Critical level topology of energy hypersurfaces

Topologies are introduced into the nuclear configuration space R of molecular systems, based upon equipotential contour hypersurfaces on the otential energy hypersurface E. Critical level topologies T fc and T fc′, based upon the number and distribution of various critical points of E, are of particular importance, since they represent convenient yet rigorous mathematical models for relations between elementary reaction mechanisms, and for relations between open sets of nuclear geometries which are classically accessible at a given total energy.