J. Phys. Chem. 1995,99, 3005-3013
3005
Ring Puckering and CH Stretching Spectra. 2. High Vibrational States of Gaseous Monohydrogenated Cyclopentene-3-hl S. Rodin-Bercion, D. Cavagnat,’ L. Lespade,” and P. Maraval Laboratoire de Spectroscopie MolCculaire et Cristalline, URA 124, UniversitC de Bordeaux I, 351 crs de la Libhation, 33405 Talence Cedex, France Received: May 16, 1994; In Final Form: October 4, 1994@
The excited vibrational states of gaseous cyclopentene 3-HCsD7 have been measured up to Av = 7. The second overtone presents essentially two main absorptions corresponding to two distinct conformers. The higher overtones are much perturbed by Fermi resonances with low-energy modes. The contribution of two types of couplings to the ring-puckering motion and to isoenergetic states involving low-energy modes are analyzed and modeled. Through the reconstruction of the spectra, the predominant pathways of the intramolecular vibrational redistribution of the energy (IVR) are discussed.
Introduction The study of vibrational motions of polyatomic molecules at energies sufficient for reaction is of great interest because of its relevance to the role of vibrational excitation and of internal vibrational energy redistribution process (IVR) in photodissociation and laser induced reactions.’-4 The interpretation of overtone spectra as a means of obtaining detailed insight into these high-energy states has received particular attention for several years. Most of these studies have been devoted to the CH or OH stretching overtones. The case of relatively small molecules like CHX3 has been extensively studied experimentally as well as t h e ~ r e t i c a l l y . ~ These - ~ ~ studies all show that energy initially localized in a CH stretch overtone undergoes a rapid relaxation as a consequence of a large effective coupling with low energy states by Fermi resonance. As shown by theoretical works,21,22the IVR dynamics appear essentially governed by a few states (in strong resonance with the initial doorway state) among the high density of states currently found at these energies for relatively large molecules. The study of these phenomena in nonrigid molecules is of particular interest as such molecules can serve as model systems for polymers, proteins, and other biological macromolecules in which flexibility is one of the most important factors in chemical reaction. The large-amplitude, low-frequency, and very anharmonic motion which characterizes the flexible molecules will play a major role in various relaxation process since it increases the density of interacting isoenergetic states and is generally coupled to several other vibrational modes of the molecule. Some recent studies have explicitely considered the mechanisms by which XH stretching energy flows into and breaks another The large-amplitude torsion motion of molecules is therefore of interest as it may be the principal component of the reaction coordinate.26 Many studies with dispersed fluorescence spectroscopy have shown that the presence of a nearly free rotating methyl group on an aromatic ring accelerates the rate of IVR in the first excited electronic This enhancement seems to be a consequence not only of the increased total density of states, but primarily because coupling strength between internal rotation and molecular vibration leads to an increased density of coupled states. Several highresolution infrared studies have shown the specific role of molecular flexibility and low-energy skeletal isomerization
* To whom correspondence should be addressed. @Abstractpublished in Advance ACS Absrrucrs, February 15, 1995. 0022-365419512099-3005$09.00/0
barrier in promoting IVR phenomena in CH stretch excited hydrocarbon^.^^^^^ In the ground electronic state, there have been only a few studies of the CH overtones in this type of molecule^.^^-^^ The overtone spectra of the perhydrogenated cyclopentene were measured in the and in the gas phase33up to the sixth overtone (Av = 7). These spectra are principally composed of two peaks, an intense and well-resolved one corresponding to the ethylenic CH bonds and a less intense broad one corresponding to the methylenic CH bonds with a complex structure, badly resolved even in the higher overtone spectrum in the gas phase.33 This lack of resolution prevents a decisive assignment of the various methylenic bands. Furthermore, Fermi resonance phenomena are expected to occur in a more complicated fashion in these large polyatomic molecules than in the small CHX3 ones as shown in the cyclohexene This should lead to caution in the assignment of multiplets of bands arising from conformers unless this assignment is established by isotope labeling. Indeed, selective deuteriation allows one to simplify the problem and to follow the evolution of one or two vibrators “chemically” decoupled from the others. It also provides a means to determine some of the mechanisms for vibrational deactivation of large molecules as it localizes most of the vibrational modes involved in the interacting combination states without strongly altering the molecular properties. However, it is not a perfect tool because changes in molecular symmetry and emergence of new coupling mechanisms in molecules containing H and D atoms bonded to the same carbon atom may complicate the vibrational mode mixing, as stressed by Baggott et al. in CHDC12I0 and CHD2C1.16 For cyclopentene, selective deuteration has allowed the CH stretching transitions to be assigned as belonging to a specific bond in the fundamental and in the two first overtone spectra of monohydrogenated -3-hl and -441 cyclopentenes. These spectra are not perturbed by Fermi resonance and reflect the coupling of the CH stretching vibration with the puckering m o t i ~ n . ~But ~ ,the ~ ~strong perturbation observed in the spectral patterns of the higher overtones, especially the third one (Av = 4), indicates the occurrence of additional coupling with lowenergy combination states by Fermi resonance.38 In this paper, the two principal couplings likely to affect the CH stretching vibration overtones of cyclopentene, coupling with the fast puckering motion and coupling with the low-energy combination states by Fermi resonance, are examined and 0 1995 American Chemical Society
Rodin-Bercion et al.
