Tight-Binding Models of Amorphous Systems: Liquid Metals

A tight-binding approach to the electronic structure of disordered systems is developed for a simple one-orbital model of a liquid metal. An equation is derived for a one-electron continuum Green's function from which the electronic density of states can be obtained. Utilizing an analogy between this Green's function and the $T$ matrix of multiple-scattering theory, results are obtained corresponding to the quasicrystalline approximation (QCA) of Lax and the self-consistent approximation (SCA) of Schwartz and Ehrenreich. Moments of the spectral function are also analyzed. Calculations were made using random and hard-sphere pair distribution functions. The QCA in this model is quite inadequate, and the SCA, while a considerable improvement, proves to involve a questionable approximation to the three-body distribution function.