Efficient O($N$) divide-conquer method with localized natural orbitals

TL;DR

This paper introduces an efficient linear-scaling divide-conquer method using localized natural orbitals for large-scale density functional theory calculations, significantly reducing computational costs while maintaining accuracy for diverse materials.

Contribution

The paper presents a novel non-iterative approach to calculate localized natural orbitals, enabling efficient large-scale DFT simulations on parallel computers.

Findings

Achieved O(N) computational scaling for large systems.

Demonstrated high parallel efficiency in benchmark tests.

Maintained accuracy for both gapped and metallic systems.

Abstract

An efficient O($N$) divide-conquer (DC) method based on localized natural orbitals (LNOs) is presented for large-scale density functional theories (DFT) calculations of gapped and metallic systems. The LNOs are non-iteratively calculated by a low-rank approximation via a local eigendecomposition of a projection operator for the occupied space. Introducing LNOs to represent the long range region of a truncated cluster reduces the computational cost of the DC method while keeping computational accuracy. A series of benchmark calculations and high parallel efficiency in a multilevel parallelization clearly demonstrate that the O($N$) method enables us to perform large-scale simulations for a wide variety of materials including metals with sufficient accuracy in accordance with development of massively parallel computers.