Learning on-top: regressing the on-top pair density for real-space visualization of electron correlation

TL;DR

This paper introduces a machine learning model that predicts the on-top pair density of molecules from their structure, enabling visualization of electron correlation effects without complex quantum calculations.

Contribution

The work presents the first ML model to accurately predict CASSCF-quality on-top pair densities solely from molecular structure, bypassing traditional computational methods.

Findings

Model trained on GDB11-AD-3165 database achieves minimal error in predicting on-top pair density.

Predicted on-top ratio effectively visualizes electron correlation and bond-breaking.

Constructed a specialized basis set for fitting on-top pair density in a single atom-centered expansion.

Abstract

The on-top pair density [$\Pi(\mathrm{\mathbf{r}})$] is a local quantum-chemical property that reflects the probability of two electrons of any spin to occupy the same position in space. Being the simplest quantity related to the two-particle density matrix, the on-top pair density is a powerful indicator of electron correlation effects, and as such, it has been extensively used to combine density functional theory and multireference wavefunction theory. The widespread application of $\Pi(\mathrm{\mathbf{r}})$ is currently hindered by the need for post-Hartree--Fock or multireference computations for its accurate evaluation. In this work, we propose the construction of a machine learning model capable of predicting the CASSCF-quality on-top pair density of a molecule only from its structure and composition. Our model, trained on the GDB11-AD-3165 database, is able to predict with minimal error the on-top pair density of organic molecules, bypassing completely the need for $\textit{ab initio}$ computations. The accuracy of the regression is demonstrated using the on-top ratio as a visual metric of electron correlation effects and bond-breaking in real-space. In addition, we report the construction of a specialized basis set, built to fit the on-top pair density in a single atom-centered expansion. This basis, cornerstone of the regression, could be potentially used also in the same spirit of the resolution-of-the-identity approximation for the electron density.