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

Alberto Fabrizio1*, Ksenia R. Briling1, David D. Girardier1, Clemence Corminboeuf1

1 Institut des Sciences et Ingénierie Chimiques, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

* Corresponding authors emails: alberto.fabrizio@epfl.ch
DOI10.24435/materialscloud:8z-2p [version v1]

Publication date: Oct 30, 2020

How to cite this record

Alberto Fabrizio, Ksenia R. Briling, David D. Girardier, Clemence Corminboeuf, Learning on-top: regressing the on-top pair density for real-space visualization of electron correlation, Materials Cloud Archive 2020.135 (2020), doi: 10.24435/materialscloud:8z-2p.


The on-top pair density [Π(r)] is a local quantum chemical property, which reflects the probability of two electrons of any spin to occupy the same position in space. Simplest quantity related to the two-particles 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.

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File name Size Description
35.3 GiB Tar ball containing: Ab initio and predicted on-top pair densities and densities, as well as training and test set geometries, OTPD basis set and reference data. See README.txt for a more detailed description of the content.


Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.


Machine Learning On-top Pair Density Strong Electron Correlation EPFL MARVEL/DD1 SNSF ERC

Version history:

2020.135 (version v1) [This version] Oct 30, 2020 DOI10.24435/materialscloud:8z-2p