J. Phys. Chem. 1992,96, 10206-10212
10246
Gas-Phase NMR Study of the Degenerate Cope Rearrangement of Bullvalene Phillip 0. Morew, C r i s h Suarez, Mohsen Tafazzoli, Nancy S. True,* Department of Chemistry, University of California, Davis, California 9561 6
and Clifford B. LeMaster Department of Chemistry, Boise State University, Boise, Idaho 83725 (Received: July 9, 1992: In Final Form: September 9, 1992)
Gas-phase 'HNMR spectra of tricyclo(3.3.2.0)deca-2,7,9-triene (bullvalene) obtained at temperatures above 340 K,display a single broad resonance 4.271 ppm down field from gaseous TMS whose line width decreases with increasing temperature and pressure. Spin-lattice relaxation does not contribute significantly to the line width over the pressure and temperature ranges studied and the observed broadening can be attributed t6 proton exchange associated with the degenerate Cope rearrangement. Infiite pressure, unimdeclilar rate constants for the Cope rearrangement of gaseous bullvalene are ca. 15% lower than those observed in solutions of bullvalene in CS2 at the same temperatures. Gas-phase kinetic parameters for the rearrangement are Eaa = 13.8 (0.2)kcal mol-', A, = 2.1 (1.5)X lOI3 s-', AG*m8 = 13.1 (0.2)kcal mol-', AH' 13.2 (0.3)kcal mol-', and AS* = 0.4 (1.2)calmol-' K-'. The pressure depndence of the rate constantsindicatesthat intramolecular vibrational redistribution in critically energized bullvalene molecule8 is statistical or nearly so.
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Introduction Since its prediction by Doering and Roth' and synthesis of the molecule by Schrbder2in 1963,the degenerate Cope rearrangement of tricyclo(3.3.2.0)deca-2,7,9-triene (bullvalene) has been extensively studied in condensed phases using NMR spectrosw One of the three possible rearrangement pathways is
Table I lists kinetic parameters for the degenerate Cope rearrangement of bullvalene in several solvents. Reported activation enthalpies, A P , range from 11.0 to 13.9 kcal mol-' and activation entropies, AS*,are small and generally positive except for early studies of C2C4and acetone-d6solutions where rate constants were determined using spin-ccho methods: Poupko et al." studied the rearrangement of deuterated bullvalene in liquid-crystalline solvents, obtaining results essentially identical with those obtained in isotropic solvents. Meier and Earl'2 reported exchangebroadened cross-polarization magic angle spinning I3C NMR spectra which demonstrate that the rearrangement takes place values which arevery similar in the solid phase with A P and a* to those in liquid solutions. Recent studies of single crystal and powder samples of deuterated bullvalene reported rate constants for the Cape narrangement similar to those obtained in dutior~s.'~ In this report we present the first gas-phase NMR study of bullvalene which demonstrates that the degenerate Cope rearrangement occurs in the gas phase. Temperature- and pressure-dependent rate constants are used to characterize the gasphase kinetics of this process and the effects of intermolecular forces on the kinetic parameters. In the gas phase the prcasure dependence of the rearrangement rate constants can provide information about intramolecular vibrational energy redistribution (IVR) in bullvalene at low internal energies. F " 4 e p e n d e n t rate constants can be compared with predictions made using statistical theories such as RictRamsperger-Kassel-Marcus (RRKM) theory which assumes that IVR is statistical and that IVR rate constants exceed ( k ( E ) ) , the average energy-dependentreaction rate constant.14 Significant differences between calculated and observed pressure-dependent rate constants may indicate that IVR is not proceeding at its statistical limit. Bullvalene has a state density of 104 states/cm-'
gasa CS," CS2b C2H2Clf CDCljd lip cryst' ClC4 acetone-dd solid'
13.1 (0.2) 12.4 (0.1) 12.4 (0.01) 12.3 (0.1) 12.6 (0.1) 12.6 12.7 12.5
13.2 (0.3) 0.4 (1.2) 12.6 (0.3) 0.5 (0.6) 12.6 (0.07) 0.8 (0.2j 13.3 (0.1) 3.4 (0.4) 13.9 (0.7) 4.4 (2.3) 13.3 2.5 12.2 -1.6 11.0 -5.2
13.8 (0.2)
21.1 (7.0)
13.2 (0.1) 23.7 (2.1) 13.9 (0.1) 100 (20) 14.5 (7) 13.9 12.8 (0.1) 8.0 15.1
40.2
This work. bReference8. CReference9. dReference7. 'Reference 11; no uncertaintica were reported. /Reference 6; AG'198, Mf', and A S , were calculated from 12 and 4 temperature-dependent rate constants reported for bullvalene in tetrachloroethylene and acetone& respectively. 'Reference
13.
