Rice-Ramsperger-Kassel-Marcus/transition

In the statistical description of ununolecular kinetics, known as Rice-Ramsperger-Kassel-Marcus (RRKM) theory [4,7,8], it is assumed that complete IVR occurs on a timescale much shorter than that for the unimolecular reaction [9]. Furdiemiore, to identify states of the system as those for the reactant, a dividing surface [10], called a transition state, is placed at the potential energy barrier region of the potential energy surface. The assumption implicit m RRKM theory is described in the next section. 

In more detail, our approach can be briefly summarized as follows gas-phase reactions, surface structures, and gas-surface reactions are treated at an ab initio level, using either cluster or periodic (plane-wave) calculations for surface structures, when appropriate. The results of these calculations are used to calculate reaction rate constants within the transition state (TS) or Rice-Ramsperger-Kassel-Marcus (RRKM) theory for bimolecular gas-phase reactions or unimolecular and surface reactions, respectively. The structure and energy characteristics of various surface groups can also be extracted from the results of ab initio calculations. Based on these results, a chemical mechanism can be constructed for both gas-phase reactions and surface growth. The film growth process is modeled within the kinetic Monte Carlo (KMC) approach, which provides an effective separation of fast and slow processes on an atomistic scale. The results of Monte Carlo (MC) simulations can be used in kinetic modeling based on formal chemical kinetics. 

Nowadays, the basic framework of our understanding of elementary processes is the transition state or activated complex theory. Formulations of this theory may be found in refs. 1—13. Recent achievements have been the Rice—Ramsperger—Kassel—Marcus (RRKM) theory of unimol-ecular reactions (see, for example, ref. 14 and Chap. 4 of this volume) and the so-called thermochemical kinetics developed by Benson and co-workers [15] for estimating thermodynamic and kinetic parameters of gas phase reactions. Computers are used in the theory of elementary processes for quantum mechanical and statistical mechanical computations. However, this theme will not be discussed further here. 

This standard mechanistic analysis has a long successful history. Organic chemistry textbooks are filled with PESs and discussions of the implication of single-step versus multiple-step mechanisms, concerted TSs, and so on. - Transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) theory provide tools for predicting rates based upon simple assumptions built upon the notion of reaction on the PES following the reaction coordinate. " ... 

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]. 

To use the master equation, one needs a general formula for the rate constant, kj, out of minimum j through transition state f. In the micro-canonical ensemble this relation is provided by Rice-Ramsperger-Kassel-Marcus (RRKM) theory [166] ... 

The rate constants were calculated with the transition state theory (TST) for direct abstraction reactions and the Rice-Ramsperger-Kassel-Marcus (RRKM) theory for reactions occuring via long-lived intermediates. For reactions taking place without well-defined TS s, the Variflex [35] code and the ChemRate [36] code were used for one-well and multi-well systems, respectively, based on the variational transition-state theory approach... 

Perhaps the point to emphasise in discussing theories of translational energy release is that the quasiequilibrium theory (QET) neither predicts nor seeks to describe energy release [576, 720]. Neither does the Rice— Ramsperger—Kassel—Marcus (RRKM) theory, which for the purposes of this discussion is equivalent to QET. Additional assumptions are necessary before QET can provide a basis for prediction of energy release (see Sect. 8.1.1) and the nature of these assumptions is as fundamental as the assumption of energy randomisation (ergodic hypothesis) or that of separability of the transition state reaction coordinate (Sect. 2.1). The only exception arises, in a sense by definition, with the case of the loose transition state [Sect. 8.1.1(a)]. 

Using Rice-Ramsperger-Kassel-Marcus (RRKM) theory (11, 12), we can model the rates of these reactions as a function of the energy difference separating the two transition states. The result of the analysis is an estimate... 

In this spirit, we will also briefly describe the basis for some of the microscopic kinetic theories of unimolecular reaction rates that have arisen from nonlinear dynamics. Unlike the classical versions of Rice-Ramsperger-Kassel-Marcus (RRKM) theory and transition state theory, these theories explicitly take into account nonstatistical dynamical effects such as barrier recrossing, quasiperiodic trapping (both of which generally slow down the reaction rate), and other interesting effects. The implications for quantum dynamics are currently an active area of investigation. 

By the end of 1972, a second cornerstone of the transition state approach was beginning to crumble significantly, for it was now quite evident that widely different transition states could be assumed for a given reaction, but the Rice-Ramsperger-Kassel-Marcus (RRKM) procedure would give the same result for the shape of the fall-off curve [72.N 72.R 74.F 79.A1]. This, as is now well known, arises through the adjustment of the model after the transition state has been chosen so as to force it to be consistent with the observed high pressure rate constant [72.R 80.P1], Perhaps it should have sounded the knell for the RRKM theory, much as the unsymmetric isotopic replacement experiments did for the Slater theory a decade earlier, but there was no other substitute available. 

Commonly applied models of reaction kinetics, such as the transition state theory or RRKM (Rice-Ramsperger-Kassel-Marcus) theory, cannot completely describe multistage catalytic cycles or even the simplest reactions in many cases. As a catalytic cycle is a nonlinear dynamic system, statements such as "the reaction is first order with respect to a component A" or "the reaction is zero order with respect to a component B" cannot be universally assumed. 

We can then calculate the transition rate matrix using Rice-Ramsperger-Kassel-Marcus (RRKM) theory. According to RRKM theory [130,157,158], the transition rate for a single transition is given by... 

Losada, M. and Chaudhuri, S. (2010) Finite size effects on alutninum/Teflon reaction channels under combustive environment a Rice-Ramsperger-Kassel-Marcus and transition state study of fluorination. J. Chem. Phys.,... 

The commonly used simplification to this approach is to use the Rice-Ramsperger-Kassel-Marcus (RRf ) expression, which invokes transition state theory (TST) to evaluate the flux through the transition state, leading to... 

This is the Rice-Ramsperger-Kassel-Marcus (RRKM) expression of the reaction rate constant at energy E [127]. For total energies E below the potential energy of the transitions state, i.e., for E < F(/ts), k E) vanishes. The canonical and the microcanonical rate constants are related by a Laplace transform, ... 

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... 

Single-pulse shock tube studies of the thermal dehydrochlorination reactions of chlorocyclopentane and chlorocyclohexane at temperatures of 843-1021 K and pressures of 1.4-2.4 bar have been carried out using the comparative rate technique. Absolute rate constants provided a self-consistent temperature scale of use in comparison with chemical systems studied with different temperature standards. Quantum chemical methods have been used to compute the structure and energies of reactants, products, and transition states. The computations were used, in conjunction with experimentally determined rate constants, to develop Rice-Ramsperger-Kassel-Marcus (RRKM)/ Master Equation models and thereby allow extrapolation of the experimental data over an extended range of temperatures. 

The RRKM (after Rice, Ramsperger, Kassel, and Marcus) theory is, basically, transition-state theory (see, in particular, the description in Section 6.2) applied to a unimolecular reaction. Thus, one focuses on the activated complex... 

Assuming that the concept of a rate constant is valid, we might consider using a microscopic theory of unimolecular chemical reactions to predict what the reaction rate should be and then check to see whether the theory is in agreement with that obtained from the computer simulation. The theory most widely used for this purpose is the RRKM theory developed by Rice and Ramsperger,36 Kassel,and Marcus and co-workers. As has been discussed in detail elsewhere,RRKM theory contains the same essential dynamical assumptions contained in transition-state theory. We discuss these assumptions briefly in the next section. 

---