RRKM theory

The RRKM theory ( Rice - Ramsperger -Kassel- Marcus ) is a microcanonical theory of the transition state, which allows the rate constants of unimolecular gas phase reactions to be calculated. It represents an extension of the RRC theory, which assumes that the rate constant depends on the energy of the reactive molecule:

It is believed that the rate constant is proportional to the number of ways to distribute the power to the various internal degrees of freedom of the reactants so that the critical energy is localized in a certain degree of freedom.

In the RRKM theory also vibrational and rotational energies are considered in compliance with the zero-point vibrational energy.

It is named after Oscar K. Rice, Herman C. Ramsperger, Kassel, Louis and Rudolph A. Marcus.

Assumptions

The molecule is considered as a system of coupled oscillators harmonics which can exchange energy with each other.

• All states of the excited molecule with the energy are accessible and immediately lead to the formation of the product.
• The power redistribution in the molecule (IVR) is much faster than the reaction itself

Derivation

Be an excited molecule:

Denotes the critical configuration with a certain minimum energy to be localized in the reaction coordinate.

Obtained for the unimolecular rate constant: