On the ab initio evaluation of Hubbard parameters .1. The analytical approach in the absence of orbital relaxation

A theoretical approach is considered for the ab initio derivation of the parameters contained in the Hubbard Model, under the fundamental assumption that the orbital relaxation represents a negligible effect for the system of interest. The approach is based on a one-to-one mapping between the states of a general empirical two-electron Hamiltonian and the results of ab initio calculations on a dimeric unit. The localization of the ab initio orbitals and its consequences are discussed in the Appendix. The analysis is carried out by distinguishing two main cases: (a) the symmetric case, in which it is possible to derive the values of the empirical parameters from a limited set of self-consistent calculations, and (b) the asymmetric case, in which several parameters have to be estimated by resorting to frozen-orbital calculations. The dependence of the effective value of the on-site Hubbard repulsion U-a on the chemical environment is discussed. Finally, making contact with an alternative approach, based on the expansion of the Hamiltonian matrix in series of overlaps between non-orthogonal functions centered on neighboring sites, the reliability of the standard Hubbard Model is investigated. It is found that off-diagonal electron-electron interaction terms such as X and W can become non-negligible, even in the absence of orbital relaxation, due to special metrical arrangements. A discussion of the capabilities and limitations of the approach, as compared with more rigorous methods, is also included. (C) 1997 American Institute of Physics.