J. Phys. Chem. 1995, 99, 2996-3004
2996
Ring Puckering and CH Stretching Spectra. 1. Theoretical Study of Gaseous Monohydrogenated Cyclopentenes-3-hl and -4-hl C. Lapouge,f,*D. Cavagnat,*$+D. Gorse: and M. Pesquers Luboratoire de Spectroscopie MolCculaire et Cristalline (URAI24-CNRS) and Luboratoire de Physicochimie Theorique (URA503-CNRS), Universitk de Bordeaux I, 351 cours de la Libhation, 33405 Talence Cedex, France Received: May 16, 1994; In Final Form: October 4, I994@
Ab-initio calculations have been performed at the HF/6-31G**level to study the conformational dependence of the geometry parameters and of the vibrational frequencies of two hydrogeddeuterium isotopomers of cyclopentene (monohydrogenated - 3 4 1 and -441). Reasonable agreement with experimental data is found. It is shown that zero-point vibrational energy effects contribute to the empirically derived puckering inversion barrier and are responsible for the asymmetry of the two potential wells in the monohydrogenated compounds, in good agreement with the previous experimental determinations. The structure of the isolated CH stretching band in the infrared ( A v = 1 and 2) and in the isotropic Raman (Av = 1) spectra of gaseous monohydrogenated cyclopentenes is well reproduced by a theoretical calculation which emphasizes that the variation of the puckering potential energy function between the fundamental and the excited states of the CH stretching vibration is only due to the conformational dependence of the CH stretching energy. For the -341 compound, a linear correlation between the CH stretching and ab-initio CH bond length yields an excellent fit to the observed spectra. For the -441 compound, some modifications must be considered to get a correct fit of the experimental spectra.
Introduction Cyclopentene constitutes a prototype of nonrigid molecules interconverting via a puckering motion between two equivalent nonplanar ring structures. In this sense, it has become one of the most thoroughly studied examples of pseudo-four-memberedring molecules. l V 4 Investigations of infrared and electron diffraction,22and m i c r ~ w a v e ~spectra ~ - ~ ~of different isotopomers of cyclopentene and several mathematical a n a l ~ s e s ~ ~have - ~ O established a double-minimum puckering potential function of the form V(x) = V& V2x2, x being the puckering coordinate, with a barrier to planarity of some 230 cm-' and an equilibrium angle between the two dihedral planes of the puckering ring in the range of 22" to 26". Several theoretical studies have also been performed in order to calculate the equilibrium geometry and the banier to planarity of cy~lopentene.~'-~~ The most recent ones report a non-negligible part of vibrational origin in the puckering barrier.37a38 A vibrational contribution to the potential barrier has also been pointed out in the spectroscopic studies of gaseous monodeuterated (3- and 4-DCgH7)17J8and monohydrogenated cyclopentenes (3- and 4-HCsD7).19-21 The isotopic monosubstitution in the allylic positions is shown to induce an asymmetry not only in the kinetic energy function but also in the potential energy function which takes the commonly used form V(x) = V2x2 V3x3 V&,39-41 where the V1 term, which accounts for the fact that the planar conformation no longer corresponds to the potential maximum, is neglected. Two spectroscopically distinct conformers for each isotopomer are thus produced,1s-21 the conformer with a CH bond in the axial position being the most stable. The asymmetry of the ring-puckering potential is shown to result primarily from the difference in the zero-point
+
+
+
* Author to whom correspondence @
should be addressed. Laboratoire de Spectroscopie MolCculaire et Cristalline. Laboratoire de Physicochimie Th6orique. Abstract published in Advance ACS Abstracts, February 15, 1995
0022-365419512099-2996$09.00/0
vibrational energies of the two conformers, which is principally related to the CH and CD stretching vibrations of the CHD group. The v(CH) stretching features in the fundamental and in the two first excited vibrational states are described by a theoretical treatment which takes into account, in the adiabatic approximation, the coupling of the fast CH stretching vibration with the slow puckering motion. 18,20,21 A correct reproduction of the experimental spectra is obtained by estimating the CH stretching-inversion coupling from the fit of the fundamental v(CH) Raman spectra. The analysis of the potential in the two first excited v(CH) states shows that the potential asymmetry increases quasi linearly with the vibrational quantum number v, confirming its vibrational origin.20-21 The higher CH stretching overtone spectra (paper 2, ref 42) are also well described with this treatment, provided that perturbations due to Fermi resonance phenomena are simultaneously m0delized.4~ However, a correct intensity ratio of the axial and equatorial v(CH) bands in these highly excited vibrational states can no longer be obtained if the V1 term of the potential is neglected. Indeed, due to the increased asymmetry of the potential, a VI term equal to 0 leads practically to the vanishing of the v(CH) axial transition in contradiction with expenmental features (paper 242). An independent determination of the V1 and V3 terms is difficult from the only fit of the spectra as these terms affect not only the frequency splitting but also the relative intensities of the axial and equatorial Y (CH) bands. Such a fit would also take into account a possible difference of the intrinsic intensity of the axial and equatorial v(CH) bands as discussed in the case of c y ~ l o h e x a n e ~ - ~ ~ . The goal of this paper is to use an alternative method to determine the CH stretching-inversion coupling from the dependence of the v(CH) frequency on the puckering coordinate x in order to analyze the high overtone ~ p e c t r a . ~This ~ - ~could ~ be achieved from the precise linear correlation found between the observed frequencies of deuterium isolated CH stretching
