Application of the method of tight binding for determining the excited bands of sodium and potassium

An accurate determination of the energy bandstructure of sodium and potassium has been performed by extending the basis set to include Bloch sums of single Gaussian orbitals of s, p, d, and f type. The results obtained using this extended basis set offer improvement over the results obtained using only Bloch sums of atomic orbitals. This increased variational freedom affected the bottom of the conduction band very little (about 0.01 a.u.) but affected the high energy bands in potassium by as much as 0.06 a.u. Comparison of energy bands using muffin-tin potential and overlapping atomic potential is also presented.