian is written in curvilinear coordinates, and the anharmonic terms are directly related to the anharmonicity of the kinetic energy; or use is made of rectilinear coordinates,and the kinetic energy is strictly quadratic. Then, the anharmonic coupling terms come from the anharmonic mixing of the rectilinear coordinates in the true vibrations. The choice between the two representations depends on the level of approximations one is prepared to treat. Sibert et a1.26 have shown that, at the first order of approximation, the two approaches are strictly equivalent. If one has to go further as, for example, in interpreting high vibrational overtones, this is no longer the case. Each of the perspectives has its own disadvantages. In curvilinear coordinates,the most important contributions of the anharmonic coupling terms, which are generally Taylor series expansion of the Wilson gr,(r) matrix elements in the displacement coordinates about the equilibrium configuration, fail in reproducing the Fermi resonance forces or crossed anharmonicity between CH stretchings and bendings. To model the spectra, one has to introduce corresponding potential terms. The Hamiltonian is an “effective” one. In the other perspective, use of rectilinear coordinates, the anharmonic coupling terms strongly depend on the anharmonicities of the CH stretching potential. What is generally known is the energy dependence E(u) = W O ( U + l/2) - x (u + ‘ / z ) ~It. is well-known that the Morse potential is only one of the potential functions which gives this energy dependence. Any quartic potential with appropriate fm, Arr, and Armgives the same dependence. Thus, this second approach needs a lot of data to permit the exact determination of the CH stretching potential surface. The phenomenon which governs the high vibrational energy flow in cyclohexeneisaseriesofshortresonances with combination states involving low-energy modes. These resonances are numerous and intricate, so they cannot be described with a high order of approximation. So we have chosen the first approach, keeping in mind that the Hamiltonian which describes the energy flow is an “effective” one. The leading terms which describe the coupling between CH stretchings and bendings (6) are the first derivatives of gaawith respect to r,z1 The first-order term
determines the Fermi resonance coupling Xr,a. The second-order term
In these expressions, the symbols have the same meaning as for e. The bendings (6) are the internal coordinate HCH angles. Theintroduction of an effective coupling “f’,which describes the indirect interactions between the two bendings via the other low-
determines the crossed anharmonicity xd.21
The Journal of Physical Chemistry, Vol. 97, No. 23, 1993 6139
Spectra of Cyclohexene-3,3,6,6-d4 The couplings between the CH stretchings and the HCC bends (e) are of the same kind.23 But the Hamiltonians Hkr and Htr which describe the Fermi resonance terms A, and crossed anharmonicities xn, must be expressed in normal coordinates and momenta:
subtracted, the diagonal elements give ,
2
2
2
3
2
2
3
2
. s
4
In these expressions, (L)ej-' are the familiar L-l matrix elements which give the dependence of the normal mode w in internal coordinates HCC, = 0,
There are also minor coupling terms in the Taylor series expansion of other terms of the C matrix. However, they are at least 1 order of magnitude below the leading terms, and they have been discarded. C. Fermi Resonance Matrix. The effective Hamiltonian presented above was expanded in a basis set whose functions were products of Morse oscillator functions for CH stretching and harmonicoscillator wave functions for lower frequency modes. The potential parameters were chosen so that the converged eigenvalues reproduced the observed spectrum inside each polyad. The Morse matrix elements r and r2 were obtained using Gallas' formula.2' Each basis function may be written as 2
2
2
3
2
2
2
2
2
3
2
