Quantum topology. IV. Relation between the topological and energetic stabilities of molecular structures

The relation between the structural stability of a molecular system as determined by the topological properties of its charge distribution and the energetic stability of the same system as determined by the properties of its potential energy hypersurface is studied. In general, it is found that one may associate a given molecular structure with an open neighborhood of an energetically stable geometry of the system. A change in molecular structure is an abrupt process, and examples are given in which the change in structure is found to occur in the immediate neighborhood of the transition state geometry. These observations suggest that topologically unstable structures correspond to energetically unstable geometries of a system. Such a correspondence can be rationalized in terms of the Hellmann–Feynman theorem which is shown to relate the gradients of the energy hypersurface to the gradient vector field of the charge density—the field whose instabilities determine the instabilities in molecular structure.