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

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