J . Phys. Chem. 1988, 92, 4056-4059
4056
momentum cross sections at the two proton sites which may reflect anisotropy in the molecule’s interaction potential. The spin-rotation cross section is roughly twice as large as the geometrical cross section of the molecule. The ratio of the angular momentum cross section and the geometric cross section allows an estimate of the number of collisions needed to completely randomize the molecule’s angular momentum. Similar results have been obtained for NH33 and benzene.8 The angular momentum reorientation cross section of furan is somewhat smaller than the cross section estimated from the second virial coefficient. Though transport properties of furan have not been reported, the second virial coefficient of furan at three temperatures has been determined from calorimetric data.22 Equating the second virial coefficients with the quantity ( b - a / R T ) , where a and b are the van der Waals m3/mol parameters, yields a molecular volume b, of 2.053 X which corresponds to a cross section of 195 A2,which, assuming a spherical molecular shape, is about 1.3 times the angular momentum reorientation cross section. The small NOE enhancements observed in the present study are surprising. In the extreme narrowing region the spin-rotation relaxation rate l/TlsR = (4*’/a)c&J, where a is defined above and T J is the angular momentum corelation time. At 300 K, the quantity (4n2/a)Cef?is 2.48 X lo9 for the a protons of furan. The analogous expression for the rate of dipolar relaxation in the extreme narrowing region is l / T D D= CDDT~,where CDDis the dipolar coupling constant and T~ is the molecular reorientation (22) Guthrie, G. B., Jr.; Scott, D. W.; Hubbard, W. N.; Katz, C.; McCullough, J. P.; Gross, M. E.; Williamson, K. D.; Waddington, G. J . Am. Chem. SOC.1952, 74, 4662-4669.
correlation time. The dipole-dipole coupling constant CDD = (447r)2h2y,2y$r4(s-~), between two protons separated by 2.75 A, is 1.905 X lo9 s - ~ . CDD is comparable in magnitude to the quantity (4r2/a)(CCf,2).If T~ = T ~ then , T,DD should be comparable in magnitude to TIsR. The small ( q = 0.02) NOE observed is consistent with TIDD values in the range 50-150 s. Using the relationship, 1/ TIDD = CDDT~,one obtains a lower limit molecular reorientation correlation time of ca. lo-’’ s at 300 Torr which is an order of magnitude shorter than the T J at this pressure. The free rotor model derived in ref 6 shows that the ratio of the correlation times T J / T ~= 5 for a spherical top, while and extrapolation of the extended rotational diffusion theory of McClung finds the ratio to be equal to 4.23 In the case of furan, a slightly asymmetric top treated as symmetric, the relationship between T~ and T J is very ~ o m p l i c a t e d .Although ~~ furan is an asymmetric top and these analyses do not rigorously apply in this case, it has been shown that the diagonal elements of the correlation time matrix for an asymmetric molecule display the same general behavior as symmetric and spherical top molecule^.^' Further studies relating to these quantities and their meaning are in progress and will be reported elsewhere.
Acknowledgment. We are pleased to acknowledge support from the National Science Foundation through Grants CHE-8351 11698-PYI and CHE-85-03074, the National Institutes of Health through Grant PHS-GM-29985-06, and the Alfred P. Sloan Foundation. Registry No. Furan, 110-00-9 (23) McClung, R. E. D. J . Chem. Phys. 1971, 55, 3459-3467.
Ring-Puckering Potential Energy Function and Unusual Rigidity of Silacyclopent-2-ene M. B. Kelly and J. Laane* Department of Chemistry, Texas A& M University, College Station, Texas 77843 (Received: October 29, 1987)
The far-infrared spectrum resulting from the ring-puckering vibration of silacyclopent-2-ene-1, l - d z has been recorded, and several transitions have been observed between 100 and 200 cm-l. The data confirm that the ring system is planar. The reduced masses for both undeuteriated and d2 molecules have been calculated as a function of an SiH2rocking parameter. When a small amount of rocking is mixed with the puckering motion, the same one-dimensional potential energy function can be used to fit the far-infrared spectra of both isotopic species. The function derived is V = 20.75 X 105x4+ 19.59 X 103x2,where x is the puckering coordinate. The large potential constants imply that an extremely rigid ring system is present. Molecular mechanics calculationsbased on standard force constants, which result in satisfactory predictions for related molecules, predict the ring should be nonplanar and much less rigid. Modifications of torsional and angle bending force constants, which are expected to be increased in magnitude by silicon-x orbital interactions, yield a much better agreement between the molecular mechanics and experimental potential energy function.
