RRKM modeling

Figure A3.12.2. Relation of state oeeupation (sehematieally shown at eonstant energy) to lifetime distribution for the RRKM theory and for various aetiial situations. Dashed eiirves in lifetime distributions for (d) and (e) indieate RRKM behaviour, (a) RRKM model, (b) Physieal eounterpart of RRKM model, (e) Collisional state seleetion. (d) Chemieal aetivation. (e) Intrinsieally non-RRKM. (Adapted from [9].)...

It is straightforward to introduce active and adiabatic treatments of K into the widely used RRKM model which represents vibration and rotation as separable and the rotations as rigid rotors [41,42]. Eor a synnnetric top, tlie rotational energy is given by... 

In these models the treatment of K is the same for the molecule and transition state. It is worthwhile noting that mixed mode RRKM models are possible in which K is treated differently in the molecule and transition state [39],... 

To analyze the trajectory N(t)/N(0) distributions with a RRKM model in which only the three intermolecular modes of the C1"-CH3C1 complex are active and exchange energy, it is necessary to average over the angular momentum j of the CT-CHjCl complexes, i.e. ... 

An RRKM model was used to calculate a high-pressure limit rate coefficient, and thermochemistry was used to obtain Arrhenius parameters for the reverse reaction, the addition of methyl to isobutane. 

The experimental results follow the predictions of a serial IVR/VP mechanism in which IVR is described by Fermi s Golden Rule and VP is described by a restricted RRKM model. 

These remarks apply equally to the complementary unimolecular reaction and it is helpful to look at the unimolecular reaction to begin with, always bearing in mind that association and dissociation are connected via the equilibrium constant. In Section 2.4.4 it was shown that for the RRKM model, the microcanonical rate coefficient is proportional to the sum of states, G, at the transition state, which is a function of the energy, E. Application of the minimum flux criterion means that G must be altered... 

In Tsang s evaluations the pressure-dependent factors in the expression for the rate constant are handled differently [45]. Using the RRKM model a factor governing the pressure dependence is calculated and presented in tables as a function of the energy transferred per collision. The user may then select a typical value for this energy for the collision partners involved and read the pressure-dependent factor from the tables. Satisfactory application depends on the ability to select the correct energy transferred which may be derived from experimental data on the particular reaction concerned but, more often, may have to be estimated from data on analogous reactions which, usually, are quite limited. 

A much more detailed microscopic picture of a unimolecular reaction may be obtained from time-domain experiments in which the number of reactant and/or product molecules is followed in real time [20-26]. At this level of experimental measurement, differences with the RRKM model have been observed. The unimolecular reactions studied in this manner include HjOj 20H [20], NCNO CN + NO [21], HOCO — HO -b CO [22,23], N02 N0-b0 [24,25], and CH3CO CO + CH3 [26]. Pronounced non-RRKM kinetics were observed for the latter two reactions. 

It is interesting to note that the flexible variational RRKM model approaches PST as the energy is lowered and the separation between the product fragments becomes very large at the variational transition state. This is because the /2pJ 2 and V terms in equation (7.36) become negligible so that the flexible Hamiltonian becomes... 

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