  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.
