Deformed transition-state theory: Deviation from Arrhenius behavior and application to bimolecular hydrogen transfer reaction rates in the tunneling regime.

A formulation is presented for the application of tools from quantum chemistry and transition-state theory to phenomenologically cover cases where reaction rates deviate from Arrhenius law at low temperatures. A parameter d is introduced to describe the deviation for the systems from reaching the thermodynamic limit and is identified as the linearizing coefficient in the dependence of the inverse activation energy with inverse temperature. Its physical meaning is given and when deviation can be ascribed to quantum mechanical tunneling its value is calculated explicitly. Here, a new derivation is given of the previously established relationship of the parameter d with features of the barrier in the potential energy surface. The proposed variant of transition state theory permits comparison with experiments and tests against alternative formulations. Prescriptions are provided and implemented to three hydrogen transfer reactions: CH4  + OH → CH3  + H2 O, CH3 Cl + OH → CH2 Cl + H2 O and H2  + CN → H + HCN, widely investigated both experimentally and theoretically.