High-performance linear-scaling electronic structure method via chromatic superposition states

TL;DR

This paper presents a novel linear-scaling electronic structure method using chromatic superposition states (CSS) that significantly improves computational efficiency for large-scale Kohn-Sham calculations while maintaining high accuracy.

Contribution

The introduction of CSS as a low-dimensional, high-fidelity basis for electronic structure calculations, enabling orders of magnitude faster computations for large systems.

Findings

Outperforms previous linear-scaling methods by over ten times in speed.

Successfully simulates 10,000 water molecules and 1 million water molecules with modest resources.

Maintains high accuracy in large-scale molecular dynamics and self-consistent calculations.

Abstract

We introduce a high-performance linear-scaling electronic structure method that employs chromatic superposition states (CSS) as a low-dimensional, high-fidelity representation, which can be orders of magnitude smaller than the full Hilbert space. Grounded in the system's finite correlation length, the CSS representation aggregates the uncorrelated orbitals into a single basis via a graph-coloring scheme, and is independent of the system size yet accurately preserves all sparse operators in solving the Kohn-Sham equations. The projection onto CSSs is efficiently computed by employing the block-Lanczos Krylov method which features high hardware efficiency and linear-scaling cost, enabling fast calculation of large-scale Kohn-Sham density matrix. We show that this method already outperforms previous linear-scaling density matrix purification method by more than one order of magnitude in computational speed at even small scale, while preserving high accuracy. The practical utility of the CSS method is demonstrated through molecular dynamics simulation of a 10000 $H_2O$, and self-consistent calculation of a 1-million $H_2O$ with modest resources.