Resonance Orbital, Off-Resonance Orbital and Pseudo-Greenian

概要

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The method of calculating the Greenian by use of a set of auxiliary orbitals besides a complete set of functions, which was proposed prevously by the authors, is elaborated with new developments and supplementary discussions. An expression of the T matrix in which the auxiliary orbitals play the role of the intermediate states is derived to describe the scattering of an electron whose unperturbed motion can be chosen arbitrarily. An approximation to the expression of the T matrix which retains the most dominant term only is shown to be useful not only for the case of resonance but also for the case of off-resornance where the pseudopotential theory may be justified. A variational principle which determines the best choice of arbitrary operators brought in by the overcompleteness of employed functions is discussed on the basis of a generalization of the pseudo-Hamiltonian of the psedopotential theory. These discussions are applied to the band structure calculation of a transition metal. An approach which corresponds to an extension of the OPW or pseudopotential calculation is discussed. It is shown also that a specialization of the general formalism leads to the Ziman and Hubbard equations. Finally a practical method of calculating the Greenian on the basis of the energy spectra determined by these equations is developed.
1971-04-25