2000
J. Phys. Chem. 1982, 86, 2000-2006
acetaldehyde and ethanol (GC) per mole of peroxide (iodometry). Under our GC conditions it decomposes completely to acetaldehyde/ethanol (60%) and ethyl acetate (40%). In dilute aqueous solution it is stable for many weeks. It has a R value of 0.59 in acetone/CCl,/benzene (1:2:1), developed as above. With the amine-naphthol reagents it developed only slowly (severalminutes) whereas H202and 1-ethoxyethyl hydroperoxide reacted instantly. To identify the organic peroxidic products, we concentrated a diethyl ether solution (2 X low2M, N20/02-saturated, irradiated at 0.39 W kg-' to 20% conversion), spotted it on a silica gel plate, and compared it with authenic H202,1-ethoxyethyl hydroperoxide and bis( l-ethoxyethyl) peroxide. After elution and spraying as described above, HzOz (Rf = 0.10) and l-ethoxyethylk hydroperoxide) (Rf = 0.42) could be identified as irradiation products. There was only a very faint indication of the presence of bis(1-ethoxyethyl) peroxide (Rf = 0.59; G < 0.05). Besides, two unknown organic peroxides (Rf= 0.24
and 0.31) of minor yields were also detected but not investigated further. The relative yields of 1-ethoxyethyl hydroperoxide vs. that of Hz02in irradiated diethyl ether solutions were obtained by following spectrophotometrically the rate of I,- formation at 350 nm. H202reacts very fast with the KI reagent at pH 4.2 ( t l 1 2< 15 s), whereas the peroxidic products (mainly 1-ethoxyethyl hydroperoxide) reacts much more slowly ( t l I 2 4 min). No apparent enhancement of I,- yields was observed when the KI reagent was acidified to pH 1.0. This is further evidence that bis(1ethoxyethyl) peroxide is not a product in irradiated diethyl ether solutions. Oxygen consumption was determined by an oxygenspecific membrane electrode manufactured by Wiss. Techn. Werkst., Weilheim, West Germany.
-
Acknowledgment. We thank Miss E. Bastian for the GC measurements and Mrs. R. Paulini for technical assistance.
Two-Dimensional Potential Energy Surface for the Ring Puckering and Ring Twisting of Cyclopentene-do,- 1-d,, - 1,2,3,3-d,, and -d8 L. E. Bauman, P. M. Klllough, J. M. Cooke, J. R. Vlllarreal, and J. Laane' Department of Chemistry, Texas AbM Universw, College Station, Texas 77843 (Received: September 8, 1981; In Final Form: Februaty 1, 1982)
The far-infrared and Raman spectra of four isotopic species of cyclopentene have been assigned in order to obtain a detailed energy map for the low-frequency ring modes. The data for each molecule, consisting of a main series of ring-puckering bands, a series of side bands, and a series of ring-twisting absorption peaks (for the asymmetrically deuterated dl and d4 molecules), have been analyzed by means of a two-dimensional potential energy calculation. The calculation yields a potential function of V = 7.880 X 105x1*- 0.2706 X lO5xI2+ 0.5158 X 1 0 5 ~ 2+2 1.904 X 1 0 5 ~ 1 2 ~ where 2 2 , x1 and x 2 represent the ring-puckering and ring-twisting coordinates, respectively. The barrier to inversion is calculated to be 232 cm-' and the sign of the cross term reflects the fact that twisting of the ring tends to hinder the puckering process.
Introduction We have previously recorded the far-infrared and Raman spectra of cyclopentene,'P2 cyclopentene-l-dl,3 cyclo~entene-l,2,3,3-d,,~ and cyclopentene-dt and analyzed these in terms of one-dimensional ring-puckering potential energy functions. If the one-dimensional approximation is valid, then the kinetic energy (reduced mass) terms in the wave equation should vary from compound to compound but the same potential function should be applicable to all species. However, our analyses have shown3 that the potential parameters a and b in the function V = ax4 - bx2 (1) vary by as much as 8%. Moreover, the calculated barrier to inversion was calculated to change from 233 to 231, to 224, and to 215 cm-' in going from the do to dl, to d4, and to d, species, respectively. Various models allowing CH2 rocking to mix with the ring puckering were utilized in an attempt to account for the variation in potential param(1)J. Laane and R. C. Lord, J. Chem. Phys., 47,4941 (1967). (2) T.H. Chao and J. Laane, Chem. Phys. Lett., 14,595 (1972). (3) J. R. Villarreal, L. E. Bauman, and J. Laane, J.Phys. Chem., 80, 1172 (1976). (4)J. R.Villarreal, L. E. Bauman, J. Laane, W. C. Harris, and S. F. Bush, J. Chem. Phys., 63, 3727 (1975).
