Tight-binding models and density-functional theory

Semiempirical tight-binding models have been widely used but the details of their relationship to more fundamental theories have never been clear and so they have usually been treated as fitting and interpolation schemes rather than as quantitative calculational tools. In this paper, we show how simple tight-binding models can be understood as stationary approximations to self-consistent density-functional theory and give prescriptions for calculating all the required potentials and matrix elements. Some preliminary applications have given encouraging results.