Additivity and Transferability of Group Properties

Even a property as sensitive as the energy can exhibit additive group contributions as was once again first demonstrated in the experimentally determined heats of formation of the normal hydrocarbons . Benson has demonstrated how this and other thermodynamic properties of molecules and the changes in these properties upon chemical reaction can be usefully tabulated and predicted in terms of group contributions. 

The properties of the alkanes, both acyclic and cyclic, are so well ordered and classified in terms of atomic and group contributions that the use of the theory of atoms in molecules as the basis for the theoretical discussion of alkane chemistry is most appropriate. The theory, in addition to predicting these properties from fundamental principles, leads directly to an understanding of their additive and constitutive nature. 

On the other hand, it is at the limit of near-perfect transferability of group properties as exhibited by the alkanes that one can detrmine whether or not a proposed theory meets the requirements of experiment, for at this limit one may experimentally determine to high precision the properties of atoms in molecules via their additive contributions. By demonstrating that the atoms defined by quantum mechanics account for and recover the experimentally measured properties of atoms in molecules, one establishes that the atoms of theory are the atoms of chemistry. There is no test of theory other than the demonstration that it predicts what can be measured. 

There have been many previous attempts to define certain properties of atoms in molecules, particularly atomic charges. Arbitrary definitions of an atom or of some of its properties do not account for the characteristics ascribed to the atom within the molecular structure hypothesis and hence play no operational role in the prediction and understanding of chemical observations. Aside from the obvious statement that all definitions should follow directly from quantum mechanics using only information 

The first requirement stems from the necessity of two identical pieces of matter exhibiting identical properties, with the important understanding that the form of a substance in real space is determined by its distribution of charge. Thus two systems, macroscopic or microscopic, are identical only if they have identical charge distributions. This requires that atoms be defined in real space and that their properties be directly determined by their distribution of charge. Thus if an atom has the same form in the real space of two systems, i.e. the same distribution of charge, then it contributes the same amount to every property in both systems. This condition demands in turn that the atomic contributions M(Q) to some property M are additive over the atoms in a molecule to yield the molecular average M (equation 1). The boundary of the atom. 

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