Definition of atomic interactions

As discussed in Chapter 2, the interaction of two atoms leads to the formation of a critical point in the charge density at which p has one positive curvature, labelled xj and two negative curvatures labelled Aj and Aj. The phase portrait of such a (3, — 1) critical point is displayed in Fig. 2.6. The position coordinate of the critical point is denoted by r . he pair of 

The sum in eqn (7.8) runs over the atoms, f2, neighbouring atom fi—over each atom linked to D by an atomic interaction line. Thus eqn (7.8) provides the physical basis for the model in which a molecule is viewed as a set of interacting atom It isolates, through the definition of structure, the set of pairwise atomic interactions which determine the force acting on each atom in a molecule for any configuration of the nuclei. 

There is, therefore, an intimate link between the topological properties of p(r) and its Laplacian, the trace of the Hessian of p, and, through the properties of the Laplacian, one may begin to bridge the gap between the form of the charge distribution and the mechanics which govern it. 

The classification of interactions in both bound and unbound states is presented first, followed in Section 7.5 by a discussion relating the parameters of this scheme to the requirements for obtaining a bound state. 

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