The topology of catchment regions of potential energy hypersurfaces

A simple proof is presented for a fundamental topological property of catch ment regions of potential energy hypersurfaces: each catchment region C(lam bda, i), representing a chemical species and its conformational range on th e potential energy hypersurface, is simply k-connected for each dimension k = 1,2,...3N - 6 - lambda, where i is the index of the catchment region. Th e consequences of this property on the structure of the fundamental group o f reaction mechanisms (the one-dimensional homotopy group of reaction paths ) is discussed.