RRKM theory rate constant calculation

Pressure-dependent gas phase NMR studies of syn-anti exchange in alkyl nitrite/C02 mixtures reported PiP values of 312,166,26, and <3 torr for MeONO, ethyl nitrite, n-propyl nitrite, and n-butyl nitrite, respectively [75], For all the nitrites studied, experimental rate constants were modeled using RRKM theory. This study concluded that the agreement between the rate constants calculated using RRKM... 

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 ... 

The reactions of the bare sodium ion with all neutrals were determined to proceed via a three-body association mechanism and the rate constants measured cover a large range from a slow association reaction with NH3 to a near-collision rate with CH3OC2H4OCH3 (DMOE). The lifetimes of the intermediate complexes obtained using parameterized trajectory results and the experimental rates compare fairly well with predictions based on RRKM theory. The calculations also accounted for the large isotope effect observed for the more rapid clustering of ND3 than NH3 to Na+. 

Vibrational frequencies for various normal modes must be estimated and active as well as inactive energies should be decided. Numerical methods may be used to calculate rate constant k at various concentrations obtained by RRKM theory. The rate constant has been found to be same as given by conventional transition state theory, i.e. 

Activation parameters for the high pressure gas-phase approach of 1,2-d2-cyclopropanes to cis, trans equilibrium (equation 1) have been reported as log A, a(kcal mol"1) of 16.0,64.2 and 16.4,65.176,77. From pressure-dependent measurements of rate constants and calculations based on RRKM theory, the threshold energy E for the cis, trans isomerization has been estimated to be 61.1 kcal mol"1 and 61.3 kcal mol"11 16 1, s. 

RRKM theory, an approach to the calculation of the rate constant of indirect reactions that, essentially, is equivalent to transition-state theory. The reaction coordinate is identified as being the coordinate associated with the decay of an activated complex. It is a statistical theory based on the assumption that every state, within a narrow energy range of the activated complex, is populated with the same probability prior to the unimolecular reaction. The microcanonical rate constant k(E) is given by an expression that contains the ratio of the sum of states for the activated complex (with the reaction coordinate omitted) and the total density of states of the reactant. The canonical k(T) unimolecular rate constant is given by an expression that is similar to the transition-state theory expression of bimolecular reactions. 

Second, we calculate the unimolecular rate constant at the internal energy E via the RRKM theory. We use Eq. (7.54), where the rotational energy is neglected and where the sum and density of vibrational states are evaluated classically. Thus at E = 184 kJ/mol we get... 

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. 

The VP rate is calculated by a restricted (to vdW modes) RRKM theory. By assuming a tight binding model for the cluster transition state, the resulting expression for the VP rate constant is (Forst 1973 Gilbert and Smith 1990 Kelley and Bernstein 1986 Levine and Bernstein 1987 Pritchard 1984 Robinson and Holbrook 1972 Steinfeld et al. 1989),... 

Reported gas-phase NMR studies have compared experimental pressure-dependent rate constants obtained from lineshape analyses with those calculated using RRKM theory which assumes stochastic IVR. This method is sensitive to significant departures from RRKM theory but cannot distinguish smaller departures due... 

Figure 6. Logarithmic plot values of LUm/fc versus pressure for the Cope rearrangement of bullvalene (torr at the experimental temperature of 356 K). Experimental values are signified by solid circles. Pressures are the total sample pressure at 356 K. Errors in frUni/fc are reported to 2o. The solid (upper) line represents the values calculated from RRKM theory using the biradicaloid transition state model. The lower line represents calculated rate constants using the aromatic transition-state model. The collision diameter was 3.6 A in both cases.

For most of the molecules discussed above, the experimentally determined pressure-dependent gas-phase rate constants can be modeled adequately with RRKM theory. SF4 and possibly aziridine are the exceptions. Due to uncertainties in the model parameters used in RRKM calculations, and the sensitivity of the calculations to these parameters, only qualitative conclusions can be drawn from the observed agreement. Since major departures are not observed, it can be... 

With this simplification, Gray, Rice, and Davis obtained reasonably accurate values for the predissociation rate constant as a function of initial vibrational excitation. The rate constant thus obtained is larger than that from exact trajectory calculations by about a factor of two. By contrast, the RRKM theory would give a rate constant that is about three orders of magnitude larger than is observed. 

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