TransitionState

Transition state is the fleeting arrangement of atoms at the highest point along the reaction pathway between reactants and products. Also called the activated complex, it represents the configuration that reactants must pass through to form products. It is not isolable under normal conditions and exists only briefly as the system traverses the minimum energy path on the potential energy surface.

On the potential energy surface, the transition state is a first-order saddle point: all but one vibrational mode have positive curvature, while along the reaction coordinate the curvature is negative. The corresponding normal mode approximates the motion from reactants toward products. In quantum chemical calculations, a transition state is confirmed by locating a stationary point with one imaginary frequency from frequency analysis.

Transition state theory provides a framework for estimating reaction rates from the properties of the transition state. A common expression for the rate constant is k = (kB T/h) exp(-ΔG‡/RT), where ΔG‡ is the Gibbs free energy of activation. Activation enthalpy ΔH‡ and activation entropy ΔS‡ describe energy and disorder changes between reactants and the transition state, shaping temperature dependence.

Practically, transition states are located with computational methods such as density functional theory or ab initio approaches, using algorithms that converge on saddle points and are followed by frequency calculations to verify a single imaginary mode. Experimentally, evidence comes from kinetic isotope effects, rate measurements, and, when possible, observation of transient catalytic intermediates or activated complexes outside of equilibrium.

Transition states are central to catalysis: catalysts stabilize the transition state of the rate-determining step, effectively lowering the activation free energy and accelerating the reaction.