3006 J. Phys. Chem., Vol. 99, No. 10, 1995 modeled. Both couplings and vibration-rotation structure are explicitly taken into account in the theoretical reconstruction of the spectra. The experimental overtone spectra of monohydrogenated -3-hl cyclopentene are then presented. They are analyzed and discussed in the framework of the previously developed theoretical calculations.
where the Wilson matrix g(rJ is a function of curvilinearinternal coordinates and atomic masses.46 The most anharmonic vibrations, the CH or CD stretchings, must be described by anharmonic potentials like the Morse potential energy function47,48which depend on the molecular conformation, Le., on x. The lower frequency vibrations are better described by harmonic normal modes Q,:
Experimental Section Monohydrogenated cyclopentene -3-hl (3-HCsD7) was synthesized by the organotin route according to the procedure described in ref 40. Isotopic purity was higher than 96%. The product was degassed by freeze-pump-thaw method and transferred under vacuum into the cells to avoid contamination. The room-temperature vapor-phase spectra were obtained by using two different techniques. The near infrared spectra (Av = 1-4) were recorded by standard absorption spectroscopy on a Nicolet 740 FTIR spectrometer (resolution 1 cm-I) between 3000 and 8600 cm-' and a BioRad FTS-60A spectrometer (resolution 2 cm-I) between 8600 and 11500 cm-'. The sample was contained in a 10 cm path length gas cell with CaF2 windows for the Av = 2 overtone and in a 7 m path length Infrared Analysis, Inc. cell for the other spectra. The visible spectra (Av = 5-7) were recorded with the intracavity photoacoustic spectrometerwhich has been described in detail e l ~ e w h e r e . ~A~Coherent Innova 70 Ar+ Laser was used to pump a CR599 dye laser fitted with high reflectance optics for the following dyes: Pyridine 2 (Av = 5), DCM (Av = 6), and Rhodamine 110 (Av = 7). A stainless steel photoacoustic cell was placed inside the dye laser cavity. The spectra were obtained by discrete scanning of the tunable laser. The wavenumber difference between successive data points was typically of 0.7 cm-' which is less than the laser resolution (1 cm-I). Each point record was accumulated 800 times. At each wavelength, the signal from the electret microphone (WM064 National Panasonic) placed inside the intracavity cell was amplified and processed by an EG&G Model 5207 lock-in amplifier. The laser intracavity power was monitored by a photodiode by means of a reflection from one of the cell windows, and amplified by an EG&G Model 5101 lock-in amplifier. The two signals (microphone and diode) were sent to a PC 286 personal computer via an VO device cart. The absorption spectra were proportional to the ratio of the two signals corrected for the photodiode response. The tunable laser wavelength was calibrated every 200 steps with a PHO monochromator. The absolute wavenumber was thus determined to within &2 cm-'.
Theoretical Approach (A) Coupling of the CH Bond Stretching Vibration and the Large-Amplitude Motion. The theoretical approach used to analyze the v(CH) profiles has already been described in paper 1 (ref 45 and references therein) and will be only retraced briefly here to stress the important points in the study of the high overtones. Therefore, the ring-puckering motion may be described by an Hamiltonian H I (eq 1 in paper 1) with an intrinsic potential V(x) depending on the ring-puckering coordinate x. The vibrational Hamiltonian for polyatomic molecules can be written in terms of curvilinear internal coordinates ri and their conjugate momenta pr,:
where Hintecdescribes the interactions between the internal coordinates ri and the interactions between ri and Qj. The coupling of the vibrational and the large-amplitude motions is modeled by the total Hamiltonian HT = H I H2 which is solved in the adiabatic appr~ximation.~~
+
H2(x,ri,Qj)y(x,rj,Qj>= 44 q(x,ri,Qj)
{H,(4 + @)I W x ) = E W x )
(3)
In this second equation, the vibrational energy e(x) acts as an additional potential for the ring-puckering motion. Thus, even in the ground vibrational state, the effective potential Vefdx,O)of the ring-puckering motion depends on the molecular zero point vibrational energy (paper 1). When the CH bond stretching is excited with v quanta of energy, the effective potential of the ring-puckering motion is increased by the corresponding vibrational part: VefdW)= V,&,O>
+ w,(x)v - x ( x ) v(v + 1)
(4)
x
where wo and are the harmonic frequency and the anharmonicity of the excited bond stretch which derive directly from the a and D parameters of the Morse function.47 The form of wo(x) is calculated from the ab initio optimization of the geomet@ and ~ ( x can ) be deduced as explained in ref 45. The vibrational transitions between the two ring-puckering motion potentials V,fdx,O) and Vefdx,v) are calculated as explained in paper l.45 Their intensities are calculated from the following r e l a t i ~ n s h i p : ~ ~ ~lO,n)-lv.n,)
P(J
J
Q)*"(lJ) ~*",,(X) &JX)
qo(rJ) Y O n ( X )
drI2 (5)
where P i s the Boltzmann factor, exp[-(Eon -Ew)/kTJ, and IO,n) and Iv,n') are, respectively the nth and n'th ring-puckering levels in the ground and excited states of CH bond stretching. For the higher overtones, the dipole moment function ,u can no more be developed only to the first order in the vibrational coordinate r. But, as the spectrum of each CH bond stretching overtone is calculated independently, we do not need to know the exact form of the dipole moment. Nevertheless, the integrals in x and in r of eq 5 can still be separated if, as in paper some assumptions are made: (i) the magnitude of the dipole moment transition is independent of conformation which yields an excellent fit to the observed Av = 1 and 2 infrared spectra.45 For the higher overtones, recent calculation^^^ performed on the intensities of the transjtions of cyclohexane, where a conformational dependence of the axial or equatorial transition intensities has been measured,51show that the intensity ratio is not strongly modified from one overtone to another. Thus, the assumption of no conformational dependence of the magni-
