MōLe-Λ: Learning the Coupled-Cluster Response State for Energies, Gradients, and Properties
MōLe-Λ: 学习耦合簇响应态以获取能量、梯度和性质
Andreas Burger, Luca Thiede, Abdulrahman Aldossary, Jorge A. Campos-Gonzalez-Angulo, Alex Zook, Jérôme Florian Gonthier, Alán Aspuru-Guzik
AI总结 提出MōLe-Λ模型,通过联合学习左右手振幅预测耦合簇响应态,高效计算能量、梯度及多类分子性质。
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- ICML 2026 AI4Physics
耦合簇理论常被视为量子化学的金标准,但其高计算成本限制了准确能量、力和响应性质的常规获取。虽然右手$T$-振幅决定了相关波函数,但许多实际重要的可观测量还需要左手$Λ$-振幅。我们引入MōLe-$Λ$,它是分子轨道学习(MōLe)的扩展,通过从局域化的Hartree-Fock分子轨道联合学习右手振幅$(T_1,T_2)$和左手振幅$(Λ_1,Λ_2)$,预测完整的基态耦合簇单双激发(CCSD)响应态。在架构上,MōLe-$Λ$扩展了MōLe,增加了$Λ_1$和$Λ_2$读出模块,这些模块镜像了$T_1$和$T_2$头的对称性约束,同时保留了原始的等变轨道编码器、奇符号等变解码、局域性和大小广延性。所得模型能够提供准确的CC级能量和力,同时恢复偶极矩、四极矩、极化率、电子密度以及双电子可观测量如对密度。我们表明,MōLe-$Λ$进一步扩展了MōLe相对于完整CCSD的速度优势,同时大幅扩展了可访问的性质,为相关量子化学的波函数级替代模型提供了途径。
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.