SQDFT: Spectral Quadrature method for large-scale parallel $\mathcal{O}(N)$ Kohn-Sham calculations at high temperature

TL;DR

SQDFT introduces a scalable spectral quadrature method for large-scale, high-temperature Kohn-Sham DFT calculations, achieving near-linear scaling and high parallel efficiency on supercomputers.

Contribution

The paper develops an efficient, parallel finite-difference implementation of the spectral quadrature approach for large-scale Kohn-Sham DFT at high temperature, demonstrating its accuracy and scalability.

Findings

Achieves systematic convergence with reference methods.

Exhibits near-perfect linear scaling with system size.

Performs efficient quantum molecular dynamics simulations.

Abstract

We present SQDFT: a large-scale parallel implementation of the Spectral Quadrature (SQ) method for $\mathcal{O}(N)$ Kohn-Sham Density Functional Theory (DFT) calculations at high temperature. Specifically, we develop an efficient and scalable finite-difference implementation of the infinite-cell Clenshaw-Curtis SQ approach, in which results for the infinite crystal are obtained by expressing quantities of interest as bilinear forms or sums of bilinear forms, that are then approximated by spatially localized Clenshaw-Curtis quadrature rules. We demonstrate the accuracy of SQDFT by showing systematic convergence of energies and atomic forces with respect to SQ parameters to reference diagonalization results, and convergence with discretization to established planewave results, for both metallic and insulating systems. We further demonstrate that SQDFT achieves excellent strong and weak parallel scaling on computer systems consisting of tens of thousands of processors, with near perfect $\mathcal{O}(N)$ scaling with system size and wall times as low as a few seconds per self-consistent field iteration. Finally, we verify the accuracy of SQDFT in large-scale quantum molecular dynamics simulations of aluminum at high temperature.