Modeling the kinetics of bimolecular reactions.

ion reaction, after the ZPE contributions are included there is no barrier in the effective potential along the reaction coordinate, so important variational effects are expected. Both VMEP and the vibrationally adiabatic potential are plotted along the path in Figure 1. At room temperature the maximum of the free energy (see eq 2.4.36) is located at s* CVT ) -0.364 a0, whereas s* μVT is energy dependent (see eq 2.4.76). Figure 2 shows the variation of s* μVT with energy; it moves in the interval [-0.70 a0, -0.22 a0] at low energies and remains almost constant above 55 kcal/mol, where the zero of energy is the potential energy at the equilibrium structure of reactants. Despite the variation of s* , the CVT and μVT rate constants are quite similar at room temperature with values of 6.54 × 10-11 and 6.08 × 10-11 cm3 molecule-1 s-1, respectively, and at higher temperatures they are even closer. This example shows that even for reactions with variable transition states the CVT rate constants are reasonable and economical alternatives to μVT rate contants. However, the conventional TST rate constant is 2.33 × 10-10 cm3 molecule-1 s-1 and seriously overestimates the experimental406 value of 5.75 × 10-11. Another interesting example is the comparison of CVT, ICVT, and μVT with QCT for the room-temperature abstraction of a bromine atom in the bimolecular HgBr + Hg f Hg + Br2 reaction.249 In this case, the QCT rate constants are smaller than the CVT, ICVT, and μVT rate constants by factors of 1.58, 1.36, and 1.16, respectively. For cases in which the transition state is “tight” and no light particle participates in the reaction, so tunneling is not important, conventional TST can still provide a reliable determination of thermal rate constants, and it also provides insight into reaction mechanisms.407 In the examples just discussed, VTST is applied to study a particular system, so if we want to study another system, even if similar, the entire procedure, starting with building the potential energy surface, has to be repeated. To make it easier to study a series of reactions, Truong and coworkers408-412 have presented a method called reaction class transition state theory (RC-TST), which profits from recognizing the common aspects of a given set of chemical reactions. Thus, reactions with similar characteristics form what is called a class, and it is expected that they also share some similarity in their kinetics parameters. The procedure involves accurate calculations for one of the reactions, called the principal reaction, and all the other thermal rate constants are obtained from empirical relations. Truong applied these ideas to hydrogen abstraction reactions by hydrogen atoms with encouraging results.408-412 An important point to keep in mind in using either conventional or variational transition state theory is that extra assumptions are required to predict more than the overall reaction rate. We will present some discussion of product state distributions in Section 3. Sometimes not only the product states but even the identity of the products is inaccessible. This problem arises if two or more products share a given transition state. This can occur if the reaction path bifurcates after the transition state.413-421 2.4.3. Anharmonicity Conventionally, one would compute the reactant partition function accurately by a sum over states, although in practice this has only recently become possible for molecules with more than 3-4 atoms.422 An alternative method to compute accurate vibrational-rotational partition functions is the Figure 2. Variation with energy of the location of the minimum sum of states for the Cl + C2H6 f ClH + C2H5 reaction. ∆Va (s) ) Va (s) Va G (reactants) (2.4.79) Figure 1. Plots of VMEP and relative vibrationally adiabatic potential ∆Va G along the reaction path for the Cl + C2H6 f ClH + C2H5 hydrogen abstraction reaction. 4538 Chemical Reviews, 2006, Vol. 106, No. 11 Fernández-Ramos et al.