Bipartite Cholesky Graph Networks for Many-Body Quantum Chemistry

Abstract

Accurate prediction of molecular correlation energies from first principles requires resolving the {O}(N^4) electron repulsion integral (ERI) tensor. Existing graph neural network approaches to the electronic structure problem often compress this tensor into low-rank scalar features, discarding higher-order interaction structures relevant to electron correlation. In this work, we demonstrate that tensor factorization of the ERI naturally induces a structured bipartite message-passing architecture that preserves access to higher-order interaction structure more effectively than compressed orbital representations. By utilizing the density-fitted Cholesky decomposition of the ERI tensor, we derive a bipartite graph network that models orbital degrees of freedom and auxiliary interaction nodes as distinct sets, maintaining interaction topology at a reduced theoretical complexity of {O}(N^3). Evaluated on 132 geometries of six diatomic molecules with Full Configuration Interaction (FCI) reference energies, our factorized representation achieves an in-distribution Mean Absolute Error (MAE) of 0.0296 Ha under five-fold cross-validation, a substantial improvement over compressed-integral baselines. Leave-one-molecule-out validation reveals that zero-shot generalization varies by nearly a factor of four across molecular species and correlates with the structural similarity of the held-out molecule's orbital environment to the training distribution, rather than with nuclear charge asymmetry alone.