Transition State Theory

Theory

In the transition state theory, the mechanism of interaction of reactants is not considered; the important criterion is that colliding molecules must have sufficient energy to overcome a potential energy barrier (the activation energy) to react.

For a bimolecular reaction, a transition state is formed when the two molecules’ old bonds are weakened and new bonds begin to form or the old bonds break first to form the transition state and then the new bonds form after. The theory suggests that as reactant molecules approach each other closely they are momentarily in a less stable state than either the reactants or the products. In the example below, the first scenario occurs to form the transition state:

It takes a lot of energy to achieve the transition state, so the state is a high-energy substance. The potential energy of the system increases at this point because:

The approaching reactant molecules must overcome the mutual repulsive forces between the outer shell electrons of their constituent atoms
Atoms must be separated from each other as bonds are broken

Bond Transition

This increase in potential energy corresponds to an energy barrier over which the reactant molecules must pass if the reaction is to proceed. The transition state occurs at the maximum of this energy barrier.

The transition state is an unstable transitory combination of reactant molecules that occurs at a potential energy maximum

The combination can either go on to form products or fall apart to return to the unchanged reactants.

The energy difference between the reactants and the potential energy maximum is referred to as the activation energy

The equation for an enzymatic reaction is:

is the concentration equilibrium constant, defined as:

Use the following equation to find the rate constant (k):

, where kB is Boltzmann’s constant, h is Planck’s constant and T is the temperature

Thermodynamics

resembles the equilibrium constant used to describe Gibbs free energy, defined as:

where c^o is the standard state concentration. DG^t can be defined as the Gibbs energy of activation. The Gibbs energy difference between the ground and transition state can be used to predict the rate of reaction. The binding energy associated with the specific substrate-enzyme interaction is a significant factor in lowering the Gibbs free energy change required for reaction. The large binding energies of substrates are due in part to the complementary shape of the active site of the enzyme. The Gibbs energy can be considered to be composed of two terms, DG_t, the binding energy and DG_s, the activation energy involved in the making and breaking of bonds leading to the transition state from enzyme-substrate intermediate (ES). They are related as follows:

DG^t = DG_t + DG_s

This can be seen on the energy diagram below:

The above equation can be substituted into the equation for the rate constant k, and k is defined as a second order constant (k_cat/K_M).

Entropy is composed of translational, rotational, and internal entropies. When two molecules react without a catalyst there is a loss of rotational and translational entropies. An enzyme brings together the reactants as an effective intramolecular adduct that will not suffer the previous losses. There will only be a small loss of internal entropy. Therefore this reaction will be entropically favored.

A sample calculation can be done below to find the entropic contribution to a reaction for the following equation:

Enter in values with appropriate units
Temperature		K
Rate Constant		s^-1
Enthalpy Difference		J/mol