0 1995 American Chemical Society
Ring Puckering and CH Stretching Spectra
J. Phys. Chem., Vol. 99, No. 10, 1995 2991
puckering coordinate. In a first approximation, the ringpuckering motion may be de~cribed'~-~l by a Hamiltonian of the form
E! hc = - $$)dx)($)
+ V(x)
where x is the unidimensional ring-puckering coordinate defined in Figure 5 , g(x) the inverse of the reduced mass of the motion and V(x) the potential function. g(x) is calculated by using the basic bisector model of Malloy2' where the motions of the ring atoms are assumed to be curvilinear and the HCH angle bisectors are constrained to be collinear with the CCC angle bisectors. No real improvement of the fit to the experimental spectra is obtained by using a more elaborate model where the CH2 rocking motion, the bond length, and angle variations during the puckering motion (calculated by ab-initio geometrical optimization) are introduced. The potential can be satisfactorily described by a fourth-order polynomial of the form V(x) = V1x v*x2 vp3 v d . The vibrational Hamiltonian for polyatomic molecules can be written in terms of curvilinear internal coordinates ri and their conjugate momenta pr,:
+
+
+
where the Wilson matrix g(ri) is a function of curvilinear internal coordinates and atomic masses.56 Figure 1. Experimental (top solid line) and calculated from Aw&) The coupling of the vibrational and the large-amplitude (eq 11) (dashed line) and from AY(x)(eq 12) (bottom solid line) Raman motions is modeled by the total Hamiltonian HT = HI H2 CH stretching spectra in gaseous cyclopentene-341. which is solved in the adiabatic approximation. The total wavefunction (PTis written as a product of two wave funcvibrations and the ab-initio calculated CH bond l e n g t h ~ . ~ OIt- ~ ~ tions: yl(ri,x) which describes the fast vibrational motions and has been shown that a variation of 1 x 8, of a CH bond depends slowly on x, and Y(x), which describes the much slower length corresponds to a variation of 10-18 cm-l of its stretching ring-puckering motion. Thus, the Schrodinger equation can be frequency. In this paper, the conformational variation of the separated into two equations, one which describes the vibrations CH bond lengths is calculated by ab-initio method and related of the molecule for each x value and the other which describes to the CH stretching change. The isolated CH stretching spectra the large-amplitude motion and depends on the vibrational of monohydrogenated cyclopentenes are then reconstructed from energy e(x). this estimation and compared to the experimental data.
+
H2(x,ri) q(x,ri)= e(x> q(x,ri)
Theoretical Review The Raman (Av = 1) and infrared (Av = 1 and 2) spectra of the monohydrogenated -3-hl and -4-hl cyclopentenes (Figures 1-4) are not perturbed by Fermi resonance and reflect the coupling of the CH stretching vibration with the puckering motion. They exhibit a triplet structure which has been interpreted in terms of transitions IO,n) Iv,n) between ringpuckering levels (n) from the ground to v(CH) excited-state potential. The two most intense bands of the triplet are assigned to transitions l0,O) Iv,O)and l0,l) \v,l). They correspond to the axial and equatorial v(CH) vibrations. The central features are assigned to transitions involving puckering levels with higher energy than the potential barrier.20,21 The theoretical approach used to analyze these v(CH) profiles is very similar to that used for the study of the internal rotation of the methyl group54355and developed to analyze the f i s t excited v(CH) states in cyclopentene.20,21It is briefly recalled and developed in order to interpret and reconstruct the higher overtone experimental infrared spectra. (a) Coupling of the CH Bond Stretching Vibration and the Large-Amplitude Motion. The basic idea of this theory is to suppose that the fast methylene group vibrations and particularly the v(CH) stretching vibration are coupled to the slow puckering motion of the ring and therefore depend on the
-
-
{H,(x)
+ e(x)) W X ) = Jww
(3)
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 of the ring-puckering motion depends on the molecular energy. (4)
-
i
'/&ei(x) is the zero-point vibrational energy of the 3N - 7 vibrations other than the puckering motion. 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:
+
V,fxx,v> = v,fXx,o> o i J ( 4 v - x(4 v(v+1)
x
(5)
w oand are the harmonic frequency and the anharmonicity of the CH bond stretch. The Schrodinger equations of the ring-puckering motion corresponding to the two vibrational levels Av = 0 and Av = v are diagonalized on a basis set of 80 harmonic oscillators. They give the ring-puckering energy levels and their cor-
Lapouge et al.