Introduction In 1970 Laane’ studied the far-infrared spectrum of sila-
,
j
cyclopent-2-ene, CH=CHSiH2CH2CH2, and demonstrated that this molecule has a planar ring system. This result was unexpected in view of the fact that the related molecules 2,3-dihydrofuran,*
,
1
CH=CHOCH2CH2, and 2,3-dihydr0thiophene,~CH=CHSC-
recently developed a computer program for calculating the reduced masses for the ring puckering of asymmetric five-membered ring molecule^.^ In order to quantitatively determine the potential energy function for silacyclopent-2-ene, we have now recorded the ring-puckering spectra of a second isotopic species and then utilized the reduced mass programs to find the common potential function for both molecules.
7
H2CH2,are nonplanar with inversion barriers of 85 and 325 cm-l, respectively. Moreover, it became clear that the silacyclopent2-ene ring system is unusually rigid. However, a quantitative potential function in terms of a dimensioned coordinate could not be calculated since methods for accurately calculating reduced masses for asymmetric molecules were not available. We have (1) Laane, J. J . Chem. Phys. 1970, 52, 358. (2) Green, W. H. J . Chem. Phys. 1969, 56, 716. (3) Ueda, T.; Shimanouchi, T. J . Chem. Phys. 1967, 47, 5018
0022-3654/88/2092-4056$01.50/0
Experimental Section Silacyclopent-2-ene-J,l-d2 was prepared in a manner similar to that described for the undeuteriated molecule’ except that LiAID, was used as the reducing agent in place of LiAIH4. Far-infrared spectra were recorded with a Digilab FTS-20 infrared spectrophotometer. Vapor-phase samples were contained in a (4) Schmude, R W , Jr., Harthcock, M A : Kelly. hl B , Laane, J J Mol Spectrosc 1987, 124. 369
1988 American Chemical Society
Ring Puckering of Silacyclopent-2-ene
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988 4057
I 120
140
160
cn-1
Figure 1. Far-infrared spectrum of silacyclopent-2-ene-1,1-d2 recorded at 50-Torr pressure and 4.9-m path length.
TABLE I: Potential Energy Parameters' for Silacyclopent-2-ene as a Function of Rockine Parameter R R O H (Xi@) U D (Xi@) bH (Xi@) b~ (Xlo') -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
16.83 17.50 18.28 19.17 20.21 21.37 22.69
14.87 15.83 16.96 18.30 19.86 21.64 23.68
17.62 17.97 18.36 18.81 19.31 19.86 20.46
16.60 17.12 17.73 18.41 19.17 20.02 20.95
'The units of a and b are cm-'/A4 and cm-l/A2, respectively.
t15
-0.4
Figure 2. Variation of the parameters a and b in the potential function V = ax4 + bx2 for the two isotopic species of silacyclopent-2-ene as a function of rocking parameter
0- 1 1-2 2-3 3-4 4-5 5-6 6-7 7-8
Figure 1 shows the far-infrared spectrum recorded for silacyclopent-2-ene-1,l -d2. Six transition frequencies can be seen in the figure between 116 and 173 cm-I. In addition, a weak doublet was observed at 176.9 and 184.9 cm-l, but no other bands were detected between 30 and 250 cm-l. The spectrum is similar to that observed for the undeuteriated molecule except that each transition frequency is shifted down in frequency by about 7-12 cm-I. Again the pattern is regular and characteristic of a planar molecule. The far-infrared spectrum of the undeuteriated molecule was previously fitted' with a reduced potential function5of the form
Society: Washington, D.C., 1982.
0-1 1-2 2-3 3-4 4-5 5-6 6-7
+ 2.40Z2)
( 5 ) Laane, J. Appl. Spectrosc. 1970, 24(1), 73. (6) Laane, J.; Harthcock, M. A,; Killough, P. M.; Bauman, L. E.; Cooke, J. M. J . Mol. Specrrosc. 1982, 91, 286. (7) Harthcock, M. A,; Laane, J. J. Mol. Spectrosc. 1982, 91, 300. (8) .Malloy, Jr., T. B. J . Mol. Spectrosc. 1972, 44, 504. (9) Allinger, N. L.; Burket, U.Molecular Mechanics; American Chemical
R.
