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This paper introduces M\=oLe-$\Lambda$, a neural network that predicts both right-hand ($T$) and left-hand ($\Lambda$) amplitudes in coupled-cluster singles and doubles (CCSD) theory from localized Hartree-Fock molecular orbitals. By jointly learning these amplitudes, M\=oLe-$\Lambda$ enables the accurate prediction of energies, forces, and a wide range of response properties like dipoles and polarizabilities, all at a significantly reduced computational cost compared to full CCSD. The model preserves key physical constraints like equivariance, locality, and size-extensivity, making it a promising surrogate model for correlated quantum chemistry.
Get accurate CCSD energies, forces, dipoles, polarizabilities, and more, all from a single neural network that learns both T and Lambda amplitudes.
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 $\Lambda$-amplitudes. We introduce M\=oLe-$\Lambda$, an extension of Molecular Orbital Learning (M\=oLe) 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 $(\Lambda_1,\Lambda_2)$ from localized Hartree--Fock molecular orbitals. Architecturally, M\=oLe-$\Lambda$ extends M\=oLe with $\Lambda_1$ and $\Lambda_2$ 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 M\=oLe-$\Lambda$ further extends the speed advantage of M\=oLe over full CCSD while substantially expanding the accessible properties, providing a route to wavefunction-level surrogate models for correlated quantum chemistry.
