Unified Deep Learning Framework for Many-Body Quantum Chemistry via Green's Functions

Quantum many-body methods provide a systematic route to computing electronic properties of molecules and materials, but high computational costs restrict their use in large-scale applications. Due to the complexity in many-electron wavefunctions, data-driven machine learning models capable of capturing fundamental many-body physics remain limited. Appreciating the success of Green's function methods in computational chemistry and materials science, we present a deep learning framework targeting the many-body Green's function (MBGF-Net), which unifies predictions of electronic properties in ground and excited states, while offering deep physical insights into electron correlation effects. By learning the GW or coupled-cluster self-energy from mean-field features, our graph neural network achieves competitive performance in predicting one- and two- particle excitations and quantities derivable from one-particle density matrix. We demonstrate its high data efficiency and good transferability across chemical species, system sizes, molecular conformations, and correlation strengths in bond breaking, through multiple molecular and nanomaterial benchmarks. Our method trained on 2,000 small organic molecules from QM9 can predict band gaps on a test set of 13,165 molecules with a mean absolute error of 29 meV. Meanwhile, MBGF-Net trained on nanoclusters up to 36 silicon atoms can achieve small band gap and optical gap errors less than 206 meV for clusters up to 4 times the size. This work opens up new opportunities for utilizing machine learning to solve many-electron problems.