Localization of electrons and excitations

Electrons, electron holes, or excitations in finite or infinite 'multimer systems' may be localized or delocalized. In the theory of Hush, localization depends on the ratio Δ/ λ ( Δ/2 = coupling; λ = reorganization energy). The latter theory has been extended to the infinite system [S. Larsson, A. Klimkāns, Mol. Cryst. Liq. Cryst. 355 (2000) 217]. The metal/insulator transition often takes place abruptly as a function of Δ/ λ. It is argued that localization in a system with un-filled bands cannot be determined on the basis of Mott-Hubbard U alone, but depends on the number of accessible valence states, reorganization energy λ and coupling Δ (=2t). In fact U = 0 does not necessarily imply delocalization. The analysis here shows that there are many different situations for an insulator to metal transition. Charge transfer in doped NiO is characterized by Ni ²⁺ - Ni ³⁺ exchange while charge transfer in pure NiO is characterized by a disproportionation 2Ni ²⁺ → Ni ⁺ + Ni ³⁺. In spite of the great differences between these two cases, U has been applied without discrimination to both. The relevant localization parameters appear to be Δ and λ in the first case, with only two oxidation states, and U, Δ and λ in the second case with three oxidation states. The analysis is extended to insulator-metal transitions, giant magnetic resistance (GMR) and high T_c superconductivity (SC). λ and Δ can be determined quite accurately in quantum mechanical calculations involving only one and two monomers, respectively.