reaction, namely . In terms of the ground state and transition state energies, the product ratio can therefore be written as: . Importantly, inspection of the energy diagram above allows us to identify with the energy difference of the transition states, giving us a simplified equation that captures the essence of the Curtin-Hammett principle: Thus, although the product ratio depends on the equilibrium constant between A and B and the difference in energy between the barriers from A to C and from B to D, both of these factors are automatically taken into account by the energy difference of the transition states leading to the products, ΔΔG‡. Classes of reactions under Curtin–Hammett control Three main classes of reactions can be explained by the Curtin–Hammett principle: either the more or less stable conformer may react more quickly, or they may both react at the same rate. Case I: More stable conformer reacts more quickly One category of reactions under Curtin–Hammett control includes transformations in which the more stable conformer reacts more quickly. This occurs when the transition state from the major intermediate to its respective product is lower in energy than the transition state from the minor intermediate to the other possible product. The major product is then derived from the major conformer, and the product distribution does not mirror the equilibrium conformer distribution. Example: piperidine oxidation An example of a Curtin–Hammett scenario in which the more stable conformational isomer reacts more quickly is observed during the oxidation of piperidines. In the case of N-methyl piperidine, inversion at nitrogen between diastereomeric conformers is much faster than the rate of amine oxidation. The conformation which places the methyl group in the equatorial position is 3.16 kcal/mol more stable than the axial conformation. The product ratio of 95:5 indicates that the more stable conformer leads to the major product. Case II: Less stable conformer reacts more quickly A second category of reactions under Curtin–Hammett control includes those in which the less stable conformer reacts more quickly. In this case, despite an energetic preference for the less reactive species, the major product is derived from the higher-energy species. An important implication is that the product of a reaction can be derived from a conformer that is at sufficiently low concentration as to be unobservable in the ground state. Example: tropane alkylation The alkylation of tropanes with methyl iodide is a classic example of a