Effect of potential on electronic energy bands in crystalline sodium

Abstract

The central problem in the calculation of the band structure of a crystal is the choice of the potential appearing in the set of one electron equations. The potential under consideration is intended to represent the effective interaction between a given electron and the rest of the crystal. The aim of the present work is to study how far the calculated electronic band structure of a crystal depends upon the choice of the particular potential. Two forms of potential are chosen. One is the famous Prokofjew potential for sodium used and recommended by many workers. The other potential is constructed considering the most important interactions on a basis of one constructed by V. Heine for Aluminium. Calculations are made using O.P.W method with both potentials of the energy at points of symmetry within the Brillouin Zone. The values obtained with our potential for T1, T15,N1,N1,P4(l) are in closer agreement with other worker's values than the values obtained with Prokofjew's potential. On the other hand the energy at P4(l) with both potentials seems unreasonable. The closer agreement thus gives an indication that the construction of our potential is near self consistent and the results obtained by us may be in closer agreement with experimental results.