capturing one another (with more glancing collisions not leading to reaction as the higher momentum carries the colliding particles out of the potential well), expressed as a reaction cross section that decreases with increasing temperature. Such a situation no longer leads itself to direct interpretations as the height of a potential barrier. Some multistep reactions can also have apparent negative activation energies. For example, the overall rate constant k for a two-step reaction A B, B → C is given by k = k2K1, where k2 is the rate constant of the rate-limiting slow second step and K1 is the equilibrium constant of the rapid first step. In some reactions, K1 decreases with temperature more rapidly than k2 increases, so that k actually decreases with temperature corresponding to a negative observed activation energy. An example is the oxidation of nitric oxide which is a termolecular reaction . The rate law is with a negative activation energy. This is explained by the two-step mechanism: and . Certain cationic polymerization reactions have negative activation energies so that the rate decreases with temperature. For chain-growth polymerization, the overall activation energy is , where i, p and t refer respectively to initiation, propagation and termination steps. The propagation step normally has a very small activation energy, so that the overall value is negative if the activation energy for termination is larger than that for initiation. The normal range of overall activation energies for cationic polymerization varies from =40 to +60 kJ/mol. Activation energy in a 2D potential energy surface Activation energy can be represented in 2D potential energy surfaces (PES), where the relation between the geometry of the reactants and the energy involved is represented as a topographic map. In the following graphic there is a representation of a reaction between hydrogen in the gas phase and a metal: tungsten. The potential energy is obtained with PES calculations and consistent with the position of H from the NEB method calculations. A 2-dimensional interpolation with the spline method can be used to evaluate the potential energy at these positions. Products and reactants can be found in the blue surface, however the red surface corresponds to the steady-state approximation. The depics correspond to the trajectories. The bluer the surface, the stronger the hydrogen bonds, so blue colors represent minima energy and red colors are maxima. Tungsten’s PES is symmetric, and has a dip at the bridge