Unimolecular reactions as radiationless transitions. Calculation of the rate of decomposition of N₂O

Abstract

We attempt an a priori calculation of the rate of a particular reaction, in a treatment in which all quantum states associated with nuclear motion are identified either as reactant states or product states. The validity of this separation is discussed in some detail. It is particularly appropriate for non-adiabatic reactions. Passage between reactant levels presents a standard problem in collision theory; passage from reactant levels to product is treated by procedures already well explored in the theory of radiationless transitions between electronic states. A matrix formalism, which draws on the work of Schlag and others, permits all these processes to be handled conveniently. Calculations are then carried out for the reaction                           N₂O(¹Σ⁺) → N₂(1Σ⁺_g) + O(³P) for which experimental data are extensive. The spectroscopic data are incomplete, however, and the product potential surface has still to be defined in terms of adjustable parameters. Practical approximations, needed to handle the thousands of vibrational levels of N₂O, are proposed and found to meet a convergence test. The calculations are performed on models with one (NO stretch) and two (NO, NN stretches) degrees of freedom. Even with the neglect of anharmonicity in the ground state, and with other approximations, the computational elaboration involved in including the second degree of freedom is large. Agreement with experimental rates and activation energies can be obtained in both high and low pressure limits with reasonable values of the upper state parameters, though the fit to the intermediate pressure region is apparently no better than that obtained by the simple Lindemann-Hinshelwood approach.