A theoretical formalism based upon simple bifurcation theory aimed at rationalizing elementary chemical processes is presented. The study of a generic potential representing the evolution from reactants to products leads us to determine a local bifurcation condition on the parameter space. Our formalism leads us to define topological regions where chemical processes can be analyzed within the Hammond postulate and the principle of maximum hardness framework. Furthermore, if a Gibbs-like potential is assumed to represent the profile of any global property (energy, hardness, and chemical potential) along the reaction coordinate, then a canonical bifurcation which is isomorphous to the fold catastrophe is obtained.