Tensor-structured algorithm for reduced-order scaling large-scale Kohn-Sham density functional theory calculations

TL;DR

This paper introduces a tensor-structured algorithm that constructs a localized Tucker tensor basis for large-scale Kohn-Sham DFT calculations, achieving exponential convergence and sub-quadratic scaling for systems with thousands of atoms.

Contribution

The paper develops a novel tensor-structured approach using a Tucker basis tailored to the Hamiltonian, enabling efficient large-scale DFT calculations with improved scaling.

Findings

Exponential convergence of ground-state energy with Tucker rank

Sub-quadratic scaling with system size for large systems

Outperforms plane-wave DFT for systems beyond 2,000 electrons

Abstract

We present a tensor-structured algorithm for efficient large-scale DFT calculations by constructing a Tucker tensor basis that is adapted to the Kohn-Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn-Sham Hamiltonian and an $L_1$ localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2,000 electrons.