Quantum embedding for material chemistry based on domain separation and open subsystems

This perspective considers two theories we recently proposed to perform quantum embedding calculations for chemical systems: domain-separated density functional theory (DS-DFT) and locally coupled open subsystems (LCOS). The development includes both the fundamentals of each theory as well as potential applications, some technical aspects, and related challenges. DS-DFT is suited to study intramolecular effects, where one can apply a high level of theory (based on DFT or wave function theory) to a region of interest inside a molecule or solid and lower level theory elsewhere, with smooth switching between the regions. LCOS, in contrast, is a fragment-based embedding, which offers computational advantages to study intermolecular behavior such as electron hopping, spin-environment interaction, and charge-transfer excitations. However, both theories can exchange roles when appropriate. In addition, these theories allow for control of computational scaling of their algorithms. We explore paths to determine the charge-transfer operator used in LCOS, and suggest an auxiliary energy minimization that can provide a practical estimate to this operator. We also briefly discuss how to implement density fitting techniques in domain separation, and how domain separation can be used for pure wave function-based embedding.