Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion

TL;DR

This paper introduces PEXSI, a method that accelerates atomic orbital-based DFT calculations by avoiding eigenvalue computations, achieving linear scaling for large systems and enabling efficient simulations of thousands of atoms.

Contribution

The paper applies the PEXSI technique to atomic orbital-based DFT, providing analytic expressions for key quantities without eigenvalues, and demonstrates its efficiency and accuracy for large systems.

Findings

PEXSI achieves linear scaling for quasi-1D systems.

It enables DFT calculations for systems with over 10,000 atoms.

PEXSI maintains accuracy comparable to traditional methods.

Abstract

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellman-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8,0) boron-nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of accuracy required in a practical DFT calculation.