Short‐Range Three‐Body Potential in the First‐Order Exchange Energy and the Relative Stability of Alkali Halide Crystals

Abstract

Using the Heitler-London approach a simple expression for the first-order exchange energy between a system of interacting atoms or ions is obtained in the S2 approximation. It is shown that this expression leads t o two-body, three-body, and four-body interactions only. A specific expression for the three-body interaction is evaluated using several different approximations. Assumptions which lead to the expression previously obtained by Lundqvist are discussed. It is found that these expressions vanish for neutral particles.Some modification in the assumption is made and an expression for three-body interaction for neutral particles is obtained. Numerical calculations are made for argon, xenon, and helium and the results compared with those obtained by others. The three-body interaction is also applied to study the relative stability of different alkali halide structures. It is found that this three-body potential has a strong preference for CsCl structure.Mit der Heitler-London-Methode wird ein einfacher Ausdruck fur die Austauschenergie erster Ordnung zwischen einem System wechselwirkender Atome oder Ionen in der S2-Naherung erhalten. Es wird gezeigt, daB dieser Ausdruck nur zu Zwei-Teilchen-, DreiTeilchen-und Vier-Teilchen-Wechselwirkungen fuhrt. Fur Drei-Teilchen-Wechselwirkung wird mit verschiedenen Naherungen ein spezifischer Ausdruck abgeleitet. Annahmen, die zu dem kurzlich von Lundquist erhaltenen Ausdruck fiihren, werden diskutiert. Es wird gefunden, daB diese Ausdriicke fur neutrale Teilchen verschwinden. Numerische Berechnungen werden fur Argon, Xenon und Helium durchgefiihrt und die Ergebnisse mit denen anderer Autoren verglichen. Die Drei-Teilchen-Wechselwirkung wird auch zur Untersuchung der relativen Stabilitat verschiedener Alkalihalogenidstrukturen benutzt. Es wird gefunden, daB dieses Drei-Teilchen-Potential eine starke Bevorzugung der CsC1-Struktur ergibt.

On the change of electronic polarisability of an ion in a crystal

“…Assuming an average value for (2;) for all the states a t the ion site G and using the exchange charge model (see for example [9]) in which the overlap is concentrated a t a point 0 midway between the nearest neighbour ions a t G and G', where OG/Oa' = ZQ/ZQ*, we Put where 10 is the ionic radius of the G-th ion. We get from (21),…”

“…The product functions Ybo and Ybv are built in the same way as in [9]. We take the electric field in the z-direction and consider the ions to be spherically symmetric.…”