Pseudopotential Calculation of the Elastic Constants of Simple Metals

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Abstract
On the basis of the local-pseudopotential perturbation formulation of the energy of a metal, the elastic coefficients are calculated for a primitive cubic lattice by the method of homogeneous deformation and also by the method of long waves. Comparison of the two methods leads to two results which are valid for any lattice structure. Firstly, the Hubbard-Sham exchange and correlation screening parameter is determined by requiring agreement between the two calculations for the exchange and correlation contribution to the bulk modulus. Secondly, it is shown that certain screening corrections are contained to a higher order in the homogeneous-deformation calculation than in the long-waves calculation. This leads to a difference in the longitudinal elastic coefficients as calculated by the two methods; the difference does not represent a disagreement with the well-known equivalence of the two methods, but merely results from the use of a finite-order pseudopotential perturbation. These results are illustrated by a simple model calculation of the elastic coefficients and their pressure derivatives for sodium and potassium.

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