TABLE 11: Observed and Calculated Ring-Puckering Frequencies (em-') for Isotopic Forms of Silacyclopent-2-ene transition observed calculated Ab
Results and Discussion
where Z is the puckering coordinate in reduced (undimensioned) form. Since the kinetic energy (reciprocal reduced mass) expansion was not calculated, accurate dimensioned potential energy constants could not be determined. Use of the potential function in eq 1 implies that the reduced mass is constant, but it, in fact, varies as a function of puckering c ~ o r d i n a t e . ~ , ~ * ~ The data now available for both isotopic forms for the silacyclopent-2-ene along with methods for calculating the kinetic energy expansions for different vibrational models make it possible to determine an accurate dimensioned potential function which fits the spectroscopic data for both isotopic species. The simplest model for the ring puckering is the bisector m0de1~8~-* which assumes that no other motions couple with the puckering. The reduced masses calculated for this model for the undeuteriated and deuteriated molecules are 129.6 and 138.6 au, respectively. The structural parameters necessary for the calculation were determined by using the molecular mechanics (MM2) programs of Allinger.' When the dimensioned potential functions are determined for the two isotopic species independently with these reduced mass values, the potential energy constants for the two isotopomers differ by about 2%. While this difference is minor, it can be totally eliminated by using a rocking parameter4s6which
0.8
R
modified 4.9-m-path Perkin-Elmer cell with polyethylene windows.
V (cm-I) = 31.45(Z4
0.4
0.0
Silacyclopent-2-ene 123.7 123.1 139.3 141.5 155.6 155.2 167.6 166.4 177.4 176.2 184.9 184.8 192.1 192.7 199.2 199.9 Silacyclopent-2-ene- 1,I -d2 116.7 116.9 131.2 132.9 145.9 145.5 156.8 156.0 165.0 165.0 172.9 173.1 180.4 76.9" } 184.9"
0.6 -2.2 0.5 1.2 1.2 0.1 -0.6 -0.7 0.7 -1.7 0.4 0.8
0.0 -0.2 -0.5
uprobable Fermi doublet with origin near 180.9 cm-'. bobserved calculated.
mixes a small amount of SiH2 (or SiD2) rocking with the puckering. Table I shows how the potential energy parameters determined for the function
v = ax4 + bx2
(2) vary with the rocking parameter R for the two isotopic species. Figure 2 shows this graphically, and it is evident that for R = 0.5 the a and b constants for the two species become essentially identical V(cm-') = 20.75 where x is in A. to R = 0.5 are gH = 1/KH = 0.0072358
X
10sx4
+ 19.59 x
103x2
(3) The kinetic energy expansions corresponding
- 0 . 0 1 0 3 5 4 ~-~0 . 1 4 1 4 7 1 ~+~ 0 . 4 4 9 8 6 5 ~(4) ~
and gD
= 1/WD = 0.0065275 - 0 . 0 0 5 3 2 2 7 ~-~0 . 1 3 8 4 9 9 ~+~ 0 . 3 6 5 6 0 0 ~(5) ~
Table I1 shows the calculated frequencies based on the potential function in eq 3 and the kinetic energy expansions in eq 4 and 5 and compares them to the observed values. As can be seen, the fit is good. Figure 3 shows the potential function and the observed transitions for silacyclopent-2-ene-1 ,I -dz. As compared to the potential functions of similar molecules containing different
4058
The Journal of Physical Chemistry, Vol. 92, No. 14, 1988
Kelly and Laane
TABLE 111: Potential Energy Parameters for Five-Membered Ring Molecules 1o-b, cm-'/A4
CH=CHCH,XCH, 7.23
X
CH2
0 S SiH2 1200'
CH=CHXCH2CH, 7.88 9.68 6.66 20.75
6.31
3.05 1.97
I
1046, cm-'/A2 CH=CHCH2XCH2 -2.59 0.92 1.os
-0.03
6H=CHXCH2CH2 -2.71 -1.87 -2.95 1.96
I
c
> 600'
I
156.a
, 200*
pJ2
-0.3 -02 W
!3! 2
-0.1
0.0
PucKEReJo C-AE
0.3
-0.3 -02 -0.1 0.0 0.1 02 PUCKERW COORDhlATP d l
0.3
Figure 4. Comparison of ring-puckeringpotential energy functions for silacyclopent-3-ene(left curves) and 2,3-dihydrothiophene (right curves)
determined (a) experimentally and (b) from molecular mechanics calculations.
