Eur. Phys. J. H 38, 519–534 (2013)
https://doi.org/10.1140/epjh/e2013-30056-8

On lower bounds for polarisability

¹ Chemistry Program, Centre College Danville KY 40444, USA
² Laboratory of Molecular Structure and Quantum Mechanics, Department of Chemistry, Lomonosov Moscow State University Moscow, 119991, Russia

^a e-mail: ed.montgomery@centre.edu

Received: 16 October 2012
Received in final form: 6 June 2013
Published online: 26 July 2013

Abstract

The response of molecular systems to external fields was one of the first areas studied after development of the new quantum mechanics. Early work by Kirkwood and Buckingham developed polarisability lower bounds that are still used today. This work uses an inequality proposed by Linderberg to develop a treatment of polarisability lower bounds that unifies the work of Kirkwood and Buckingham with Hylleraas’ variational perturbation theory. In particular, the prehistory of the works of Kirkwood and Buckingham is described. Numerical examples are presented to demonstrate the convergence of approximate wavefunctions in the confined atom problem. The applicability of dimensional scaling and its utility in the analysis of confined systems are also discussed.