eters and barrier height, but little improvement in the correlation between isotopic forms was obtained. It seemed reasonable to assume, therefore, that the apparent variation in the one-dimensional potential functions resulted primarily from the coupling of the ring-puckering and ring-twisting motions. Support for this idea comes from the fact that the spectra show "side bands" which result from ring-puckering transitions when the molecules are in the first excited state of the twisting mode. Moreover, spectra showing the ring-twisting hot bands for the asymmetrically substituted dl and d4 species have been observed, and these provided data which are of great value for the analysis of the coupling. In this work we present a two-dimensional analysis, using the ring-puckering and ring-twisting motions as the two coordinates, in order to fit the spectra of all four isotopic forms of cyclopentene with the same potential energy surface. A two-dimensional anharmonic oscillator calculation has previously been carried out for the two out-of-plane ring modes of 2,5-dih~drofuran.~ Only the data for the ringpuckering series with its side bands were available for the determination of the potential energy function, however. (5) L. A. Carreira, I. M. Mills, and W. B. Person, J . Chem. Phys., 56, 1444 (1972).
0022-3654/82/2086-2000$0 1.25/0 0 1982 American Chemical Society
The Journal of Physical Chemistry, Vol. 86, No. 1 1, 1982
Potential Energy Surface for Cyclopentene
2001
TABLE I: Reduced Masses and Kinetic Energy Coefficients for Cyclopentene Species ~
kinetic energy coeff, au-' .KJ
reduced masses, au molecule
p1
P2
d,, d, d, d,
117.88 119.78 138.95 191.9ab
24.02 27.06 (28.56)" 32.44 (35.08) 34.98 (36.13)
g:
gl(2)
8.4843 X 10'' 8.3502 X l o e 3 7.1977 x 5.2095 x
-2.1692 X lo-* -2.2287 X 10.' -1.0362 X lo-* -0.5488 X l o T 2
g1(4)
-0.22270 -0.20647 -0.23456 -0.18297
g,@)
g;
1.00680 0.86214 0.80003 0.58924
0.04163 0.03695 0.03083 0.02859
The reduced mass used for the d , is about 4% higher than the calculated value3 of Calculated values in parentheses. 184.51 for the bisector model. This is apparently due t o some additional vibrational mixing.
Experimental Section The preparations of the deuterated cyclopentene species3 as well as the far-infrared and Raman spectra for these have been previously presented. A detailed tabulation of the low-frequency (20-400 cm-') spectra is presented in this work. Hamiltonian The two-dimensional Hamiltonian selected has the form
blX12
+ a2x324 + b,x,2 + cx12x,2
(2)
where x1 and x 2 represent the ring-puckering and ringtwisting coordinates, respectively, and where the gi are the reciprocal reduced mass expansions gi = l / p i = g:
+ g1(2)x? + gi(4)xi4 + gi(6)x:
(3)
The constants a,, bl, a,, b2, and c are potential energy parameters while the gib) are the kinetic energy coefficients. Because both the potential energy and kinetic energy involve only even power terms, they are symmetric with respect to both x1 and x2. Thus the solution b,, the eigenvalueeigenvedor problem may be separated into four parts according to the evenness (e) or oddness (0)of the coordinates (i.e.: ee, eo, oe, and 00). If odd power terms were present, this separation would not be possible.
