RRKM analysis

Rate constants for elementary reactions involving tin compounds are even rarer. In an important recent investigation, Takahashi et al. performed shock-tube measurements and RRKM analysis from which they obtained rate constants for several important reactions involved in mechanism for SnCU pyrolysis [50] ... 

H.K. Moffat, K.F. Jensen, and R.W. Carr. Determination of the Arrhenius Parameters for Si2H6 SiH4 + SiH2 and AHJ (SiH2) by RRKM Analysis of Forward and Reverse Reaction Rate Data. J. Phys. Chem., 96 7683-7695,1992. 

These estimates bracket the NASA-JPL and lUPAC recommendations of 6.5x10 and 7.7 x 10 cm molecule s [9,60]. It is therefore possible fo reconcile fhe thermochemistry proposed here with the observed lO + NO2 recombination kinetics while employing reasonable input parameters for the unimolecular model. Nevertheless it must be stressed, as emphasized earlier [16], that there is considerable uncertainty in some of the input parameters to an RRKM analysis, especially the Frot term. It is of interest to compare the present kinetic calculations with the Multiwell [61] Master Equation calculations on this system by Golden [16]. He used a Morse potential to locate the centrifugal maximum, and from the bond extension Frot 2.1 is derived, about 1/7 of fhaf used here. On the other hand, the higher Eo value yields a density of sfafes larger by a facfor of 6, and fhese two factors largely cancel. 

On the other hand, a recent study of energy flow in CH,OOCH3 (54) reported qualitative agreement with RRKM analysis and with experimental rate constants, using the Miller et al. (45) method. 

Equations (28) and (29) differ in that latter contains contributions from the rotational partition functions. This contribution is lost in a RRKM analysis unless one includes the total angular momentum, J, and thus formulates the microcanonical rate constants as k E, J). In many cases, the geometries of the transition state and the reactant are very similar and consequently the ratio of the rotational partition functions is very... 

The analysis is performed for the calculations with rrot=0 K for the CH3C1 reactant, so that the angular momentum distribution for the complex P(j) is the distribution of orbital angular momentum for complex formation P(i). This latter distribution is given in ref. 37. Jm , the quantum number for j, varies from 282 for Enl = 0.5 kcal/mol to 357 for rel = 3.0 kcal/mol. The term k iEJ) in equation 24 is written as k (.EJ)=k Ejyf E), where k EJ) is the classical RRKM rate constant with the CH3C1 intramolecular modes inactive and / ( ) is treated as a fitting factor. 

In 1991 Moffat, Jensen and Carr employed RRKM theory in the form of a nonlinear regression analysis of experimental data to estimate the high-pressure Arrhenius parameters for elimination of H2 from SM4 as logA = 15.79 0.5 s 1, E = 59.99 2.0 kcalmor1 and A//j(SiH2) = 65.5 1.0 kcalmorl62. 

The lowest-lying potential energy surfaces for the 0(3P) + CH2=C=CH2 reaction were theoretically characterized using CBS-QB3, RRKM statistical rate theory, and weak-collision master equation analysis using the exact stochastic simulation method. The results predicted that the electrophilic O-addition pathways on the central and terminal carbon atom are dominant up to combustion temperatures. Major predicted end-products are in agreement with experimental evidence. New H-abstraction pathways, resulting in OH and propargyl radicals, have been identified.254... 

Table XXIII displays the rate constants obtained from the MRRKM theory and the reaction path analysis. It is seen that the former are about a factor of two smaller, and the latter about a factor of two larger, than those derived from direct trajectory calculations. We infer that, since both the RRKM and the MRRKM calculated rate constants are smaller than that calculated from trajectory calculations, there is a nonstatistical contribution to the isomerization rate that is not captured by the MRRKM theory.

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. " ... 

As in the development of RRK theory, the analysis starts with the assumption that the dynamics of the molecule are classical. The essential approximations of the classical RRKM treatment are that... 

Another advantage of the quantum calculations is that they provide a rigorous test of approximate methods for calculating dissociation rates, namely classical trajectories and statistical models. Two commonly used statistical theories are the Rice-Ramsperger-Kassel-Marcus (RRKM) theory and the statistical adiabatic channel model (SACM). The first one is thoroughly discussed in Chapter 2, while the second one is briefly reviewed in the Introduction. Moreover, the quantum mechanical approach is indispensable in analyzing the reaction mechanisms. A resonance state is characterized not only by its position, width and the distribution of product states, but also by an individual wave function. Analysis of the nodal structure of resonance wave functions gives direct access to the mechanisms of state- and mode-selectivity. 

As a result, the attempts to quantify the observed structures in k E) using RRKM lead to inconsistencies. In NO2, the observed steps are separated by 100 cm - which should be considered as the lowest TS-frequency. In contrast, the lowest adiabatic potential curves obtained from the ab initio PES of Grebenshchikov et al. [271] have no or only very small barriers, i.e., the TS-frequency is certainly much smaller than 100cm Discrepancies between the RRKM predictions of the TS-frequency and ab initio calculations were also found in triplet ketene, for which the analysis of the step-like structures in the observed energy profile of k E) was completed by Kim et al. [33]. In this molecule, tunneling through one-dimensional adiabatic potential barriers plays an important role and must be included in the statistical treatment. The barrier transparency, semiclassically related to the imaginary frequency at the barrier top, becomes an adjustable... 

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