Accelerating Density Matrix Embedding with Stochastic Density Fitting Theory: An Application to Hydrogen Bonded Clusters

In this work, we demonstrate how using semistochastic density fitting (ss-DF) can accelerate self-consistent density matrix embedding theory (DMET) calculations by reducing the number of auxiliary orbitals in the three-indexed DF integrals. This reduction results in significant time savings when building the Hartree-Fock (HF) Coulomb and Exchange Matrices and in transforming integrals from the atomic orbital (AO) basis to the embedding orbital (EO) basis. We apply ss-DF to a range of hydrogen-bonded clusters to showcase its effectiveness. First, we examine how the amount of deterministic space impacts the quality of the calculation in a (H2O)