Self-averaging stochastic Kohn-Sham density functional theory

TL;DR

This paper introduces a stochastic formulation of Kohn-Sham DFT that achieves sublinear scaling by using self-averaging properties, enabling efficient and reliable electronic structure calculations for large systems.

Contribution

It presents the first sublinear scaling KS-DFT method based on stochastic averaging, bypassing density matrix calculations and improving scalability for large systems.

Findings

Achieves sublinear scaling in KS-DFT calculations.

Demonstrates effectiveness on silicon nanocrystals.

Ensures reliable estimates with controlled statistical error.

Abstract

We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is deter-mined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the forces on nuclei, the density and its moments, etc. The fluctuations in the total energy per electron are guaranteed to decay to zero as the system size increases. This facilitates "self-averaging" which leads to the first ever report of sublinear scaling KS-DFT electronic structure. The approach sidesteps calculation of the density matrix and thus is insensitive to its evasive sparseness, as demonstrated here for silicon nanocrystals. The formalism is not only appealing in terms of its promise to far push the limits of application of KS-DFT, but also represents a cognitive change in the way we think of electronic structure calculations as this stochastic theory seamlessly converges to the thermodynamic limit.