Ring Puckering and CH Stretching Spectra tude of the dipole moment transition also seems reasonable for the higher overtones. (ii) The bond dipole approximation is used in calculating the transition intensities. p is supposed to be colinear to the CH bond and we have used the components ,UX(X), p&), and PAX)along the molecular moments of inertia determined by the ab initio calculation^.^^ In a monohydrogenated molecule, this approximation only can be verified by simulating the vapour phase infrared contours as done in paper 145where it has given satisfactory results. In the higher overtones, this approximation can no more be checked since the band shapes are progressively lost. Nevertheless, to model the spectra, we have convoluted the theoretical vibrationrotation infrared spectra by a Lorentzian whose half-width is more and more important in the higher overtones. (B) Couplings of the CH Bond Stretching Overtones with the Low-Energy States by Fermi Resonances. Fermi resonances between CH bond stretching and bending modes are very common in the high vibrational states of organic molecule^.^-^^ Whereas the existence of such Fermi resonances has been known for a long time,5's52only much more recently has this been analyzed systematically and recognized as one of the major pathways of intramolecular energy flow in organic molecule^.^-^^ In particular, Quack and co-workers have thoroughly studied the high vibrational states of CHX3 molecules and compared effective Hamiltonians formulated in different coordinates (rectilinear or curvilinear, internal or normal) with ab initio calculations. For the molecules they studied, the best choice was a treatment based on rectilinear normal coordinates using a polar coordinate representation of the potential.Il The most serious limitations of the curvilinear internal coordinates models seemed to be the neglect of coupling to the motions of the heavy atom CX3 frame which is important in the case of relatively small molecules like CHX3. However, the advantage of the treatment in curvilinear coordinates is that it allows a selection of the modes which anharmonically couple with the CH bond stretching overtones. In large molecules like cyclopentene, the number of modes which could be involved in Fermi resonances with the CH bond stretching overtones is important and we have chosen the curvilinear representation to model the experimental spectra with the smallest possible number of parameters. This treatment is based on an idea of Sibert et al.,53 who proposed that the Fermi resonance problem be formulated in curvilinear, internal coordinates, with the hope that, in this representation, the Fermi resonance coupling constants might be deduced from the G matrix alone. In reality, for most of the molecules studied, couplings in the potential also have to be introduced to satisfactorily reproduce the spectra.54 Thus, the Fermi resonance couplings are deduced from the most important anharmonic terms of the Taylor expansion of the kinetic matrix and from their corresponding potential part. In cyclopentene -3-hl,as in c y ~ l o h e x e n efour , ~ ~ kinetic terms lead to couplings larger than 10 cm-I. They involve the first and second derivatives of the HCD or HCC deformation mode G matrix elements with respect to the CH bond stretching and lead to coupling terms between lv,j,n) and Iv-ljf2,n) states, where v, j , and n are respectively the quantum numbers of CH bond stretching, deformation mode, and ring-puckeringmotions. Fermi resonances also occur when there is a matching of the frequencies. For this reason, only modes with frequencies lying between 1450 and 1100 cm-' can be involved in Fermi resonances with CH bond stretching overtones up to Av = 7. In cyclopentene -3-hl, the frequencies of five to six modes are in this range (Table 4 of ref 45). Fortunately, because of the partial deuteration of the molecule, the modes corresponding to the CHD methylenic group are localized and their assignment
J. Phys. Chem., Vol. 99, No. 10, 1995 3001 can roughly be made with symmetry coordinates. The first two modes are respectively the CHD deformation (at 1305 cm-I) and the wagging (at 1255 cm-I). There are also two ring modes at 1180 and 1145 cm-' and two CD2 bendings at 1105 and 1090 cm-I. The first bending mode contains a small part of HCC deformation. Thus, in the curvilinear approach, only three modes are strongly anharmonically coupled to the CH bond stretching overtones, the two modes at 1305 and 1255 cm-l and, to a lesser extent, the CD2 bending at 1105 cm-I. In a first approach, to simplify the modeling of the experimental spectra, we have considered only the most important modes, that is to say the CHD bending and the wagging. We have also discarded the weak interactions between the CH or CD bond stretchings of different methylenes. Thus, we have restricted our attention to the CHD chromophore and the HCC angles. To model the Fermi resonance patterns, we have restricted the vibrational Hamiltonian of relation (3) to the CH and CD bond stretching, and HCD and HCC deformation modes and developed it up to the second order retaining only the most important terms. The effective spectroscopic Hamiltonian is the sum of three terms:39
H2 = Zf
+ HI + H2
(6)
In the zero-order term, the CH or CD bond stretchings are considered as weakly coupled Morse oscillators and the deformation modes are considered as weakly anharmonic oscillators.
