Projection-Based Correlated Wave Function in Density Functional Theory Embedding for Periodic Systems

We present a level shift projection operator based embedding method for systems with periodic boundary conditions where the active subsystem can be described using either density functional theory (DFT) or correlated wave function (WF) methods and the environment is described using DFT. Our method allows for k-point sampling, is shown to be exactly equal to the canonical DFT solution of the full system under the limit that we use the full system basis to describe each subsystem, and can treat the active subsystem either with periodic boundary conditions in what we term periodic-in-periodic embedding or as a molecular cluster in cluster-in-periodic embedding. We explore each of these methods and show that cluster WF-in-periodic DFT embedding can accurately calculate the absorption energy of CO on to a Si(100)-2X1 surface.