Band structure of lithium using a method suitable for a self- consistent calculation

Some of the essential requirements for a self-consistent field band structure calculation in a solid are discussed and a method is suggested, similar to that used in atomic and molecular calculations, which is based upon the expansion of the one-electron crystal wave functions in terms of a set of basis functions. Using a mixture of tight-binding Bloch orbitals (TBBO's) and varying numbers of separate plane waves as basis functions, test calculations have been performed for bcc Li with a = 6.5183 a.u. using the Seitz potential in place of the true SCF potential. The convergence behaviour indicates that a set of 13 separate plane waves and 6 TBBO's is potentially able to give core and conduction band energies accurate to within 0.001 ryd for Li. The results of a band structure calculation are presented which, although not realising the full accuracy because of approximations in dealing with the TBBO's, nevertheless provide a description of the conduction band structure for the Seitz potential accurate to 0.003 ryd at 40 inequivalent points on a cubic grid. Conduction band energies for the symmetry points, with the exception of Γ, are obtained to within 0.0005 ryd