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arXiv · 2309.02536

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

Nadine C. Bradbury·Tucker Allen·Minh Nguyen·Daniel Neuhauser
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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.

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Nadine C. Bradbury, Tucker Allen, Minh Nguyen, Daniel Neuhauser. 2023-09-05. Deterministic/Fragmented-Stochastic Exchange for Large Scale Hybrid DFT Calculations. https://arxiv.org/abs/2309.02536

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