RECONSTRUCTION OF THE TRUE WAVE-FUNCTIONS FROM THE PSEUDOWAVEFUNCTIONS IN A CRYSTAL AND CALCULATION OF ELECTRIC-FIELD GRADIENTS

Eight schemes for the reconstruction of the true aspherical wavefunctions from the pseudowavefunctions in a crystal are developed. The schemes are distinguished by four different choices of the boundary conditions for the self-consistent solution of the Kohn-Sham equation for the true wavefunction in a reconstruction sphere (the boundary conditions being supplied by the pseudopotential calculation) and by two different ways of solving the Kohn-Sham equations (numerically or by the use of a basis set). The methods are tested by calculating the electric field gradients in hexagonal metals and on atoms near a vacancy in Na The comparison with ad-electron calculations and with experiments demonstrates that the reconstruction schemes represent powerful tools for the calculation of electric field gradients within the framework of the pseudopotential methods for situations with moderate or large electric field gradients. Altogether, the reconstruction schemes extend the applicability of the pseudopotential method to situations where the nodal structure of the true wavefunctions of the valence electrons in the core regime is essential.