Virtual transition states

Many organic reaction mechanisms are complex and may involve both multiple steps in series and multiple pathways in parallel. Consequently, for many reactions occurring in condensed media (including enzyme-catalyzed reactions) there is no single rate-determining step associated with a unique transition state (TS): in general, any 'transition-state structure' derived from experimental kinetics investigations of a complex mechanism is an average corresponding to a virtual TS. Computational simulation is now capable of yielding valuable insight, complementary to experiment, for minima and saddle points on potential-energy surfaces, corresponding to intermediates and TSs on Gibbs-energy surfaces for complex reactions with multiple TSs in parallel or in series. For a reaction with multiple steps in series, the apparent Gibbs energy of activation (corresponding with a virtual TS) is a sum of terms, one for each contributing real TS_j; the kinetic significance w_j of each is given by exp(Δ^‡G_j/RT)/exp(Δ^‡G_app/RT). An analogous expression applies to the kinetics of reaction steps in parallel, except that each Gibbs energy is preceded by a minus sign, and the contribution w_i of each real TS to Δ^‡G_app is its Boltzmann weighting, and the mole fraction of the lowest-energy reactant conformer must be factored in. Examples of both types of reaction are discussed to illustrate the concept of the virtual TS.