RRKM theory extension

J. Manz Let me add a comment on Professor W. H. Miller s remark that he would never make himself, but I can express this as the chairman of this session. In fact, Professor Miller s extension of the standard RRKM-theory allows to predict not only the statistical mean values of the rate coefficients, but also their fluctuations. This is an important achievement in the theory of chemical reaction theory over the past couple of years and it should be adequate to call it the RRKMM theory (Ramspeiger-Rice-Kassel-Marcus-Miller) [1]. 

The MP2/6-31G direct dynamics simulation study was later extended to cover the dynamics from the central barrier for the SN2 reaction of Cl I C2H5CI.104 The majority of the trajectories starting from the saddle point moved off the central barrier to form the Cl- C2H5CI complex. The results were different from those obtained previously for the CH3C1 reaction, in which extensive recrossing was observed. The reaction of C2H5CI was, in this sense, consistent with the prediction by the RRKM theory. However, some of the... 

Rice et al. [99] developed a global potential energy surface based on the Mowrey et al. [103] results and performed extensive classical trajectory calculations to study the dynamics of the CH2NN02 dissociation reactions. They calculated rates for reactions (III) and (IV) with classical barriers of 35 and 37 kcal/mol, respectively. They found that N-N bond fission dominates at low energy but that HONO elimination is competitive. Chakraborty and Lin [104] predict the opposite on the basis of their ab initio barriers and RRKM theory calculations. The two dissociations channels are closely competitive and it is not clear that ab initio methods are sufficiently reliable to distinguish between two reactions that have such similar energy requirements. Also, the Zhao et al. results [33] are not in accord with the theoretical predictions. 

Extensions of variable reaction coordinate RRKM theory... 

The most accepted modern activation theory for the outer electron transfer is that of Rudolph A. Marcus (Nobel Prize in Chemistry in 1992) [14], which is different from the transition state theory. His studies on unimolecular reactions and the transition and collision theories committed him to elaborate on the Rice-Ramsperger-Kassel-Marcus (RRKM) theory in 1952. This theory is an extension of the previous RRK theory proposed by Rice, Ramsperger, and Kassel between 1927 and 1928. Moreover, Hush and Marcus further extended the electron transfer theory of Marcus for inner electron transfers [15-17]. 

With the development of computers, accurate calculations using theoretical models better able to represent the behavior of real molecules has become widespread. A very important extension of the original theory, due to Marcus, is known as RRKM theory. Here, the real vibrational frequencies are used to calculate the density of vibrational states of the activated molecule, N E). The number of ways that the total energy can be distributed in the activated complex at the transition state is denoted W E ). Note that the geometry of the transition state need not be known, but the vibrational frequencies must be estimated in order to calculate W E ). n calculating the total number of available levels of the transition state, explicit consideration of the role of angular momentum is included. The RRKM reaction rate constant is given by ... 

Extensions of this statistical thermodynamical approach to estimating reaction rates include the RRK and RRKM theories of unimolecular decay rates, and the information theoretic formulation of reaction dynamics. These theories are remarkably successful, although generally more successful at interpreting experimental data and correlating results than at deriving results a priori. 

RRKM theory is also at the basis of localization of loose transition states in the PES. Another assumption of the theory is that a critical configuration exists (commonly called transition state or activated complex) which separates internal states of the reactant from those of the products. In classical dynamics this is what is represented by a dividing surface separating reactant and product phase spaces. Furthermore, RRKM theory makes use of the transition state theory assumption once the system has passed this barrier it never comes back. Here we do not want to discuss the limits of this assumption (this was done extensively for the liquid phase [155] but less in the gas phase for large molecules we can have a situation similar to systems in a dynamical solvent, where the non-reacting sub-system plays the role... 

Our application of this approach to the benzene ion dissociation in collaboration with Klippenstein was noted in Section II. When it can be carried out, this is by far the most satisfactory way currently available for extrapolation to E. The necessary VTST calculations, whether by way of the Marcus variational RRKM approach or other approaches (e.g., statistical adiabatic channel theory ) are laborious, involving the quantum chemical construction of large potential maps for the interaction of the separating fragments and extensive statistical calculations for the dissociation process. Application of this approach to a variety of interesting systems is one of the outstanding opportunities for future work. 

Schindler and coworkers verified the formation of hydroxyl radicals kinetically and further RRKM calculations by Cremer and coworkers placed the overall concept on a more quantitative basis by verifying the measured amount of OH radical. An extensive series of calculations on substituted alkenes placed this overall decomposition mechanism and the involvement of carbonyl oxides in the ozonolysis of alkenes on a firm theoretical basis. The prodnction of OH radicals in solution phase was also snggested on the basis of a series of DFT calculations . Interestingly, both experiment and theory support a concerted [4 4- 2] cycloaddition for the ozone-acetylene reaction rather than a nonconcerted reaction involving biradical intermediates . 

More sophisticated treatments of Lindemann s scheme by Lindemann— Hinshelwood, Rice—Ramsperger—Kassel (RRK) and finally Rice— Ramsperger—Kassel—Marcus (RRKM) have essentially been aimed at re-interpreting rate coefficients of the Lindemann scheme. RRK(M) theories are extensively used for interpreting very-low-pressure pyrolysis experiments [62, 63]. 

---