kinetic energy of the products. For a reaction such as F + H2 → HF + H in which atom A is heavier than B and C, there is mixed energy release, both vibrational and translational, even though the PES is repulsive. For endothermic reactions, the type of surface determines the type of energy which is most effective in bringing about reaction. Translational energy of the reactants is most effective at inducing reactions with an attractive surface, while vibrational excitation (to higher vibrational quantum number v) is more effective for reactions with a repulsive surface. As an example of the latter case, the reaction F + HCl(v=1) → Cl + HF is about five times faster than F + HCl(v=0) → Cl + HF for the same total energy of HCl. History The concept of a potential energy surface for chemical reactions was first suggested by the French physicist René Marcelin in 1913. The first semi-empirical calculation of a potential energy surface was proposed for the H + H2 reaction by Henry Eyring and Michael Polanyi in 1931. Eyring used potential energy surfaces to calculate reaction rate constants in the transition state theory in 1935. H + H2 two-dimensional PES Potential energy surfaces are commonly shown as three-dimensional graphs, but they can also be represented by two-dimensional graphs, in which the advancement of the reaction is plotted by the use of isoenergetic lines. The collinear system H + H2 is a simple reaction that allows a two-dimension PES to be plotted in an easy and understandable way. In this reaction, a hydrogen atom (H) reacts with a dihydrogen molecule (H2) by forming a new bond with one atom from the molecule, which in turn breaks the bond of the original molecule. This is symbolized as Ha + Hb–Hc → Ha–Hb + Hc. The progression of the reaction from reactants (H+H₂) to products (H-H-H), as well as the energy of the species that take part in the reaction, are well defined in the corresponding potential energy surface. Energy profiles describe potential energy as a function of geometrical variables (PES in any dimension are independent of time and temperature). We have different relevant elements in the 2-D PES: The 2-D plot shows the minima points where we find reactants, the products and the saddle point or transition state. The transition state is a maximum in the reaction coordinate and a minimum in