Thermal rate coefficient

Wahnstrom G and Metiu H 1988 Numerical study of the correlation function expressions for the thermal rate coefficients in quantum systems J. Phys. Chem. JPhCh 92 3240-52... 

Thachuk M and Schatz G C 1992 Time dependent methods for calculating thermal rate coefficients using flux correlation functions J. Chem. Phys. 97 7297-313... 

Fig. 9. The thermal rate coefficient for H2 + OH - H + H2O on the WDSE, YZCL1, and YZCL2 surfaces are compared with experimental results.74...

We can calculate the thermal rate constants at low temperatures with the cross-sections for the HD and OH rotationally excited states, using Eqs. (34) and (35), and with the assumption that simultaneous OH and HD rotational excitation does not have a strong correlated effect on the dynamics as found in the previous quantum and classical trajectory calculations for the OH + H2 reaction on the WDSE PES.69,78 In Fig. 13, we compare the theoretical thermal rate coefficient with the experimental values from 248 to 418 K of Ravishankara et al.7A On average, the theoretical result... 

Fig. 15. Comparison of the theoretical thermal rate, fc(T), with experimental results.74 Also shown are the initial state selected rate coefficient for the (0,0) state, and an approximate theoretical thermal rate coefficient, fcest(T).

Even in J-type shock models, it is not appropriate to use thermal rate coefficients because the internal degrees of freedom will cool rapidly (via radiation) in the low density medium, whereas the translational degree of freedom will cool much more slowly. Appropriate rate coefficients are then those in which only translation is strongly excited such rate coefficients can be considerably lower than thermal rates for systems in which vibrational energy is the most efficient at inducing reaction. 

Fig. 9.5 Energy dependence of reactive cross section for reactive hard sphere model. Now the thermal rate coefficient is given by...

A further advance occurred when Chesnavich et al. (1980) applied variational transition state theory (Chesnavich and Bowers 1982 Garrett and Truhlar 1979a,b,c,d Horiuti 1938 Keck 1967 Wigner 1937) to calculate the thermal rate coefficient for capture in a noncentral field. Under the assumptions that a classical mechanical treatment is valid and that the reactants are in equilibrium, this treatment provides an upper bound to the true rate coefficient. The upper bound was then compared to calculations by the classical trajectory method (Bunker 1971 Porter and Raff 1976 Raff and Thompson 1985 Truhlar and Muckerman 1979) of the true thermal rate coefficient for capture on the ion-dipole potential energy surface and to experimental data (Bohme 1979) on thermal ion-polar molecule rate coefficients. The results showed that the variational bound, the trajectory results, and the experimental upper bound were all in excellent agreement. Some time later, Su and Chesnavich (Su 1985 Su and Chesnavich 1982) parameterized the collision rate coefficient by using trajectory calculations. 

Applications of RRKM theory often focus on the high pressure limit of the dissociation rate coefficient. The presence of multiple collisions prior to reaction generally maintains a Boltzmann population distribution. Correspondingly, the thermal rate coefficient is then expressed as a Boltzmann average over the energy and angular momentum resolved rate coefficient, which reduces to... 

The generation of pressure-dependent thermal rate coefficients from such microcanonical rate coefficients involves some averaging over a collision induced distribution. This averaging can once again reduce some of the errors due to the neglect of vibrational anharmonicities. In particular, at fairly high pressures, the distribution function is close to Boltzmann. In the calculation of thermal rate coefficients the errors in the distribution function then cancel with those in the microcanonical rate coefficients, just as in the high pressure limit. 

So far our discussion has focused on the measurement of thermal rate coefficients for a number of different classes of reactions involved with low temperature combustion. A significant proportion of the kinetics community is interested in looking beyond thermally averaged rate coefficients k T)) towards quantum state specific data the rate coefficient for reagents in the quantum state vj. The two quantities are related via equation (2.71)... 

This paper draws a parallel between the (full) six-dimensional H + H2O —> H2 -I- OH and the (reduced) seven-dimensional H -l- CH4 —> H2 + CH3 abstraction reactions. In Sec. 2, we briefly present the initial state TD quantum wave packet approach for the A -I- BCD and X + YCZ3 reactions. The Hamiltonians, body-fixed (BE) parity-adapted rotational basis functions, initial state construction and wave packet propagation, and extraction of reaction probabilities, reaction cross sections, and thermal rate coefficients from the propagated wave packet to compare with experiments are discussed. In Sec. 3 we briefly outline the potential energy surfaces used in the calculations. Some... 

Figure 13. Comparison of the best fit experimental thermal rate coefficient with the total value for the JG PES. the ab initio PES. and the contribution from the initial CH stretch (nOO). HCH bend (OnO), and umbrella (OOn) states.

For the H + CH4 reaction, it is shown that (a) there is substantial difference between the reaction probability calculated with the new ab initio global PES versus the semi-empirical Jordan-Gilbert PES, (b) CH4 molecules with an excited CH bond stretch have high reactivity and accounts laigely for the overall reaetivity of CH4 above 450K, and (c) the thermal rate coefficients calculated with the ab initio global PES agree very well with experimental data. 

The thermal rate coefficients calculated for the inverse power law excitation functions for the (04)o state on both the WSLFH and the OC potential surfaces are in very good agreement with the experiments [23]... 

As has been mentioned in Section 2.1, the most fundamental and the most useful quantities in ion—molecule reactions are the microscopic cross-section a(v) and thermal rate coefficient k T), respectively. Thus it is desirable that the phenomenological cross-section Q can be converted into either of these quantities. The desired relationship is obtained, as was first derived by Light [37], from eqn. (31) or its equivalent... 

In this article, we do not discuss various experimental techniques developed for studying ion—molecule reaction rates. Some techniques measure the microscopic cross-sections or thermal rate coefficients directly, while others measure the phenomenological cross-sections or some apparent rate coefficients relevant to. particular experimental situations. Detailed descriptions and assessments of these techniques are found in refs. 28 and 34. In particular. Chapter 5 of ref. 34 gives critical comparisons of rate data obtained with different techniques and also comparisons with theory. The reader is referred to these excellent reviews. 

It is well established that the parent ion C2H reacts with acetylene to produce the principal secondary ions C4H2 and C4H3. For these two principal reactions, the thermal rate coefficients in units of cm molecule sec are [311],... 

This rate coefficient can be averaged in a fifth step over a translational energy distribution P (E ) appropriate for the bulk experiment. In principle, any distribution P (E ) as applicable in the experiment can be introduced at this point. If this distribution is a thermal Maxwell-Boltzmann distribution one obtains a partially state-selected thermal rate coefficient... 

In a final, sixth step one may also average (sum) over a thermal (or other) quantum state distribution I (and F) and obtain the usual thermal rate coefficient... 

A comprehensive listing of absolute thermal rate coefficients for hydrogen abstraction and olefinic addition reactions by atomic fluorine has been given in Table X. 

Reduced-Dimensionality Quantum Calculations of the Thermal Rate Coefficient for the Cl + HCl — HCl -I- Cl Reaction Comparison with Centrifugal-Sudden Distorted Wave, Coupled Channel Hyperspherical, and Experimental Results. 

Key words Quasiclassical trajectory method -Reactive cross section - Thermal rate coefficient -Potential-energy surface - Quantum scattering... 

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