RRKM theory

The Rice–Ramsperger–Kassel–Marcus (RRKM) theory is a theory of chemical reactivity.[1][2][3] It was developed by Rice and Ramsperger in 1927 [4] and Kassel in 1928[5] (RRK theory[6]) and generalized (into the RRKM theory) in 1952 by Marcus[7] 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:

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

Unimolecular rate constant is obtained as follows.[8]

  

See also

References

  1. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Rice–Ramsperger–Kassel–Marcus (RRKM) theory".
  2. ↑ Di Giacomo, F. (2015). "A Short Account of RRKM Theory of Unimolecular Reactions and of Marcus Theory of Electron Transfer in a Historical Perspective". Journal of Chemical Education. 92 (3): 476. Bibcode:2015JChEd..92..476D. doi:10.1021/ed5001312.
  3. ↑ Lindemann, F. A.; Arrhenius, S.; Langmuir, I.; Dhar, N. R.; Perrin, J.; Mcc. Lewis, W. C. (1922). "Discussion on ?the radiation theory of chemical action?". Transactions of the Faraday Society. 17: 598. doi:10.1039/TF9221700598.
  4. ↑ Rice, Oscar Knefler; Ramsperger, Herman Carl (1927), "Theories of unimolecular gas reactions at low pressures", Journal of the American Chemical Society, 49 (7): 1617–1629, doi:10.1021/ja01406a001
  5. ↑ Kassel, Louis Stevenson (1928), "Studies in Homogeneous Gas Reactions I", The Journal of Physical Chemistry, 32 (2): 225–242, doi:10.1021/j150284a007
  6. ↑ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Rice–Ramsperger–Kassel (RRK) theory".
  7. ↑ Marcus, Rudolph A. (1952), "Unimolecular Dissociations and Free Radical Recombination Reactions", J. Chem. Phys., 20 (3): 359–364, Bibcode:1952JChPh..20..359M, doi:10.1063/1.1700424
  8. ↑ J. I. Steinfeld; J. S. Francisco; W. L. Hase (1998). Chemical Kinetics and Dynamics (2 ed.). Prentice Hall. ISBN 978-0-13737123-5.


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