Incremental embedding: A density matrix embedding scheme for molecules

Abstract

The idea of using fragment embedding to circumvent the high computational scaling of accurate electronic structure methods while retaining high accuracy has been a long-standing problem for quantum chemists. Traditional fragment embedding methods mainly focus on systems composed of weakly correlated parts and are insufficient when division across chem. bonds is unavoidable. Recently, d. matrix embedding theory (DMET) and other methods based on the Schmidt decompn. have emerged as a fresh approach to this problem. Despite their success on model systems, these methods can prove difficult for realistic systems because they rely on either a rigid, non-overlapping partition of the system or a specification of some special sites (i.e. "edge" and "center" sites), neither of which is well-defined in general for real mols. In this work, we present a new Schmidt decompn.-based embedding scheme that allows the combination of arbitrary overlapping fragments without the knowledge of edge sites. This method forms a convergent hierarchy in the sense that higher accuracy can be obtained by using fragments involving more sites. The computational scaling for the first few levels is lower than that of most correlated wave function methods. We present results for several small mols. in atom-centered Gaussian basis sets and demonstrate that Incremental Embedding converges quickly with fragment size and recovers most static correlation in small basis sets even when truncated at the second lowest level.