In this Hamiltonian, the local CH and CD bond stretching modes are weakly coupled via the kinetic and potential matrices. 6 is the normal HCD bending mode and w is the normal HCC wagging mode. Because of the partial deuteration, they are quasi-pure symmetry coordinates. 5
5
with el = HCD, &,3 = HCC, and t?4,5= DCC. In these relationships, (Lei)-' are the familiar L-' matrix elements which give the dependence of the normal modes in internal coordinates. As already mentioned, the coupling terms which describe the Fermi resonances arise from a Taylor series expansion of the Wilson G matrix elements in the displacementcoordinates about the equilibrium configuration and the corresponding potential energy terms.54 The fist-order term of the Hamiltonian corresponding to the bending 6 or to the wagging w modes
5
2
determines the Fermi resonance couplings Ard,,(x).
Rodin-Bercion et al.
3008 J. Phys. Chem., Vol. 99, No. 10, 1995 The second-order term
determines the crossed anharmonicities x,d,w. One has to notice that, for each CH or CD bond stretching, only three derivatives of the G matrix elements are different from zero:
(%),
In this relationship, a and k are Morse parameters: k = wdx. They evidently depend on x and on the v(CH) transition. There are two kinds of off-diagonal couplings. The first accounts for the interaction of the CH and CD oscillators in terms of an interbond coupling parameter related to the potential fl2 and kinetic coupling matrix elements. It is relevant only in the higher overtones.10,16The Fermi resonance is described by a second type of off-diagonal element, which is deduced from the first-order Hamiltonian HI.
for the CH bond stretching and
(%)o
for the CD bond stretching. To calculate the energy, the effective Hamiltonian is expanded in a basis set whose functions are products of Morse oscillators functions for CH or CD bond stretchings and harmonic oscillators wavefunctions for bending and wagging modes. The energy flow which takes place via the Fermi resonance is rapid or ( 5 100 fs)55compared to the ring-puckering motion (1300 f ~ ) . ~ ~ Furthermore, for the overtones, the effective potential barrier to puckering becomes larger (up to 504 cm-' at Av = 7) leading to a slower motion regime. Thus, we can separate the two phenomena and suppose that the Hamiltonian expansion can be done for each transition between the two ring-puckering potentials which has a noticeable intensity. Thus, each basis function may be written as IV) = (VCH, V'CD, v6, vw, nn,), where VCH, V'CD, vd, and vw are respectively the quantum numbers in To model the experimental spectra, the Schrodinger equation CH and CD bond stretching, bending, and wagging motions. for the vth manifold expressed in matrix form Itn' indicates the transition between the nth and n'th ringpuckering levels in the ground and excited states of v(CH). C H j j c i ,= hcwncjn When the zero-point energy contribution is subtracted, the 1 diagonal elements of the Hamiltonian expansion lead to the unperturbed energies: is solved by diagonalization of the Hamiltonian matrix H. The resulting eigenvalues w n are compared to the observed band 1 positions. The fitting procedure of the effective parameters -((VCH,VCD,V,,V,,~,,IHO hc + H' H ~ I V ~ ~ , V ~ ~ , V ~ , V , , =~ , , ) ) displayed in Table 3 also takes into account the mode intensities 2 (wIJCH(nn') - XcH(nn')>vcH - XcH(nn')vCH + (uC€D(nn') inside each polyad. If cln is the eigenvector of the transition 2 with wavenumber ancorresponding to the (v,O,O,m,,( state, the XcD(nn'))vcD - XCD(nn')vCD + - X d V d - XSv62 + intensity of that transition is proportional to 2
+
(ow
-X I Y )~ ~X w v w - XrcH6(nnt)VCHV6 - XrcD6(nn')VCDVd x'CKw (nn,>vw - X ~ ~ ~ ~ ( ~ , ' ) V C D(11) V,
x
The harmonic wavenumbers wo and anharmonicities of the CH or CD bond stretchings depend on the ring-puckering transitions. The ab-initio calculations indicate a small dependence of wg and wwin the ring-puckering coordinate x but, for simplicity, we have assumed these parameters to be constant. The cross anharmonicities are defined by the relationship
or
-
The intensity of the unperturbed (0,rnl (v,m'l transition is calculated according to the relationship 5. We have supposed that all the band intensities inside each polyad come from the CH bond stretching overtones. In the fitting of the experimental spectra, we have also taken into account the transition band shapes as described in paper 145 and in the previous paragraph. (C) Modeling of the Spectra. The procedure we have applied to model the spectra can be briefly summarized as follows. The effective potentials of the ring-puckering motion corresponding to the overtones of CH bond stretching are calculated
J. Phys. Chem., Vol. 99, No. 10, 1995 3009
Ring Puckering and CH Stretching Spectra
Figure 1. Definition of the ring-puckering coordinate x when the molecule is in its bent equilibrium conformation. m
-
I
I
N
11200
-
11000
10800
I
10600
10400
cm-1
m
Figure 3. Observed and calculated spectra of the third CH stretching overtone (Av = 4). The observed spectrum (top full line) was obtained by FTIR with a 7 m path length cell and a pressure of 100 Torr. The bottom full line represents the calculated spectrum obtained by summing all the CH stretching transitions between the two effective potentials of ring-puckering (see text) and the circle dots represent the calculated profile resulting of Fermi resonances perturbation on this latter spectrum.
