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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.

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The OH radical is the most important radical in combustion and in the atmosphere, and methanol is a fuel and antifreeze additive, model biofuel, and trace atmospheric constituent. These reagents are also present in interstellar space. Here we calculate the rate constants, branching ratios, and kinetic isotope effects (KIEs) of the hydrogen abstraction reaction of methanol by OH radical in a broad temperature range of 30-2000 K, covering interstellar space, the atmosphere, and combustion by using the competitive canonical unified statistical (CCUS) model in both the low-pressure and high-pressure limits and, for comparison, the pre-equilibrium model. Coupled cluster CCSD(T)-F12a theory and multi-reference CASPT2 theory were used to carry out benchmark calculations of the stationary points on the potential energy surface to select the most appropriate density functional method for direct dynamics calculations of rate constants. We find a significant effect of the anharmonicity of high-frequency modes of transition states on the low-temperature rate constant, and we show how tunneling leads to an unusual negative temperature dependence of the rate constants in the range 200 K > T > 100 K. The calculations also demonstrate the importance of the extent of stabilization of the pre-reactive complex. The capture rate for the formation of the complex is the dominant dynamical bottleneck for T < 100 K, and it leads to weak temperature dependence of the rate below 100 K in the high-pressure-limit of the CCUS model. We also report the pressure dependence of branching ratios (which are hard to measure so theory is essential) and the KIEs, and we report an unusual nonmonotonic variation of the KIE in the high-pressure limit at low temperatures.