Locally Updated Bootstrap Embedding

Bootstrap Embedding (BE) has recently demonstrated an impressive ability to produce highly accurate single-point energies at a low computational cost, utilizing systematically determined fragments that overlap with each other. In many chemical applications, such as scanning the potential energy surface, one performs numerous single-point calculations that differ by local geometric changes. This often leads to a frustratingly time-consuming process, even with computationally affordable methods like BE. We present here a locally updated version of BE that dramatically accelerates these types of calculations with a minimal loss in accuracy. Specifically, we propose a method that updates only the fragments that involve the change in geometry, while reusing information from a single correlated calculation at a reference geometry for all other fragments. We illustrate the key characteristics of this method and compare it with conventional BE. This novel scheme can potentially lead to a correlation method that scales sub-linearly in time with respect to system size. It exhibits chemical accuracy (<1 kcal/mol energy error) for bond stretches of about 1 Å or rotations of tens of degrees relative to the reference geometry, while recomputing only a small number of fragments, independent of system size. We discuss potential applications in simulating realistic chemical phenomena, such as scanning the potential energy surface, reaction pathway studies, molecular dynamics simulations, and geometry optimizations.