Energy randomisation. How much of rotational phase space is explored? How long does it take? Page: 3 of 30
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The central assumption in the RRKM theory of unimolecular reactions is
that the energy distribution within energised molecules is randomised on a time
scale short compared to the reaction time. The randomisation is constrained by
the conservation of the total energy, E, and total angular momentun, J. In most
applications,I it is assumed that the projections, Ka or Kc, of the angular
momentum on a molecule-fixed axis are ramdomised as well as the vibrations.
An alternative to this "K-active" approach is the "K-adiabatic" approach in which
these projections are treated as conserved quantities.1
In specific cases, 3, there is evidence that. the relaxation of the Ka and
Kc quantum numbers may not be complete. The lack of complete energy
randomisation could be apparent because the Ka and Kc quantum numbers relax
too slowly to complete with the reaction rate or intrinsic in the sense that the
whole of phase space consistent with E and J would not be explored by the
collisionless molecule even at long times.
The question of whether or not Ka and Kc are conserved affects the
dynamics of unimoledular reaction in a number of ways. For example, consider
the case of a near-prolate asymmetric top molecule in which the rotational
constant A is much larger than B. or C and consider only K - Ka.
First, we note that the rate of the reaction may depend on the extent that K
is conserved. A thermal distribution of rotational levels populates mainly states
with KJ. After randomisation of K, there will be a comparable probability of
the system having. K-J which ties. up several kBT of the available activation
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Perry, D. S.; Bethardy, G. A.; Davis, M. J. & Go, J. Energy randomisation. How much of rotational phase space is explored? How long does it take?, article, December 1995; Illinois. (digital.library.unt.edu/ark:/67531/metadc668965/m1/3/: accessed April 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.