MōLe-Λ: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties

• URL: http://arxiv.org/abs/2605.29622v1
• Date: Thu, 28 May 2026 08:56:22 GMT
• Title: MōLe-Λ: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties
• Abstract summary: We introduce MLe-$$, an extension of Molecular Orbital Learning (MLe) that predicts the full ground-state coupled-cluster singles and doubles.<n>We show that MLe-$$ further extends the speed advantage of MLe over full CCSD while substantially expanding the accessible properties.
• Score: 5.972018694065695
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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