9
U Y
za
$6 0
a mm
a
m
N
i 8600
I
8435
8270
8105
7940
cm-1 Figure 2. Observed and calculated spectra of the second CH stretching overtone (Av = 3). The observed spectrum (top full line) was obtained by FTIR with a 21 m path length cell and a pressure of 100 Torr. The bottom full line represents the calculated spectrum obtained by summing all the CH stretching transitions between the two effective potentials of ring-puckering (see text) and the circle dots represent the calculated profile resulting of Fermi resonances perturbation on this latter spectrum.
from relationship 4 with the variations of the harmonic frequencies wo and anharmonicities determined by the abinitio cal~ulations.4~ Because of its vibrational part, the effective potential becomes more and more asymmetric when the vibrational energy increases. The calculated overtone spectra, which are not perturbed by Fermi resonances, roughly exhibit two main absorptions corresponding to the axial and equatorial CH positions. Hence, we have completed a first calculation of the perturbed spectra with only the two principal axial and equatorial transitions in order to determine the coupling parameters and to refine the values of the hannonic frequencies wo and of the anharmonicities of the CH bond stretches for the two positions.
x
x
I
13730
I
13540
13350
13160
12970
12780
cm- 1 Figure 4. Observed and calculated spectra of the fourth CH stretching overtone (Av = 5). The observed spectrum (top full line) was obtained with the photoacoustic apparatus described in the text and a 11 cm path length cell. The pressure of the sample was 300 Torr. The bottom full line represents the calculated spectrum obtained by summing all the CH stretching transitions between the two effective potentials of ring-puckering (see text) and the circle dots represent the calculated profile resulting of Fermi resonances perturbation on this latter spectrum.
As stressed in ref 45, these two latter parameters are important to refine the vibrational part of the effective potential. The final complete calculations are performed by including all the transitions between the two refined effective potentials. The results of these calculations are displayed in Figures 2-6.
Rodin-Bercion et al.
3010 J. Phys. Chem., Vol. 99, No. IO, 1995 VtXl
wi'
I
A
Y
'B
I H. 3
..
J
. .......
1.1
16060
15783
15505
15228
14950
cm-1
Figure 5. (Left) Calculated effective potrentials of the ring-puckering motion in the ground state and in the Av = 6 excited state of CH bond stretching. The most intense transitions are indicated by arrows and the squared wave functions of the first puckering levels are drawn for each vibrational state to show the localisation in each potential well. (Right) Observed and calculated spectra of the fifth CH stretching overtone (Av = 6). The observed spectrum (top full line) was obtained with the photoacoustic apparatus described in the text and a 11 cm path length cell. The pressure of the sample was 300 Torr. The bottom full line represents the calculated spectrum obtained by summing all the CH stretching transitions between the two effective potentials of ring-puckering (see text) and the circle dots represent the calculated profile resulting of Fermi resonances perturbation on this latter spectrum.
/
-
\ I
I
18160
17865
17570
Coupling with the Ring-Puckering Motion. Because of the difference of the axial and equatorial bond stretch wavenumbers, the effective potential of the ring-puckering motion becomes more and more asymmetric and the height of the barrier increases with increasing CH excitation. As illustrated in Figure 5 for the fifth overtone of CH bond stretching, a strong localization in each potential well of the wave functions corresponding to the levels labeled 0 and 1 in the ground state and to the levels labeled 0 and 3 in the fifth excited CH stretching state leads to the two most intense transitions l0,O) 16,O) and l O , l > 16,3>. These transitions correspond to the CH bond in the axial and equatorial positions, respectively. The other transitions occur between ring-puckering levels with less localized wave functions but, due to the strong asymmetry of the potential of the excited vibrational state, they also can be assigned to nearly axial or equatorial conformations. Only the weak )0,2) 16,2) and 10,4) 16,4) transitions correspond to the planar conformation. The most intense transitions between the two effective potentials (at Av = 0 and Av = 6) are indicated by arrows and with a bar diagram in Figure 5. Thus, the calculated overtone spectra, which are not perturbed by Fermi resonances, roughly exhibit two main absorptions corresponding to the axial and equatorial CH positions. This localization phenomenon is very clearly observed in comparing the spectra of the fundamental and of the two first overtones (Figures 3a, 4a, and 4b of ref 38) where the Fermi resonance effect is weak and principally shifts the whole spectrum toward high frequency. In the Av = 1 and 2 spectra, an important intermediate band due to the transitions between levels with an energy higher than the potential barrier is ~ b s e r v e d . ~At ~ ~Av~ *= 3 (Figure 2), the intensity of the central band decreases. The calculations show that this localization
17275
1
16980
c m -1
Figure 6. Observed and calculated spectra of the sixth CH stretching overtone (Av = 7). The observed spectrum (top full line) was obtained with the photoacoustic apparatus described in the text and a 11 cm path length cell. The pressure of the sample was 250 Torr. The bottom full line represents the calculated spectrum obtained by summing all the CH stretching transitions between the two effective potentials of ring-puckering (see text) and the circle dots represent the calculated profile resulting of Fermi resonances perturbation on this latter spectrum.
