Tempering stochastic density functional theory

TL;DR

This paper presents t-sDFT, a tempering stochastic density functional theory method that significantly reduces statistical errors and biases in electronic structure calculations by splitting the density into warm and colder components, improving accuracy and efficiency.

Contribution

Introduction of t-sDFT, a novel tempering approach that enhances stochastic DFT by reducing errors through a warm-cold component decomposition, enabling more accurate large-scale simulations.

Findings

Energy systematic error reduced by over an order of magnitude.

Statistical fluctuations in total energy decreased by factors of 4-5.

Force errors and fluctuations also significantly quenched.

Abstract

We introduce a tempering approach with stochastic density functional theory (sDFT), labeled t-sDFT, which reduces the statistical errors in the estimates of observable expectation values. This is achieved by rewriting the electronic density as a sum of a "warm" component complemented by "colder" correction(s). Since the "warm" component is larger in magnitude but faster to evaluate, we use many more stochastic orbitals for its evaluation than for the smaller-sized colder correction(s). This results in a significant reduction of the statistical fluctuations and the bias compared to sDFT for the same computational effort. We the method's performance on large hydrogen-passivated silicon nanocrystals (NCs), finding a reduction in the systematic error in the energy by more than an order of magnitude, while the systematic errors in the forces are also quenched. Similarly, the statistical fluctuations are reduced by factors of around 4-5 for the total energy and around 1.5-2 for the forces on the atoms. Since the embedding in t-sDFT is fully stochastic, it is possible to combine t-sDFT with other variants of sDFT such as energy-window sDFT and embedded-fragmented sDFT.