J. R. Villarreal, L. E. Bauman, and J. Laane
1172
Ring-Puckering Vibrational Spectra of Cyclopentene- 7 - 4 and Cyclopentene- 7,2,3,3-d4 J.
R. Villarreal, L. E. Bauman, and J. Laane*
'
Department of Chemistry, Texas A&M University, College Station, Texas 77843 (Received January 13, 1976)
The far-infrared and low-frequency Raman spectra of cyclopentene-1-dl and -1,2,3,3-d4have been recorded. For each molecule approximately a dozen infrared bands in the 60-200-cm-l region and a like number of Raman bands in the 90-250-cm-l region were assigned to ring-puckering transitions. A series of ring-twisting infrared Q branches was also obtained for each molecule, near 370 cm-l for the d 1 and near 338 cm-l for the d4. The d4 molecule showed a series of side bands resulting from the ring-twisting excited state. The seventh excited state (u = 7 ) of the ring puckering was found to be split by an unusual Fermi resonance with the u = 2 puckering state in the twisting excited state. Extensive potential energy calculations were carried out using various models (with and without CH2 rocking) for the puckering vibration for the do, dl, d4, and d8 molecules. Inclusion of rocking gave slight improvement for the frequency fit, but rocking parameters could not be well determined. The barriers to inversion of the four molecules were found to be 233, 231, 224, and 215 cm-l in order of increasing deuteration. The dihedral angle of each isotopic form was determined to be 26'.
Introduction The barrier to inversion of cyclopentene was first determined by Laane and Lord2 to be 0.66 kcal/mol (232 cm-l). Their analysis of the far-infrared spectrum established the ring-puckering potential energy function for this molecule and showed conclusively that the cyclopentene ring is bent with a dihedral angle exceeding 20'. Low-frequency Raman studies later confirmed these far-infrared result^.^,^ Very recently the far-infrared and Raman spectra of cyclopentene-de were reported and analyzed by Villarreal and c o - ~ o r k e r sThe . ~ results for the de derivative were very similar to those of the do compound except that the inversion barrier had apparently decreased to 215 cm-l and the one-dimensional potential energy function had changed slightly. These differences were attributed to the mixing of other motions, including CH2 (or CD2) rocking, into the ring-puckering normal coordinate. In order to better understand the ringpuckering motion and to examine the effect of isotopic substitution on the potential function and barrier height, we have prepared cyclopentene-1-dl and cyclopentene-1,2,3,3-d4 and recorded their far-infrared and low-frequency Raman spectra. The data were then analyzed using various one-dimensional models for the ring-puckering motion. Experimental Section Cyclopentene-l,2,3,3-d4 was prepared according to the following reaction scheme. Cyclopentene-1 -dl was prepared similarly except that the undeuterated cyclopentanone was used instead of the d4 derivative.
S-Y-SCH,
P
Cyclopentanone-2,2,5,5-d4.Cyclopentanone (Aldrich, The Journal of Physical Chemistry, Vol. 80, No. 11, 1976
99.5%),anhydrous K2C03 (Mallinckrodt Analytical reagent), and D20 (Stohler, 99.8%) were mixed according to the procedure of Ellis and MacieL6Three successive exchanges were required for complete deuteration. l-Cyclopentanol-1,2,2,5,5-d5. Cyclopentanone-2,2,5,5-d4, 14.9 g (0.17 mol) in 110 ml of anhydrous ether, was added dropwise to 2.9 g (0.062 mol) of LiAlD4 (Stohler, 99.8%) suspended in 225 ml of anhydrous ether. The procedure used was that of L i p n i ~ kExcess .~ LiAlD4 was destroyed with saturated ammonium chloride solution. Filtration, concentration, and vacuum distillation gave 10.8 g (0.119 mol, 70%) of the deuterated alcohol. 0-1,2,2,5,5-Cyclopentyl S-Methyl Xanthate. 