Discussion The aim of this study is to contribute to a detailed understanding of vibrational redistribution in the excited vibrational states of cyclopentene-3-hl. We have thus investigated the anharmonic couplings between the CH stretching vibrations and the two types of low-energy modes, the ring-puckering motion, and the HCD or HCC deformation modes, and tried to quantify their respective contributions.
-
-
-
J. Phys. Chem., Vol. 99, No. 10, 1995 3011
Ring Puckering and CH Stretching Spectra
TABLE 1: Observed and Calculated Fundamental Vibrations Involved in the Modelization of the Spectraa v(obs) (k0.5 cm-') fundamental vibrations IR
Raman
v(ca1c) (cm-')
1305 1255 2885.5
1305 1256.0 2885.5 2893.0 2907.0 2909.5 2924.5 2933.0
1304 1253 2885.5
2933.0
2933.1
eigenvectors
0.99 (l0,O) 0.99 (10.2) 0.99 (10,4) 0.99 (lad 0.99 (10,3) 0.99 (l0,l)
----
I1,O)) 11,2)) 11,4)) I l d (44)) 11.3)) 11.1))
assignment LHCD deformation (6) LHCC deformation (w) axial CH stretching axial CH stretching planar CH stretching planar CH stretchings equatorial CH stretching equatorial CH stretching
The eigenvectors are indicated by their quantum numbers in CH stretching and ring-puckering vibrations.
TABLE 2: Observed and Calculated CH Stretching Excited State@ ~~
excited vibrational state polyad
Av = 1.5
v(obs) (cm-')
v(c1ac) (cm-])
eigenvector
assignment
4177
4177
0.99 (l0,O) Il,O)+6) 0.99(10,n) Il,n)+6) (n)4) 0.99 (10.1)- Il,l)+S) 0.97(/0,0) 12,O)) 0.98(IO,n) (44) 0.98 (10.1) 12,l)) 0.95 (l0,O) 12,0)+6) 0.97 (l0,l) I2,1)+6) 0.31 (l0,O) 13,O)) 0.36 (10.0) 13,O)) 0.28 (l0,O) 13,O)) 0.87 (10.0) 13,O)) l0,n) 13,n) ( 4 4 ) 0.92 (I0,l) 13,2)) 0.42 (l0,O) 13,0)+6) 0.37 (10,O) 13,O)fd) 0.37 (l0,l) 13,2)+6) 0.81 (l0,O) /3,0)+6) 0.27 (l0,l) 13,2+6) 0.88 (l0,l) /3,2)+6) 0.29 (l0,O) I4,O)) 0.69 (l0,O) I4,O)) 0.47 (l0,O) KO)) 0.41 (l0,O) 14,O)) 0.61 (l0,l) 142)) 0.34 (l0,l) /4,2)) 0.68 (l0,l) 142)) 0.20 (l0,O) l5,O)) 0.36 (l0,O) I5,O)) 0.24 (l0,O) l5,O)) 0.52 (l0,O) l5,O)) 0.37 (l0,O) l5,O)) 0.39 (l0,O) l5,O)) 0.31 (l0,O) l5,O)) 0.40 (l0,l) 15,3)) 0.49 (l0,l) l5,3)) 0.61 (l0,l) 15.3)) 0.26 (l0,l) 15,3)) 0.37 (l0,O) 16,O)) 0.57 (l0,O) 16,O)) 0.39 (l0,O) 16,O)) 0.26 (l0,O) I6,O)) 0.39 (l0,l) 16,3)) 0.62 (l0,l) 16,3)) 0.39 (I0,l) 16,3)) 0.26 (I0,l) 16,3)) 0.21 (I0,l) /6,3)) 0.58 (l0,O) 17,O)) 0.41 (10.1) 17,4)) 0.35 (I0,l) 174) 0.44 (IOJ) 174) 0.33 (l0,l) 17.4))
axial combination planar combination equatorial combination axial first overtone planar first overtone equatorial 1st overtone axial combination equatorial combination axial combination axial combination axial combination axial second overtone planar second overtone equatorial 2d overtone axial combination axial combination equatorial combination axial combination equatorial combination equatorial combination axial combination axial third overtone axial combination axial combination equatorial 3d overtone equatorial combination equatorial 3d overtone axial combination axial combination axial combination axial fourth overtone axial combination axial combination axial combination equatorial combination equatorial combination equatorial 4th overtone equatorial combination axial combination axial fifth overtone axial combination axial combination equatorial combination equatorial 5th overtone equatorial combination equatorial combination equatorial combination axial sixth overtone equatorial combination equatorial combination equatorial combination equatorial combination
4201 Av=2
4224 5643
4223 5643
5692,5 Av = 2,5 (512)
5740 6927 7022
5743 6926 7022
Av=3
8098 8210
8102 8181 8207
8284
8283
8360 Av = 3.5 (712)
8430
9549
8432
9380 9422 9483 9564
9522 9690
Av=4
Av = 5
9705
10617 10700
10708
10860
10955
10782 10855 10874 10944
11022
11025
12900
12870 12984 13013
13058
13057
13107 13214
13107 13131 13206 13228
13326 13386
13322 13390
13530
13579 15190
15270
15255
Av = 6
15338 15363 15522
Av = 7
15610
15618
15690 15840
15683 15748 15860
17325
17325
17698 17720 17780
17759
17836
---
---- ---------------------
As for Table 1, the quantum numbers of the eigenvectors correspond respectively to the CH bond stretching and ring-puckering transitions. The bold wavenumbers indicate the most intense absorptions. In the assignment, the modes which are too mixed are indicated as combinations. In the sixth overtone, the Fermi resonance coupling gives rise to a great number of modes; none of them has a sufficiently important eigenvector in equatorial CH stretching to be assigned as equatorial sixth overtone. a
Rodin-Bercion et al.
3012 J, Phys. Chem., Vol. 99, No. IO, 1995
