Shift equations iteration solution to n-level close coupled equations, and the two-level nonadiabatic tunneling problem revisited

The shift equations iteration (SEI) solves the n-level quantum scattering problem in one dimension, i.e., the close-coupled equations, free from exponential instability arising from closed channels. SEI provides exponential-instability-free transmission and reflection coefficients, and is well suited to two-sided scattering problems such as conduction in molecular wires. Our most efficient implementation of SEI utilizes an adaptation of the log-derivative symplectic integrator described by Manolopoulos and Gray in (J Chem Phys 102:9214, 1995). The two-level nonadiabatic tunneling system is investigated—in the tunneling regime, above the barrier, and at resonance. Nonadiabatic components in the upper channel wavefunction (and lower channel wavefunction at resonance energies) are found to be non-adiabatic, i.e., not describable by WKB functions. Their behavior is characterized in terms of an empirical model relating these components to adiabatic components in the lower (upper) channel and the potential energy coupling.