Real-space method for calculation of the electric field gradient in systems without symmetry

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Abstract
The authors present a new scheme for obtaining the electronic contribution to the electric field gradient at the nucleus in systems which are well represented by a tight-binding Hamiltonian. They show that for close-packed metallic systems the linear muffin-tin orbital method in the recently developed tight-binding representation provides a realistic tight-binding Hamiltonian which can be used in this context. The scheme is based on the recursion method and can be applied to systems without symmetry such as amorphous metals, where k-space methods cannot be used. Test calculations were done for HCP Zr with the z axis of the coordinate system taken along the c axis of the crystal and also along an arbitrary direction. The results are independent of the choice of the system, showing that the procedure works in absence of symmetry. When compared with the experimental results for HCP Zr, calculations give the correct sign and a reasonable value for the magnitude. Considering the approximations made when obtaining the Hamiltonian and the subtlety of the effect, the results are very encouraging. In the following paper, other HCP metals are studied. A comparison between real-space and k-space calculations in these metals gives a good idea of the advantages and limitations of the proposed real-space scheme.