2998 J. Phys. Chem., Vol. 99, No. 10, 1995
A b
A
b a
a
0
0
b
P b
r
a n
I
n
E E
C
e
I
58%
3020
2980
29u)
2900
m4
1820
cm.1
5’190
5730
5670
5610
55%
Figure 2. Experimental (top solid line) and calculated from Av(x) (eq 12) (bottom solid line) infrared fundamental (Av = 1) and fist overtone (Av = 2) CH stretching spectra in gaseous cyclopentene-341 (px= 0.168 -I- 0 . 4 2 -I-0.68~~; py = 0.631 -I-2 . 0 ~- 2 . 0 ~ p~z;= 0.870 - 1 . 5 ~- 2.09 as determined by ab-initio calculations).
structed by adding the CH stretching transitions calculated between the energy levels of the two ring-puckering potentials Ve~x,v) and V e ~ x , 0separated ) by an arbitrary energy chosen so that the l0,O) Iv,O)transition wavenumber corresponds to the axial CH stretching wavenumber. The intensities of these transitions are calculated from the following relationship:
-
‘lo,n)-lv,n?
p(J
=
J Q)”(~J) v*vn*(x>A ( ~ J )
vO(~J)
von(x>
dr12 (6)
where P is the Boltzmann factor, exp[-(Eo,-Em)/kT], and l0,n) and Iv,n’)are respectively the nth and n’th ring-puckering levels in the ground and excited states of CH bond stretching. A(r,x) is the transition operator, i.e., the mean polarizability for the isotropic Raman spectrum and the dipole operator p for the infrared one. It is expanded around the equilibrium position r = 0. As the fiist-order term is dominant for Av = 1,45 eq 6 can be written
I
2x0
2960
I
2940
I
2920
em-1
Figure 3. Experimental (top solid line) and calculated from AWO(X) (eq 14) (chain line), from Aw’o(x) (eq 16) (dashed line), from Av(x) (eq 15) (bottom solid line) Raman CH stretching spectra in gaseous cyclopentene-441.
responding wave functions in the two CH stretching vibrational states. The CH bond stretching overtone spectra are recon-
Since q(r,x)depends slowly on x (adiabatic approximation), the two integrals of eq 7 can be separated. Since we are only interested in the relative intensities of the puckering fine structure components in calculating the CH stretching spectrum, the first integral in eq 7 can be considered as a constant as this factor will simply scale the entire spectrum. For the first overtone Av = 2, the fist- and second-order terms of the dipole moment expansion have generally equal contribution^.^^ In this work, as each overtone spectrum is analyzed independently, the exact form of the dipole moment is not examined and the same calculation is done for Av = 1 and Av = 2. Raman Spectrum. The isotropic v(CH) Raman spectrum is calculated by assigning a Lorentzian profile to each transition
J. Phys. Chem., Vol. 99, No. IO, 1995 2999
Ring Puckering and CH Stretching Spectra
A
b a 0
A
r
b a
a
b
n
0
C
r b
a
a n E
e
58s
5810
5no
51M
56W
J
5650 c m '
Figure 4. Experimental (top solid line) and calculated from Av(x) (eq 15) (bottom solid line) infrared fundamental (Av = 1) and fist overtone (Av = 2 ) spectra of the CH stretching in gaseous cyclopentene-4-hl (ux= 0; p , = 0.650 3 . 5 ~- 1.02; p x = 0.870 - 2 . 1 ~ 3 . 5 as ~ ~determined by ab-initio calculations).
+
.
Figure 5. (a, upper) Definition of the inversion coordinate x (A) and of the puckering angle f3 ("). (b, lower) Representation of the planar and puckered conformations of cyclopentene with the numbering of
the atoms. between the levels of the first excited v(CH) vibrational state and the ground-state ring-puckering potentials as done in the previous studies.20.21 The dependence of the polarizability derivative (da(x)ldr)o on the conformation of the CH bond and hence on the puckering coordinate x has been checked as done for cyclopentane4' or c y ~ l o h e x a n e .But, ~ ~ ~the ~ best fit of the experimental features is obtained when no conformational variation is assumed. Infrared Spectrum. The dipole moment derivative is supposed to be collinear to the CH bond and decomposed along the three molecular moments of inertia X,Y,Z. These three components can be expressed as a function of the ring-puckering coordinate x. The infrared transition intensity is the result of the combination of these three contributions. The dipole moment modulus derivative (dp(x)ldr)o is assumed to be independent of conformation. Indeed, polarizability and dipole moment derivatives present generally similar conformation dependence, as checked in cyclohexane where similar Raman and infrared conformational dependence of the axial and equatorial transition intensities has been e v i d e n ~ e d . ~ - ~ ~ Cyclopentene is very close to a symmetrical oblate top (ZA = ZB < IC) with the greatest principal moment of inertia (ZZ) perpendicular to the ring plane. To account for the effect of the overall rotation of the molecule, neglecting any interaction
between this motion and the ring puckering, each transition has been convoluted by the theoretical vibration-rotation profile corresponding to each component of the spectrum (A, B, or C type depending on whether the considered transition involves the px,p~y,or pz dipole component).20 To calculate the spectra, we have assigned to each transition its corresponding theoretical profile convoluted by a Lorentzian whose half-width has been adjusted for the considered overtone. Such a simulation allows in addition to check the validity of the bond dipole approximati~n.~~ The principal parameters used for the reconstruction of the CH stretching spectra (wo(x), ~ ( x ) PAX), , PAX), and pdx) variations) are determined from ab-initio calculations, the molecular geometry being optimized for different constrained puckering angle values (from 0" to 25"). (b) Method of Calculation. As shown in previous works, ab-initio calculations must be performed with high-level electron correlation treatments with extended basis sets to converge the predicted puckering inversion A double-zeta basis set, including polarization functions on the carbon atoms (DZ(d)) and electron correlation by perturbation methods MP2, predicts a value equal to 23.4" for the puckering angle and 159.9 cm-I for the puckering barrier (26" and 232 cm-I experimentally). In this work, as we are essentially interested in the accuracy of the calculated conformational variation of the CH bond lengths A), we have used a 6-31G** basis set including polarization functions on all the atoms. Geometry optimizations and frequency calculations were performed with the program Gaussian 88.58-60 Results (a) Molecular Orbital Calculations. The structural parameters resulting from the geometry optimization, leading to the puckered conformation, are listed in Table 1 (the numbering of the atoms and the inversion coordinate x are represented in Figure 5). They compare well with the experimental data.23,22 The calculated electronic part of the inversion barrier is 115.3 cm-' and the puckering angle 20.6".
