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Transition state theory (TST) assumes that reactants are in quasi-equilibrium with the activated complex (transition state), and that the rate is proportional to the concentration of transition states multiplied by their rate of crossing the barrier. The Eyring equation k = (k_B T/h)·κ·exp(−ΔG‡/RT) provides the rate constant from the free energy of activation ΔG‡ = ΔH‡ − TΔS‡. Unlike collision theory, TST uses thermodynamic quantities for the transition state, making it straightforward to separate enthalpic (barrier height) and entropic (geometric constraint) contributions. The transmission coefficient κ accounts for recrossing trajectories and quantum tunneling (important for proton transfer reactions).
Analyze Eyring plots (ln(k/T) vs 1/T) for several reactions to extract ΔH‡ and ΔS‡. Interpret negative ΔS‡ as an ordered transition state (bimolecular associations) and positive ΔS‡ as a looser one (unimolecular dissociations).
Transition state theory builds directly on potential energy surfaces, which describe how a system's energy changes as bonds break and form during a reaction. The reaction coordinate traces the path of lowest energy from reactants to products, and the highest point along that path — the saddle point — is the transition state (or activated complex). TST asks a precise question: given that the transition state exists, how fast does the reaction proceed?
The key assumption is quasi-equilibrium: the population of transition states is assumed to be in rapid equilibrium with the reactant population, governed by the Boltzmann factor exp(−ΔG‡/RT). The rate constant then equals the frequency at which transition states cross over the barrier multiplied by their equilibrium concentration. This gives the Eyring equation: k = (k_BT/h) · κ · exp(−ΔG‡/RT), where k_BT/h is a universal frequency (≈ 6 × 10¹² s⁻¹ at 298 K) and κ is the transmission coefficient. Because ΔG‡ = ΔH‡ − TΔS‡, the rate depends on both the height of the energy barrier (ΔH‡) and how constrained the geometry of the transition state is (ΔS‡). This is TST's major advantage over the Arrhenius equation, which lumps both effects into a single empirical E_a.
The entropy of activation is particularly informative. A large negative ΔS‡ means the transition state is highly ordered relative to the reactants — two molecules must find each other with precisely the right orientation, severely restricting the number of accessible configurations. This is common in bimolecular association reactions. A positive ΔS‡ indicates the transition state is looser than the reactants — a bond is substantially broken while little new constraint has been imposed — typical of unimolecular dissociations.
The transmission coefficient κ corrects for two effects that classical TST ignores. First, some trajectories that reach the barrier top recross back to reactants without proceeding forward, making κ < 1. Second, quantum tunneling allows light particles (most importantly protons) to pass *through* the barrier rather than over it. For proton transfer reactions, tunneling can make rates far higher than the classical Eyring equation predicts, explaining large kinetic isotope effects when hydrogen is replaced by deuterium.
Eyring plots — graphs of ln(k/T) versus 1/T — let you extract ΔH‡ from the slope (−ΔH‡/R) and ΔS‡ from the intercept. This separates the two thermodynamic contributions to reactivity, giving insight into whether a slow reaction suffers from a high barrier, an unfavorable geometric requirement, or both. The limitation to keep in mind is that TST is an approximation: real reaction dynamics on multidimensional potential energy surfaces do not always obey the no-recrossing assumption, and modern trajectory calculations often find κ significantly less than 1 for complex systems.