A theory of the rates of elementary reactions which assumes a special type of equilibrium, having an equilibrium constant \(K^{\ddagger }\), to exist between reactants and activated complexes. According to this theory the rate constant is given by: \[k=\frac{k_{\rm{B}}\ T}{h}\ K^{\ddagger }\] where \(k_{B}\) is the Boltzmann constant and \(h\) is the Planck constant. The rate constant can also be expressed as: \[k=\frac{k_{\rm{B}}\ T}{h}\ \exp (\frac{\Delta ^{\ddagger }S^{\,\unicode{x26ac}}}{R})\ \exp (- \frac{\Delta ^{\ddagger }H^{\,\unicode{x26ac}}}{R\ T})\] where \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), the entropy of activation, is the standard molar change of entropy when the activated complex is formed from reactants and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\), the enthalpy of activation, is the corresponding standard molar change of enthalpy. The quantities \(E_{a}\) (the energy of activation) and \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) are not quite the same, the relationship between them depending on the type of reaction. Also: \[k=\frac{k_{\rm{B}}\ T}{h}\ \exp (- \frac{\Delta ^{\ddagger }G^{\,\unicode{x26ac}}}{R\ T})\] where \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\), known as the Gibbs energy of activation, is the standard molar Gibbs energy change for the conversion of reactants into activated complex. A plot of standard molar Gibbs energy against a reaction coordinate is known as a Gibbs-energy profile; such plots, unlike potential-energy profiles, are temperature-dependent. In principle the equations above must be multiplied by a transmission coefficient, \(\kappa \), which is the probability that an activated complex forms a particular set of products rather than reverting to reactants or forming alternative products. It is to be emphasized that \(\Delta ^{\ddagger}S^{\,\unicode{x26ac}}\), \(\Delta ^{\ddagger}H^{\,\unicode{x26ac}}\) and \(\Delta ^{\ddagger}G^{\,\unicode{x26ac}}\) occurring in the former three equations are not ordinary thermodynamic quantities, since one degree of freedom in the activated complex is ignored. Transition-state theory has also been known as absolute rate theory, and as activated-complex theory, but these terms are no longer recommended.