Lapouge et al.
3000 J. Phys. Chem., Vol. 99, No. 10, 1995 TABLE 1: Calculated and Experimental Geometrical Parameters of Cyclopentene (Bond Length in di and Angle in Degrees) coordinate 6-31G** microwave" electron diffractionb ClC2
1.3188 1.5103 c3c4 1.5433 CiH6 1.0760 C3Hs 1.0864 C3H9 1.0892 C4H10 1.0853 W i i 1.0842 ClC2C3 112.23 c2c3c4 102.87 c3c4c5 105.58 CiC2H7 124.59 W3Hs 112.82 C2C3H9 110.48 C4C3Hs 112.25 C4C3H9 111.92 C3caio 109.28 C3C4Hll 112.69 CiC2C3C4 12.60 C ~ C ~ C ~ C S- 19.51 8' 20.60 energyd -193.99023
c2c3
1.350 1.518 1.540 1.085 1.095 1.095 1.095 1.095
1.341 1.519 1.544 1.096 1.096 1.096 1.096 1.096 111.2 103.0 104.0 121.8
106.30
109.50
22.30
28.8
Reference 23. Reference 22. 8 is the puckering angle. Energy in hartrees.
In order to study the conformational variation of the CH bond lengths, the geometry was optimized with the puckering angle constrained at different values: 0", 5", lo", 15", and 25" (Table 2). A detailed analysis of the variation of all the parameters shows the presence of additional motions to the puckering (Table 3). Three of them are significant: the first one concerns the ethylenic Hg and H7 atoms which move until 2.2" below the C5ClC2C3 plane (Figure 6 ) . The two others are the rocking motions of the methylenic (i) P(CH2) group (H atoms attached to the carbon number 4) in phase with the puckering with a magnitude of 7.0" and (ii) a(CH2) group (H atoms attached to the carbon number 3) out of phase with the puckering with a magnitude of only 1.5" (Figure 6). In order to evaluate the
electronic origin of these motions, we have optimized the geometry of the -4.4H2CsF6 derivative in the planar and 20.6" Duckered constrained conformations. As seen in Table 3. the a(CF2) and P(CH2) groups present the same rocking motions as in the perhydrogenated derivative with comparable magnitude. Repulsion between the adjacent CHz groups cannot be advanced to explain these phenomena. These rocking motions were empirically estimated by MalloyZ7and characterized by the parameters 6 = f 0 . 1 (ratio of P(rocking/puckering) angle) and y = -0.1 (ratio of a(rocking/puckering) angle) at the potential minimum. Our calculations give a very similar value for y (-0.06) but a higher 6 value (+0.28) close to that determined for cyclobutane (6 = +0.22).61,62 In each CH2 group, both CH bond lengths have the same value in the planar conformation (1.0876 8, for the C3Hs and C3H9 bond lengths (a(CH) bonds) and 1.0839 A for the C4H10 and bond lengths @(CH))), but their evolution differs during the puckering motion in the same CH2 group and also between the two groups (Figure 7). The aCH bond length decreases regularly from the axial (1.0892 A) to the equatorial position (1.0864 A). Hyperconjugation effects can explain the major part of this variation. Actually, in the axial position, the CH bond is almost parallel to the n electronic cloud of the adjacent C=C double bond leading to a strong attraction of the hydrogen atom and to a bond lengthening. On the contrary, in the equatorial position, the CH bond lies in almost the same plane as the double bond and is not affected by the hyperconjugation effect. The P(CH) bond length also decreases from the axial position (1.0853 A) to the quasi-planar one but then it increases as becoming more and more equatorial (1.0842 A). This phenomenon is also observed for all the used basis sets38and for other CH2 groups in cyclic molecules in similar environment as in c y ~ l o b u t a n eand ~ ~ tetrahydrofuran.64 For the nonstrained alkanes, a precise linear correlation has been established between the observed frequencies of deuterium isolated CH stretching vibration and the CH bond length rCH calculated using ab-initio methods:
TABLE 2: Geometry Optimization Parameters for Different Values of the Puckering Angle of Cyclopentene (Bond Length in
A and Angle in Degrees) coordinate CIC2 c2c3 c3c4
clH6 C3H8 C3H9 W i o
GHII CIC2C3 c2c3c4
c3c4c5
CiC2H7 C2C3Hs CzC3H9 C4C3Hs C4C3H9 C3C4Hio C3C4Hii CIC2C3C4 c2c3c4c5
HioC4Hi I HsC3H9 8"
energyb a
planar
puckered 5"
puckered 10"
puckered 15"
full optimizn
puckered 25"
1.3176 1.5078 1.5517 1.0762 1.0876 1.0876 1.0839 1.0839 112.84 103.86 106.60 124.79 111.38 111.38 112.00 112.00 110.89 110.89 0.00 0.00 106.80 106.33 0.00 - 193.98970
1.3177 1.5079 1.5512 1.0762 1.0872 1.0880 1.0842 1.0838 112.80 103.80 106.55 124.80 111.75 111.05 112.00 112.03 110.39 111.38 3.20 -4.81 106.78 106.35 5 .OO -193.98977
1.3179 1.5084 1.5499 1.0762 1.0869 1.0884 1.0845 1.0838 112.69 103.61 106.38 124.84 112.12 110.78 112.02 112.04 109.94 111.86 6.35 -9.60 106.88 106.39 10.00 -193.98993
1.3182 1.5091 1.5479 1.0761 1.0866 1.0889 1.0849 1.0839 112.51 103.32 106.08 124.91 112.49 110.58 112.10 112.01 109.54 112.31 9.39 -14.33 107.05 106.46 15.00 -193.99012
1.3188 1.5103 1.5453 1.0760 1.0864 1.0892 1.0853 1.0842 112.23 102.87 105.58 124.99 112.82 110.48 112.25 111.92 109.28 112.69 12.60 -19.51 107.29 106.60 20.60 -193.99023
1.3192 1.5116 1.5430 1.0759 1.0863 1.0894 1.0855 1.0845 111.95 102.43 105.07 125.06 113.06 110.47 112.45 111.77 109.15 112.94 14.97 -23.51 107.51 106.74 25.00 -193.99012
8 is the puckering angle. Energy in hartrees.