TABLE 3: Effective Parameters Used in the Modelization of the Fermi Resodance Perturbed Spectra“ local parameters for CH stretching modes (cm-’) effective coupling between CH stretches (mdynlA)
xa= 66.0 f 0.5 ze= 65.0 f 0.5
w a= 3011.O f 0.5 we= 3061.5 f 0.5
fae
= 0.05 f 0.01
Low-Frequency Mode Parameters (cm-’) h a d = 16 f 2 Area = 16 f 2 xr,6 = 14 -+ 1 XreS = 15 i 1 Lraw = 20 f 3 Lrew = 24 -+ 3 xr,w = 10 f 1 p e w = 10 f 1 w,, = 1262 f 2 X*=5fl Xrew = 12 -+ 3 X’rew = 14 f 5 Zraw = 10 f 3 x’w = 5 -+ 1 x’raw = 5 f 5 w’,+ = 1115 f 2 The third line of the low-frequencymode parameters gives the values cI f the parameters of the third mode used in the calculation of the spectra of Figure 7 only. 06
= 1316.5 iz 2.0
X6=lf1
(1
r 18160
1
17865
T
17570
17175
16480
cm- 1
I
16060
I
15783
I
I
15505
15228
I
14950
cm- 1 Figure 7. Observed and calculated spectra of the fifth and sixth CH stretching overtones when the combinations of the third mode at 1105 cm-’ are added in the calculations. The other spectra are not modified.
goes on at the third overtone (Figure 3). For higher energies, some weak “planar” transitions seem to appear again (Figures 5 and 6). Thus, the theoretical analysis shows that the coupling of the CH stretching with the ring-puckering motion contributes less and less to the redistribution of the vibrational energy with increasing CH excitation. For all the overtones, the most stable conformer is the one with the CH bond in the axial position. It corresponds to the l0,O) Iv,O) transition between two puckering levels with the wave function strongly localized in the deeper well. The other, more intense, transition is situated in the second potential well and occurs when the CH bond is in the equatorial position. The relative intensities of the two transitions depend essentially on the first coefficient VI of the effective potential for the ring-puckering motion which determines the position of the maximum of the potential.45 The value determined by the ab-initio calculations leads to transitions with more or less equal intensities from Av = 3 to 5. At higher energies, the l0,l) 16,3) and l0,l) 17,4) transitions become slightly less intense than the axial ones, but due to the weak satellite transitions the global intensities of the absorptions
-
-
-
corresponding to the two conformers become almost equal. This is in good agreement with the experimental spectra. Modification of the Band Shapes. Three types of infrared vibration-rotation profiles characterized by the value of the separation of the P-R wings and by the intensity of the Q branch can be distinguished for each dipole moment component.45 To reconstruct the spectra, the theoretical vibrationrotation profiles are convoluted with the spectral resolution (typically 1-2 cm-I). However, even at Av = 1, a broader profile must be used for this c o n v ~ l u t i o n . ~ ~ As the energy increases, the analysis of the spectra shows that the vibration-rotation structure, still clearly observed at Av = 1 and 2,45 disappears and that the bands become Lorentzian-like. Indeed, when the vibrational molecular energy increases, the density of states weakly bonded to the CH bond stretching becomes more and more important, leading to a broadening of the profiles. To model this phenomenon, we have convoluted the vibration-rotation theoretical profiles by a Lorentzian whose half-width depends on the excited state (fwhh = 2.5, 10, 14, 25,45, 60, 80 cm-’ from Av = 1 to 7). As this width becomes larger than the PR splitting, the characteristic vibration-rotation band shapes are progressively lost, until at the higher energies all the transitions show similar patterns which can be fitted with Lorentzian band shapes. Coupling with Deformation Mode Combinations by Fermi Resonances. As displayed in Figures 2-6, strong Fermi resonances, which completely modify the spectra for energies higher than 9.000 cm-I occur in the excited states of cyclopentene-3-hl. This phenomenon leads to a large redistribution of the vibrational energy. To model these couplings, all the possible combinations of the relevant low-energy states must be included in the calculations. In particular, the combinations which contain both bending and wagging modes have to be taken into account. These combinations have no direct Fermi resonance coupling with the CH stretching overtones because the two low energy modes are orthogonal in the 8I1t9z, 03 space but they couple indirectly via other modes. Calculationswithout these combinations lead to slightly different effective parameter~.