Simplified local-density theory of the cohesive energy of metals

Abstract

A simplified but accurate theory of the cohesive energy of metals has been developed from the density-functional formalism of Kohn and Sham. In this theory, the total energy of both the free atom and the solid is expressed as a sum of a core and a valence binding energy, and the cohesive energy is reduced (apart from a zero-point vibrational term) to a difference in binding energies. The free-atom binding energy is directly calculated, and accurately (to within 3%) matches the experimental ionization energy in nonrelativistic elements. The binding energy of the metal, on the other hand, is obtained by the generalized pseudopotential method developed previously by the author. This latter step permits all band-structure and self-consistent screening effects to be incorporated analytically. The calculated cohesive energy agrees well with both experiment (to about 20%) and heavy numerical computation (to about 10%) in simple as well as $d$-band metals. More importantly, the method permits the physical origins of the cohesion to be identified in each case, and these are discussed for 22 nontransition metals. It is found that band-structure effects are important in all nonalkali metals and, in particular, that $\mathrm{sd}$ hybridization contributes 30%-60% of the cohesion in the alkaline-earth and noble metals. In addition, the large relativistic energy shifts inherent in the binding energies of the heavy metals are seen to approximately cancel in the cohesive energy.