M olecular P hysics, 1996, V ol. 89, N o. 2, 595±605 Transferability of topologically partitioned polarizabilities : the case of n-alkanes By ANTHONY J. STONE University Chemical Laboratory, Lens®eld Road, Cambridge CB2 1EW, UK CHRISTOF HA $ TTIG Institut fu $ r Physikalische und Theoretische Chemie, Universita $ t Bonn, Wegelerstr. 12, D-53115 Bonn, Germany GEORG JANSEN and JA ! NOS G. A ! NGYA ! N Laboratoire de Chimie The ! orique, Universite ! Henri Poincare ! , URA CNRS No 510, B.P. 239, F-54506 Vandúuvre-le ’ s-Nancy Cedex, France (Recei Šed 1 December 1995; accepted 17 March 1996) Distributed polarizabilities of a series of n-alkanes C n H # n+ # (n ¯ 2±7) in various conformations have been determined using Bader’s topological theory of atoms in molecules. Using an appropriate localization scheme, a simple distributed model is constructed, where the methyl and methylene groups are characterized by their dipole polarizability tensors in local frames, and all charge ¯ow polarizabilities between them are retained. A set of average polarizability parameters is proposed that takes into account the local environment of the methyl and methylene groups, and that not only reproduces the polarizability tensor for any member of the n-alkane series in an arbitrary conformation, but also is suitable for the calculation of induction energies. 1. Introduction Additivity and transferability of group polarizabilities is well established ex- perimentally. One of the most extensively studied cases is that of the alkanes, where it has been found that the addition of a methylene unit increases the average polarizability by about 11 ±98 au for the higher members of the series. More sophisticated additivity schemes, based on bond polarizability tensors whose longitudinal and transverse components may diŒer, have been compiled by Le Fe ’ vre [1]. The theoretical basis for such additivity has been questioned on the grounds that the local ®eld experienced by a given atom or bond is quite diŒerent from the external ®eld, and strongly dependent on the actual molecular structure, because of induced moments on other parts of the molecule [2]. This role of the local ®eld has been emphasized by Applequist’s model, where a dipole±dipole interaction scheme is used to take the in¯uence of the molecular environment into account [3]. Nevertheless, it seems that the `in-molecule’ eŒective polarizabilities are reasonably transferable, which can be explained by the relative constancy of the immediate environment of a given atom or bond in various molecular systems [4]. The rigorous theory of distributed polarizabilities [5] overcomes the limitations of earlier approximate models used to describe the interactions between subunits within the molecule. All intramolecular interactions are handled by quantum mechanics, and 0026± 8976 }96 $12± 00 ’ 1996 Taylor & Francis Ltd