1-Cyclopentanol-1,2,2,5,5-d~(10.8 g) was added to a suspension of NaH in mineral oil (5.63 g, K & K) following the procedure of Roberts and Sauer.8 After addition of CS2 (10.9 g, Fischer Scientific Reagent Grade) and CH3I (21.6 g, Fischer Scientific, Certified) the mixture was stirred overnight. The xanthate was concentrated using a 1-ftbeaded glass column and used without further purification. Cyclopentene-1,2,3,3-d4. Crude 0-1,2,2,5,5-cyclopentyl S-methyl xanthate was dropped into boiling biphenyl (Matheson Coleman and Bell) under a fast N2 purge.8 The products were collected in two successive dry idacetone traps. Distillation of the trapped products resulted in 4.1 g of cyclopentene-1,2,3,3-d4(48%from cyclopentanol-d5).The purity and authenticity of the product was verified by its NMR, ir, and mass spectra. Cyclopentene-1-dl. Cyclopentanone (Aldrich 99%+) was reduced with LiAlD4 (as above) to 1-cyclopentanol-1-d 1. Formation of the xanthate of this alcohol and its subsequent pyrolysis were accomplished in the same manner (and with comparable yields) as in the cyclopentene-1;2,3,3-d4synthetic scheme. The far-infrared spectra were recorded on a Digilab FTS-20 vacuum spectrophotometer using a Wilks multiple-reflection long-path cell. Raman spectra were recorded on a Cary 82 spectrophotometer using a Coherent Radiation 53 argon ion laser as the exciting source. Experimental conditions for both kinds of spectra were similar to those previously d e ~ c r i b e d . ~ Infrared frequencies are accurate to f 0 . 2 cm-l whereas the broader Raman lines are f0.5 to f l . O cm-l. Infrared resolu-
1173
Ring Puckering of Deuterated Cyclopentenes
2
0
-l
a LT 0
cn
m
a
I 60
80
120
100
140
160
CM-I Figure 1. Far-infrared ring-puckering spectrum of cyclopentene- 741: path length, 5.3 m; vapor pressure, 80 Torr; resolution, 1.0 cm-l. The ordinate scale is 0 to 100% transmittance.
tions ranged from 0.25 to 1.0 cm-l and Raman band widths were 2 to 4 cm-1.
l
,
250
l
,
230
l
,
210
l
,
l
,
170 CM-'
190
l
,
l
,
130
150
l
,
110
l
90
Figure 2. Raman spectrum of cyclopentene- 741: vapor pressure, 300 Torr; resolution, 3 cm-l.
Results Ring-Puckering Spectra. Figures 1 4 show the far-infrared and Raman spectra of cyclopentene-1-dl and cyclopentene1,2,3,3-d4 vapors in the ring-puckering region. Tables I and I1 list the recorded band maxima and assignments along with the calculated frequencies which will be discussed later. As in the previous studies on cyclopentene-do and -d8, the farinfrared frequencies correspond to single quantum transitions (except for several triple jumps originating from levels below the barrier) and the Raman bands correspond to changes of two in the ring-puckering quantum number v. The complementary nature of the two types of spectra and the excellent correlation between the data make the interpretation clear cut for each molecule. The cyclopentene-1-dl spectrum is very similar to that of the undeuterated species with most frequencies being shifted by about 1 cm-I or less. The d4 spectra show evidence €or an extra ring-puckering level a t v = 7 and this will be discussed later in the section on Fermi resonance. The d4 infrared spectrum also shows a side band series (see Table 111) resulting from the excited state of the ring-twisting mode (see Figure 7), similar to the series reported for the undeuterated molecule.2 Three or four such bands can also be seen for the d l molecule but a series sufficient for determining a potential function was not obtained. Ring-Twisting Spectra. Due to the reduction of symmetry, the cyclopentene-dl and -d4 molecules give rise to ringtwisting Q branches in the infrared and these spectra can be seen in Figures 5 and 6. The fundamental twisting frequencies are at 369.3 and 337.6 cm-l for the d l and d4, respectively. The other Q branches in the spectra arise from transitions between various twisting states, and some of these may also be associated with excited puckering levels. No definite assignment is presented a t this time, but these will be analyzed in greater detail a t a later time using a two-dimensional potential function involving both ring-puckering and ring-twisting coordinates. In the Raman spectra of the do, d l , dq, and d8 compounds the broad twisting bands (with no Q branches) have center gaps at 392,369,338, and 325 cm-l, respectively. Fermi Resonance. The far-infrared and Raman spectra of cyclopentened4 show a remarkable case of Fermi resonance involving one of the puckering levels. If we designate the twisting and puckering quantum numbers as UT and up, re-
C M-'
Figure 3. Far-infrared spectrum of cyclopentene- 1,2,3,3,44: path length, 6.3 m; vapor pressure, 84 Torr; resolution, 1.0 cm-l. The ordinate scale is 0 to 60% transmittance.
