Deterministic/Fragmented-Stochastic Exchange for Large Scale Hybrid DFT Calculations

TL;DR

This paper introduces a hybrid deterministic-stochastic method for efficiently calculating range-separated exact exchange in large-scale GKS-DFT, enabling accurate and scalable simulations of complex molecular systems.

Contribution

It presents a novel fragmented-stochastic approach combined with a subspace projection technique for efficient large-scale hybrid DFT calculations.

Findings

Accurately computes HOMO and LUMO energies with few states.

Enables tuning of long-range hybrids for large systems.

Successfully applied to chlorophyll hexamer with 1,320 electrons.

Abstract

We develop an efficient approach to evaluate range-separated exact exchange for grid or plane-wave based representations within the Generalized Kohn-Sham DFT (GKS-DFT) framework. The Coulomb kernel is fragmented in reciprocal space, and we employ a mixed deterministic-stochastic representation, retaining long wavelength (low-$k$) contributions deterministically and using a sparse ("fragmented") stochastic basis for the high-$k$ part. Coupled with a projection of the Hamiltonian onto a subspace of valence and conduction states from a prior local-DFT calculation, this method allows for the calculation of long-range exchange of large molecular systems with hundreds and potentially thousands of coupled valence states delocalized over millions of grid points. We find that even a small number of valence and conduction states is sufficient for converging the HOMO and LUMO energies of the GKS-DFT. Excellent tuning of long-range separated hybrids (RSH) is easily obtained in the method for very large systems, as exemplified here for the chlorophyll hexamer of Photosystem II with 1,320 electrons.