A log derivative formulation of reaction rate theory

The reaction rate theory of Miller, Schwartz and Tromp is reformulated using a complex Bloch boundary value operator to enforce the scattering boundary conditions. This Bloch operator requires a knowledge of the log derivative of the outgoing wave function on the boundary of the interaction region, and this in turn can be approximated semiclassically from a knowledge of the interaction potential on the boundary. The resulting absorbing log derivative boundary conditions are shown to work well in practice, reducing the range over which the quantum-mechanical problem has to be solved to a narrow region enclosing the relevant turning points. For example they are. shown to be at least three times more effective in reducing the required size of the interaction region for a standard barrier tunnelling problem than more conventional absorbing potentials.