RRKM theory

The Rice–Ramsperger–Kassel–Marcus (RRKM) theory is a theory of chemical

• 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.
• As a corollary to the above, the potential energy surface does not have any "bottlenecks" for which certain vibrational modes may be trapped for longer than the average time of the reaction

Derivation

Assume that A^* is an excited molecule:

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

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

The unimolecular rate constant ${\displaystyle k_{\mathrm {uni} }}$ is obtained as follows:^[8]

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

where ${\displaystyle k(E,J)}$ is the microcanonical transition state theory rate constant, ${\displaystyle G^{\ddagger }}$ is the sum of states for the active degrees of freedom in the transition state, ${\displaystyle J}$ is the quantum number of angular momentum, ${\displaystyle \omega }$ is the collision frequency between ${\displaystyle A^{*}}$ molecule and bath molecules, ${\displaystyle Q_{r}}$ and ${\displaystyle Q_{v}}$ are the molecular vibrational and external rotational partition functions.

See also

• Transition state theory

References