Energy Level Computations Kinetic Energy Expansions. A computer program was written3p6for the numerical evaluation of the reduced mass for the ring-puckering motion. The reduced mass pl(xl) and its reciprocal gl(xl) for various different values of the puckering coordinate x1 were determined, and the Newton-Raphson method was used to determine the coefficients g,G) which gave the best numerical fit to the calculated values. As described previously3 various different ring-puckering models, such as those including CH2 rocking, may be used for the calculation. However, the basic bisector model' without rocking was found to be satisfactory. Table I lists the ring-puckering reduced masses ( p J and the kinetic energy coefficients (g,") determined for the four isotopic cyclopentene species. Reduced mass calculations were also carried out for the ring-twisting motion with the model described elsewhere.83 Since the twisting is of smaller amplitude than the puckering and since a number of different vibrational models are possible, only one fixed reduced mass value, corresponding to motion away from a planar structure, was calculated for each isotopic form of cyclopentene. For this (6) L. E. Bauman and J. Laane, unpublished results; L. E. Bauman, Ph.D. Thesis, Texas A&M University, 1977. (7)T. B. Malloy, J. Mol. Spectrosc., 44,504 (1972). (8)J. Laane, M. A. Harthcock, P. M. Killough, J. M. Cooke, and L. E. Bauman, J. Mol. Spectrosc., 91,286 (1982). (9)M. A. Harthcock and J. Laane, J.Mol. Spectrosc., 91,300(1982).
type of calculation it is necessary to know the relative magnitudes of the out-of-plane vectors at carbon atoms 1and 2 as compared to atoms 3 and 5. For cyclopentene-do and -d8 the use of symmetry principles facilitates the evaluation of these vectors.8 For the dl and d4 molecules, however, the asymmetry of the molecules complicates the calculation considerablyin that the vectors at atoms 1and 2 no longer should have the same magnitude. Likewise, 3 and 5 take on different values. For our calculations on the dl and d4 species we did not evaluate these changes but instead assumed the same model as for the symmetric doand d8models. These calculated values then only served as approximations for the asymmetrically deuterated species. The values used for the potential energy calculations were determined from the relation pD/pH = v H 2 / ~ , where the subscripts D and H refer to a deuterated (d, or d4) molecule or the unsubstituted species, respectively. Table I lists both sets of reduced mass values for the ring twisting. For the do molecule the value calculated from the reduced mass program was used without correction. However, for the reasons described above, the computed d, and d4 results had to be reduced by about 5 and 7%, respectively. The calculated twisting reduced mass for the d8 molecule was also reduced by about 3% in order to fit the observed frequency shift. Apparently a small amount of mixing (perhaps from CH2 twisting motions) slightly alters the form of the ring twisting. The cross kinetic energy term g,, is exactly zero for a planar configuration but takes on small values for puckered structures. However, the effect of this term is expected to be negligible and it was not used for the computations. Basis Functions. The energy level computation was carried out by using three different basis sets in order to ensure numerical accuracy, especially for the higher levels. The first basis set used was that of the isotropic harmonic oscillator in polar coordinates. This is similar to that previously described5 except that the Wang transformationlo was used to separate the Hamiltonian into four symmetry blocks instead of two. The matrix elements have been listed elsewhere6and compared in part to those previously published."J2 A least-squares adjustment routine based on that of Ueda and Shimanouchi13was incorporated into the program and was used to find the potential energy parameters in eq 2 that yield the best agreement with the experimental data. Although the extra symmetrization made the computer program more efficient than that used for the analysis of 2,5-dihydrof~ran,~ two disadvantages for its use were encountered. First, the higher order kinetic energy terms of eq 3 could not be readily incorporated into the calculation. Second, the basis set is really not the best for analyzing the two vibrations, one of which is highly anharmonic. As a result, some of the higher energy levels could not be accurately determined (10)S. C. Wang, Phys. Reo., 34,243 (1929). (11)W.H.Shaffer, Reu. Mod. Phys., 16,245(1944).Some errors have been corrected in ref 6. (12)S. Bell, J.Phys. B, 3,745 (1970). (13)T.Ueda and T.Shimanouchi, J . Chem. Phys., 47,4042 (1967).
2002
Bauman et al.
