Rice-Ramsperger-Kassel-Marcus rate unimolecular reaction

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. 

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. 

Rate constants for unimolecular homogeneous PH3 decomposition were calculated by the Rice-Ramsperger-Kassel-Marcus (RRKM) theory and by the use of estimated values for the activation energies. Rate constants at the high-pressure limit for reaction (5), log(k/s)= 14.18-11 610/T [5] or 14.00-12610/T [4], include activation energies of 222 or 241 kJ/mol, respectively. Calculated rate constants for reaction (6) are log(k/s)=15.74-18 040/T with an activation energy of 345 kJ/mol. At 900 K PH formation is thus predicted to exceed PH2 formation by a factor -10. Calculated fall-off pressures for both reactions which indicate the onset of second-order decomposition, are quite high, about 10 Torr in an H2 bath gas [5]. 

The QET is formally identical to the Rice-Ramsperger-Kassel-Marcus (RRKM) theory of unimolecular decay, in which the rate constant for dissociation to reaction products of an energized species with total angular momentum J and internal energy E over a barrier of Eq is given by the following relation ... 

Transition state theory (TST) and Rice-Ramsperger-Kassel-Marcus (RRKM) theory are the theories most widely used to calculate the rate constant. TST is used to study bimolecular reactions and RRKM theory is the generalization of TST which is applicable for unimolecular reactions. 

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. 

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