Ring Puckering and CH Stretching Spectra
J. Phys. Chem., Vol. 99, No. 10, 1995 3001
TABLE 3: Variation of the Rocking Angle of the Methylene Groups and Ethylenic Out-of-Plane Bending as a Function of the Puckering Angle of Perhydrogenated and -4,4HzCsF,j Cyclopentenes planar puckered 5" CsHs(4Y 0.00 2.21 0.00 -0.32 C5Hs(3)b 0.00 -0.62 CsHs(1,2)' 0.00 CsF6Hz(4) CsFsHz(3) 0.00 CsF&z(1,2) 0.00 a ,9(CH2)group. a(CH2)group. Ethylenic CH.
puckered 10" 4.19 -0.62 -1.14
puckered 15" 5.76 -0.93 -1.71
full optimized
puckered 25" 7.01 -1.51 -2.20
6.53 -1.24 -2.04 5.86 -0.34 -2.33
a ,
b 4
k
1
0
.-a
c
'O
//
t
U
- 68
-40 - 3 0
-20
-10
U
0 8 ("1
10
20
30
l
40
,
-0,l
-0,05
0 x
Figure 6. Variation of the rocking angle of the B(CH2) group (filled circles),a(CH2) group (squares), and out-of-plane bending of the vinyl hydrogens (crosses) of cyclopentene against puckering angle 8. The variation of the rocking angle of the CH2 group (open circles) of cyclobutane is given for comparison.60 The points are the values predicted by molecular orbital methods and the lines represent regression fits of these points. 2
-0,15
0,os
0,l
0,15
(A)
Figure 8. Variation of the CH stretching vibrational energy of the cyclopentene-3-hl as a function of the inversion coordinate x. The CH stretching frequency of the planar conformation is taken as reference. The open circles are the values determined by the molecular orbital methods; the dashed line represents the regression fits to these points Aw&) (eq 11) and the solid line AY(x)(eq 12).
AY(x)= Awo(x)v
+ Ax(x) v(v+l)
(9)
1
where v is the vibrational quantum number, Aoo(x) the harmonic frequency variation, and Ax(x) the vibrational anharmonicity variation. At the Av = 1, the measured energy difference between the axial and equatorial CH stretching vibration (47.5 cm-' for cyclopentene-341 and 25.5 cm-l for cyclopentene4-h120) is equal to g
o
t The study of the overtones (till Av = 7) shows that
-1.5
L
.0.15
-0.1
-0.05
0
0.05
0.1
0 15
1 IA)
Figure 7. Variation of the a(CH) bond length (open circles) and of the B(CH) bond length (filled circles) as a function of the inversion coordinate x. The CH bond length values of the planar conformation (1.0876 and 1.0839 A) are taken as reference.
OJ(CH)= w(cH0)
Oleq-
xax)is equal to 1 cm-l Olax= 66 cm-' and xes = 65 cm-' cyclopentene-3-h1, xax= 63.5 cm-' and xes = 62.5 cm-l
+ l;I(rCH-rocH)
where o(CHo) is the reference frequency, +CH the reference bond length, and 7 = Aw(CH)/ATCHwith 7 ranging from -10 OOO to -18 000 cm-' 8,-1.50-53 Thus, the variation of the CH stretching frequencies w&) can be determined from the ab-initio calculations of the variation of the CH bond length IC&). The scaling factor in eq 8 is determined by the experimental range of the CH stretching frequency variation.
