Ligand-field theory multiplet model

As we know, a few first-principles calculations for multiplet structure have been tried by several researchers. Ohnishi and Sugano calculated the energy positions of the (R line) and Ti (U band) states in ruby, under one-electron approximation (12). Xia et al. carried out similar calculations using more realistic model cluster (13). They could, however, only consider the energies of lower-lying two states in multiplet structure. Watanabe and Kamimura combined one-electron calculations with ligand field theory, and carried out first-principles calculation for the "full" multiplet structure of several transition metal impurities... 

Under the second topic of Ligand-field Theory and its Extensions we describe the basic concepts behind the various versions of LFT - the angular-overlap model (AOM) and its extensions. In the section named The physical background conditions for the applicability of the ligand-field approach we sketch briefly the theoretical foundation and limits of applicability of the effective-hamiltonian approach with special attention to electronic multiplets. In the theory section, we describe various approaches in current calculations of electronic structure, such as LFDFT, SORCI and TDDFT, with the various applications detailed in the following section, before an outlook for further developments. 

LFT originated as a purely electrostatic model - crystal-field theory (CFT) [18], in which d-electronic multiplets of transition metals are perturbed by ligands as point charges or point dipoles. The CF operator (Equation 1) acts within the space of Slater determinants (SD) composed of purely d-spin-orbitals in which two-electron energies are taken into account with the Coulomb operator and one-electron energies with a crystal-field potential (vcp), the first and second terms in Equation 1, respectively. 

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