Linear Scaling Density Matrix Real Time TDDFT: Propagator Unitarity \& Matrix Truncation

TL;DR

This paper introduces a linear-scaling real-time density matrix TDDFT method that uses matrix truncation to efficiently compute optical properties of large systems while maintaining propagator unitarity.

Contribution

The paper presents a novel implementation of density matrix TDDFT with matrix truncation, enabling linear scaling and accurate optical spectra for large systems.

Findings

Matrix truncation preserves propagator unitarity.

Optical spectra accuracy depends on basis set size and truncation range.

Computational cost scales linearly with system size.

Abstract

Real time, density matrix based, time dependent density functional theory proceeds through the propagation of the density matrix, as opposed to the Kohn-Sham orbitals. It is possible to reduce the computational workload by imposing spatial cut-off radii on sparse matrices, and the propagation of the density matrix in this manner provides direct access to the optical response of very large systems, which would be otherwise impractical to obtain using the standard formulations of TDDFT. Following a brief summary of our implementation, along with several benchmark tests illustrating the validity of the method, we present an exploration of the factors affecting the accuracy of the approach. In particular we investigate the effect of basis set size and matrix truncation, the key approximation used in achieving linear scaling, on the propagator unitarity and optical spectra. Finally we illustrate that, with an appropriate density matrix truncation range applied, the computational load scales linearly with the system size and discuss the limitations of the approach.