The Journal of Physical Chemistry, Vol. 86, No. 7 1, 1982
TABLE 11: RingTwisting Hot-Band Transition
and fourth terms of eq 2 represent those used for obtaining the one-dimensional ring-puckering solution while the second and sixth terms represents a harmonic oscillator Hamiltonian for which the solutions are known. As a result eq 6 can be rewritten as
Frequencies (cm-’) cyclopentene-1-d, transition (0,O )-(I, O ) ( O J )-(1J 1
obsd
inferred
obsd
inferred
369.3 369.3
369.3 (369.5)“ 368.7
337.4 337.6 330.8 332.5 335.2 333.2 336.8 338.5 339.3 342.5
337.4 (337.5) 329.1? 332.2 335.1 333.4 336.8 338.5 (338.8) (342.2) (34 3.3)
(0,2)-( 1 , 2 ) (0,3)-(I , 3 ) (0,4)-(1,4) (0,5)-(1,5) (0,6)-(I , 6 ) (0,7)-(1,7)* (0,8)-(1,8) (0.9)-( 1 . 9 ) (0,lO)-(1,lO)
cyclopen tene1,2,3,3-d,
367.1 365.6 367.8 368.8 -369.9
367.1 365.4 367.4 (368.9) (370.2)
371.2 372.2 373.5
(371.0) (372.2) (373.4)
Hu,,uI,I
u # u’,u # u’
“ Frequencies in parentheses are based o n calculated values for the side band transitions. The (0,7) and (1,2) levels of cyclopentene-l,2,3,3-d4are in Fermi resonance. even when the matrix sizes were 105 X 105, 91 X 91, 91 X 91, and 91 X 91.14 The second computer program used to calculate the energy levels for the two-dimensional cyclopentene potential function utilized the product of two harmonic oscillator basis sets in Cartesian c00rdinates.l~ The matrix elements for this basis are ~ ~ o w I Iand , ~ Jthe ~ higher order kinetic energy terms can be easily accomodated. However, even after symmetry factoring into four blocks, the desired accuracy in the calculated higher energy levels could not be attained by using reasonable sized Hamiltonian matrices. It should be noted that accurate calculations were necessary for about 30 energy levels and for energies extending above 1500 cm-’ for each molecule. So that the desired accuracy in the energy level calculations could be achieved a third computer program was written which utilizes the products of harmonic oscillator functions with ring-puckering functions as the basis set. The latter are obtained by solving the one-dimensional ring-puckering problem with the potential of eq 1 and a one-dimensional harmonic oscillator basis set.17 The one-dimensional potential energy parameters are selected so that the best agreement with the experimental data is attained. The ring-puckering functions IC/; are then represented as a linear combination of harmonic oscillator functions xi n iF/i
=
Ccijxj I
(4)
where n represents the.dimension of the one-dimensional Hamiltonian matrix, usually between 50 and 100. For the two-dimensional calculation the basis set is the product of the IC/i and harmonic oscillator functions *lI”
=
+uxu
(5)
and the matrix elements are determined by evaluating terms of the type
H,,,,,,,
= ( U U ~ H’U~’) U
+ ( U + ‘/z)h~z + (UuIcx12x221uu)+ ( ~ 1 ~ 2 x 2 ~ 1 ~ ) = ( u u ~ c x ~ ~ x ~ ~+~(uu/o+x~~~u’) ’u’) (7)
Hu,,u, = A,
(6)
where the Hamiltonian H is given by eq 2. The first, third, (14) This corresponds to ,u of 26 while that in ref 5 had u, = 20 when 121 X 121 and 110 X 110 matrix sizes were used. (15) J. M.Cooke and J. Laane, unpublished results. (16) E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, “Molecular Vibrations”, McCraw-Hill, New York, 1955. (17) J. Laane, Appl. Spectrosc., 24,73 (1970).
