Valence Electron Wave Functions Research Articles

The electronic energy bands of the alkali metals and metallic beryllium

The applicability of various electronic energy band interpolation schemes to the alkali metals and metallic beryllium is discussed. An ‘l-dependent’ pseudo-potential method using only a very small number of plane waves in the expansion of the valence electron wave functions is then applied to these metals. The density of states curves and the Fermi surfaces are calculated. It is found that for lithium the Fermi surface may touch the Brillouin zone boundaries. The calculated and observed low temperature electronic specific heat coef­ficients and valence band widths are compared.

The use of the repulsive potential in the quantum theory of solids

A new method is proposed for calculating the energy in certain special points of the Brillouin zone. The wave functions of valence and conduction electrons are given in the form of the linear combination of plane waves and the orthogonality condition of these functions to the wave functions of lower states is replaced by the repulsive potential. The practical application of this very simple method is illustrated on the energy spectrum of silicon in the centre of the Brillouin zone. It is proved that the results are comparable with some other methods, e. g. the orthogonalized plane-wave method.

Fourier Coefficients of Crystal Potentials

A method is developed for the calculation of the Fourier coefficients of the electrostatic potential of a given distribution of valence electrons in a solid. The valence electron wave functions are expressed as combinations of orthogonalized plane waves. The treatment takes full account of the nonspherical character of the atomic polyhedron. Application is made to lithium.