It took a relatively long time to develop methods capable of determining the detailed electronic structure of solids. In contrast, for gases, unraveling the mysteries of atomic energy levels went hand in hand with the development of quantum theory. Atomic optical spectra yielded sharp lines that could be interpreted in terms of excitations of electrons from occupied to empty states. These studies provided important tests of the theory. However, compared to atomic spectra, solid-state spectra are broad, since the interactions between the atoms spread the allowed occupied and empty energy levels into energy bands. This made interpretation of spectra in terms of electronic transitions very difficult. Trustable precise electronic energy band structures were needed to interpret solid-state spectra, but these were difficult to obtain.

In principle, the Schr dinger equation can describe the behavior of electrons in solids; but without approximations, solutions for the electronic energy levels and wavefunctions are extremely difficult to calculate. Despite considerable effort, the situation around 1960 was still unsatisfactory. Creative models of solids had been introduced to explain many physical phenomena such as electronic heat capacities and superconductivity with spectacular success. However, calculations capable of yielding band structures and other properties for specific materials were not available.

An important intermediate step was the introduction of the empirical pseudopotential model (EPM). Pseudopotentials had been around since 1934, when Fermi introduced the concept to examine the energy levels of alkali atoms. Since he was interested in highly excited atoms, he ignored the oscillations of the valence electron wavefunctions...