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

We demonstrate how using semi-stochastic 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 results in time savings in building the Hartree Fock (HF) Coulomb and the Exchange Matrix and in integral transformation from the Atomic Orbital (AO) basis to the Embedding orbital (EO) basis. We then apply ss-DF to a range of hydrogen bonded clusters. First, we examine how the amount of deterministic space impacts the quality of the calculation in a (H2O)10 cluster. Next, we test the computational efficiency of ss-DF when compared to deterministic DF (d-DF) in water clusters containing 6 to 30 molecules of water using a triple-ζ basis set. Finally, we perform numerical structural optimisations on water and hydrogen fluoride clusters, revealing that DMET can recover weak interactions when using a back-transformed energy formula. This work therefore demonstrates the potential of using stochastic resolution of identity in quantum embedding theories and their potential to recover weak interactions.