Here, the A, represent the eigenvalue solutions of the one-dimensional calculation and v2 = 2’J27r-l b2’J2g21J2 is the harmonic frequency for the second vibration (ring twisting). In most calculations the anharmonicity of the ring twisting was not considered (i.e., u2 = 0). Thus, the terms involving u2 could be neglected. Evaluation of the matrix elements primarily involved solving for (uu~cx,2x22~u’u’) = c(uJx121u’)(u(x221u’) (8) Evaluation of the terms in u and u give respectively (uIxZ21u’) = ( u
= [(u
+ ‘/)h/(2av2)
+ l ) ( u + 2)]’J2h/(47rv2)
for u ’ = u for u’ = u
+2
(9)
and (uIx12/u’)=
h ”
CC,iC,di 4TVl i
+ 72) +
cu~cut,i+2[(i + l)(i + 2)]”2
+ CUiC,.,i-2[i(i
- 1)]1’2
(10)
where the cui were determined from the one-dimensional solution and where v1 is the harmonic frequency selected for the first coordinate (ring puckering) for computational purposes. Since the one-dimensional approximation does a good job of representing the ring puckering and since the ring twisting is expected to be nearly harmonic, the basis functions of eq 5 are already very close to the final twodimensional solutions. Thus, after symmetry factoring into four matrix blocks, few basis functions were required to calculate the energy levels. The maximum matrix dimension used for each block was 150 X 150 (15 functions in u and 10 in u ) although 50 X 50 matrices produced satisfactory results.
Results and Discussion The far-infrared and Raman spectra of the various cyclopentene species have been previously published.14 The ring-twisting hot-band spectra for the dl and d4 molecules were shown in ref 3 and these are tabulated in Table I1 along with the assignments. Figure 1 shows the energy level diagram for the puckering and twisting vibrations along with the observed transitions from these molecules. The hot-band values observed can be seen to be in excellent agreement with the inferred values derived from the main and side band ring-puckering transitions. Since the do and d8 selection rules tend to conform to C2, symmetry, no infrared hot bands for the ring twisting were observed for these molecules. Only broad bands with missing Q branches were observed in the gas-phase Raman spectra. Table I11 lists the experimentally derived ring-puckering energy level separations for both the ground and excited states of the twist. These have been determined from the main band and side band series in the far-infrared spectra and confirmed and extended by use of the ring-twisting (18) J. R. Villarreal, J. Laane, S. F. Bush, and W. C. Harris, Spectrochim. Acta, Part A , 35,331 (1979).
The Journal of Physical Chemistry, Vol. 86, No. 7 1, 7982
Potential Energy Surface for Cyclopentene
T t
t A
2003
1200
-- 800
ll0.
-- 600
E (cM-’)
-- 400 -- 200
-0
PUCKER
PUCKER
TWIST
TWIST
Flgure 1. Infrared transitions involving the ring-puckering and ring-twisting vibrations for cyclopentene- 7 4 , and - 7,2,3,3-d,.
’
TABLE 111: Experimentally Derived Energy Level Separations (cm- ) for Cyclopentene Species do UP-UP
0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10
10-11 0-3
ut=
0
0.91 127.1 25.2 83.1 76.6 92.0 99.8 107.5 113.3 119.4 128.4 152.6
d4
dl
ut=
1
(1.15)“ 126.1 23.2 81.5 77.0 93.5 101.3 108.8 114.5 150.2
ut=
0
(0.85) 126.0 24.2 82.8 76.1 91.5 99.5 106.2 112.6 118.1 123.5 151.3
‘Values in parentheses are based o n calculated values.
ut=
ut= 0
1
(1.07) 125.4 22.8 81.1 78.1 92.5 100.6 107.5 113.6 119.4 149.1
(0.50) 120.0 18.3 76.5 66.0 81.7 87.9’ 94.6’ 100.5 106.0 110.4 138.8
d8 ut=
1
(0.63) 113.1b 21.7 74.6 69.6 83.4 90.4
136.5
’Average of two interacting levels.
