Projection-Based quantum embedding for high spin multiplicities

Projection-based quantum embedding is a formally exact density functional theory embedding. By implementing an appropriate post-Hartree Fock method, the electron correlation of a chosen embedded subsystem can be recovered from the mean-field approximation in a systematically improvable way. However, partitioning the embedded subspace to include all local entanglement with the embedded subsystem is not trivial, and there have been many proposed partitioning methods involving localized orbitals. Using a singular value decomposition (SVD) to guide the partitioning of the embedded subspace is a robust way to ensure the invariance of the chosen subspace against orbital deformation while capturing the local correlation energy. Additionally, using an SVD to truncate the virtual subspace is a cost conscience way of prioritizing those virtual orbitals that most contribute to the correlation energy in the chosen active space. To date, SVD partitioning of the embedded subspace has been successfully demonstrated for singlet ground-state systems. Here we present an extension of the SVD-informed subsystem projected atomic orbital decomposition partitioning method to systems with higher spin multiplicities. This method is built on restricted open-shell mean-field orbitals that ensure the fidelity of the subsystem spin, a necessary condition of a well-defined embedding method. Furthermore, the same formalism is naturally extended to an SVD-informed concentric localization and subsequent truncation of the virtual space.