Consistency condition in the energy expression of the pseudopotential theory of metals

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Abstract
The consistency condition for the energy expression of a metal obtained from the pseudopotential theory is found to be equivalent to the statement that the static and dynamic elastic constants must agree. If the band-structure energy and the coupling parameter are both confined to the second order of the perturbation theory then this consistency condition is violated. It is pointed out that the reason for this violation lies in the fact that the homogeneous deformation theory takes note of the change in the dielectric function due to strain, while the long-wave theory partly ignores it. It is shown that by suitably coupling the local strain to the ionic coordinates one can get the missing terms in the long-wave theory and the consistency condition is satisfied. The effect of these terms on the phonon dispersion curves for A1 is analyzed.