at 13 kcal mol-' indicating that RRKM theory may provide a valid description of the kinetics of the Cope rearrangement of this molecule. Several conformationalp r m in molecules at low internal energies with comparable state densities have been adequately modeled using RRKM kinetics.'521 The axiakquatorial fluorine exchange process in SF4 is a notable exception.22 Bullvalene is more symmetric than other molecules studied and symmetry restrictions may prevent statistical IVR with rate constants in excess of k Q . The direction and magnitude of solvent effects on the Cope * by comparing rate rearrangement of bdvalene can be detemud constantsfor gas-phasc samples with those obtained for w * e solutions. previous studies have shown that increasing the preesure applied to a solution of bullvalene in CS2 by 500 MPa increases the rearrangement rate constant by 10% at 19.8 0C?3 The small negative activation volume, AV,of -0.5 cm3 mol-', consistent with theeeresults, indicates that sisnificant charge separation does not o a u r in the transition state in solution. If the Cope rearrangement in bullvalene is predominantly an intramolecular proass which is facilitated by solvent interactions, one would predict that rate constants would be slightly slower in the gas phase, based on the pressuredependent solution-phase results. A significant change in the rearrangement mechanism with sample phase would produce a larger phase dependence of the rate constants. ExperimeaW Section Sample Preparation. Our sample of bullvalene was provided by Professor G. Schr&ier(University of Karlsruhe). The gas-phase sample used to determine temperature-dependent Cope rear-
0022-3654/92/209610206$03.00/0 Q 1992 American Chemical Society
Cope Rearrangement of Bullvalene rangement rate constants was prepared by placing a small (-2 mg) crystal of bullvalene in the bottom of a 3-cm-long 12-mm insert tube which was then attached to a vacuum line. Air was evacuated from the tube, 0.25 TOKof carefully degassed tetramethyhilane (TMS, Aldrich, NMR grade) was added as a frequency and field inhomogeneity reference, followed by 1750 Torr (at 297 K) of SF6(Liquid Carbonic, Grade A) which was used to narrow spectral lines and ensure fmt-order rate constants. The tubes were sealed as previously deacribed.16 Samples with different bath gas pressures were prepared by placing small (-3 mg) crystals of bullvalene in the bottoms of 3-cm-long 12-mm insert tubes which were then attached to a glass manifold. The manifold was constructed from a 1-L flask fitted with 16 0.25-in.-o.d. glass stems at the bottom and attached to the vacuum line at the top. The tubes were evacuated, 0.25 TOKof TMS was added, and then the appropriate amount of SF6 was added as a bath gas. The lowest pressure of bath gas was added fmt, the system was allowed to equilibrate for 30 min, and one tube was sealed. More bath gas was then added to the manifold and allowed to equilibrate and then the next tube sealed. This process was used for all samples below ambient pressure. Gas-phase samples with pressures above 760 Torr were prepared by condensing the appropriate amount of bath gas into the sample tube from a calibrated glass bulb. The liquid-phase sample was prepared by dissolving bullvalene, 5% by weight, in CS2with TMS (
