Properties of atoms in molecules: Group additivity

Every property of a molecule is given by the sum of the contributions from each of its constituent atoms or groups, the groups being defined as proper open systems. The observation of experimental group additivty requires that in addition to the propel-ties of the groups being additive, the group and its properties be transferable from one molecule to another, different molecule. It is shown that such transferability of a group and its properties is in general, only apparent, being the result of compensatory transferability wherein the changes in the properties of one group are compensated for by equal but opposite changes in the properties of the adjoining group. These compensating changes are in some cases vanishingly small, but even when the energy changes are in excess of 20 kcal/mol, the experimental heat of formation is still predicted to be additive to within 0.1 kcal/mol, The operation of compensatory transferability is illustrated for the linear homologous series of hydrocarbons and polysilanes and for the formation of pyridine from fragments of benzene and pyrazine. The properties considered are the energy and the delocalization of the electrons, the former determined by the one-electron density matrix and the latter by the pair density. It is shown that the transferability of the degree of localization of the electrons to a given group, a property of the pair density, is a result of the conservation of the delocalization of its electrons over the remaining groups in the molecule. The results presented here emphasize the important observation that all the properties of a proper open system-a functional group-whether determined by the first-order density matrix, the pair density, or field-induced charge and current densities, are all functionally related to its form in real space, that is, to its distribution of charge.