MODIFIED TIGHT-BINDING EQUATIONS FOR WAVE-FUNCTIONS OF SEMIINFINITE CRYSTALS AND INTERFACES

An infinite set of equations for wave functions of semi-infinite crystals or interfaces in the tight-binding approximation is transformed into a finite one for coefficients of basis functions in the disturbed region and coefficients of the Bloch waves. The solutions of this set of equations permit us to construct the wave function of the whole system. The expressions for the local density of states, transmission, and reflection coefficients on the interface are obtained. As a model example the wave functions, the local densities of states, the transmission and reflection coefficients for the Pt(111) surface, treated as an interface between the crystal and empty space, are calculated for the center of the surface Brillouin zone in the linear-muffin-tin-orbital-tight-binding approximation.