$\mathbb{i}$CAS: Imposed Automatic Selection and Localization of Complete Active Spaces

Abstract

It is shown that a prechosen set of occupied/virtual valence/core atomic/fragmental orbitals can be transformed to an equivalent set of localized occupied/virtual pre-molecular orbitals (pre-LMO), which can then be taken as probes to select the same number of maximally matching localized occupied/virtual Hartree-Fock (HF) or restricted open-shell Hartree-Fock (ROHF) molecular orbitals as the initial local orbitals spanning the desired complete active space (CAS). In each cycle of the self-consistent field (SCF) calculation, the CASSCF orbitals can be localized by means of the noniterative ``top-down least-change'' algorithm for localizing ROHF orbitals, such that the maximum matching between the orbitals of two adjacent iterations can readily be monitored, leading finally to converged localized CASSCF orbitals that overlap most the guess orbitals. Such an approach is to be dubbed as ``imposed CASSCF'' ($\mathbb{i}$CASSCF or simply $\mathbb{i}$CAS in short) for good reasons: (1) it has been assumed that only those electronic states that have largest projections onto the active space defined by the prechosen atomic/fragmental orbitals are to be targeted. This is certainly an imposed constraint but has wide applications in organic and transition metal chemistry where valence (or core) atomic/fragmental orbitals can readily be identified. (2) The selection of both initial and optimized local active orbitals is imposed from the very beginning by the pre-LMOs (which span the same space as the prechosen atomic/fragmental orbitals). Apart from the (imposed) automation and localization, $\mathbb{i}$CAS has an additional merit: the CAS is guaranteed to be the same for all geometries for the pre-LMOs do not change in character with geometry. Both organic molecules and transition metal complexes are taken as showcases to reveal the efficacy of $\mathbb{i}$CAS.