(b) Comparison of Simulated and Experimental Spectra. The conformational variation of the CH stretching vibrational energy added to V,ft(x,O)in eq 5 is equal to
for for ~yclopentene-4-hl)~~ (paper 2, ref 42). The harmonic CH stretching frequency differences (woes- worn)are thus equal to 45.5 cm-' for cyclopentene-3-hl and 23.5 cm-l for cyclopentene-4-hl. Cyclopentene-3-hl. The Aoo(x) harmonic frequency variation is calculated from eq 8 by multiplying TCH(X) (Figure 7) by a parameter equal to -15 300 cm-l (Figure 8, open circles). It is reported in Figure 8 with respect to the value for the planar conformation. Its fit leads to the following expression (dashed line Figure 8): Ao,(x) = 2 5 2 - 4 3 9 ~ 4300x3 ~
+ 1 1000x4
(1 1)
where x (the inversion coordinate) is in 8, and A@&) in cm-l The isotropic v(CH) Raman profile calculated by adding this ab-initio determined Aog(x) to the already known ground-state potential energy function V,~~(X,O)'~ (V,&,O) = -26 4 5 b 2 952x3 754 0242) is in good agreement with the experimental one (Figure 1). However, due to the neglect of the conformational dependence of anharmonicity, the calculated axial and
+
+
Lapouge et al.
3002 J. Phys. Chem., Vol. 99, No. IO, 1995 equatorial v(CH) splitting is smaller than the experimental one. A better fit of the experimental spectrum can be achieved by evaluating the expansion in x of the anharmonic CH stretching variation Av(x) (eq 9). However, the vibrational anharmonicity variation Ax(x) cannot be determined straightforward from the CH bond length variation. It seems reasonable to suppose that it can be expanded in a polynomial function of x similar to (eq 1l), the first term of Ax(x) being proportional to the first term of Awo(x) in the ratio kes - xax)/(woe,- worn). The first term of Av(x) expansion in x is thus fixed and the other terms are fitted to the fundamental v(CH) Raman experimental spectrum. The polynomial variation reported in Figure 8 (solid line) is obtained:
+
Av(x) = 2 6 3 ~ 300~'- 4 1 2 2 ~ ~6 0 0 0 ~ ~ (12) where x (the inversion coordinate) is in 8, and Av(x) in cm-'. The anharmonic contribution on each term of the potential variation is deduced from the half the difference (Av; A~i)/2:
+
+
A~(x= ) 5 . 5 ~ 6 9 ~ ' 89x3 - 2 5 0 0 ~ ~ (13) Av(x) and Ao(x) plots are very similar as, at Av = 1, the anharmonic contribution is small. But, at higher energy, it is multiplied by a factor v(v 1) and contributes for a nonnegligible part to the vibration energy variation. The isotropic v(CH) Raman profile calculated by adding Av(x) (eq 12) in eq 5 to the ground-state potential energy function V,ftjx,O) reproduces very well the experimental Raman spectrum (Figure 1). In this work, for the first time, the infrared spectra are also reconstructed. The component ,UX gives rise to a A type profile (APR = 19 cm-l, Q intensity 8%) and contributes weakly to the infrared spectrum. The components ,UY and pz give rise to a B type profile (APR = 19 cm-', no Q intensity) and to a C type profile (APR = 27 cm-', Q intensity 40%), respectively. The agreement of the calculated profiles with the experimental spectra is very good as well for the CH stretching fundamental as for the first overtone spectra (Figure 2). In paper 2,"2 a correct analysis of the high-energy overtones (Av = 3-6) is also obtained with this vibrational energy variation (eq 12). The other frequencies, calculated in the harmonic approximation for the full optimized geometry, their scaled values, and their assignments are tabulated in the supplementary material (Table 4). The Raman and infrared frequencies are well reproduced (to within an average value of 7 cm-'). Of the 32 vibrational modes other than the ring-puckering motion, the frequencies of 10 change more than 10 cm-' on going from the puckered to the planar conformations. Despite substantial cancellations among the frequency shifts, a significant contribution (+21 cm-') of the zero-point vibrational energy (ZPVE) of these higher frequency modes to the effective barrier height for ring-puckering potential is found in agreement with previous works.37,38$63 A significant axial to equatorial conformation ZPVE change of +5 cm-' is also calculated. This confirms the ZPVE origin of the cyclopentene-3-hl potential asymmetry determined from the experimental spectra (4.4 Cyclopentene-4-hj. The Awo(x) harmonic frequency variation is calculated from the r C H ( x ) variation determined by ab-initio calculations (Figure 7) multiplied by 17 (17 = -15 300 cm-' (filled circles in Figure 9). Its fit leads to the following expression (chain line in Figure 9):
+
+
Aw0(x) = 1 1 9 ~ 1 6 0 2~ ~3 8 6 5 ~ ~3 2 0 0 0 ~ (14) ~
IS
L
k
5
--20 I5 -25
I
E
EJ 1 " " " ' " ' ' 1 ' " " " ' 1 " " ' '
-0,15
-0,l
-0,05
0
0,05
0,l
0,15
(A) Figure 9. Variation of the CH stretching vibrational energy of the cyclopentene-4-hl as a function of the inversion coordinate x. The CH stretching frequency of the planar conformation is taken as reference. The filled circles are the values determined by the molecular orbital methods; the chain line represents the regression fits to these points Ao&) (eq 14), the solid line Av(x) (eq 15), and the dashed line A d & ) (eq 16). x
This variation is added to the aldready known ground-state potential Ve&,O)lg (Ve&,O) = -25 5212 370x3 737 1242) to obtain the puckering potential Vefr(x,l) in the first excited v(CH) vibrational state. The such calculated isotropic v(CH) Raman spectrum presents only two bands (Figure 3), a lower frequency band corresponding to the axial v(CH) vibration and a twice intense band at a higher frequency corresponding to the addition of the equatorial and the planar conformation v(CH) vibrations, as predicted from the calculated quasi equal CH bond lengths for these two positions. This is in complete discrepancy with the experimental spectrum (Figure 3). As the v(CH) energy variation cannot be straightforwardly deduced from the CH bond length change, we have supposed, according to the similarities between the -341 and -4-hl CH stretching spectra (Figures 1-4), that the first term of Av(x) for the -4-hl derivative is proportional to that found for the -3-hl derivative in the ratio (A.~~-aglhv,-,~). The other terms of the Av(x) expansion are fitted to the Raman experimental spectrum. The difference between the two series of Vedx,O) and Veft(x,1) parameters contains implicitly the v(CH)/ringpuckering coupling and gives the polynomial variation reported in Figure 9 (solid line):
+
Av(x) = 1 4 1 -~ 2 0 0 ~ '- 2030x3
+
+ 1 6 0 0 0 ~ ~(15)
The spectrum calculated with these parameters reproduces the three most important peaks of the Raman experimental spectrum within 2 cm-l, and the two others within 5 cm-' (Figure 3). As the anharmonicity difference between the axial and equatorial CH stretching mode is the same for both derivatives, Ax(x) is kept equal to that previously calculated for the -3-hl derivative (eq 13). The harmonic variation is then (dashed line in Figure 9):
+.
