Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low rank approximation of the dielectric matrix

TL;DR

This paper introduces a low rank dielectric matrix preconditioner that significantly accelerates and stabilizes self-consistent field iterations in large-scale Kohn-Sham DFT calculations, reducing computational cost by up to 3.4 times.

Contribution

The paper develops a novel low rank approximation of the dielectric matrix (LRDM) for preconditioning in Kohn-Sham DFT, including adaptive and spin-polarized variants, improving convergence and efficiency.

Findings

LRDM preconditioner converges within 20-30 iterations across benchmarks.

Achieves up to 3.4x reduction in computational cost.

Outperforms other preconditioners in robustness and speed.

Abstract

We present an efficient preconditioning technique for accelerating the fixed point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low rank approximation of the dielectric matrix (LRDM) based on G\^ateaux derivatives of the residual of fixed point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these G\^ateaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous SCF iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from $\sim$ 100-1100 atoms ($\sim$ 500--20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized $d$ orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20--30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed point iteration in some cases. Finally, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4$\times$ reduction in computational cost for the total ground-state calculation compared to other preconditioners.