The interactions which occur between nuclear and electronic motions in electronically degenerate states of octahedral molecules are investigated.frequency" polarizations of the electronic motions: if V is the electronic Hamiltonian, which difFers from the total Hamiltonian in the absence of the nuclear kinetic energies alone, then
A unified formal treatment of the two-state potential-curve-crossing problem in atomic collision theory is presented, and the case of close crossings analyzed in detail. A complete solution for this case, including necessary computations, is given using a suitable generalization of the linear model originally suggested by Landau, Zener, and Stueckelberg. Our solution is based upon a hierarchy of approximations concerned with (i) choice of a discrete basis set for electronic coordinates, (ii) semiclassical treatment of the nuclear motion, (iii) an appropriate model for the two-state electronic Hamiltonian, and (iv) a complete solution to that model.
The time-dependent equations of the classical picture of inelastic collisions (classical-trajectory equations) are derived using the momentum-space semiclassical approximation.Thereby it is shown that the classical-trajectory equations remain valid in the vicinity of classical turning points provided that (a) the momentum-space semiclassical approximation is valid, (b) the trajectories for elastic scattering in the various internal states differ only slightly, and (c) the slopes of the elastic scattering potentials have the same sign. A brief review of the existing derivations of the classical-trajectory equations is given, and the general conditions for their validity are discussed.
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