Transition state theory ($k=(k_{\mathrm{B}}T/h)\exp [-\Delta G^{‡\circ }/(RT)]$)

Transition state theory relates an elementary reaction's rate constant to a Gibbs energy of activation. The Eyring expression used in the catalyst example assumes every passage counted at the transition state succeeds. More generally, a factor accounting for unsuccessful passage multiplies it. Comparing barriers alone gives the quoted speedup only when the remaining prefactors agree. Free-energy profiles can depend on temperature, so the example's values at $300\mathrm{K}$ do not determine a temperature curve. See the IUPAC Gold Book: transition state theory.

A constant tensile force changes a one-coordinate free-energy landscape from $G_0(x)$ to $G_0(x)-Fx$. To first order, an escape barrier decreases by $F\Delta x$, where $\Delta x$ is the saddle-to-initial-minimum displacement at zero force. An approximately fixed attempt prefactor gives the displayed rate law. Its characteristic force is $F_0=k_{B}T/\Delta x$. Large changes in saddle location or competing pathways invalidate a constant activation distance. The barrier is measured relative to the initial state; an absolute saddle energy is not enough to determine an escape rate.

The pressure derivative of the standard Gibbs energy of activation: $\Delta V^{‡\circ }=(\partial \Delta G^{‡\circ }/\partial p{)}_T$. In the corresponding rate convention, $\Delta V^{‡\circ }=-RT(\partial \ln k/\partial p{)}_T$. A negative value makes increasing pressure accelerate the reaction. Solvent reorganization can contribute as well as the intrinsic reacting geometry.

The standard entropy difference between the activated-complex reference state and the reactants. Its numerical value depends on standard-state conventions; association, molecular reorientation, internal motions and solvent reorganization can all contribute.

The standard enthalpy difference between the activated-complex reference state and the reactants at the same temperature and pressure. Under the usual Eyring assumptions it controls the slope of $\ln (k/T)$ against $1/T$.

A transition state theory expression relating a rate constant to the standard free energy of activation. For a bimolecular reaction expressed in concentration units, $k_2=(k_{\mathrm{B}}T/h)(c^{\circ }{)}^{-1}\exp [-\Delta G^{‡\circ }/(RT)]$ in the unit-transmission approximation.

The Gibbs energy of activation is the standard molar Gibbs free energy change associated with going from the starting reactants to the transition state in transition state theory. It specifies the directional barrier, rather than the overall endpoint change in Gibbs free energy. Use consistent standard states when comparing Gibbs energies of activation and rate constants. See the IUPAC Gold Book: Gibbs energy of activation.

The standard molar enthalpy difference between the transition state and the starting reactants, at the same temperature and pressure, in transition state theory.^[ref]

The standard molar entropy difference between the transition state and the starting reactants, at the same temperature and pressure, with specified standard states, in transition state theory.^[ref]