Calculation of the Cohesive Energies and Bulk Properties of the Alkali Metals

Abstract

The cohesive energy and zero-pressure density of the alkali metals have been calculated using the self-consistent augmented-plane-wave method and the statistical ($X\alpha$) exchange-correlation approximation. For the value of $\alpha$ which makes a single determinant of atomic spin orbitals satisfy the virial theorem, the lighter alkali metals are computed to have cohesive energies and zero-pressure densities which are too large (errors of 22 and 16% for Li) with respect to experiment. To test the sensitivity of these results to the choice of $\alpha$, the same calculations have been performed with $\alpha$ set equal to $\frac{2}{3}$. This choice of $\alpha$ produced more uniformly good results for all the alkali metals with the largest errors occurring for cesium (errors of 7 and 9%, respectively). It is suggested that these results may be a consequence of the large change in the valence electronic charge density that occurs when the lighter alkali-metal atoms come together to form the solid. It is not suggested, however, that $\alpha =\frac{2}{3}$ be used in all energy-band calculations.