feasible. For these systems a possible approach is to calculate only a reduced set of points on the PES and then use a computationally cheaper interpolation method, for example Shepard interpolation, to fill in the gaps. Application A PES is a conceptual tool for aiding the analysis of molecular geometry and chemical reaction dynamics. Once the necessary points are evaluated on a PES, the points can be classified according to the first and second derivatives of the energy with respect to position, which respectively are the gradient and the curvature. Stationary points (or points with a zero gradient) have physical meaning: energy minima correspond to physically stable chemical species and saddle points correspond to transition states, the highest energy point on the reaction coordinate (which is the lowest energy pathway connecting a chemical reactant to a chemical product). Attractive and repulsive surfaces Potential energy surfaces for chemical reactions can be classified as attractive or repulsive by comparing the extensions of the bond lengths in the activated complex relative to those of the reactants and products. For a reaction of type A + B—C → A—B + C, the bond length extension for the newly formed A—B bond is defined as R*AB = RAB − R0AB, where RAB is the A—B bond length in the transition state and R0AB in the product molecule. Similarly for the bond which is broken in the reaction, R*BC = RBC − R0BC, where R0BC refers to the reactant molecule. For exothermic reactions, a PES is classified as attractive (or early-downhill) if R*AB > R*BC, so that the transition state is reached while the reactants are approaching each other. After the transition state, the A—B bond length continues to decrease, so that much of the liberated reaction energy is converted into vibrational energy of the A—B bond. An example is the harpoon reaction K + Br2 → K—Br + Br, in which the initial long-range attraction of the reactants leads to an activated complex resembling K+•••Br−•••Br. The vibrationally excited populations of product molecules can be detected by infrared chemiluminescence. In contrast the PES for the reaction H + Cl2 → HCl + Cl is repulsive (or late-downhill) because R*HCl < R*ClCl and the transition state is reached when the products are separating. For this reaction in which the atom A (here H) is lighter than B and C, the reaction energy is released primarily as translational