Modifications and Extensions to Harrison's Tight-Binding Theory
  Harrison's tight-binding theory provides an excellent qualitative description of the electronic structure of the elements across the periodic table. However, the resulting band structures are in significant disagreement with those found by standard methods. We developed a new procedure to generate both the prefactors of Harrison's hopping parameters and the onsite energies. Our approach gives an impressive improvement and puts Harrison's theory on a quantitative basis. Our method retains the most attractive aspect of the theory, in using a revised set of universal prefactors for the hopping integrals. In addition, a new form of onsite parameters allows us to describe the lattice constant dependence of the bands and the total energy, predicting the correct ground state for all transition metals. This work represents not only a useful computational tool but also an important pedagogical enhancement for Harrison's books. 
L. Shi, D. A. Papaconstantopoulos