The Cohesive Energy and Charge-Density Form Factors of Beryllium as a Test on the Langreth–Perdew–Mehl Approximation

In order to assess the accuracy of the approximation to exchange and correlation recently presented by Langreth, Predew, and Mehl (LPM) we have used it to calculate the cohesive energy and the charge density of metallic Be. In accordance with previous results on bulk Si we find the LPM approximation to be superior to the LD approximation for both the energy and the density. The LD energy error is reduced by approximately a factor of three in the LPM approximation. We also show that a comparison between theoretical and experimental form factors cannot be used to distiguish between different approximations used in computing the density of the valence electrons. Differences in valence densities are overshadowed by errors in the core density. Finally we have discovered an error in previous pseudopotential calculations of the electronic density of solids. We also present a procedure for correcting the error, which enables us to obtain accurate valence densities within the ab initio pseudopotential approach.