The effect of non-orthogonality and previously neglected diagonal terms in the tight-binding approximation for the electronic structure of liquid metals and alloys

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The averaged Green's function for an electron in non-simple liquid metals and alloys is evaluated in the tight-binding approximation (LCAO) when the effect of non-orthogonality and previously neglected diagonal terms are taken into account. The actual formalism is given on the basis of self-consistent single-site approximations (SSSA)-particularly of the coherent potential approximation (CPA) for liquid metals and of the Ishida-Yonezawa theory. The averaged Green's function is well known to be related to one-electron properties such as the density of states and, within SSSA assumptions, even to the electric conductivity, the Hall coefficient, etc. Calculated densities of states with and without non-orthogonal terms are given for comparison and discussion.