The Rice–Ramsperger–Kassel–Marcus (RRKM) theory is a theory of chemical
reactivity.
It was developed by
Rice
Rice is the seed of the grass species '' Oryza sativa'' (Asian rice) or less commonly ''Oryza glaberrima'' (African rice). The name wild rice is usually used for species of the genera '' Zizania'' and '' Porteresia'', both wild and domesticat ...
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
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit ...
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 , 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 is an excited molecule:
:
where stands for product, and for the critical atomic configuration with the minimum energy along the
reaction coordinate.
The unimolecular rate constant
is obtained as follows:
:
where
is the microcanonical transition state theory rate constant,
is the sum of states for the active degrees of freedom in the transition state,
is the quantum number of angular momentum,
is the collision frequency between
molecule and bath molecules,
and
are the molecular vibrational and external rotational partition functions.
See also
*
Transition state theory
References
External links
An RRKM online calculator
Chemical physics
Quantum chemistry
Molecular physics
Chemical kinetics
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