Accurate time propagation method for the coupled Maxwell and Kohn-Sham equations.

An accurate method for time propagation of the coupled Maxwell and time-dependent Kohn-Sham (TDKS) equation is presented. The new approach uses a simultaneous fourth-order Runge-Kutta-based propagation of the vector potential and the Kohn-Sham orbitals. The approach is compared to the conventional fourth-order Taylor propagation and predictor-corrector methods. The calculations show several computational and numerical advantages, including higher computational performance, greater stability, better accuracy, and faster convergence.

Accuracy and computational efficiency of real-time subspace propagation schemes for the time-dependent density functional theory.

Time-dependent Density Functional Theory (TDDFT) has become successful for its balance of economy and accuracy. However, the application of TDDFT to large systems or long time scales remains computationally prohibitively expensive. In this paper, we investigate the numerical stability and accuracy of two subspace propagation methods to solve the time-dependent Kohn-Sham equations with finite and periodic boundary conditions. The bases considered are the Lánczos basis and the adiabatic eigenbasis. The results are compared to a benchmark fourth-order Taylor expansion of the time propagator. Our results show that it is possible to use larger time steps with the subspace methods, leading to computational speedups by a factor of 2-3 over Taylor propagation. Accuracy is found to be maintained for certain energy regimes and small time scales.