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The on-top pair density [$\Pi(\mathrm{\mathbf{r}})$] is a localquantum-chemical property that reflects the probability of two electrons of anyspin to occupy the same position in space. Being the simplest quantity relatedto the two-particle density matrix, the on-top pair density is a powerfulindicator of electron correlation effects, and as such, it has been extensivelyused to combine density functional theory and multireference wavefunctiontheory. The widespread application of $\Pi(\mathrm{\mathbf{r}})$ is currentlyhindered by the need for post-Hartree--Fock or multireference computations forits accurate evaluation. In this work, we propose the construction of a machinelearning model capable of predicting the CASSCF-quality on-top pair density ofa molecule only from its structure and composition. Our model, trained on theGDB11-AD-3165 database, is able to predict with minimal error the on-top pairdensity of organic molecules, bypassing completely the need for $\textit{abinitio}$ computations. The accuracy of the regression is demonstrated using theon-top ratio as a visual metric of electron correlation effects andbond-breaking in real-space. In addition, we report the construction of aspecialized basis set, built to fit the on-top pair density in a singleatom-centered expansion. This basis, cornerstone of the regression, could bepotentially used also in the same spirit of the resolution-of-the-identityapproximation for the electron density.

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