I
240
/
,
,
220
I
200
/
,
180
,
,
I
I60
,
140
,
,
120
,
l
100
/
,
80
CM-I
Figure 4. Raman spectrum of cyclopentene- 7,2,3,3d4: vapor pressure, 300 Torr: resolution, 3 cm-l. The Journal of Physical Chemistry, Vol. 80, No. 1 I, 1976
J. R. Villarreal, L. E. Bauman, and J. Laane
1174
TABLE I: Observed and Calculated Ring-Puckering Transitions of Cyclopentene-1 -d from Far-Infrared and Raman Spectra Transition 0-1
1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-1 0 10-1 1 0-3 2-5 0-2 1-3 2-4 3-5 4-6 5-7 6-8 7-9 8-10 9-1 1
Frequency, cm-' Obsd Calcd Ia Calcd IIb Far-Infrared Spectrum 0.85 0.87 126.0 125.9 125.8 24.0 24.0 82.8 81.8 81.9 76.1 75.7 75.8 91.5 90.9 91.0 99.5 98.9 98.9 106.2 106.5 106.5 112.6 113.1 113.0 118.1 119.1 119.0 123.5 124.5 124.3 151.3 150.6 150.8 182.9 181.3 181.8 127.2 150.0 107.9 159.0 168.3 190.1 205.2 218.8 231.0 -242
Raman Spectrum 126.7 126.7 149.8 149.9 105.6 105.9 157.5 157.8 166.6 166.8 189.8 189.9 205.4 205.4 219.6 219.5 232.2 232.0 243.7 243.3
Rel. intensity Obsd Calcd
0.4
1.0
1.4 0.7
1.1 0.9
(1.0)
(1.0)
0.9 0.7 0.5 0.3 0.2 1.1 0.4
0.7 0.7 0.5 0.3 0.2 1.1 0.2
0.7
0.7
(1.0) 1.0
(1.0)
0.5 0.8 0.7 0.7 0.6 0.5 0.3 0.2
0.9 0.7 0.6 0.5 0.4 0.3 0.1
25.05 (Z4- 6.072') cm-' ; no rocking model. b V = 25.22 (Z4- 6.052') cm-';rocking included (y = -0.10; 6 = +0.10). spectively, and label our levels as (UT,UP),the resonance occurs between levels (0,7)and (1,2). Evidence for the Fermi interaction comes from the fact that extra bands are present in both the infrared and Raman puckering spectra. These extra bands are readily explained if the (0,7) level is considered to be a doublet split by 3.4 cm-l. Two infrared bands (86.2 and 89.6 (0,7) doublet trancm-l) can then be assigned to the (0,6) sition and two (92.9 and 96.3 cm-l) to the (0,7) doublet (0,8) transition. Two Raman bands at 167.6 and 171.5 cm-l correspond to the (0,5) (0,7) doublet jump and the very broad band (-194 and -196 cm-l) corresponds to the (0,7) doublet (0,9) transition. By summing five infrared transition frequencies up to the u p = 7 state, the pair of (0,7) levels are calculated to be 449.2 and 452.6 cm-' above the ground state. The pair of (1,2) levels are calculated to be a t 452.7 and 456.3 (1,O) transition frequency (337.6 cm-l by summing the (0,O) cm-l) and the (1,l) (1,2) frequencies (114.6 and 118.2 cm-l) and adding the calculated (1,O) (1,l)separation of 0.5 cm-l. Although the two calculations are not in exact agreement, it is highly probable that the (1,2) and (0,7) levels are in resonance. Both levels have A" symmetry for the C, point group. [The (0,8) and (1,4) levels are also calculated to be similar in energy but have A' and A" symmetry representations, respectively, and therefore no resonance is possible.] It should be remembered that band maxima do not normally correspond exactly to band origins (for trimethylene sulfide, differences of about 0.5 cm-l for each puckering band were cald a t e d g ) , consequently the difference in the two frequency summations of less than 4 cm-l resulting from combining eight frequencies is not entirely unexpected. Another possibility is that the (0,O) (1,O) transition actually corresponds to one of the bands in Figure 6 a t a frequency below 337 cm-l.
