Eur. Phys. J. D 32, 45-49 (2005)
https://doi.org/10.1140/epjd/e2004-00174-3

Some remarks on generalised multipole expansions

¹ Istituto Nazionale per la Fisica della Materia e Dipartimento di Fisica “A. Volta”, Università di Pavia, via A. Bassi 6, 27100 Pavia, Italy
² Biblioteca Unificata di Giurisprudenza, Servizio Informatico, Università di Pavia, Corso Strada Nuova 65, 27100 Pavia, Italy

Corresponding author: ^a Silvano.Romano@pv.infn.it

Received: 30 June 2004
Revised: 23 September 2004
Published online: 30 November 2004

Abstract

Models for the mutual potential energy between two molecules proposed in the scientific literature often contain a sum of inverse-power interactions involving pairs of sites belonging to the two particles; in turn, these quantities are functions of a few scalar invariants involved in the problem at hand, and one is often interested in directly obtaining an explicit expression of the potential in terms of the latter; the extensively studied two-centre multipole expansion for the mutual electrostatic energy between two charge distributions is a well-known example of this procedure and of its restrictions. We consider here another, less widely known and possibly complementary, approach, proposed by Šebek some years ago [J. Šebek, Czech. J. Phys. B 38, 1185 (1988)];
the resulting formulae show that this procedure can become computationally favourable for sufficiently high molecular symmetry.