A multichannel semiclassical collision theory, based on Feynman's path-integral formulation of quantum mechanics and developed by Pechukas, is discussed. The theory is applied to low-energy, elastic and inelastic, collisions between ${\mathrm{He}}^{+}$ and Ne. The calculation involves the solution of a boundary-value problem, and a numerical method for obtaining this solution is presented. The numerical results and the qualitative interpretation of them are compared with the predictions of other available theories.
A model system consisting of two electronic manifolds coupled through a nontotally symmetric mode of vibration is solved exactly and self-consistently by the method described in Paper I [J. Chem. Phys. 65, 2071 (1976)]. As in I, the model is defined in terms of harmonic diabatic potentials, but the restriction to harmonic adiabatic potentials, applied in I, is lifted here. As a result, the adiabatic coupling operator which has the same analytical form as in I, can assume a much wider range of values. It leads to adiabatic potentials which in general are anharmonic and may exhibit a double minimum. The coupling is taken to be an odd function of the vibrational coordinate so that it describes the (pseudo-) Jahn–Teller effect. Absorption and emission spectra are calculated for selected combinations of four spectroscopic parameters: (1) the electronic energy gap; (2) the diabatic harmonic frequency difference; (3) a linear adiabatic coupling parameter; and (4) a nonlinear (quasiquadratic) adiabatic coupling parameter. In the appropriate limits, the results are shown to reduce to analytical weak- and strong-coupling results, but the model is shown to differ from the molecular dimer model which also permits exact numerical solution for arbitrary coupling. The calculated spectra are interpreted in terms of a number of basic characteristics. Recognition of these characteristic spectral patterns may be helpful in the analysis of vibronically contaminated spectra. For certain combinations of parameter values, the model predicts strong and possibly anomalous solvent and isotope effects. As an example, the vibrational structure of the lowest singlet absorption band of pyrazine is analyzed and shown to indicate evidence for nonlinear vibronic coupling.
Using an exponential transition probability model normalized in the (0,∞) energy domain, we have obtained an analytical solution for the time-dependent population density below threshold, c (x,t), in the form of the eigenfunction expansion where x is internal energy, t is time, A0 and Aj are constants that depend on initial conditions, S and Rj are solutions of a determinant of a matrix of coefficients and k0−1 and τj are the relaxation times, the lowest of which (subscript 0) represents the reciprocal of the steady-state rate constant. From c (x,t) we then obtain all other time-dependent properties such as the non-steady-state rate constant and average energy, as well as incubation times and dead times for both number density and vibrational energy. Calculations relative to shock tube decomposition of N2O, CO2, and O2 in inert gas are compared with experiment, with generally good results. For the triatomics, average energy transferred per collision, as calculated from the experimental relaxation time, compares well with that calculated from the Schwartz–Slawsky–Herzfeld theory. The calculated diatomic rate constants (but not the relaxation and incubation times) are too low. Calculations relative to shock tube decomposition of cyclopropane are compared with numerical calculations of Malins and Tardy using a stepladder model. It is concluded that non-steady-state effects are unlikely in the cyclopropane shock tube work, and that diatomic rate constants are sensitive to rotational energy transfer.
A simple analytical model of rotational effects in thermal decomposition is developed. The model describes the non-equilibrium population distribution of the reactant, as a function of the average vibrational energy lost per deactivating collision. The corresponding non-equilibrium rate constant is evaluated, and the results are compared to two previous models.
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