A Compact Latent Space Representation of Molecular Electronic Structure

Encoding physically-informed, spherically-averaged atomic electron density basis functions into the latent space of a neural network allows for a compact and transferable representation of a larger molecular system. We show how to construct atomic radial basis density functions, with formal asymptotic constraints, to implement a neural network description of molecular systems. This induces an ensemble atom-in-molecule (AIM) decomposition that partitions a molecule into constituent atomic-like entities. The ensemble AIM framework is expressed in terms of weighted superpositions of basis electron densities for individual ground, charge, and excited states of the constituent atoms. The neural network optimizes the weights to define the contributions of individual atomic states to the overall molecular density. This framework leads to a deeper understanding of the interplay of ionic and covalent contributions of individual atoms to various molecular properties and interactions, as a function of molecular structure. We present results on the radial basis electron density functions and highlight their ability to capture complex quantum mechanical information defining a molecule with a compact atomic representation. The framework’s ability to describe nuances of chemical bonding is demonstrated through results for diatomics, including LiF as an exemplar of ionic bonding, Li₂ and H₂ as examples of excited state-dominated homonuclear bonding, and CO for covalent bonding.