-
-+
- -
-+
-
The Journal of Physical Chemistry, Vol. 80, No. 11, 1976
Transition
Obsd
1-2 2-3 3-4 4-5 5-6 6-7
(2: {E 100.5
7 -8 8-9
9-10 10-11 11-12 0-3 2-5 0-2 1-3 2-4 3-5 4-6 5-7 6-8 7 -9 8-10 9-11
Frequency, cm-I Calcd Ia Calcd IIb
Far-Infrared Spectrum 0.53 0.56 120.0 119.5 119.6 18.0 17.8 76.5 75.4 75.8 66.0 65.5 65.7 81.7 81.2 81.1 88.2 88.2
0-1
aV=
-
TABLE 11: Observed and Calculated Ringpuckering Transitions of Cyclopentene-1,2,3,3-d4from Far-Infrared and Raman Spectra
106.0 110.4 114.6 138.8 161.2 120.5 138.0 95.0 143.1 148.5 c171.5 167'6 182.8 194 (-196 206.3 215.0
-
95.4 101.5 107.1 112.2 116.9 137.9 158.7
101.2 101.2 106.7 111.6 116.2 138.3 159.5
Raman Spectrum 120.1 120.2 137.3 137.7 93.2 93.8 140.9 141.5 146.6 146.9 169.3 169.4 183.6 183.5 196.9 208.6 219.3
196.5 207.9 218.3
Rel. intensity Obsd Calcd
0.3
0.9 0.01
1.1 0.6 (1.0) 0.3 0.4 0.2 0.4 0.4 0.3 0.2 0.1 0.6 0.2 1.0 (1.0) 1.0
1.0 0.7 (1.0)
Oe7
0.5 0.4 0.3 0.2 1.0
0.4 0.7 (1.0)
0.4 0.9 0.7
0.9 0.3 0.3 0.3
0.5 0.3 0.3 0.3
0.7 Oe6
0.5 0.3
0.3
a V = 22.40 (Z4 - 6.322') cm-'; no rocking model, b V = 22.77 (2'- 6.272*) cm-'; rocking included (YH = -0.10; YD = -0.25; 6 = +0.10).
TABLE 111: Observed and Calculated Far-Infrared Frequencies for the Cyclopentene-l,2,3,3-d, Side Band Seriesa Frequency, crn-' Transit ion
Obsd
Calcd
A
0-1 0.73 118.2 1-2 115.6 0.8 114.6 21.3 2-3 3 -4 74.6 74.6 0.0 4 -5 69.6 68.9 0.7 5 -6 83.4 83.0 0.4 131.7 -1.2 0-3 136.5 Q V = 22.63 (Z4- 6.132') cm-'; no rocking model, Barrier = 213 cm-'.
At any rate, five pairs of transition frequencies with a consistent separation of about 3.4 cm-l support the existence of a doublet at about 450 cm-' above the ground state. Only the ring-puckering and ring-twisting modes can combine to give levels in this region. All other vibrations have frequencies above 500 crn-l.lo Figure 7 summarizes the scheme of levels and transitions observed in the vicinity of the Fermi doublet. On the left of the diagram are shown pure ring-puckering (infrared and Raman) transitions; on the right are those involving the ring-twisting excited state, including the "sideband" series.
