Integrating Coupled-Cluster Theory Within AI Workflows for Accurate Molecular Geometries

We introduce a hybrid data-driven coupled-cluster (DDCC) framework that enables efficient coupled-cluster singles and doubles (CCSD)-level geometry optimizations through direct prediction of wavefunction parameters. In conventional CCSD, each optimization step requires solving the nonlinear $t$ -amplitude equations and the linear $\Lambda$ -equations, both scaling as $O\left(N^6\right)$ , making geometry optimizations computationally demanding. The $\Lambda$ data-driven CC ( $\Lambda$ DDCC) scheme replaces these iterative solvers with neural network predictions of the $t$ and $\lambda$ amplitudes, thereby removing the dominant computational bottleneck. The model utilizes a physically grounded representation of electron correlation, combining excitation-based descriptors with a molecular orbital (MO) framework defined through orbital centroids. This design enables accurate recovery of the CC wave function parameters, which in turn yields reliable nuclear gradients throughout the optimization process. Across a diverse set of thermally perturbed geometries and out-of-sample molecules, $\Lambda$ DDCC reproduces CCSD geometries with near-quantitative agreement, while reducing computational cost by over an order of magnitude. These results establish $\Lambda$ DDCC as an effective and transferable strategy for accelerating high-level electronic structure calculations, providing a practical route toward routine CCSD-quality geometry optimization in larger and more complex molecular systems.