In this expression, wa, we, war and ww/ are the harmonic wavenumbers of the considered motions. The crossed anharmonicities may be different for the two kinds of CH bonds-pseudoaxial and pseudoequatorial-as they depend on the potential parameters of the second-order Hamiltonian H2 and also, for the lower frequency motions, on the Le1 elements. Two kinds of off-diagonal couplings have been introduced. The first accounts for the interaction of the CH oscillators in terms of an interbond coupling parameter related to the potential A,,, and kinetic coupling matrix elements or for the interaction between the two bending motions. This coupling gives rise to in-plane and out-of-phasesymmetric and antisymmetric normal modes and are only relevant for the first excited state, Av = 1. The Fermi resonance requires the introduction of a second type of off-diagonalelement,described by the first-order Hamiltonian P.It connects basis functions differing by two quanta in the bending or lower frequency mode motions. As for the crossed anharmonicity, the Fermi resonance coupling constants Ana, A d , Amw/, or /A, which depend on I9 parameters may be different for the axial and equatorial CH bonds. The SchrMinger equation for the vth manifold expressed in matrix form
is solved by diagonalization of the Hamiltonian matrix H. Such a matrix is block diagonal in u. The resulting eigenvalues o,are compared to the observed band positions. But the fitting procedure takes into account also the mode intensities inside each polyad. D. Intensities. The intensities arecalculated from the following relation:28
where ji is the electric dipole moment operator of the molecule and NOis Avogadro's number. IVn)is the part of the eigenstate of the mode of wavenumber onwhich receives contributions from stretching states only:
3
where vpl, vq, Oak, and vW1are the quantum numbers in the ith pseudoaxial CH bond stretchingJth pseudoequatorialCH bond stretching, kth bending motion, and Ith lower frequency normal modes, respectively. When the zero-point energy contribution is
The calculations have been performed according to the bond dipole approximation;28 that is to say, for every polyad, (~~,0,0,01ji(O,O,O) has been supposed colinear to the ith CH bond. The intensities of each transition moment corresponding to pseudoaxial or pseudoequatorial bonds have been supposed identical. It is well-known that the intensities of the transition moments of the axial and equatorial bond stretchings of the
6140 The Journal of Physical Chemistry, Vol. 97, No. 23, 1993
TABLE IIk List of the Panmetens Used in tbe Calculations of the Frequenciee md Intensities of the CH Stretching Overtone Spectra of CycIohexene-3,3,6+4 on = 3026 cm-l = 1282 ~ m - ' X,,Q = 5 cm-1 we = 3056 cm-1 ww3 = 1244 cm-1 x, = 63 cm-l xw3 = 5 cm-1 xe = 63 cm-l Anwl = 24 cm-1 fu = -0.032 mdyn/A fie
= 0.07 mdyn/A = 0.005 mdyn/A = 1468 cm-1
fo0
08
= 6 cm-1 = 0.005 mdyn/rad* A8, = 22 cm-1 A d = 20 cm-1 x d = 32 cm-I = 32 cm-l wwl = 1348 cm-1
XJ fM
xwl
= 5 cm-1
Awl
A&, zA,, Anw3 3A ,
= 24 cm-1 17 cm-l = 10 cm-1 = 22 cm-1
= 4 cm-1 5 cm-I 10 cm-1 h W z = 14 cm-1 = 17 cm-1 h W 3 = 16 cm-I h 3 = 18 cm-l xnwl = h l =
cyclohexene molecule are different.Z9 But their ratio is the same in the Raman and in the infrared ~pectra.3~ It is very difficult to measure the relative intensities of the CH stretching impurities in the infrared spectrum of the fully deuterated cyclohexene because of the complicated band shapes. But the corresponding Raman spectrum is isotropic with no structure. The fitting to Lorentzianband shapes indicates that the intensity ratio between the pseudoequatorialand the pseudoaxial transitions is equal to 1.05 f 0.05. The evolution of this ratio with the overtone order may be compared with the one for the cyclohexane molecule. Recent calc~lations3~ have been performed on the intensities of these transitions, showing that the ratio is not strongly modified from one overtone to another. So we have supposed that the ratio in the cyclohexene molecule was the same for all the overtones of the infrared spectrum, and since our calculations are not accurateto within 1096,we have taken the two transition intensities to be equal. Thus, for each mode of wavenumber, on,the relative intensity inside each polyad is calculated proportional to
The values of pix, pi,,, and pfz are deduced from an ab initio optimization of the geometry.32 With the set of calculated wavenumbers and intensities, we have tried to reconstruct the spectra of each polyad. From Au = 3 to 6 and for the Raman spectrum,each band has been assigned a Lorentzian band shapewith a constanthalf-width which depends only on the number u of the polyad. For Au = 1 and 2, such an approach was not applicable due to the large variation of the band shapes of all the modes considered. The Raman intensities of the Au = 1spectrumhave been calculated with theelectrooptical parameters of the paraffinic methylenes determined by Gussoni et al.33
