On real-space Density Functional Theory for non-orthogonal crystal systems: Kronecker product formulation of the kinetic energy operator

TL;DR

This paper introduces a novel Kronecker product approach to real-space Density Functional Theory that efficiently handles non-orthogonal crystal systems, reducing computational costs and maintaining accuracy.

Contribution

The paper develops a new Kronecker product formulation of the kinetic energy operator for non-orthogonal systems, significantly improving computational efficiency.

Findings

Reduces scaling with finite-difference order from quadratic to linear.

Maintains high accuracy in non-orthogonal crystal simulations.

Demonstrates efficiency gains through example validations.

Abstract

We present an accurate and efficient real-space Density Functional Theory (DFT) framework for the ab-initio study of non-orthogonal crystal systems. Specifically, employing a local reformulation of the electrostatics, we develop a novel Kronecker product formulation of the real-space kinetic energy operator that significantly reduces the number of operations associated with the Laplacian-vector multiplication, the dominant cost in practical computations. In particular, we reduce the scaling with respect to finite-difference order from quadratic to linear, thereby significantly bridging the gap in computational cost between non-orthogonal and orthogonal systems. We verify the accuracy and efficiency of the proposed methodology through selected examples.