An efficient algorithm for time propagation within time-dependent density functional theory

TL;DR

This paper introduces a computationally efficient and stable algorithm for propagating the time-dependent Kohn-Sham equations in density functional theory, suitable for magnetic systems and large time steps.

Contribution

The authors develop a novel algorithm that divides the Hamiltonian into small steps and assumes constancy, enabling efficient time propagation in TDDFT for magnetic systems.

Findings

Algorithm is stable for non-magnetic and magnetic systems

Large time steps can be used without loss of accuracy

Significant efficiency improvements over previous methods

Abstract

An efficient 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 stability and efficiency of the algorithm are tested not just for non-magnetic but also for fully non-collinear magnetic systems. We show that even for delicate properties, like magnetization density, large time-step sizes can be used indicating the stability and efficiency of the algorithm.