Exchange Correlations in Statistical Model and the Cohesive Energy of Solids

✍ Scribed by S. Olszewski

• Publisher: John Wiley and Sons
• Year: 1963
• Tongue: English
• Weight: 805 KB
• Volume: 3
• Category: Article
• ISSN: 0370-1972
• DOI: 10.1002/pssb.19630031204

✦ Synopsis

Abstract

A method of calculating the cohesive energy of solids, using a statistical approximation, is presented.

The cohesive energy is found by introducing, into a statistical model, the local density correction which takes into account the finite volume produced by the exchange holes in the electron gas. The correction reduces the density of the electron gas, so that its influence is opposite to that of the charge accumulation due to the energy reduction by the exchange term.

As a result two distinct states occur for atoms in which exchange is considered. In one state, that of the free atom, the electron density at the boundary is zero and the boundary of the atom lies at infinity. The second state represents the atom in a crystal; the atomic dimensions are finite and the electron density at the boundary is equal to that of the Thomas‐Fermi‐Dirac model. The difference in energy between the atom in the first and second states is positive and provides the energy of cohesion. The lattice parameter can be obtained from the atomic radius in the second state. Numerical calculations are performed for the Kr atom.