Sublinear scaling for time-dependent stochastic density functional theory

TL;DR

This paper introduces a stochastic method for time-dependent density functional theory that achieves sublinear scaling in computational resources, enabling efficient analysis of large nanocrystals.

Contribution

The paper develops a stochastic TDDFT approach using a small set of orbitals, achieving sublinear scaling in time and memory for large systems.

Findings

Sublinear scaling of the algorithm with computational time and memory.

Accurate absorption spectra and RPA correlation energies with few stochastic orbitals.

Effective application to silicon nanocrystals using real-space grids.

Abstract

A stochastic approach to time-dependent density functional theory (TDDFT) is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (? 16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals (NCs) using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.