Time independent quantum theory of electron transfer collisions using a nonorthogonal basis and R-matrix propagation

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Abstract
We briefly review the difficulties associated with the traditional adiabatic quantum treatment of low energy charge transfer collisions between atoms and suggest that the charge transfer problem can be most conveniently treated by using atomic‐centered basis functions and expressing the Hamiltonian simultaneously with respect to two separate atomic origins. As a result, we must solve the quantum nuclear equations of motion in a nonorthogonal basis. We demonstrate that this may be efficiently done by building the R‐matrix propagator in this basis. Flux is automatically conserved even though the R matrix is built up from a series of nonunitary transformations. A simple model problem designed to represent the radial coupling in the reaction Li++Na→Li+Na+ is solved to illustrate the technique.