Calculation of the electric field gradient tensor from energy band structures

The electric field gradient tensor (EFG) can be measured accurately by various experimental techniques. The theoretical understanding, however, was restricted to point charge models, Sternheimer antishielding factors and model calculations for a restricted number of compounds. We have developed a method which obtains the EFG from a full potential linearized augmented plane wave (LAPW) energy band structure calculation. Starting from the total crystal charge density (including the core electrons) the EFG is obtained numerically without further approximations. We have applied our method successfully to all hep metals up to Cd, to semiconductors, and to insulators such as lithiumnitride or cuprite. Good agreement with experiment is found and we predict interesting changes in the sign of the EFG in the 3d and 4d transition metal series. The aspherical distribution of the valence electrons determines 80 or 90% of the total EFG and the influence of the core electrons is small. Even for the 3d and 4d metals the asphericity of the valence p electrons dominates over the d contribution to the EFG due to the different radial behavior of p and d wave functions.