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

2020/10/31 by Alberto Fabrizio, Ksenia R. Briling, David D. Girardier +1 · 1 citation
Chemistry · Materials Science · Physics and Astronomy · #Ab initio #Advanced Chemical Physics Studies #Basis (linear algebra) #Density functional theory #Electron #Electron density #Electronic correlation #Machine Learning in Materials Science #Metric (unit) #Molecular spectroscopy and chirality #Visualization #Wave function #physics.chem-ph #quant-ph

paper · pdf · doi:10.1063/5.0033326

published as J. Chem. Phys. 153, 204111 (2020) · Article and Supporting Information

openalex created_date 2020/10/22 · openalex publication_date 2020/11/28 · arxiv created 2020/11/30 · arxiv updated 2020/12/01 · openalex updated_date 2026/08/05

Abstract

The on-top pair density [Π(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 Π(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 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.

Citations

• Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
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Cited by

• Clémence Corminboeuf [wikipedia]

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