Calculation of Electron Velocity in Crystal ab Initio. Results of Computation by Green's Function Method for Vanadium

Abstract

Using the Hellman-Feynman theorem and the perturbation theory for the matrix, an expression for the electron velocity in crystals is derived. Calculations are carried out on a mesh of 55 points in 1/48 th of the b.c.c. Brillouin zone for six energy bands of vanadium. The comparison with the data of numerical differentiation demonstrates the excellent accuracy of the technique presented. The influence of higher angular-momentum terms in the expansion of the wave function on the velocity value is discussed. [Russian Text Ignored].