RRKM theory rotational-vibrational energy transfer

Of course, in a thermal reaction, molecules of the reactant do not all have the same energy, and so application of RRKM theory to the evaluation of the overall unimolecular rate constant, k m, requires that one specify the distribution of energies. This distribution is usually derived from the Lindemann-Hinshelwood model, in which molecules A become activated to vibrationally and rotationally excited states A by collision with some other molecules in the system, M. In this picture, collisions between M and A are assumed to transfer energy in the other direction, that is, returning A to A ... 

A more carefully constructed approach to energy transfer explicitly accounts for the energy distribution of the chemically activated product (5,6,26,27), The initial distribution of energies upon production as well as the transient distributions formed by collisional relaxation of internal energy are used to calculate rate constants for imimolecular reaction. The formalism of Bunker (7,8,9) based on general RRKM theory is convenient for recoil chemical activation, since it explicitly accounts for both rotational and vibrational excitation in the product. In the cyclobutane model system reported, a stepladder approach to deactivation was incorporated, with the step size being a parameter determined by the best fit to the data (6). The overall processes considered are illustrated in Equation 4. 

TST calculations apply in the high-pressure hmit pressure-dependent reactions can be analyzed via more complex kinetic analyses such as Pace—Ramsperger—Kassel—Marcus (PJkKM) theory. The RRKM theory is used to model the energy transfer in the transition state (or activated complex) of a molecule, using statistical mechanical methods that describe the density of energy states, which depend upon the vibrational and rotational partition functions for the molecule. 

Chemical dynamics simulations of the gas phase 5 2 reactions of methyl halides have been carried out at many different levels of theory and compared with experimental measurements and predictions based on transition state theory and RRKM (Rice-Ramsperger-Kassel-Marcus) theory. Although many 5 2 reactions occur by the traditional pre-reaction complex, transition state, post-reaction complex mechanism, three additional non-statistical mechanisms were detected when the F -CH3-I reaction was analysed at an atomic level (i) a direct rebound mechanism where F attacks the backside of the carbon and CH3-F separates (bounces off) from the iodine ion, (ii) a direct stripping mechanism where F approaches CH3-I from the side and strips away the CH3 group, and (iii) an indirect reaction where the pre-reaction complex activates the C-I bond causing a CH3-I rotation and then the 5 2 reaction. The presence of these processes demonstrate that three non-statistical effects, (i) recrossing of the transition state is important, (ii) the transfer of the translational energy from the reactants into the rotational and vibrational modes of the substrate is inefficient, and (iii) there is... 

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