Global error control of the time-propagation for the Schrdinger 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 Schrdinger equation describing the interaction of a molecule with a time-dependent field. Based on this result, we design a class of h, p-adaptive MagnusLanczos 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.
global error control h time-dependent schrdinger equation p-adaptivity magnuslanczos propagator