Quantum Rice-Ramsperger-Kassel

In chapter 2, computational methods used for the determination of thermodynamic data of the compound, and the kinetic calculations performed in this work are presented. We give a brief review of the computational methods ab initio, and Density Functional Theory, Statistical Mechanics methods. Group Additivity method, and multifrequency Quantum Rice-Ramsperger-Kassel (QRRK). 

Multifrequency Quantum Rice-Ramsperger-Kassel (QRRK) is a method used to predict temperature and pressure-dependent rate coefficients for complex bimolecular chemical activation and unimolecular dissociation reactions. Both the forward and reverse paths are included for adducts, but product formation is not reversible in the analysis. A three-frequency version of QRRK theory is developed coupled with a Master Equation model to account for collisional deactivation (fall-off). The QRRK/Master Equation analysis is described thoroughly by Chang et al. [62, 63]. 

Chemaster code is based on the quantum Rice-Ramsperger-Kassel (QRRK) analysis for k(E) and Master Equation analysis for fall off Chemaster will be employed to determine kinetic parameters in complex reaction systems, such as CeHs + O2. The source code for the QRRK... 

High Pressure limit kinetic parameters are obtained from canonical Transition State Theory calculations. Multifrequency Quantum Rice-Ramsperger-Kassel (QRRK) analysis is used to calculate k(E) data and master equation analysis is applied to evaluate fall-off in this chemically activated reaction system. 

The kinetic parameters of each path are determined as a function of temperature and pressure using the bimolecular chemical activation analysis. High Pressure limit kinetic parameters from the calculation results are obtained with the canonical Transition State Theory. The multifrequency Quantum Rice-Ramsperger-Kassel analysis is utilized to obtain k(E) and Master Equation analysis is used for the evaluation of pressure fall-off in this complex bimolecular chemical activation reaction. Results are applicable to elementary experiments at low pressures, ambient combustion studies at one atmosphere, as well as higher-pressure turbine systems. 

Marcus developed a quantum mechanical formulation of Kassel-Rice-Ramsperger theories in which zero point energies have been taken into account (see flow chart). However, due to lack of data for individual molecules it is difficult to apply the theory of Rice-Ramsperger-Kassel-Marcus (RRKM)... 

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. 

Theoretical Expressions. The Rice-Ramsperger-Kassel-Marcus (RRKM14) theory of unimolecular reactions employs a quantum statis-... 

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. 

S. K. Klippenstein and J. D. Kress, Comparison of variational Rice-Ramsperger-Kassel-Mar-cus theory with quantum scattering theory for the He + H2 - HeH + H reaction, J. Chem. Phys. 96 8164 (1992). 

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. 

Energy Constrained and Quantum Anharmonic Rice-Ramsperger-Kassel-Marcus and Phase Space Theory Rate Constants For AI3 Dissociation. 

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. 

Rice, Ramsperger, and Kassel [206,333,334] developed further refinements in the theory of unimolecular reactions in what is known as RRK theory. Kassel extended the model to account for quantum effects [207] this treatment is known as QRRK theory. 

While the Slater model does not lend itself to a simple solution in terms of the quantum theory, the fact that it agrees in form with the simple quantum model of Rice-Ramsperger and Kassel suggests that we can write the following expression for the mean rate of decomposition of a critically energized molecule of energy E E ... 

RRKM theory is the well-known and consolidated statistical theory for unimolecular dissociation. It was developed in the late 1920s by Rice and Ramsperger [141, 142] and Kassel [143], who treated a system as an assembly of s identical harmonic oscillators. One oscillator is truncated at the activation energy Eq. The theory disregards any quantum effect and the approximation of having all identical is too cmde, such that the derived equation for micro canonical rate constant, k(E),... 

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