Observational basis for a quantum atom

A theory is only justified by its ability to account for observed behaviour. It is important, therefore, to note that the theory of atoms in molecules is a result of observations made on the properties of the charge density. These observations give rise to the realization that a quantum mechanical description of the properties of the topological atom is not only possible but is also necessary, for the observations are explicable only if the virial theorem applies to an atom in a molecule. The original observations are among the most important of the properties exhibited by the atoms of theory (Bader and Beddall 1972). For this reason and for the purpose of emphasizing the observational basis of the theory, these original observations are now summarized. They provide an introduction to the consequences of a quantum mechanical description of an atom in a molecule. 

The postulation of an atomic virial theorem for the topologically defined atoms leads to a numtjer of important conclusions (Bader and Beddall 1972). 

The total energy of a molecule is expressible as a sum of atomic energies. 

The average potential energy of an atom is defined as the average of the virial of the forces exerted on it—as demonstrated later, this is the only non-arbitrary way of partitioning potential energies of interaction between systems. 

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