~~ The results of our calculationsfor the two axial and equatorial positions are displayed in the Tables 1 and 2. The effective parameters we have used for the CH bond vibrations are indicated in the two first lines of Table 3. In this table, we have given the total Fermi resonance couplings Arb and A, instead of the potential parameters Frdand F , because a small variation of the Lei can lead to significant variations of the anharmonic potential parameters. In the same way, only the values of x r d and xrware given in Table 3. The values of the cross anharmonicities involving the bending motion can be deduced from the spectra of the 312, 512, and 712 polyads. We cannot measure the corresponding spectra of combinations with wagging motions. The effective parameters of the CD vibrations are not well determined in the calculations of the CH stretching overtones. Contrary to what is observed in selectively deuter-
J. Phys. Chem., Vol. 99, No. IO, 1995 3013
Ring Puckering and CH Stretching Spectra ated dichloromethane, the interactions between the CH and the CD bond are not efficient.10,’6 As displayed in Figures 2-6, the modeling of the Fermi resonances with only two low-energy modes gives satisfactory results until the fifth overtone of CH bond stretching. At Av = 7, some discrepancy between the calculated and observed frequencies of the equatorial overtone is observed. The relative intensities of the two observed transitions must be considered with some caution at this energy. We had some trouble with the baseline and the relative intensities were reproducible only within 50%. The discrepancy between the calculated and the observed frequencies of the equatorial overtone is not well understood. The addition of the third mode at 1105 cm-’ which begins to enter in resonances at these high energies leads to only marginal improvement in the fit of the fifth and the sixth overtone spectra, as shown in Figure 7 . At these energies, the number of states which couple directly or indirectly to the CH bond stretching overtone is very important. Fermi resonances essentially lead to a broadening of the absorptions. The modifications of the frequencies are not important.
Conclusion We have measured the vapor-phase overtone spectra of cyclopentene-3-h, in the regions corresponding to AVCH = 3-7. The isolation of the CH chromophore in this isotopomer provides a window to look at the dominant anharmonic interactions between the CH stretching and the other lowfrequency vibrations up to high vibrational energies. The broadened structure of the spectra is for the most part due to the competition between two phenomena: localization of the energy in the potential wells of the ring-puckering effective potential and large energy flow through Fermi resonances with combination states involving HCD or HCC deformation modes. The vibrational part of the effective ring-puckering motion potential is shown to be at the origin of an increase in the barrier of the effective ring-puckering potential with increasing CH stretching energy and of a strong asymmetry of the two potential wells. This leads to a localization of the CH stretching transitions in each potential well. Despite this asymmetry, the respective intensities of the axial and equatorial transitions are approximately equal up to the Av = 7 overtone. The second coupling phenomenon, which is more rapid than the coupling with the ring-puckering motion, can be modeled independently. We have shown that the spectra could be satisfactorily reproduced with a model including all the combinations of the CH bond stretching overtones with two lower energy modes only: the HCC and HCD deformation modes. The ring modes seem to have no strong anharmonic coupling with the CH stretching vibrations and the large energy flow which is evidenced at these energies in these types of molecules occurs principally through a small number of the isoenergetic states. The origin of the additional broadening of the band shapes may come from the harmonic couplings between the combination modes involved in the Fermi resonances and isoenergetic combinations of other modes of the molecule.
Acknowledgment. We are grateful to J. C. Cornut and J. J. Martin for assistance in experiments. L.L. and D.C. acknowledge support of this research by the “Region Aquitaine” through the award of equipment grants. References and Notes (1) Diibal, H. R.; Crim, F. F. J . Phys. Chem. 1985, 83, 3863. (2) Ticich, T. M.; Likar, M. D.; Diibal, H. R.; Butler, L. J.; Crim, F. F. J . Chem. Phys. 1987, 87, 5820. (3) Carpenter, J. E.; Weinhold, F. J. Phys. Chem. 1988, 92, 4295.
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