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.
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