Ring Puckering of Deuterated Cyclopentenes
1175
600
I
500
400
Figure 5. infrared ring-twisting spectrum of cyclopentene- 7d7:path length, 75 cm; vapor pressure, 84 Torr; resolution, 0.5 cm-'. The ordinate scale is 5 to 100% transmittance.
300
0 Flgure 7. Ring-puckering (left) and ring-twisting (right) energy levels showing Fermi resonance between the (0,7) and (1,2) levels.
CM-' Flgure 6. ifrared ring-twisting spectrum of cyclopentene- 1,2,3,3d4: path leng..i, 7 m; vapor pressure, 84 Torr; resolution, 0.25 cm-'. The ordinate scale is 0 to 100% transmittance.
Calculations The use of the quartic-quadratic one-dimensional potential energy function, V = ax4 f bx2, for analyzing ring-puckering vibrations is well e ~ t a b l i s h e d . l l -This ~ ~ kind of double-minimum potential has been applied215to cyclopentene-doand -dg, and it is also used in this study. In addition to the potential function, which for mathematical purposes is used in reduced (undimensioned) form, the calculated transition frequencies depend to a lesser extent on the model assumed for the puckering motion. This model determines the reduced mass expansion used in the kinetic energy part of the matrix calculation. We have selected three different types of reduced mass functions to be used in the calculations. First, a fixed reduced mass, independent of puckering coordinate x, is utilized. Even though this is not realistic, many ring-puckering calculations have been carried out in this fashion, and we include this calculation for comparison purposes. In the second type of calculation, a reduced mass function depending on the puckering coordinate is made use of. This function is calcu-
lated by a computer program which we have written and which assumes the basic bisector model described by Mal10y.l~The motion of the ring atoms is assumed to be curvilinear and the HCH angle bisectors are constrained to be colinear with the CCC angle bisectors. That is, no CH2 rocking is allowed. In the third type of calculation rocking of the both the a and @ CH2 groups is allowed. For consistency, the rocking motion and parameters are identical in definition to that of Mal10y.l~A positive 6 represents a motion of the P-CH2 group rocking in the same direction as the @-carbonatom moves during the puckering; a positive y measures equal rocking motions of each of the ( Y - C Hgroups ~ in the direction of the puckering of the a-carbon atoms. For cyclopentene-dl, YH and y~ are used to distinguish between the independent a-CH2 and a-CD2 rocking motions. The rocking angle is assumed to vary linearly with the dihedral angle of the ring and no rocking (6 = y = 0) is assumed for the planar cyclopentene structure. Although this rocking model may not be the most realistic, it is virtually the only one which can be accommodated into a one-dimensional analysis of the potential function. Malloy has analyzed the cyclopentene-do data and has shown that use of y = -0.10 and 6 = +0.10 improves the frequency agreement. We have used these rocking parameters