The Simplest Ab Initio Theory of Electronic Structure

Abstract

It has long been thought that electronic states in molecules and solids could be viewed as combinations of free-atom states. This idea even appeared in the thesis of Bloch [2.1] in 1928 but was thought to be so crude as to only be useful for illustrative purposes. Hückel [2.2] used this concept for molecular orbitals in 1931, noting that for estimating electron energies one needed only a few parameters, which could be calculated or guessed, with many taken equal to zero. This theory is called tight-binding theory. By 1963 Hoffmann [2.3] had proposed the extended Hückel theory, in which he reintroduced many of the discarded parameters and found approximate ways to compute them. There was a flexibility to these theories in the sense that, once they were programed and used to calculate a property, it was easy to modify the program to improve the result and the next application used the new scheme, with a new name. See [2.4] for a comprehensive discussion of such approaches.