This article, written in honor of Eleftherios N. Economou, contains a short
summary of work one of us carried out some 20 years ago in collaboration w
ith Lefteris and reports on recent developments on the use of tight-binding
Hamiltonians to perform accurate and efficient electronic structure calcul
ations. More specifically. in this work we use the newly developed NRL tigh
t-binding method to explore the existence of metastable phases in transitio
n metals, present new Slater-Koster parametrizations of cubic perovskite ma
terials and provide an extension of the Slater-Koster approach that include
s the spin-orbit interaction. (C) 2001 Elsevier Science B.V. All rights res
erved.