Matching-pursuit∕split-operator Fourier-transform simulations of nonadiabatic quantum dynamics

A rigorous and practical approach for simulations of nonadiabatic quantum dynamics is introduced. The algorithm involves a natural extension of the matching-pursuit∕split-operator Fourier-transform (MP∕SOFT) method [Y. Wu and V. S. Batista, J. Chem. Phys. 121, 1676 (2004)] recently developed for simulations of adiabatic quantum dynamics in multidimensional systems. The MP∕SOFT propagation scheme, extended to nonadiabatic dynamics, recursively applies the time-evolution operator as defined by the standard perturbation expansion to first-, or second-order, accuracy. The expansion is implemented in dynamically adaptive coherent-state representations, generated by an approach that combines the matching-pursuit algorithm with a gradient-based optimization method. The accuracy and efficiency of the resulting propagation method are demonstrated as applied to the canonical model systems introduced by Tully for testing simulations of dual curve-crossing nonadiabatic dynamics.