Awb(x) = 1 3 0 ~ 3 3 8~ 2~ 2 0 8 ~ ~21000x4
(16)
In this case, the correlation r C H / v C H is no more valid. The introduction of the rocking motion of the CHD group in the calculation of the reduced mass does not improve the agreement of the calculated spectra with the experimental spectra, showing that the kinetic effect is negligeable as already noted by Champion et a1.37,63and by M a l l ~ y . ~We * have no explanation for this discrepancy.
J. Phys. Chem., Vol. 99, No. IO, 1995 3003
Ring Puckering and CH Stretching Spectra The infrared spectra are also reconstructed. The component px does not contribute to the infrared spectra. The components py and pz give rise to a B type profile (APR = 19 cm-l, no Q
intensity) and to a C type profile (APR = 27 cm-', Q intensity 41 %) respectively. The calculated profiles agree satisfactorily with the experimental spectra as well for the CH stretching fundamental as for the first overtone spectra (Figure 4). A correct analysis of the higher energy overtones (Av = 3-6) is also obtained with this vibrational energy variation (to be published). The other frequencies, calculated in the harmonic approximation for the full optimized geometry, their scaled values and their assignment are tabulated in the supplementary material (Table 5). The Raman and infrared frequencies are well reproduced (to within an average value of 6 cm-I). A ZPVE contribution of +17 cm-I to the effective barrier height of the puckering potential is found. Conclusion The aim of this work is to test if the theoretical calculation used to explain the structure of the fundamental CH stretching spectra associated with the puckering dynamics of cyclopentene ring in previous papers20,21can be applied to the higher overtones analysis (paper 2).42 In particular, the reduction of the problem to two degrees of freedom (CH stretching and puckering motion) and the use of adiabatic approximation to separate them are checked. In this paper, the CH stretching-puckering coupling is not determined by fitting the experimental spectra as done previously,20,21but it is estimated by assuming a linear correlation between deuterium isolated CH stretching frequencies and abinitio CH bond lengths. The variations of the geometrical parameters of this molecule and more particularly the CH bond lengths are calculated with a 6-31G** basis set for constrained puckering angles varying from 0" (planar) to 25" (puckered). In addition, the vibrational frequencies of the two monohydrogenated derivatives -3-hl and -4-hl have been calculated for the planar and puckered conformations. A significant zero-point vibrational effect (ZPVE) on the effective inversion barrier of cyclopentene (with a contribution of about 20 cm-l) and on the asymmetry of the potential (as previously supposed from the experimental data) has been found. For the -3-hl monohydrogenated derivative, an excellent agreement is found between the calculated and the experimental Raman (Av = 1) and infrared (Av = 1 and 2 ) spectra with coupling potential parameters evaluated from the ab-initio calculated CH bond lengths. Only minor adjustments of the predicted ab-initio data are made to take into account the anharmonicity dependence of the stretching mode on the puckering motion. For the -4-hl monohydrogenated derivative, the coupling potential directly determined from the CH bond length calculation yields a poor fit to the observed spectra. This can hardly be connected with the precision of the calculation method. Indeed, ab-initio calculations provide quite reliable CH bond length conformational variations even though the calculated CH bond length absolute values are generally too low. The linear correlation between these variations and the relative CH stretching frequencies provides a correct determination of the coupling parameters for the a(CH) oscillator in cyclopentene and for the CH oscillator in many other molecules~7-49The disagreement observed for the P(CH) oscillator in cyclopentene appears as a characteristic of the methylene groups in a constrained cycle. Indeed, a similar CH bond length variation
