Global error control of the time-propagation for the Schrödinger equation with a time-dependent Hamiltonian

We use a posteriori error estimation theory to derive a relation between local and global error in the propagation for the time-dependent Schrödinger equation describing the interaction of a molecule with a time-dependent field. Based on this result, we design a class of h, p-adaptive Magnus–Lanczos propagators capable of controlling the global error of the time-stepping scheme by only solving the equation once. We provide results for models of several different small molecules including bounded and dissociative states, illustrating the efficiency and wide applicability of the new methods.

Research highlights
► We consider efficient and accurate solution of time-dependent.
► Schrödinger equations arising from femto-second chemistry.
► We derive a posteriori estimates for the time-dependent Schrödinger equation.
► We devise an adaptive algorithm for time-propagation that is specially tailored towards our application problem.
► We compare the proposed method with traditional duality -based error estimates.