Exponential Integrators in Time-Dependent Density Functional Calculations

TL;DR

This paper implements and compares exponential integrator methods with traditional approaches for solving time-dependent Kohn-Sham equations, showing significant accuracy improvements especially in nonlinear potential-driven dynamics.

Contribution

It introduces exponential integrator methods into time-dependent density functional calculations and demonstrates their superior accuracy over conventional methods.

Findings

Exponential integrators improve accuracy by multiple orders of magnitude for nonlinear potential dynamics.

They match or outperform traditional methods in external potential-driven dynamics.

The methods are computationally efficient and robust for time-dependent density functional simulations.

Abstract

The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches, are compared to these exponential integrator methods in order to judge the relative merit of the computational schemes. We determine an improvement in accuracy of multiple orders of magnitude when describing dynamics driven primarily by a nonlinear potential. For cases of dynamics driven by a time-dependent external potential, the accuracy of the exponential integrator methods are less enhanced but still match or outperform the best of the conventional methods tested.