Instability in chemical bonds from broken-symmetry single-reference to symmetry-adapted multireference approaches to strongly correlated electron systems

Theoretical descriptions of strongly correlated electron systems have been investigated from the view point of generalization of molecular orbital (MO) concepts; namely from broken-symmetry (BS) single reference (SR) MO theories to symmetry-adapted (SA) multi-reference (MR) MO theories. Generalized Hartree-Fock (GHF) MO and generalized Kohn-Sham (GKS) DFT methods are first introduced as the BS SR approach, whereas the MR-X (X=configuration interaction (CI), perturbation (PT), coupled-cluster (CC) and density fianctional theory (DFT)) are discussed as the SA MR approach. The quantum resonance (R) of the degenerated BS MO solutions is also examined as a powerful procedure for recovery of the broken spin and spatial symmetries in finite systems. The RBS MO CI has been applied to elucidate electronic structures of triangular and tetrahedral systems with strong spin frustrations. The RBS MO method also gives rise to an approximate spin projection (AP) scheme of the spin-contaminated BS solutions. The natural orbitals (NO) analysis of BS and RBS solutions provides symmetry-adapted (SA) NOs and their occupation numbers, which are useful for construction of complete active space (CAS) for successive MR-X computations. The occupation numbers of NOs are also used to define several chemical indices such as effective bond order (b and B) and unpaired electron density (U), which are common conceptual bridges between BS SR and SA MR methods. Applications of these theoretical methods have been performed for elucidation of chameleonic reactivity of molecular oxygen and transition-metal oxo species, and the nature of chemical bonds in ion-radicals and mixed-valence (MV) iron-sulfiar clusters as typical examples with strongly correlated electron systems.