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This paper introduces MEHnet-MG, an equivariant neural network that predicts an effective one-electron Hamiltonian from a single B3LYP/def2-SVP calculation, enabling the accurate prediction of multiple molecular properties at coupled-cluster accuracy across nine main-group elements. By training on a new dataset of multi-property labels computed at the CCSD(T) level, the model significantly reduces prediction errors by a factor of 3.8 to 230 compared to various DFT methods, while maintaining a computational cost comparable to a single DFT calculation. The architecture's design allows it to accurately extrapolate trends in larger molecular systems, demonstrating that its performance is driven by inductive bias rather than the limitations of the training data.
Achieving coupled-cluster accuracy for molecular properties with the computational cost of a single DFT calculation could revolutionize molecular modeling in chemistry.
Coupled-cluster theory defines the accuracy standard for molecular electronic-structure properties but scales too steeply for routine application, whereas density-functional theory is affordable yet systematically biased. We resolve this trade-off with a single equivariant network, MEHnet-MG, that predicts an effective one-electron Hamiltonian from one inexpensive B3LYP/def2-SVP calculation and derives a broad suite of properties from it (energy, optical gap, dipole, quadrupole, polarizability, Mulliken atomic charges, and Mayer bond orders) at coupled-cluster accuracy across nine main-group elements, including the under-served phosphorus, sulfur, and chlorine chemistries. The model is trained on a new in-house dataset of multi-property labels computed at the CCSD(T) level for all nine elements. On a held-out test set, it reduces the error of every property by a factor of 3.8 to 230 relative to semi-local, hybrid, and double-hybrid DFT (referenced to composite CCSD(T)/cc-pVTZ; Methods), while adding only ~25 ms wall time per molecule, delivering coupled-cluster-quality predictions at the cost of a single DFT calculation. Critically, deriving every property from a predicted Hamiltonian rather than pooling per-atom features builds the correct size-scaling into the model architecture: on pi-conjugated oligothiophenes it matches finite-field CCSD polarizability and the EOM-CCSD optical gap to ~2% at the largest sizes where those references remain affordable (44 and 37 atoms, where a single CCSD field point already costs ~500x the model's entire inference) and extrapolates the corrected trends to 58-atom chains, a regime where pooling-based architectures fail by construction. Accurate extrapolation is therefore set by the model's inductive bias rather than by the training data.
