Exactly-embedded multiconfigurational self-consistent field theory using density matrix embedding: the localized active space self-consistent field method.

Density matrix embedding theory (DMET) is a fully quantum-mechanical embedding method which shows great promise as a method of defeating the inherent exponential cost scaling of multiconfigurational wave function-based calculations by breaking large systems into smaller, coupled subsystems. However, we recently [JCTC 2018, 14, 1960] encountered evidence that the single-determinantal bath picture inherent to DMET is sometimes problematic when the complete active space self-consistent field (CASSCF) is used as a solver and the method is applied to realistic models of strongly-correlated molecules. Here, we show this problem can be defeated by generalizing DMET to use a multiconfigurational wave function as a bath without sacrificing attractive features of DMET, such as a second-quantized embedded subsystem Hamiltonian, by dividing the active space into unentangled active subspaces each localized to one fragment. We introduce the term localized active space (LAS) to refer to this kind of wave function. We obtain the LAS wave function by the DMET algorithm itself self-consistently, and we name this approach the localized active space self-consistent field (LASSCF) method. LASSCF exploits a modified DMET algorithm, but it requires no ambiguous error function minimization, produces a wave function with exact embedding, is variational, and reproduces CASSCF where comparable DMET calculations fail. Our results for test calculations on the nitrogen double-bond dissociation potential energy curves of several diazene molecules suggest that LASSCF can be an appropriate starting point for a perturbative treatment. Outside of the context of embedding, LAS is an attractive alternative to a CAS wave function because its cost scaling is exponential only with respect to the size of individual fragment active subspaces, rather than the whole active space of the entire system.