Towards a Full Configurational Accuracy calculation of an arbitrary molecule via fragment embedding and a stochastic solver

We demonstrate the feasibility of using a stochastic solver, Full Configuration Interaction Quantum Monte Carlo with the initiator approximation(i-FCIQMC), to converge fragment em- bedding calculations, namely Bootstrap Embedding (BE). We first propose and test a general protocol to converge BE-i-FCIQMC calculations, then suggest how the quality of the calcu- lation compares against deterministic BE-FCI using different numbers of walkers. We then demonstrate that BE-i-FCIQMC can perform as well as BE-FCI in the large walker limit, and how different factors, including the size of the Hilbert space of the fragments, the number of walkers and the nature of the chemical system affect the achievable matching error. This work demonstrates the potential of performing FCI quality calculations in realistic systems using BE.