hot bands. The analysis of the hot bands not only allowed the determination of upper puckering levels for ut = 1 but also showed previous assignments to be in error. For example, the assignment of the 128.4 (0,lO -,0,111 and 126.1 cm-’ (1,1-, 1,2) bands was previously reversed. It should be noted in Table I1 that the hot-band series are rather irregular with the frequencies first decreasing and then changing directions. The reason for this can be seen from Table 111; the excited-state separations up to 3-4 are less than for the ground state but beginning with the 4-5
ut= 0
(0.14) 108.2 9.3 68.3 47.3 64.8 69.6 75.6 80.7 85.3 89.3 117.7
ut=
1
(0.17)
separation they are larger in the excited state. Once all of the relevant energy levels had been determined for the four isotopic species, the kinetic energy expansions gland g2were determined as described above. The potential parameters in eq 2 were then adjusted to obtain the best fit with the observed data. This was accomplished by first selecting a reasonable trial function based on the experimental data. Initial values for al and bl were taken to be the one-dimensional constants in eq 1 as determined in previous work.I4 The calculated values
2004
The Journal of Physical Chemistry, Vol. 86, No. 11, 7982
Bauman et ai. h
?
rl v
2 hl
ri
4
m
h
2
????
?
Y??"?
riofiokokoooori
'?
0
c?
""c?
O k O O O
-
mm
199 050 00
c:
0
Y1"11
oooori
2
2
c?c?
0 0
m 0
0 5
m 0
1
0
@?
0
1
0
W m ri3oori 5 0 0 0 0 0
3 Q)
m U
0
E
i
s
0,
3ridrlri
ri
hh
h r l
-0
CJ
4 3
hhh
m
Potential Energy Surface for Cyclopentene
h
??????"??"?"
0 ~ 0 0 0 0 0 0 0 0 0 0
The Journal of Physical Chemistry, Vol. 86, No. 11, 1982 2005
for the far-infrared ring-puckering sequence are most sensitive to these constants. The constant b2 is the harmonic constant for the ring twisting and the initial value is found from the harmonic oscillator relationship b2 = 0.O1526vT2/g2,where UT is the fundamental frequency for the ring twisting. The constant u2 reflects the anharmonicity of the twisting mode and is expected to be very small. Since no experimentally observed hot bands could be assigned for the pure twisting, u2 was set equal to zero. The last potential constant c represents the interaction between the two vibrational motions. Its initial value was taken to be zero. From the initial potential energy function a set of energy levels for each of the four isotopic forms of cyclopentene was calculated and these were quite close to those experimentally determined except that the perturbation of the puckering levels in the excited state of the twisting was not accounted for. The adjustment of the potential parameters to obtain the best experimental potential function was aided by a least-squares fitting routine. Primarily the interaction constant c needed to be varied in order to account for the shift of the puckering frequencies in the ut = 1 excited state. Changes in c then required smaller but not insignificant changes to be made in the other parameters a,, bl, and b2. After adjustment of the four potential parameters, the following potential energy function was found to give the best fit:
V (cm-') = 7.880 X 105x14- 0.2706 X 105x12+ 0.5158 X io5$ + 1.904 x 105x12x22(11)
h
??Y=!?? 0 ~ 0 0
u)":
0 00 0
mrir!
0 0 0
The units of x1 and x 2 are given in Angstroms. The constants al and bl are very similar to the one-dimensional values u = 7.93 X lo5 cm-l/A4 and b = -0.272 X lo5 cm-l/A2 found for cyclopentene-do3. Table IV presents a compilation of the available experimental data and compares the observed and calculated values. It should be evident that the four-parameter potential function does a satisfactory job of fitting the 140 experimental frequencies for the four molecules. Most calculated values are within 1 cm-' of the experimental. A few, such as the up = 1-2 transitions for ut = 0 and 1,are more poorly fit, however. These differences are not unexpected since the transitions occur within the potential well and are very sensitive to the exact shape of the potential surface. Higher order potential parameters could be added to improve the fit in such transitions, but due to the excellent fit of most other frequencies, their use was not warranted. Figure 2 shows the two-dimensional potential energy surface calculated for cyclopentene. The barrier at the planar configuration is 232 cm-l (0.66 kcal/mol) and the minimum of the potential surface is at x1 = f0.131 A and x 2 = 0. The positive sign of the cross term in the potential function reflects the fact that the two motions hinder each other somewhat. That is, twisting of the ring tends to make the puckering more difficult and vice-versa. In a previous analysis of only the cyclopentene-dospectra (with no twisting hot-band data) Malloy and Carreira,lgusing Van Vleck perturbation theory, calculated a negative value for the cross term. Most likely, this discrepancy is due to the limited set of data that they had available. A two-dimensional potential energy surface for the puckering and twisting of 2,5-dihydrofuran was previously ~alculated.~ However, the reduced masses used for the puckering (155.7 au) and twisting (20.0 au) were not accurately determined and the values of the dimensioned (19)T.B. Malloy and L.A. Carreira, J.Chem. Phys., 71,2488 (1979).