to generate a set of kinetic energy expressions for cyclopentene-dl, -d4, and -dg, realizing that the contribution of rocking to the puckering motion will change upon deuteration. We have also generated more than 30 other reduced mass expansions for the $4 and dg species in order to investigate which sets of rocking parameters lead to the best frequency fit. Our basic conclusion is that a wide variety of rocking parameters will improve the calculation somewhat, but the degree of improvement is relatively insensitive to the rocking model. Consequently, not much physical significance can be ascribed to the 6 and y values which yield the optimum calculated frequencies. Table IV summarizes a few selected calculations which were The Journal of Physical Chemistry, Vol. 80, No. 1I, 1976
J. R. Villarreal, L. E. Bauman, and J. Laane
1176
TABLE IV : Ring-Puckering Potential Energy Functions for Cyclopentene and Its Deuterated Derivatives Potential functions Reduced C,H* species mass, aua d, 117.88 117.88 + p o ( x ) 115.00 + y,R(x) d, 119.78 119.78 + & ( x ) 117.01 + p,R(x) d, 138.95 138.95 + p , ( x ) 132.72 + p,R(x) 122.88 + p,T(x) d, 184.51 184.51 + & ( x ) 178.43 + p,R(x) 142.79 + p , T ( x )
Reduced: V = A(Z4 - B Z 2 )
Rocking parameters
6
A , cm-l
B
0 0 +0.1 0 0 +0.1 0 0 +0.1 +0.1
24.36 25.31 25.50 24.12 25.05 25.22 21.86 22.40 22.58 22.77
6.17 6.06 6.04 6.20 6.07 6.05 6.40 6.32 6.30 6.27
7.06 7.93 7.72 7.08 7.93 7.72 7.11 7.63 7.13 6.27
x 105 x 105 x 105
x 105 x 105 x 105
25.6 27.2 26.8 25.5 27.0 26.7 25.3 26.1 25.3 23.7
0
17.92 18.27 18.41 18.63
6.95 6.87 6.84 6.79
6.89 7.30 6.99 4.63
x 105 x 105 x 105 x 105
24.4 25.1 24.5 19.9
Y 0 0 -0.1 0 0 -0.1 0 0 -0.1
{ 2: E:I 0
11
0
0 +0.1 -0.1
-0.1 -0.2
Dimensioned: V = ax4 a,
cm-'/A4
Barrier, Dihedral AvC cm-I angleb A2
b , cm-'/A2
lU5 x 105 X
x 105 x 105
x x x x x x x x x x x x x x
103 103 103
io3 io3 io3 io3
103 103 103 103 103 103
io3
232.1 232.7 232.8 231.8 230.6 230.4 224.0 223.9 223.9 224.0
26.5 25.8 26.0 26.5 25.8 25.9 26.4 25.9 26.3 27.2
216.4 215.3 215.1 214.5
26.5 26.0 26.3 29.2
1.64 0.50
0.25 3.40 0.48 0.34 2.31 0.93 0.62
0.44 0.74 0.32 0.23 0.09
a p o ( x )= 3 1 9 . 1 ~ '+ 2 7 9 2 3 ~ + ~1 9 492x6;poR(x)= 400.3~'+ 2901x4 + 21 5 3 5 ~p ~l ( ;k ) = 1 9 9 . 7 ~ +' 3 7 0 2 3 ~+~17 9 5 4 ~ ' ; 277.6~'+ 3544x4 + 19 616x6;p4(x)= 219.5~'+ 3701x4 + 18 448x6;p,R(x) = 298.6~'+ 3544x4 + 20 1 6 0 ~ ~ ; ::T(x) = 343.0~'+ 3 3 6 1 +~ 20 ~ 8 0 3 ~&~( x;) = 2 2 2 . 4 ~ '+ 5 0 6 6 +~ 23 ~ 148x6; p , R ( x ) = 345.82 + 4882x4 + 26 0 4 8 3 ~ ~ ; p,T(x) = 2 9 9 . 6 ~ + ~4281x4 + 22 369x6. bcalculated by averaging extremes of the potential function for the ground state. R(x) =
C Taken
for the ten most prominent far-infrared frequencies.
1000 -
1
1000-
I
I
IO 118.1
231.0
800
9
800
-
600
-
110.4
215.0
218.8
112.6
8 106.2
600
205.2
7
190. I
v (chi9
6
4001
5
v (d') 400
-
200
-
4
3
200
2 I
0
OL
0-
I
-0.2
- 0.2
0.2
0
0.2
0
X (8) I
-2
,
I
I
0
I
i
2
2 (REDUCED)
L
l
'
-2
l
l
0
l
'
2
2 (REDUCED)
Flgure 8. Ring-puckering potential energy function for cyclopentene1-di .
