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

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.

arXiv comment13 pages, 4 figures, 1 table

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• M-SPARC: MATLAB-Simulation Package for Ab-initio Real-space Calculations