4. Discussion The results of the calculations are displayed in Figures 2-7. One can notice that the general trends of the experimentalspectra are correctly reproduced. In particular, thedifference in intensity between the lower and higher frequency bands at Au = 5 and 6 is well accounted for. The infrared and Raman fundamental spectra require the set of the 14 first parameters of Table I11 to be reproduced with a standard deviation of 1.5 cm-1. The analysis of the calculationsshows that the higher frequencybands at 2949 and 2942 cm-l correspond to the two in-phase and out-of-phase pseudoequatorial transitions. Only the in-phase transition of symmetry A has a significant Raman intensity. The other strong band of the infrared spectrum at 2932 cm-1 corresponds to the out-of-phase pseudoaxial CH stretching which is in strong resonance with the bending overtone at 2873 cm-1. The in-phase
Lespade et al. modes are very mixed with the pseudoequatorialstretching and bending overtones. They have very weak infrared intensities, but one of them, at 2874 cm-1, possesses a large Raman intensity, withashoulderat 2871 cm-' whichcanbeassignedtoa progression band due to the internal motion. Such progression bands can also be observed in the infrared spectrum on the lower frequency side of the out-of-phase pseudoaxial stretching bands at 2932 and 2873 cm-l. The Au = 1 spectra are only perturbed by resonances with the bending overtones. In the higher overtones, this resonance is progressively detuned because of the great anharmonicity of the CH stretching motions, but other resonances occur with combinations involving lower frequency modes. The choice of these modes for the calculationof the spectra is not an evident one. The Raman spectrum shows three weak bands between 1400 and 1200cm-lat 1338,1272,and 1234cm-l. Theyhavebeenassigned to HCC deformations in ref 24. The infrared spectrum exhibits an extra band near 1396cm-l which appears also in the spectrum of the totally hydrogenated cyclohexene. It has been attributed by Net0 et aLZ4to a combination mode. So we have retained only the three Raman modes in the calculation of the high overtones spectra. The description of the anharmonic couplings with the combinations involving these three modes requires a lot of parameters which are not independent of each other. Even if each mode combination seems to interact with a particular overtone, the 1338-cm-l one with the Au = 3 and 4 transitions, the 1272-cm-l one with the Au = 4 and 5 overtones, and the lower frequency modecombination with the highest overtone, the Fermi resonance forces or anharmonicities of each mode are not independent. For example, a small changeof the Fermi resonance force of one of the combinations involving the overtone of the mode at 1234 cm-l, which enters in resonance only at Au = 6, would change completely the intensities of the lower frequency modes of Au = 4 at 10 686 and 10 776 cm-1. Thus, in order to understand the complicated intramolecular energy redistribution which is present in that sort of molecule, it is important to perform complete calculations which involve all the possible couplings. It is evident that the set which is displayed in Table I11 is only one the possiblesets which describe theovertone spectra, in particular because we have discarded the combinations involving modes with frequencies lower than 1200cm-1. The introductionof these modes would not change the frequencies very much but would have an influence on the intensities. In particular, the discrepancy that we have found between the two Fermi forces XAW3 and ,A,, may come from the neglect of these combinations. The problem of including these extra modes is that it still increases the number of parameters. Thus, the values of the parameters displayed in Table 111, which are connected with the third deformation combinations, must be considered with some caution. However, we have found that the calculations lead to two important conclusions, whatever the values of the parameters: (1) Up to Au = 4, the modes are not purely pseudoaxial or pseudoequatorialtransitions, and it is often difficult to give them an assignment. In the higher overtones, the vibrational energy no longer flows from one CH bond to the other