Linear scalability of density functional theory calculations without imposing electron localization

TL;DR

This paper introduces a massively parallel, deterministic density functional theory method that achieves efficient linear wall-time complexity for large systems without relying on electron localization, suitable for high-performance computing environments.

Contribution

Develops a fully deterministic, quadratic-scaling DFT approach that maintains linear complexity in weak scalability regimes, extending stochastic DFT methods for large, delocalized systems.

Findings

Enables efficient DFT calculations on large systems without electron localization.

Achieves linear wall-time complexity in high-performance computing environments.

Extends stochastic DFT to a deterministic framework for better scalability.

Abstract

Linear scaling density functional theory approaches to electronic structure are often based on the tendency of electrons to localize even in large atomic and molecular systems. However, in many cases of actual interest, for example in semiconductor nanocrystals, system sizes can reach very large extension before significant electron localization sets in and the scaling of the numerical methods may deviate strongly from linear. Here, we address this class of systems, by developing a massively parallel density functional theory (DFT) approach which doesn't rely on electron localizationa and is formally quadratic scaling, yet enables highly efficient linear wall-time complexity in the weak scalability regime. The approach extends from the stochastic DFT method described in Fabian et. al. WIRES: Comp. Mol. Science, e1412 2019 but is fully deterministic. It uses standard quantum chemical atom-centered Gaussian basis sets for representing the electronic wave functions combined with Cartesian real space grids for some of the operators and for enabling a fast solver for the Poisson equation. Our main conclusion is, that when a processor-abundant high performance computing (HPC) infrastructure is available, this type of approach has the potential to allow the study of large systems in regimes where quantum confinement or electron delocalization prevents linear-scaling.