Natural-Orbital-Based Neural Network Configuration Interaction

TL;DR

This paper demonstrates that using approximate natural orbitals improves the efficiency of neural-network-assisted configuration interaction methods for molecular electronic structure calculations, reducing the number of determinants needed.

Contribution

It introduces the use of approximate natural orbitals in neural-network-assisted configuration interaction, enhancing efficiency over traditional canonical Hartree-Fock orbitals.

Findings

Consistent reduction in determinants needed for accuracy across benchmarks

Approximate natural orbitals outperform canonical Hartree-Fock orbitals

Enhanced efficiency in neural-network-assisted configuration interaction

Abstract

Selective configuration interaction methods approximate correlated molecular ground- and excited states by considering only the most relevant Slater determinants in the expansion. While a recently proposed neural-network-assisted approach efficiently identifies such determinants, the procedure typically relies on canonical Hartree-Fock orbitals, which are optimized only at the mean-field level. Here we assess approximate natural orbitals - eigenfunctions of the one-particle density matrix computed from intermediate many-body eigenstates - as an alternative. Across our benchmarks for H$_2$O, NH$_3$, CO, and C$_3$H$_8$ we see a consistent reduction in the required determinants for a given accuracy of the computed correlation energy compared to full configuration interaction calculations. Our results confirm that even approximate natural orbitals constitute a simple yet powerful strategy to enhance the efficiency of neural-network-assisted configuration interaction calculations.