Bipartite Cholesky Graph Networks for Many-Body Quantum Chemistry
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910253793148928 |
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| author | Khan, Abdul Samad |
| author_facet | Khan, Abdul Samad |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_25268 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bipartite Cholesky Graph Networks for Many-Body Quantum Chemistry Khan, Abdul Samad Chemical Physics Quantum Physics 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. |
| title | Bipartite Cholesky Graph Networks for Many-Body Quantum Chemistry |
| topic | Chemical Physics Quantum Physics |
| url | https://arxiv.org/abs/2605.25268 |