0. -0.2
-0.1 0.0 0.1 02 E N CobRCWATE d)
0.2
0.1
(A)
Figure 3. Ring-puckering potential energy function and observed transitions for silacyclopent-2-ene-Z,Z-d2.
heteroatoms, this potential function is very steep, reflecting an unusually rigid ring structure. In order to place into perspective the unusually large values of the potential energy parameters for silacyclopent-2-ene, Table I11 lists the a and b potential constants for this molecule along with those of several related molecules. These values are based on the recently described methods for calculating the reduced masses for asymmetric five-membered ring molecule^.^ What is most evident is that the coefficient for the quartic term for silacyclopent-2-ene is about an order of magnitude larger than might be expected. Similarly, the quadratic coefficient, which results predominantly from torsional forces, is large and positive. The analogous sulfur, oxygen, and carbon compounds are nonplanar and have negative b coefficients arising from two (or three) adjacent C H 2 groups which avoid eclipsing one another when the ring system bends out of the plane.
Molecular Mechanics Calculation We have recently tested the ability of molecular mechanics calculations (MM2) for predicting energy differences between different conformations of the same molecule.lO-ll These calculations proved to be in semiquantitative agreement with the experimental data for barrier heights and almost always correctly predicted the lowest energy conformation. For example, Figures 4 and 5 compare the experimental potential energy curves to the molecular mechanics curves for ~ilacyclopent-3-ene~~ (left) and 2,3-dihydr~thiophene~ (right), The former is correctly predicted to be planar while the latter is correctly predicted to be puckered although the calculated barrier height of 160 cm-' is only about half of the observed value of 327 cm-'. When the standard MM2 force constants are utilized to generate the ring-puckering potential function for silacyclopent-2-ene, a double-minimum potential function characteristic of a nonplanar molecule is generated. Figure 5 compares this to the experimental curve of the planar molecule. The discrepancy between the standard MM2 calculation and the experimental result must arise from an unusual interaction (IO) Cooper, C. M.S. Thesis, Texas A&M University, 1986. ( 1 1 ) Lee, R. S.: Cooper, C.; Laane, J., to be published. (12) Laane, J. J . Chem. Phys. 1970,52, 358.
-0.3 -02 -0.1
0.0 0.1 02 WCKERNG C O O R M A T E (A)
0.3
Figure 5. Ring-puckering potential energy functions for silacyclopent2-ene determined (a) experimentally, (b) from molecular mechanics
calculations using standard force constants, and (c) from molecular mechanics calculations using modified force constants. between the silicon atom and the carbon-carbon r system. In order to demonstrate this with an MM2 calculation, we have estimated reasonable increases in the values of the three force constants which we expect to be most affected by the silicon-r twofold torsion was orbital interaction: (1) the C=C-Si-C estimated (somewhat arbitrarily) to be 8 kcal/mol (typical of internal rotation about a bond with more r character than a single bond but less than a double bond) rather than the MM2 standard angle bending force value of 0.0 kcal/mol; (2) the C=C-Si constant was increased from 0.4 to 1.2 mdyn/A; and (3) the =C-Si-C bending constant was increased from 0.4 to 1.0 mdyn/A. With these values the molecular mechanics calculation predicts silacyclopent-2-eneto be. planar and produces a calculated potential energy curve which is much closer to that obtained experimentally. The modified MM2 function is also shown in Figure 5. We have not attempted to match the calculated potential curve to the experimental one. That could have been done quite satisfactorily, but the significance of the results after adjusting three parameters would have been questionable. Here we have simply tried to demonstrate that an interaction of the carbon-
J . Phys. Chem. 1988, 92, 4059-4062 carbon double bond with silicon orbitals can result in a modification of the force constants which yield a potential energy curve similar to that obtained experimentally.
Conclusions The quantitative determination of the ring-puckering potential energy function for silacyclopent-2-ene in this work demonstrates that this ring system is indeed unusually rigid. Molecular mechanics calculations, which are usually reliable in predicting the correct conformation and in estimating energy differences between conformers, fail for this molecule. This can be explained by a significant interaction between the silicon atom and the carboncarbon double bond. We are currently carrying out ab initio (GAUSSIAN 82) calculations on this molecule in order to gain an
4059
insight into the nature of the bonding. Whether silicon d orbitals or antibonding u orbitals are involved in the interaction is not clear. What is clear is that a type of bonding interaction which is relatively insignificant in the analogous oxygen and sulfur compounds is present for this cyclic silane. A similar interaction is apparently present in 2-phospholene,13 but the magnitude is much smaller.
Acknowledgment. We thank the National Science Foundation and the Robert A. Welch Foundation for financial support. Registry No. CH=CHSiH2CH2CH2, 6572-33-4; CH=CHSiD2CH2CH2, 110897-47-7.
-
(13) Harthcock, M. A.; Villarreal, J. R.; Richardson, L. W.; Laane, J. J. Phys. Chem. 1984,88, 1365.
