J . Phys. Chem. 1988, 92, 5933-5936 have enthalpies of formation in the same order as we have found from our fit. We stress that complex formation does not contradict the mechanism of spin-lattice relaxation via external heavy-atom perturbers, as outlined above: the overlap integrals between naphthalene and its complex forming partner molecules are modulated via stochastic motions of the molecules involved. Since the complex seems to be a rather loose arrangement of molecules with an ill-defined geometry, the Occurrence of TLS which involve the heavy atom is a straightforward idea.
Summary We measured the average spin relaxation at 1.5 K in the photoexcited triplet state of naphthalene in a 3-methylpentane glass doped with bromoethane. We found a pronounced dependence of the relaxation rate on the heavy-atom concentration: Around a mole fraction of 0.1 the rate shows a steep rise which
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levels off into saturation for higher concentrations. We argued that this behavior is due to spin-orbit coupling dominated spin relaxation induced by the heavy dopant. The modulation of the spin-orbit interaction by lattice motion occurs via modulation of the overlap integrals between the naphthalene ?r-orbitals and the outer orbitals of the heavy center. Since the same type of coupling matrix elements governs the electronic decay, a similar dependence on the concentration of the dopant is found in this case. The characteristic variation of the relaxation rate with concentration is well described by assuming the formation of a rather weak complex between probe molecule and heavy dopant.
Acknowledgment. We thank the Deutsche Forschungsgemeinschaft for financial support. Registry No. Naphthalene, 91-20-3; bromoethane, 74-96-4; 3methylpentane, 96-14-0.
Gas-Phase 'H NMR Studies of 1,3,5-Trimethylhexahydro-I ,3,5-triatine Clifford B. LeMaster, Carole L. LeMaster, Mohsen Tafazzoli, Cristina Suarez, and Nancy S. True* Department of Chemistry, University of California, Davis, California 9561 6 (Received: April 1, 1988)
Gas-phase 'H NMR spectra of 1,3,5-trimethyIhexahydro-1,3,5-triazine (THTRIZ) display exchange-broadened line shapes attributable to ring inversion that are both temperature and pressure dependent. Unimolecular rate constants obtained at pressures above 800 Torr in the gas phase are twice those obtained for liquid samples (15 vol 7% in CHFC12) at corresponding temperatures. The free energy of activation (AG') at 298 K (12.4 (0.1) kcal mol-') for the chair to twist-boat inversion is slightly lower than that for the liquid. Other unimolecular gas-phase chair to twist-boat activation parameters (AH* = 13.2 (0.5) kcal mol-', AS* = 2.8 (1.8) cal mol-' K-', E,, = 13.8 (0.5) kcal mol-', and A = 3.51 (5) X lOI3 s-I) are all lower. Pressure-dependent rate constants obtained at 301.4 K at pressures between 5.48 and 2000 Torr can be adequately modeled with RRKM theory; thus vibrational redistribution of THTRIZ at an internal energy of about 13.2 kcal mol-' is statistical.
Introduction This study continues our examination of gas-phase conformational kinetics in six-membered rings. Our previous studies of cyclohexane (CHX),I tetrahydropyran (THP),* and cyclohexyl fluoride (CHF)j have shown that gas-phase unimolecular inversion rates were slower and corresponding activation parameters were higher than those found in the condensed phases. These results were consistent with negative activation volumes of ca. -4, -5, and -8 cm3/mol for the inversion process. The present study of THTRIZ gives rate constants that are twice the liquid values and a directionally lower AG* of activation. This is consistent with a positive activation volume for the chair to twist-boat inversion. The AS*value of ca. 3 cal mol-' K-I supports the freely or nearly freely pseudorotating transition state proposed for carbon and carbon-xygen rings by Pickett and Strass4 and supported by our previous studies.'-3 As with the previous rings studied, the gas-phase ring-inversion constants were found to be pressure dependent. Vibrational redistribution in T H T R I Z at energies of about 13 kcal mol-' and 1 X lo7 states/cm-' was found to be statistical. This is the highest state density we have studied to date, those of CHX, CHF, and T H F being 1500/cm-', 5285/cm-', and 700/cm-', respectively, at internal energies of approximately 12 kcal mol-'. The study of six-membered rings by N M R in the gas phase is limited by low vapor pressure and low interconversion barriers (8-14 kcal mol-'). Small limiting chemical shift differences further limit the possibility of study. CHX, THP, and C H F have proton (1) (2) (3) (4)
Ross, B. D.;True, N. S . J . Am. Chem. SOC.1983, 105, 4871-4875. Chu, P.S.; True, N. S. J . Phys. Chem. 1985, 89, 2625-2630. Chu, P.S . ; True, N. S. J . Phys. Chem. 1985, 89, 5613-5616. Pickett, H. M.; Strauss, H. L. J . Am. Chem. SOC.1970,92,7281-7290.
0022-3654/88/2092-5933$01.50/0
limiting chemical shift differences of about 0.5 ppm, necessitating work at temperatures well below ambient even at 500 MHz. In the case of CHF, the volatility was so low at temperatures where reliable kinetic data could be obtained by using proton N M R that I9F spectra (F,,-F, chemical shift difference = 18.59 ppm) were used to raise the temperature region of study. In the case of THTRIZ, the limiting chemical shift difference of 0.86 ppm (259 Hz at 300 MHz) allowed 300-MHz proton spectra to be obtained at temperatures from 288 to 310 K where the vapor pressure is about 2 Torr. The large limiting chemical shift difference actually necessitated work in this temperature region, which is above coalescence because at temperatures between 278 and 288 K, the broad exchanging proton peak is so flat as to be barely discernible above the base line.
Experimental Section THTRIZ was purchased from Aldrich Chemcial Co. and sulfur hexafluoride from Matheson Gas Co. The THTRIZ was used without further purification except for five freeze-thaw-pump cycles prior to sample preparation. Pressure samples were prepared by introducing 1.5 Torr of THTRIZ into an evacuated 3-cm long, 12-mm N M R tube. SF6 was added to increase the sample pressures to those used in the study. Short, 3-cm insert tubes were used to confine the sample and thus reduce the temperature gradient within the active volume. The short tubes were inserted into a longer 12-mm tube for introduction into the probe. Details of the sample preparation are described elsewhere.' Sample pressures appearing in Table I are corrected pressures. An estimated 2% uncertainty in the pressures results from this technique. Samples used for temperature-dependent measurements were prepared in the same manner, but contained 0.5 of THTRIZ along with added SF6 to increase the total pressure to 1600 Torr. 0 1988 American Chemical Society
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The Journal of Physical Chemistry, Vol. 92, No. 21, 1988
N M R measurements were made on a General Electric NT-300 spectrometer with IH observation at 300 MHz. A 12-mm probe was used to increase signal and reduce the required number of transients. Spectra were acquired on spinning samples in unlocked mode. Acquisition time was 2.05 s/transient with a 0.75-s delay time and a pulse angle of 86' (12 p ) . Typically 300-1000 transients stored in 8 K memory were required to achieve signal-to-noise ratios of about 50 to 1. Low-pressure and/or temperature samples required more transients. Slow-exchange spectra required 4000 transients due to the extremely low vapor pressure of THTRIZ at 243 K. The free induction decays were multiplied by an exponential line-broadening factor of 1 Hz. Probe temperature was measured by using three copperconstantan thermocouples placed at different heights within a spinning N M R tube in the active volume. By proper control of the variable-temperature unit air flow at 11.6 L/min, it was possible to reduce the gradient measured by the thermocouples to