Figure 9. Ring-puckering potential energy function for cyclopentene1,2,3,3-d4.
carried out. For completeness, all four isotopic forms are included. Results for all the various rocking models could not be included, and only those leading to the smallest average A2 ( A is the difference between observed and calculated frequencies) are shown. It should be reemphasized that we do not consider this a meaningful determination of the rocking parameters, but rather an indication of how important a role rocking plays in the overall motion. The rocking parameters are not well determined and other sets of parameters may lead to average A2 nearly as small as those in Table IV. Furthermore, it should be noted that Malloy's values, y = -0.10 and 6 = +0.10, for cyclopentene-do are not consistent with our ds
values of y = -0.20 and 6 = -0.10 in that one of the rocking motions has changed directions. Tables I and I1 compare the calculated frequencies for cyclopentene-dl and -d4 to those observed, and Figures 8 and 9 show the potential energy functions determined for these compounds. For each molecule calculation I lists the frequencies for the reduced mass expansion with no rocking; calculation I1 utilizes addition of rocking into the puckering motion. In both cases calculation I1 gives slightly better agreement than calculation I. However, two additional parameters were required for this model. In addition, use of rocking parameters has a pronounced effect on the calculated
The Journal of Physical Chemistry, Vol. 80, No. 11. 1976
Ring Puckering of Deuterated Cyclopentenes
reduced masses and thus, on the dihedral angle. Since the calculated dihedral angle should be reasonably consistent from one isotopic form to another, the last calculations for the d4 and dg molecules in Table IV are in poor agreement with the other calculations indicating that these selections of rocking parameters are not good ones, even though they lead to improved frequency determinations. It is interesting that when no rocking is used, the observed isotope shift is quite well matched by the calculation. We feel, therefore, that the most meaningful potential functions determined are those with no rocking. Undoubtedly, rocking is present, but the slight improvement in the calculations does not warrant the addition of two more parameters, which are themselves ill-determined. The dihedral angles listed in Table IV were calculated by averaging the extremes of the potential for the ground state. The minima of the potential functions occur approximately a degree higher. Each of the calculations with kinetic energy expansion and no rock gives an angle (within 0.1') of 25.9'. On the other hand, the barrier to inversion drops from 233 to 231 to 224 to 215 cm-l in going from the do to d l to d4 to d g . It is interesting to note that the energy between the top of the barrier and the ground state appears to remain constant at 151 f 1cm-l for each isotopic form.
Discussion The spectra of four different isotopically substituted cyclopentene molecules were analyzed in order to examine the variation in barrier height and the effect of the rocking motion on the ring-puckering coordinate. We have found that a regular decrease in barrier height occurs in going from the do compound (233-cm-l barrier) to the d l (231 cm-l) to the d4 (224 cm-l) and to the dg compound (215 cm-l). These barrier values are very insensitive to the one-dimensional model and the inclusion of various rocking motions leaves them virtually unchanged ( f lcm-l). It is apparent, then, that mixin'g of the rocking motion can not account for the change in barrier, even though some rocking is no doubt present in the puckering normal coordinate, and use of rocking parameters does slightly improve the frequency calculation. A similar conclusion was reached by Malloy and Lafferty14 for cyclobutane and cyclobutane-d g where a barrier difference of 14 cm-l was found for the two m01ecules.l~Bauder and co-workers16also concluded that the exact form of the kinetic energy operator has only a very small effect on the barrier determination for nitroethylene. The calculated variation in barrier height may be the result of inherent deficiencies in the one-dimensional model of the puckering. The ring-twisting vibration, which is also a lowfrequency motion, may be sufficiently coupled to the puckering motion to cause the apparent decrease in barrier with deuteration. For this reason, we have begun a two-dimensional analysis, with ring-puckering and ring-twisting coordinates, on the cyclopentene molecules. A two-dimensional potential function has been calculated for the ring-puckering and twisting of 2,5-dihydrofuran,16 but no series of twisting frequencies was available for the analysis. However, the spectra of the d l and d4 derivatives make cyclopentene more suitable since the ring-twisting mode for these is infrared active and gives rise to a number of Q branches. Cyclopentene-do and - d g have C, symmetry but their spectra conform closely to the CzUselection rules expected for a planar molecule. The cll and d4 derivatives have C1 symmetry but their
