Mean-Field Density Matrix Decompositions

TL;DR

This paper presents new, robust, and lossless decompositions of mean-field density matrices using localized orbitals, enhancing interpretability and data granularity for machine learning in quantum chemistry.

Contribution

It introduces novel decompositions of density matrices that improve interpretability and data richness, aiding machine learning applications in quantum chemistry.

Findings

Decompositions allow partitioning into bond-wise or atomic contributions.

Compared to existing methods, the new approach offers better energy and dipole moment analysis.

Preliminary results suggest potential for refining structure-property relationships.

Abstract

We introduce new and robust decompositions of mean-field Hartree-Fock (HF) and Kohn-Sham density functional theory (KS-DFT) relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning 1-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regards to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.