Orbitals with intermediate localization and low coupling: Spanning the gap between canonical and localized orbitals

Localized orbitals are representations of electronic structure, which are easier to interpret than delocalized, canonical orbitals. While unitary transformations from canonical orbitals into localized orbitals have long been known, existing techniques maximize localization without regard to coupling between orbitals. Especially in conjugated π spaces, orbitals are collapsed by unitary localization procedures into nonintuitive, strongly interacting units. Over-localization decreases interpretability, results in large values of interorbital coupling, and gives unmeaningful diagonal Fock energies. Herein, we introduce orbitals of intermediate localization that span between canonical and fully localized orbitals. To within a specified error, these orbitals preserve the diagonal nature of the Fock matrix while still introducing significant locality. In systems composed of molecular fragments, π spaces can be localized into weakly coupled units. Importantly, as the weakly coupled orbitals separate, highly coupl...