within the same methylene group, but the large absorptions are the addition of several bands which may correspond to pseudoaxial and pseudoequatorial transitions with more pseudoaxial stretching overtones for the lower frequencies and more pseudoequatorial overtones for the higher frequencies. (2) The analysis of the delocalizationof the vibrational energy on the twomethylenicgroupscanexplain the near-infrared circular dichroism spectra of monoterpenes. In the energy range 40011000 cm-l, the two in-phase and out-of-phasevibrationspossess nearly equal wavenumbers (within 5 cm-1) but the contributions of the four CH stretching overtones to the vibrations are not rigorously the same. Thus, if the two methylene groups are no longer equivalent,as in the case in chiral compounds, it is possible
Spectra of Cyclohexene-3,3,6,6-d4 to calculate some modes which are completely delocalized on the two CHI groups. The result of our calculations shows that the existence of Fermi resonance couplings between CH bond stretching overtones and lower frequency combination states can inducea sufficiently large delocalization of thevibrational energy for near-infrared circular dichroism to be measured in chiral compounds like monoterpenes. Very recently, visible circular dichroism has been measured at energies corresponding to Av = 5 and 6.34 The spectrum of the fourth overtone (Av = 5 ) corresponds exactly in sign and frequency to the spectra measured in the near-infrared region (Av = 3 and 4). But the Av = 6 spectrum seems to present inverse signs. Our calculations are not precise enough to give an explanation of this surprising phenomenom. Nevertheless, it is possible that, at these energies, other modes enter in resonance, changing completely the vibrational structure of the fifth overtone of limonene. In conclusion, none of the possible explanations of this phenomenon-large amplitude motion of existence of Fermi resonances-can be excluded up to now. Only complementary studies of chiral molecules which are smaller than limonene would allow us to discriminate the participation of the two possible ways. Some work is in progress in this field.
5. Conclusion We have measured the vapor-phase overtone spectra of cyclohexene-3,3,6,6-d4 in the regions corresponding to AuCH = 1-6. The methylenicvibrationsexhibit a very distorted structure which provides evidence of Fermi resonance couplings with combination states involving lower frequency modes such as CH2 bendings and HCC deformations. To explain the spectra, a model Hamiltonian has been constructed. The result of the calculations shows that the HCC deformation modes are coupled to the CH stretching modes with anharmonic coupling forces of the same order of magnitude as the CH2 deformation. These coupling forces are large enough for the vibrational energy to flow from one CH bond to the other of the same CH2 unit, below 11 000 cm-1. Above this energy, the ‘local” pseudoaxial and pseudoequatorialmodes are energeticallydistributed on wide spectral regions which interconnect with each other. With the coupling parameters of the model, it is possible to calculate rather delocalized wave functions of twovicinousunequivalent methylene vibrationsfor energies below 11 000cm-1. Thus, thedelocalization of the vibrational energy by Fermi resonance couplings with combination states may be a possible explanationof the existence of circular dichroism in monoterpenes. Indeed, unlike the CH2 deformations,the lower frequency modes are very delocalized on the molecular ring and represent a privilegious pathway of intramolecularredistribution of the energy onto an extended chiral chromophore of the molecule. Acknowledgment. We are grateful to Raymond Cavagnat for the measurementsof the Raman spectra, Jean Claude Cornut for assistance in experiments, and Philippe Maraval for help in the
The Journal of Physical Chemistry, Vol. 97, NO. 23, 1993 6141 computational procedures. L.L., S.R., and D.C. acknowledge support of this research by the “Region Aquitaine” through the award of equipment grants. We are also grateful to the Aerospatiale Industry for having provided us the use of the BOMEM A03 FTIR spectrometer. This work was done in part under the auspices of an international collaboration program between the CNRS (France) and the University della Basilicata (Italy).
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