# RRKM theory

The Rice–Ramsperger–Kassel–Marcus (RRKM) theory is a theory of chemical reactivity. It was developed by Rice and Ramsperger in 1927  and Kassel in 1928 (RRK theory) and generalized (into the RRKM theory) in 1952 by Marcus who took the transition state theory developed by Eyring in 1935 into account. These methods enable the computation of simple estimates of the unimolecular reaction rates from a few characteristics of the potential energy surface.

## Assumption

Assume that the molecule consists of harmonic oscillators, which are connected and can exchange energy with each other.

• Assume the possible excitation energy of the molecule to be E, which enables the reaction to occur.
• The rate of intra-molecular energy distribution is much faster than that of reaction itself.

## Derivation

Assume that A* is an excited molecule:

$A^{*}{\xrightarrow {k(E)}}A^{\ddagger }\rightarrow P$

where P stands for product, and A for the critical atomic configuration with the minimum energy E0 along the reaction coordinate.

Unimolecular rate constant $k_{\mathrm {uni} }$  is obtained as follows.

$k_{\mathrm {uni} }={\frac {1}{hQ_{r}Q_{v}}}\int \limits _{E_{0}}^{\infty }\mathrm {d} E\sum _{J=0}^{\infty }{\frac {(2J+1)G^{\ddagger }(E,J)\exp \!\left({\frac {-E}{k_{b}T}}\right)}{1+{\frac {k(E,J)}{\omega }}}}$