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

2026-05-28

AI Summary

This work addresses the high computational cost of traditional coupled-cluster (CC) methods, which hinders efficient prediction of energies, forces, and diverse response properties. The authors propose the first end-to-end learning framework that jointly predicts right-hand amplitudes (T₁, T₂) and left-hand Lagrange multipliers (Λ₁, Λ₂) to construct a complete CCSD response state directly from localized Hartree–Fock orbitals. Built upon the MōLe architecture, the model incorporates a mirror-symmetric Λ output head, an equivariant orbital encoder, and a sign-equivariant decoder with odd parity. This design rigorously preserves symmetry, equivariance, and size extensivity while unifying the prediction of energies, gradients, dipole and quadrupole moments, polarizabilities, electron densities, and two-electron observables—achieving accuracy comparable to conventional CCSD at significantly reduced computational cost.

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.

Problem

• coupled-cluster
• response properties
• computational cost
• amplitudes
• quantum chemistry

Innovation

• coupled-cluster response
• left-hand amplitudes
• equivariant neural network
• surrogate quantum chemistry model
• molecular property prediction