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We introduce TheRate (THEoretical RATEs), a complete application program with a graphical user interface (GUI) for calculating rate constants from first principles. It is based on canonical variational transition‐state theory (CVT) augmented by multidimensional semiclassical zero and small curvature tunneling approximations. Conventional transition‐state theory (TST) with one‐dimensional Wigner or Eckart tunneling corrections is also available. Potential energy information needed for the rate calculations are obtained from ab initio molecular orbital and/or density functional electronic structure theory. Vibrational‐state‐selected rate constants may be calculated using a diabetic model. TheRate also introduces several technical advancements, namely the focusing technique and energy interpolation procedure. The focusing technique minimizes the number of Hessian calculations required by distributing more Hessian grid points in regions that are critical to the CVT and tunneling calculations and fewer Hessian grid points elsewhere. The energy interpolation procedure allows the use of a computationally less demanding electronic structure theory such as DFT to calculate the Hessians and geometries, while the energetics can be improved by performing a small number of single‐point energy calculations along the MEP at a more accurate level of theory. The CH4+H↔CH3+H2 reaction is used as a model to demonstrate usage of the program, and the convergence of the rate constants with respect to the number of electronic structure calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1039–1052, 1998

In many cases, variational transition states for a chemical reaction are significantly displaced from a saddle point because of zero-point and entropic effects that depend on the reaction coordinate. Such displacements are often controlled by the competition between the potential energy along the minimum-energy reaction path and the energy requirements of one or more vibrational modes whose frequencies show a large variation along the reaction path. In calculating reaction rates from potential-energy functions we need to take account of these factors and—especially at lower temperatures—to include tunneling contributions, which also depend on the variation of vibrational frequencies along a reaction path. To include these effects requires more information about the activated complex region of the potential-energy surface than is required for conventional transition-state theory. In the present article we show how the vibrational and entropic effects of variational transition-state theory and the effective potentials and effective masses needed to calculate tunneling probabilities can be estimated with a minimum of electronic structure information, thereby allowing their computation at a higher level of theory than would otherwise be possible. As examples, we consider the reactions OH+H2, CH3+H2, and Cl+CH4 and some of their isotopic analogs. We find for Cl+CH4→HCl+CH3 that the reaction rate is greatly enhanced by tunneling under conditions of interest for atmospheric chemistry.

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We have carried out ab initio calculations using Mo/ller–Plesset perturbation theory, scaling all correlation energy in second order (MP-SAC2) with several large basis sets, for the reaction OH+CH4→H2O+CH3. We found that correlation has a large effect on the geometry, barrier height, and vibrational frequencies of the transition state. The final calculated values, obtained with a correlation-balanced basis set, for the forward and reverse classical barrier heights are 7.9 and 21.2 kcal/mol, respectively. We have used these with transition state theory and an Eckart model for semiclassical tunneling calculations of the rate constants for the above reaction in the temperature range from 200 to 2000 K. We found that the present model, which requires information only at the reactants, transition state, and products, predicts rate constants of the same order of magnitude as the experimental data for this wide temperature range.