This article shows how to evaluate rotational symmetry numbers for different molecular configurations and how to apply them to transition state theory. In general, the symmetry number is given by the ratio of the reactant and transition state rotational symmetry numbers. However, special care is advised in the evaluation of symmetry numbers in the following situations: (i) if the reaction is symmetric, (ii) if reactants and/or transition states are chiral, (iii) if the reaction has multiple conformers for reactants and/or transition states and, (iv) if there is an internal rotation of part of the molecular system. All these four situations are treated systematically and analyzed in detail in the present article. We also include a large number of examples to clarify some complicated situations, and in the last section we discuss an example involving an achiral diasteroisomer.

A method for calculating quasiclassical trajectories on potential energy surfaces defined using a sequence of model quadratic surfaces (QCT/GH) is suggested, and tested for atom–diatom collisions against the traditional quasiclassical trajectory approach. A simple model is also suggested to constrain the classical energy of a bound vibrational mode to be greater than a specified amount, namely, its zero‐point energy value. Essentially the model consists of assuming that the sum of the energies in the nonrelevant vibrational modes (typically unbound modes) of the supermolecular complex acts as a pool from which energy may be taken to compensate any leak of vibrational energy in the relevant bound modes, hence preventing the latter from falling below zero‐point value. Extensive QCT/GH trajectory calculations carried out for the H+H₂ exchange reaction, which occurs over an energy barrier, as well as exploratory trajectories for the reaction O+OH→O₂+H, which occurs on a potential energy surface with a deep chemical well, have shown that the total energy and total angular momentum are conserved within a small numerical tolerance. Correcting for the leak of zero‐point vibrational energy still leaves the total energy rigorously conserved but the total angular momentum is then only approximately kept constant. For H+H₂(v=0, j=0)→H₂(v’, j’)+H, the calculated state‐to‐state QCT/GH cross sections show reasonably good agreement with those of converged quantum results reported in the literature for the same H₃ potential energy surface. This agreement does not deteriorate after correction of zero‐point energy leak. For both H₃ and HO₂, accurate global analytical potential energy surfaces based on the double many‐body expansion method have been utilized. Using these prototype systems, an assessment is made of the difficulties encountered on direct reaction dynamics using the novel QCT/GH method.

The quasiclassical trajectory (QCT) method has been used for a detailed study of the state-to-state dynamics of the reaction O(3P) + OH(2Π)→O2(X̂33Σ−g) + H(2S) over the range of translational energies 0.125 ≤ Etr/kcal mol−1≤2.0, corresponding to the temperature range 40≤T/K≤680. A novel variant of this method insuring that trajectory calculations properly account for the zero-point energy of the diatomic molecules, the so-called quasiclassical trajectory–internal-energy quantum-mechanical-threshold method, is also suggested and applied to the title reaction. The most recent and accurate double many-body expansion potential-energy surface for the ground doublet state of the hydroperoxyl radical has been employed in all calculations. The computed reactive cross sections for initial quantum rotational states of OH varying from J=0 to J=10 (the vibrational quantum number is kept fixed at v=0) are shown to have a marked decreasing dependence on translational energy, thus suggesting that long-range forces play a major role on the dynamics of the O(3P) + OH(2Π) reaction. A comparison of the thermalized rate coefficients with the results of direct experimental measurements is shown to agree best with the data of Howard and Smith over the whole range of temperatures covered by experiment. It is also shown that nonstatistical recrossing effects are important for all translational energies and rotational states, while a nearly linear dependence is shown over the range of translational energies that have been studied. Finally, appropriate averaging over the initial conditions shows that the dependence on temperature of the calculated recrossing factor is in good agreement with the corresponding estimate from recent direct thermalized QCT calculations using the same potential-energy surface while fitting well by a recently proposed model for this recrossing factor.