Accurate Molecular Properties via Bootstrap Embedding

We demonstrate the utility of back-transformed bootstrap embedding (BE) one- and two-particle density matrices (1 and 2-PDMs) by computing dipole moments and force gradients for several polar systems. The resulting mean absolute error in atomic force gradients at BE2/CCSD is approximately 0.003 au/bohr even in most polar and strained environments, and these forces further enable stable geometry optimization trajectories. We refer to this approach for generating molecular properties as Bootstrap Embedding-Direct Matrices (BE-DM). This efficient evaluation of dipole moments and atomic force gradients holds significant promise for machine learning applications, where coupled-cluster-level forces can substantially enhance the quality of machine-learned potentials.