Study of the electronic band structure of a model of the sodium chloride lattice

The aim of this work is to study how far the calculated electronic band structure of a crystal depends on the choice of a particular field. The sodium chloride structure has been investigated by carrying out a calculation of its electronic band structure, employing a simple model with a positive constant potential representing the negative ion and a negative constant potential representing the positive ion. The electronic energy levels have been determined for various values of a parameter in the chosen potential, in such a way that one may have an idea of the relative position of the various levels over the whole range from the case of free electrons to that in which the electrons are bound in a spherical potential well of infinite depth. The calculation has been carried out using the simple plane wave method. No relativistic or spin-orbit coupling effects have been considered. It has been convenient to determine the energies at points of high symmetry in the Brillouin zone and interpolate these results for general points. The effect of changes in the potential in displacing levels of certain symmetry with respect to others has been investigated. The flat behaviour of the chosen potential is in line, though differing in important details, with the behaviour suggested by the pseudo-potentials approach, and simulates orthogonalization to core states. The calculation has brought out certain features of the band structure that are characteristics of the NaCl structure and must be found with any physically acceptable potential. The energy bands obtained have been compared with those of some crystals with the NaCl structure, calculated by other authors using other methods of calculation, and with the few available experimental data. Attempts have been made to determine the effect of an assymmetry between the two types of ions, of a non-spherically symmetrical potential, and of not making the positive potential on one ion equal to the negative potential on the other. These attempts have led to no new significant effect in comparison with the former results.