Vibrational Relaxation Efficiency at Low and High Temperature Mark G . Sceats Department of Physical Chemistry, University of Sydney, N.S. W. 2006, Australia (Received: December 4, 1987)
A stochastic model of vibrational relaxation of a diatomic is developed and used to explain the deviation from Landau-Teller behavior at low temperatures. The model includes (i) attractive forces, associated with both encounter dynamics and acceleration effects, (ii) quantum effects associated with energy conservation and wavepacket spreading, and (iii) the anharmonicity of the diatomic. For a low-frequency diatomic vibration of 200 cm-I, a weak temperature dependence below 100 K is predicted for both light and heavy colliders.
Introduction Vibrational relaxation of diatomics in seeded supersonic expansions has been extensively studied'-5 and the primary observation, namely that the V-T relaxation becomes weakly temperature dependent at low temperatures, has been the subject of considerable These trends are also confirmed in bulb experiments,6.'@-I3 where deviations from classical Landau-Teller behavior become apparent at low temperature. In bulb experiments, predissociation of van der Waals complexes has been invoked,6 but the same behavior is observed in beams where selective excitation of the isolated molecule is possible. In this note a model is presented which explains the observed behavior over the entire temperature range, without change of mechanism, for the isolated molecule. Theoretical Development The quantity of interest is the collision efficiency for the transfer of vibrational energy from an oscillator AB with vibrational energy E . The efficiency Q is related to the relaxation rate kE by (1) Tusa, J.; Sulkes, M.; Rice, S. A. Proc. Narl. Acad. Sci. U.S.A. 1980, 77, 2367. (2) Sulkes, M.; Tusa, J.; Rice, S. A. J . Chem. Phys. 1980,72,5733. Tusa, J.; Sulkes, M.; Rice, S. A. J. Chem. Phys. 1979, 70, 3136. (3) Hall, G.; Liu, K.; McAuliffe, M. J.; Giese, C. F.; Gentry, W. R. J . Chem. Phys. 1984, 81, 5577. (4) McClelland, G. M.; Saenger, K. L.; Valentine, J. J.; Herschbach, D. R. J. Phys. Chem. 1979,83, 947. ( 5 ) Kable, S. H.; Knight, A. E. W. J . Chem. Phys. 1987, 86, 4709. (6) Ewing, G. Chem. Phys. 1978, 29, 253. (7) Gray, S. K.; Rice, S. A. J . Chem. Phys. 1985, 83, 2818. (8) Cerjan, C.; Rice, S. A. J. Chem. Phys. 1983, 78, 4929. Cerjan, C.; Lipkin, M.; Rice, S. A. J . Chem. Phys. 1983, 78, 4929. (9) Schwenke, D. W.; Truhlar, D. G. J . Chem. Phys. 1984, 81, 5586. (10) Lucht, R. A,; Cool, T. A. J . Chem. Phys. 1975, 63, 3962. (1 1) Zittel, P.; Moore, C. B. J . Chem. Phys. 1973, 59, 6636. (12) Billingsley, J.; Callear, A. B. Trans. Faraday SOC.1971, 67, 257. (13) Stephenson, J. C. J. Chem. Phys. 1974, 60, 4289.
where uAB,M is a reference hard-sphere diameter, p is the bath particle-diatom reduced mass, and pM is the bath density at temperature T. In the stochastic model used in this paper the energy relaxation rate is deduced from the frequency-dependent friction @(a) that the bath exerts on the oscillator. The interest in use of stochastic approaches is that they are readily extended to liquids where individual collision events may not be res01ved'~J~ and collective behavior of the bath molecules may play a role. If K ( t ) is the Fourier transform of @(o),then linear coupling theory gives16
kE = R X - K ( t ) Cvv(t) di with R = 1. Cvv(t) is the normalized velocity autocorrelation function of the unperturbed oscillator, and R is a correction factor introduced in an ad hoc manner to account for nonlinear coupling with heavy bath parti~1es.I~ For a Morse oscillator with harmonic frequency w and dissociation energy D
where 6 = E / D and a(€)= w(1 The semiclassical limits to this paper are found for a given quantum state u by using u
20 + -21 = [ l - (1 - 4 / 2 1 hw
(4)
(14) Sceats, M. G. Adu. Chem. Phys., 1988, 708, 358. (15) Nordholm, S.; Freasier, B. C.; Jolly, D. L. Chem. Phys. 1977, 23, 135. (16) Grote, R. F.; Hynes, J. T. J . Chem. Phys. 1982, 77, 3736.
0022-3654/88/2092-4059$01.50/0 0 1988 American Chemical Society
