transition state making it difficult to distinguish between the two. Determining the geometry of a transition state Transition state structures can be determined by searching for first-order saddle points on the potential energy surface (PES) of the chemical species of interest. A first-order saddle point is a critical point of index one, that is, a position on the PES corresponding to a minimum in all directions except one. This is further described in the article geometry optimization. The Hammond–Leffler postulate The Hammond–Leffler postulate states that the structure of the transition state more closely resembles either the products or the starting material, depending on which is higher in enthalpy. A transition state that resembles the reactants more than the products is said to be early, while a transition state that resembles the products more than the reactants is said to be late. Thus, the Hammond–Leffler Postulate predicts a late transition state for an endothermic reaction and an early transition state for an exothermic reaction. A dimensionless reaction coordinate that quantifies the lateness of a transition state can be used to test the validity of the Hammond–Leffler postulate for a particular reaction. The structure–correlation principle The structure–correlation principle states that structural changes that occur along the reaction coordinate can reveal themselves in the ground state as deviations of bond distances and angles from normal values along the reaction coordinate. According to this theory if one particular bond length on reaching the transition state increases then this bond is already longer in its ground state compared to a compound not sharing this transition state. One demonstration of this principle is found in the two bicyclic compounds depicted below. The one on the left is a bicyclo[2.2.2]octene, which, at 200 °C, extrudes ethylene in a retro-Diels–Alder reaction. Compared to the compound on the right (which, lacking an alkene group, is unable to give this reaction) the bridgehead carbon-carbon bond length is expected to be shorter if the theory holds, because on approaching the transition state this bond gains double bond character. For these two compounds the prediction holds up based on X-ray crystallography. Implications for enzymatic catalysis One way that enzymatic catalysis proceeds is by stabilizing the transition state through electrostatics. By lowering the energy of the transition state, it allows a greater population of the starting material to attain the energy needed to overcome the transition energy and proceed to product. See also