A Chebychev propagator with iterative time ordering for explicitly time-dependent Hamiltonians.

A propagation method for time-dependent Schrodinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time dependence of the time-dependent Schrodinger equation is rewritten as an inhomogeneous term. At each step of the iteration, the resulting inhomogeneous Schrodinger equation is solved with the Chebychev propagation scheme presented in the work of M. Ndong et al. [J. Chem. Phys. 130, 124108 (2009)]. The iteratively time-ordering Chebychev propagator is shown to be robust, efficient, and accurate and compares very favorably with all other available propagation schemes.