Invariance properties of the multipole expansion with respect to the choice of the coordinate system

✍ Scribed by Leszek Z. Stolarczyk; Lucjan Piela

• Publisher: John Wiley and Sons
• Year: 1979
• Tongue: English
• Weight: 584 KB
• Volume: 15
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/qua.560150613

✦ Synopsis

Abstract

The physical interpretation of intermolecular interactions is usually based on the well‐known multipole expansion of the inverse of the interparticle distance. The interaction energy is then interpreted as a sum of terms arising from the interaction of various multipole moments of both systems. It is supposed that the interaction energy calculated via the truncated multipole expansion generally depends on the choice of local coordinate systems through the coordinate dependence of the multipole moments. In this paper we prove that each term of the multipole expansion given in the form ∑~k = 1~ C~k~/R^k^ is invariant with respect to identical translations and arbitrary rotations of the local coordinate systems. The invariant form of the convergence criterion of the multipole expansion is given and discussed.