2006
The Journal of Physical Chemistry, Vol. 86, No. 11, 1982
Bauman et ai.
as well as its interaction with the ring puckering are very similar for both molecules. The biggest difference in the cyclopentene and 2,5-dihydrofuran potential functions, of course, is due to torsional forces. Cyclopentene has three adjacent CH2 groups and their interaction causes the molecule to take on a nonplanar structure. This also results in a negative bl value and makes a small positive contribution to al. For 2,5-dihydrofuran two CH2 groups are separated by an oxygen atom and the torsional forces help maintain the planarity of the molecule. Consequently, bl is positive, but the al value is reduced due to the negative torsional contribution to this term.
J
I
0 h)
I
-0.2
I
-0.1
I
0.0
I
0.1
1
0.2
Figure 2. Two-dimensional potential energy surface for the ringpuckering (x ') and ring-twisting (xp)vibrations of cyclopentene. Contour lines are drawn every 50 cm-'.
potential terms presented, therefore, are not meaningful. We have recalculated the reduced masses to be pp = 86.2 au and pT = 23.58 au. With these values the corrected 2,5-dihydrofuran potential function becomes V (cm-l) = 4.040 X 105x14+ 0.082 X 105x12+ 0.289 X 10~x24+ 0.525 x ~ o + 2.422 ~ xx 105x12x22 ~ ~ (12) Some caution should be used in comparing this potential function to that for cyclopentene in eq 11. The potential in eq 12 uses an ~ 2 ~ x 2term, 4 which has been set to zero for cyclopentene and we feel that there are inadequate experimental data to warrant its inclusion. Another minor flaw with the 2,5-dihydrofuran potential is that is was determined without using kinetic energy expansions. The potential constants in eq 12 are affected a few percent (less than 5%) by this. A further difference in the two potentials is that eq 11 represents a surface with a double minimum for a nonplanar molecule while eq 12 is for a planar molecule with a single minimum at the origin for the potential surface. Nonetheless,the similarities between the b2 (0.516 X lo5 vs. 0.525 X lo5) and c (1.904 X lo5 vs. 2.422 X lo5) coefficients are striking. Thus it may be concluded that the forces governing the twisting motion
Conclusions In this study we have determined the two-dimensional potential energy surface for the two interacting low-frequency ring modes of cyclopentene. The analysis of the data represent the most comprehensive two-dimensional calculation yet performed in that four isotopic species with 140 transition frequencies were fit simultaneously. The kinetic energy terms, which in previous two-dimensional analyses were only estimated, have been calculated from realistic vibrational models in order that meaningful potential energy constants could be obtained. In earlier one-dimensional it was not possible to fit the experimental data for the four isotopic molecules with the . same potential function and, in fact, the derived barrier heights varied from 215 to 233 cm-l. The single two-dimensional potential obtained in the present analysis satisfactorily reproduces all the experimental data for the four isotopic forms and shows the potential barrier to be 232 cm-l for all molecules. In addition, it lends insight into the understanding of the interaction between the two ring motions and how such interactions affect the energy level spacings in excited vibrational states. The minima of the potential energy surface, which correspond to the equilibrium molecular conformations,occur at a ring-puckering coordinate of x1 = *0.131 A or a dihedral angle of 26". This agrees well with the most recent one-dimensional determination but is higher than the microwave value of 220 *20,21 Acknowledgment. This work was supported by the National Science Foundation and the Robert A. Welch Foundation. (20) S. S. Butcher and C.C.Costain, J . Mol. Spectrosc., 15,40 (1965). (21) G. W. Rathjens, J . Chem. Phys., 36, 2401 (1962).
