Eliminating artificial boundary conditions in time-dependent density functional theory using Fourier contour deformation

TL;DR

This paper introduces a Fourier contour deformation method for propagating time-dependent density functional theory equations in free space, eliminating artificial boundary errors and enabling more accurate simulations of electronic processes.

Contribution

The authors adapt the Fourier contour deformation approach to TDDFT, providing a simple algorithm for truncating potentials and removing artificial boundary condition errors in electronic structure calculations.

Findings

Significant reduction in computational domain size needed for accurate results.

Effective elimination of boundary condition errors in TDDFT simulations.

Successful application to absorption and photoelectron spectra in model systems.

Abstract

We present an efficient method for propagating the time-dependent Kohn-Sham equations in free space, based on the recently introduced Fourier contour deformation (FCD) approach. For potentials which are constant outside a bounded domain, FCD yields a high-order accurate numerical solution of the time-dependent Schrodinger equation directly in free space, without the need for artificial boundary conditions. Of the many existing artificial boundary condition schemes, FCD is most similar to an exact nonlocal transparent boundary condition, but it works directly on Cartesian grids in any dimension, and runs on top of the fast Fourier transform rather than fast algorithms for the application of nonlocal history integral operators. We adapt FCD to time-dependent density functional theory (TDDFT), and describe a simple algorithm to smoothly and automatically truncate long-range Coulomb-like potentials to a time-dependent constant outside of a bounded domain of interest, so that FCD can be used. This approach eliminates errors originating from the use of artificial boundary conditions, leaving only the error of the potential truncation, which is controlled and can be systematically reduced. The method enables accurate simulations of ultrastrong nonlinear electronic processes in molecular complexes in which the inteference between bound and continuum states is of paramount importance. We demonstrate results for many-electron TDDFT calculations of absorption and strong field photoelectron spectra for one and two-dimensional models, and observe a significant reduction in the size of the computational domain required to achieve high quality results, as compared with the popular method of complex absorbing potentials.