Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations

TL;DR

This paper introduces a two-level Chebyshev filter-based complementary subspace method that significantly accelerates large-scale Kohn-Sham DFT calculations, enabling efficient simulations of systems with thousands of electrons.

Contribution

The novel iterative strategy reduces computational cost by avoiding full diagonalization and efficiently handling partially occupied states, advancing large-scale electronic structure calculations.

Findings

Achieves chemical accuracy for large systems within minutes per SCF iteration.

Successfully simulates a 8,000-atom silicon system at finite temperature.

Enables ab initio molecular dynamics for large systems within a feasible timeframe.

Abstract

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to: 1) compute a set of vectors that span the occupied subspace of the Hamiltonian; 2) reduce subspace diagonalization to just partially occupied states; and 3) obtain those states in an efficient, scalable manner via an inner Chebyshev-filter iteration. By reducing the necessary computation to just partially occupied states, and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the Discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 hours (of wall time).