Structural homeomorphism between p and the nuclear potential

Gradient maps of the nuclear potential V (r X) on the left and of the electronic charge density p(r X) on the right for symmetric structures of the H2O system. The pairs of maps demonstrate the existence of equivalent structures. 

A gradient path of V has a simple physical interpretation. It is a line of force—the path traversed by a test charge moving under the influence of the potential F(r X). At a critical point other than a (3, — 3) critical point, the force vanishes. Thus a critical point in the field V(r X) denotes a point of electrostatic balance between the attractors of the system. Since trajectories defining the surface which separates neighbouring basins satisfy the zero-flux condition 

One finds that the structure diagrams obtained for F(r X) and p(r X) for the HjO system are homeomorphic in the sense that both exhibit an identical partitioning of the control space yielding the same sets of structures, both stable and, as illustrated in Fig. 3.13, unstable. In addition to finding the same sets of structures for both fields, it has been found that their mechanisms of structural change are also the same. Thus, the bifurcation and conflict 

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