The Approximate Expression of Green's Function for the Calculation of Electronic Structure in Metals and Alloys

Abstract

The calculation of Green's function of the one-electron Schrödinger equation by use of an overcomplete set of functions is discussed; in addition to the plane waves a set of atomic orbitals is introduced as auxiliary functions which facilitate the calculation. A formalism which treats the auxiliary functions on an equivalent basis with the plane waves is developed; it leads to a new expression of Green's function which is useful not only for the ab initio calculation of electronic structure but also for the substantiation of model Hamiltonians such as the Anderson model. It is pointed out that there are many arbitrariness in defining the resonance orbitals, the mixing elements, etc.; the present theory takes them into account explicitly. In the absence of resonance the present theory is equivalent to the pseudopotential theory with a general choice of the pseudopotential. The Anderson model is discussed in detail as an illustrative example; an ab initio calculation of the model is presented.