Coupled Cluster con MōLe: Molecular Orbital Learning for Neural Wavefunctions

Coupled-cluster (CC) theory is often considered the gold standard of quantum chemistry, but its high computational cost limits routine access to accurate energies, forces and response properties. While the right-hand $T$-amplitudes determine the correlated wavefunction, many practically important observables additionally require the left-hand $Λ$-amplitudes. We introduce MōLe-$Λ$, an extension of Molecular Orbital Learning (MōLe) that predicts the full ground-state coupled-cluster singles and doubles (CCSD) response state by jointly learning right-hand amplitudes $(T_1,T_2)$ and left-hand amplitudes $(Λ_1,Λ_2)$ from localized Hartree--Fock molecular orbitals. Architecturally, MōLe-$Λ$ extends MōLe with $Λ_1$ and $Λ_2$ readouts that mirror the symmetry constraints of the $T_1$ and $T_2$ heads, while preserving the original equivariant orbital encoder, odd sign-equivariant decoding, locality and size-extensivity. The resulting model yields accurate CC-quality energies and forces, while simultaneously recovering dipoles, quadrupoles, polarizabilities, the electron density, and 2-electron observables such as the pair density. We show that MōLe-$Λ$ further extends the speed advantage of MōLe over full CCSD while substantially expanding the accessible properties, providing a route to wavefunction-level surrogate models for correlated quantum 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, HARP (Hamiltonian Read-out for Properties), 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 270 relative to semi-local, hybrid, and double-hybrid DFT (referenced to composite CCSD(T)/cc-pVTZ), while adding only ~0.1 s 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 to ~1% and the EOM-CCSD optical gap to ~3% 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.

Machine-learned (ML) operator models can be trained to predict density functional theory (DFT) Hamiltonian/density matrices at significantly reduced computational cost, thus extending electronic-structure calculations to previously unfeasible scales. Here, we introduce MALOQ (Massively Accelerated Learning of Operators for Quantum Transport), an application built to train on and predict electronic-structure matrices for systems made of few to 100k atoms, described by large basis sets, and covering a wide range of atomic elements. Based on a state-of-the-art, SO(2)-equivariant backbone architecture, MALOQ provides (i) custom data-processing kernels to handle high-rank Hamiltonian matrix data and (ii) a scalable edge-wise distribution of atomic graph(s). Trained on the largest molecular Hamiltonian datasets available today, it reduces time-per-epoch by over 30% compared to a molecule-wise-distributed framework, and enables inference on material graphs of arbitrary size. We demonstrate scalable training and inference for 3,000-12,000 atoms on the Alps supercomputer, up to 192 GPUs and 256 GPUs, respectively.