An efficient algorithm for time propagation as applied to linearized augmented plane wave method

An algorithm for time propagation of the time-dependent Kohn–Sham equations is presented. The algorithm is based on dividing the Hamiltonian into small time steps and assuming that it is constant over these steps. This allows for the time-propagating Kohn–Sham wave function to be expanded in the instantaneous eigenstates of the Hamiltonian. The method is particularly efficient for basis sets which allow for a full diagonalization of the Hamiltonian matrix. One such basis is the linearized augmented plane waves. In this case we find it is sufficient to perform the evolution as a second-variational step alone, so long as sufficient number of first variational states are used. The algorithm is tested not just for non-magnetic but also for fully non-collinear magnetic systems. We show that even for delicate properties, like the magnetization density, fairly large time-step sizes can be used demonstrating the stability and efficiency of the algorithm.