Efficient real space formalism for hybrid density functionals

TL;DR

This paper introduces a fast and accurate real space method for hybrid density functional calculations in DFT, significantly improving computational efficiency over traditional Fourier-based approaches.

Contribution

It develops a novel real space formalism leveraging Kronecker product structures for hybrid functionals, enabling faster solutions without boundary condition restrictions.

Findings

Achieves up to tenfold speedup compared to planewave codes.

Accurately models isolated and bulk systems with verified results.

Successfully applied to liquid water simulations with good agreement.

Abstract

We present an efficient real space formalism for hybrid exchange-correlation functionals in generalized Kohn-Sham density functional theory (DFT). In particular, we develop an efficient representation for any function of the real space finite-difference Laplacian matrix by leveraging its Kronecker product structure, thereby enabling the time to solution of associated linear systems to be highly competitive with the fast Fourier transform scheme, while not imposing any restrictions on the boundary conditions. We implement this formalism for both the unscreened and range-separated variants of hybrid functionals. We verify its accuracy and efficiency through comparisons with established planewave codes for isolated as well as bulk systems. In particular, we demonstrate up to an order-of-magnitude speedup in time to solution for the real space method. We also apply the framework to study the structure of liquid water using ab initio molecular dynamics, where we find good agreement with literature. Overall, the current formalism provides an avenue for efficient real space DFT calculations with hybrid density functionals.