1177
spectra behave close to C, selection rules. The ring-twisting is AB(infrared forbidden) in Czu for the do and d g molecules but becomes A" (infrared active) in C, for the d l and d4 derivatives. As noted in our discussion5of cyclopentene-dg the reduced mass calculations quite accurately determine the expected isotope shift for that molecule. The same is true for the dl and d4 shifts, and it can be seen that for the same type of puckering model the dimensioned potential function parameters are relatively constant. If we constrain the dimensioned potential function to be identical for all four molecules, fairly good frequency agreement is obtained for all spectra. For example, the best function for all the molecules together would be very close to that of the d4 molecule (using the kinetic energy expansion but no rocking): V = 7.62 f 0.32 X 105x4- 26.1 f 1.1 X 103x2.This calculates all the observed energy level spacings to within approximately 2 cm-I for all four molecules. While we feel that different amounts of mixing of other vibrations in the various isotopic forms should result in somewhat different one-dimensional potential functions, it appears that we have achieved about as good a picture of the kinetic and potential energy functions as can be hoped for within the limitations of the one-dimensional approximation. The dihedral angle for each of the isotopic forms is consistently calculated near 26" for the models with no rocking or with the rocking parameters as previously estimated. Large changes in the rocking parameters can have a marked effect on the calculated angles. Nevertheless, we feel the rocking contribution is sufficiently shall so that the value of 26' is a good one. This may be compared to the value of 22.3 f 2' reported from microwave studies.18J9 Acknowledgments. The authors wish to dedicate this paper to Professor R. C. Lord on his 65th birthday and retirement. His contributions to spectroscopy and chemistry are unsurpassed. This work was supported by the Robert A. Welch Foundation. The FTS-20 spectrophotometer was purchased with the aid of NSF Grant No. GP-37029. One of us (L.E.B.) wishes to thank the John and Fannie Hertz Foundation for a predoctoral fellowship.
References and Notes (1) J. Laane received his Ph.D. under the direction of Professor R. C. Lord in 1967. (2) J. Laane and R. C. Lord, J. Chem. fhys., 47,4941 (1967). (3) T. H. Chao and J. Laane, Chem. fhys. Left., 14, 595 (1972). (4) J. R. Durig and L. A. Carreira, J. Ch8m. fhys., 56, 4966 (1972). (5) J. R. Villarreal, L. E. Bauman, J. Laane, W.C. Harris, and S.F. Bush, J. Chem. fhys., 63,3727 (1975). (6) P. D. Eiiis and G.E. Maciel, J. Am. Chem. Soc., 92, 5829 (1970). (7) R. L. Lipnick, J. Mol. Struct., 21, 411 (1974). (8)J. D. Roberts and C. W. Sauer, J. Am. Chem. Soc., 71,3928 (1949). (9) T. R. Borgers and H. L. Strauss, J. Chem. fhys., 45, 947 (1966). (10) J. R. Viliarreai, J. Laane, W. C. Harris, and S. F. Bush, to be submitted for publication. (11) J. Laane, Appl. Spectrosc., 24, 73 (1970). (12) C. S.Biackweli and R. C. Lord, "Vibrational Spectra and Structure", Vol. 1, J. R. Durig, Ed., Marcel Dekker, New York, N.Y., 1972, pp 1-25. (13) T. B. Malloy, Jr., J. Mol. Spectrosc., 44, 504 (1972). (14) T. B. Malloy, Jr., and W. J. Lafferty, J. Mol. Spectrosc., 54, 20 (1975). (15) The situation for C4H.g and C4D8 is rather different, however, in that without rocking the correlation between calculated potential functions for the two species is very poor. (16) A. Bauder, E. Mathier, R. Meyer, M. Ribeaud, and Hs.H. Gunthard. Mol. fhys., 15, 597 (1968). (17) L. A. Carreira, i. M. Mills, and W. B. Person, J. ch8m. fhys.. 56, 1444 (1972). (18) G. W. Rathjens, J. Chem. Phys., 36, 2401 (1962). (19) S. S Butcher and C. C. Costain, J. Mol. Spectrosc., 15, 40 (1965).
The Journal of Physical Chemlstry, Vol. 80, No. 11, 1976
