Integration of the time-dependent Kohn-Sham (TDKS) equation, for real-time simulations of electron dynamics, is complicated by the time-dependent nature of the Kohn-Sham effective Hamiltonian. Whereas many existing TDKS algorithms are based on some kind of midpoint interpolation of the time-dependent Fock matrix, we have developed predictor/corrector approaches in which the Fock and density matrices are iterated to self-consistency over the course of each time step. These propagators remain stable even with time steps that are 10–20 times larger than those typically used with midpoint approaches, and they prove to be more efficient despite requiring more than one Fock build per time step. In addition, the new propagators come with provable bounds on their stability that are unavailable in non-self-consistent approaches. We find that midpoint algorithms can afford absorption spectra (computed from the time-dependent dipole moment function) that are significantly shifted with respect to linear-response TDDFT results, even for weakly-perturbing external fields where the two methods should agree. In the non-self-consistent TDKS approach, such shifts are preventable only by following empirical recommendations regarding an appropriate time step, but the self-consistent approaches come with built-in tools to detect divergent dynamics. These allow an appropriate time step to be selected in an automated way. Applications to study electron dynamics in ionized water will be presented, where our Gaussian orbital implementation facilitates easy use of hybrid functionals and avoids the need for a pseudopotential representation of the core hole, as required in a plane-wave implementation.

Self-consistent predictor/corrector algorithms for provably stable propagation of the time-dependent Kohn-Sham orbitals

256th National Meeting (2018)

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