Recently, density matrix embedding methods such as density matrix embedding theory (DMET), density embedding theory (DET) and bootstrap embedding (BE) have been successful at describing correlated solids and model Hamiltonians. Here, we present two different approaches, incremental embedding (IE) and a generalization of BE, to generalizing these methods to molecules. In IE, we describe the system by a one-site effective Hamiltonian for each site (localized orbitals) that is constructed by accumulating corrections to the mean-field description of the single site from two-, three-, four- ... site fragments. To compute these correction terms, we use a new mathematical tool called Schmidt reduction to "compress" the information from a large fragment to a small one, as well as an incremental scheme to properly combine the contributions from different fragments. In BE, on the other hand, we describe the system by assigning to each site a fragment that is "centered" on that site based on a heuristic strategy of determining inter-site connectivity. We then apply matching conditions to these overlapping fragments and optimize the density for each fragment self-consistently. Both approaches formulate a hierarchy with increasing fragment size. We show that the resulting hierarchy converges fast in treating strong correlation in molecules. We also generalize the orbital-based fragmentation strategy in BE to an atomistic level, and show that the atom-based fragment embedding allows fast and accurate computation of large molecules.

Quantum embedding for molecular systems

2019 Spring National Meeting

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