  A recent tight-binding scheme provides a method for extending the results of
first principles calculations to regimes involving $10^2 - 10^3$ atoms in a
unit cell. The method uses an analytic set of two-center, non-orthogonal
tight-binding parameters, on-site terms which change with the local
environment, and no pair potential. The free parameters in this method are
chosen to simultaneously fit band structures and total energies from a set of
first-principles calculations for monatomic fcc and bcc crystals. To check the
accuracy of this method we evaluate structural energy differences, elastic
constants, vacancy formation energies, and surface energies, comparing to
first-principles calculations and experiment. In most cases there is good
agreement between this theory and experiment. We present a detailed account of
the method, a complete set of tight-binding parameters, and results for
twenty-nine of the alkaline earth, transition and noble metals.
