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

• URL: http://arxiv.org/abs/2010.07116v2
• Date: Mon, 30 Nov 2020 15:22:13 GMT
• Title: Learning on-top: regressing the on-top pair density for real-space visualization of electron correlation
• Authors: Alberto Fabrizio, Ksenia R. Briling, David D. Girardier and Clemence Corminboeuf
• Abstract summary: The on-top pair density is a powerful indicator of electron correlation effects. A machine learning model capable of predicting CF ontop density molecules only its structure composition is trained on the GDB11AD-3165 database. The accuracy of the regression is demonstrated using the on-top ratio as a visual metric of electron correlation effects and bondbreaking fit in realspace.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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