The electrostatic potential generated by topological atoms: a continuous multipole method leading to larger convergence regions P.L.A. Popelier * , M. Rafat Department of Chemistry, UMIST, 88 Sackville Street, Manchester M60 1QD, UK Received 1 May 2003; in final form 28 May 2003 Published online: 27 June 2003 Abstract The electrostatic potential generated by an atom in a molecule can be conveniently expressed by traditional mul- tipole expansions. The disadvantage of such expansions is that they introduce a divergence sphere within which the expansion diverges. Because of their finite size, atoms defined according to quantum chemical topology (QCT) yield a small divergence sphere. However the introduction of an alternative continuous multipole expansion reduces the di- vergence region even further. The new method allows the electrostatic potential to be evaluated accurately at short- range, which is illustrated for a pair of simple molecules. Ó 2003 Elsevier Science B.V. All rights reserved. 1. Introduction The molecular electrostatic potential (MEP), a physical observable proposed [1] a few decades ago, has ever since been recognised as a most in- formative quantity [2–4], as witnessed by its wide range of applications. Just to name a few exam- ples, molecular electrostatics operated as a tool in the interpretation of regioselectivity [5] and reac- tivity [6] of small molecules, served as an indicator for evolutionary conservativeness near enzyme active sites [7], featured in zeolite catalysis [8], predicted adsorption sites on crystalline oxide surfaces [9], acted as the basis for force-field parametrisation [10] and hydration models for proteins [11] and nuclei acids [12], was used as a vehicle in host–guest complementarity in cyclo- dextrins [13], and was applied in structure–activity relationships of the H2 receptor antagonists [14] and in a toxicity study of dibenzo-p-dioxins [15]. Such enormous range of applications warranted efficient implementation of the MEP within the LCAO-MO-SCF formalism, which was eventually achieved [16] after a momentous development of fast techniques for Gaussian integral evaluation [17]. Since the availability of such algorithms the electrostatic potential can be routinely computed by standard ab initio packages, such as GAUS- AUS- Chemical Physics Letters 376 (2003) 148–153 www.elsevier.com/locate/cplett * Corresponding author. Fax: +441612004559. E-mail address: pla@umist.ac.uk (P.L.A. Popelier). 0009-2614/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0009-2614(03)00957-6