is also observed in other molecule^^^,^ but not compared with experimental data till now. However, estimates of the CH stretching frequency variation of the -4-hl derivative similar to that found for the -3-hl derivatives leads to a good reproduction of the experimental Raman (Av = 1) and infrared (Av = 1 and 2) spectra. The simulation of the CH stretching infrared contours shows that the orientation of the dipole change vector for the isolated CH stretch vibration coihcides with the CH bond direction. Acknowledgment. The calculation facilities were supplied by the Institut de Dtveloppement et des Ressources en Informatique (IDRIS)and by C.N.R.S. The authors also thank J. C. Leicknam and P. Maraval for their assistance in the calculation of the infrared spectra profile. Supplementary Material Available: Calculated and experimental frequencies of cyclopentene-3-hl and -4-hl (Tables 4 and 5) (2 pages). Ordering information is given on any current masthead page. References and Notes (1) Blackwell, C. S.; Lord, R. C. Vib. Spectra Struct. 1972, I , 1. (2) Wurrey, C. J.; Durig, J. R.; Carreira, L. A. Vib. Spectra Struct. 1976, 5, 121. (3) Lister, D. G.; MacDonald, J. N.; Owen, N. L. Internal Rotation and Inversion; Academic Press: New York, 1978. (4) Legon, A. C. Chem. Rev. 1980, 80, 231. ( 5 ) Laane, J.; Lord, R. C. J . Chem. Phys. 1967, 47, 4941. (6) Ueda, T.; Shimanouchi, T. J . Chem. Phys. 1967, 47, 5018. (7) Green, W. H. J . Chem. Phys. 1970, 52, 2156. (8) Durig, J. R.; Carreira, L. A. J . Chem. Phys. 1972, 56, 4966. (9) Chao, T. H.; Laane, J. Chem. Phys. Lett. 1972, 14, 595. (10) Harris, W. C.; Longshore, C. T. J . Mol. Srruct. 1973, 16, 187. (1 1) Villarreal, J. R.; Bauman, L. E.; Laane, J.; Harris, W. C.; Bush, S. F.J . Chem. Phys. 1975, 63, 3727. (12) Villarreal, J. R.; Bauman, L. E.; Laane, J. J . Chem. Phys. 1976, 80, 1172. (13) Villarreal, J. R.; Laane, J.; Bush, S. F.; Harris, W. C. Spectrochim. Acta, Part A 1979, 35, 331. (14) Bauman, L. E.; Killough, P. M.; Cooke, J. M.; Villarreal, J. R.; Laane, J. J . Phys. Chem. 1982, 86, 2000. 115) Besnard. M.: Lasseeues. J. C.: Guissani. Y.: Leicknam. J. C. Mol. phis. i984, 53,45. (16) Lascombe. J.; Cavamat, D.; Lassemes, J. C.; Rafilipomanana, C.; Biran, C. J . Mol. Struct. l d 4 , 113, 179. (17) Rafilipomanana, C.; Cavagnat, D.; Cavagnat, R.; Lassegues, J. C.; Biran, C. J . Mol. Struct. 1985, 127, 283. (18) Rafilipomanana, C.; Cavagnat, D.; Lassegues, J. C. J . Mol. Struct. 1985, 129, 215. (19) Cavagnat, D.; Banisaeid-Vahedie,S.; Gngnon-Dubois, M. J . Phys. Chem. 1991, 95, 5073. (20) Cavagnat,D.; Banisaeid-Vahedie, S. J . Chem. Phys. 1991,95,8529. (21) Cavagnat, D.; Banisaeid-Vahedie, S.; Lespade, L.; Rodin, S. J . Chem. SOC.,Faraday Trans. 1992, 88, 1845. (22) Davis, M. I.; Muecke, J. W. J . Phys. Chem. 1970, 74, 1104. (23) Rathjens, G. W. J . Chem. Phys. 1962, 36, 2401. (24) Butcher, S. S.; Costain, C. C. J. Mol. Spectrosc. 1965, 15, 40. (25) Scharpen, L. H. J . Chem. Phys. 1968, 48, 3552. (26) Lopez, J. C.; Alonso, J. L.; Charro, M. E.: Wlodarczak, G.; Demaison, J. J . Mol. Spectrosc. 1992, 155, 143. (27) Malloy, T. B. J . Mol. Spectrosc. 1972, 44, 504. (28) Malloy T. B.; Carreira, L. A. J. Chem. Phys. 1979, 71, 2488. (29) Pyka, J. J . Mol. Spectrosc. 1992, 151, 423. (30) Sztraka, L. Spectrochim. Acta 1992, 48A, 65. (31) Allinger, N. L.; Sprague, J. T. J . Am. Chem. SOC. 1972, 94, 5734. (32) Rosas, R. L.; Cooper, C.; Laane, J. J . Phys. Chem. 1990,94, 1830. (33) De Alti, G.; P. Decleva, P. J . Mol. Struct. 1977, 41, 299. (34) Saebo, S.; Cordell, F. R.; Boggs, J. E. J . Mol. Struct. (THEOCHEM) 1983, 104, 221. (35) Miller, M. A,; Schulman, J. M.; Disch, R. L. J . Am. Chem. SOC. 1988. 110. 7681. (36) Schulman, J. M.; Miller, M.; Disch, R. L. J . Mol. Struct. (THEOCHEM) 1988, 169, 563. (37) Champion, R.; Godfrey, P. D.; Bettens, F. L. J . Mol. Struct. 1991, 147. 488. (38) -Allen, W. D.; Csaszar, A. G.; Homer, D. A. J . Am. Chem. SOC. 1992, 114, 6834.
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