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

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We present systematic direct ab initio dynamics studies of proton transfer in hydrogen-bond systems using the tautomerization in gas phase formamidine and its monohydrated complex as model reactions. The thermal rate constants were calculated using a canonical variational transition state theory (CVT) with multidimensional semiclassical tunneling corrections within a small-curvature ground-state approximation. The reaction valleys were calculated at the second-order Mdller-Plesset (MP2) perturbation theory, Hartree-Fock (HF) and nonlocal Becke's half-and-half exchange and Lee-Yang-Parr correlation (BH&H-LYP) density functional theory (DFT) levels of theory using the 6-3 1 G(d,p) basis set. For accurate rate constants, the potential energy along the minimum energy path was scaled to match the single-point coupled cluster calculations including single and double excitations plus correction for triple excitation [CCSD(T)] at the MP2/6-3 1 G(d,p) classical barrier for each reaction. In the HF rate calculations, the HF frequencies were also scaled by a factor of 0.9. We found that adding a water to assist the proton transfer significantly enhances the tautomerization rate. Tunneling contributions in both systems are quite substantial and cannot be corrected by the Wigner approximation. We found that vibrational excitation of the solvent symmetriclike stretching mode would significantly enhance the rate of proton transfer in the formamidine-water complex. We also found that nonlocal DFT methods, particular the BH&H-LYP functionals studied here, can provide accurate potential energy information for dynamical calculations. Due to the computational advantage of DFT methods, prospects for dynamical studies of large polyatomic chemical reactions are quite encouraging.

Direct ab initio dynamics calculations based on a canonical variational transition-state theory with several multidimensional semiclassical tunneling approximations were carried out to obtain rate constants for the water-assisted tautomerization of formamide. The accuracy of the density functionals, namely, B-LYP, B3-LYP, and BH&H-LYP, were examined. We found that the BH&H-LYP method yields the most accurate transition-state properties when comparing it to ab initio MP2 and QCISD results, whereas B-LYP and B3-LYP methods predict barrier heights too low. Reaction path information was calculated at both the MP2 and nonlocal hybrid BH&H-Ž . LYP levels using the 6-31G d, p basis set. At the BH&H-LYP level, we found that the zero-point energy motion lowers the barrier to tautomerization in the formamide᎐water complex by 3.6 kcalrmol. When tunneling is considered, the activation energy at the BH&H-LYP level at 300 K is 17.1 kcalrmol. This is 3.4 kcalrmol below the zero-pointcorrected barrier and 7.0 kcalrmol below the classical barrier. Excellent agreement between BH&H-LYP and MP2 rate constants further supports the use of BH&H-LYP for rate calculations of large systems.

We present an ab initio direct dynamics study of the primary and solvent kinetic isotopes effects (KIEs) for the water-assisted tautomerization in the formamidine-water complex. These calculations are based on a variational transition state theory plus multidimensional semiclassical tunneling corrections with potential energy information calculated at the MP2 level of theory using the 6-31G(d,p) basis set. We found that both the primary and solvent KIEs are large at low temperatures and are due not only to tunneling but also to quantum effects in vibrational motions. The primary KIEs were larger than the solvent KIEs. This results from differences due to the effect of deuteration on vibrational modes. Bending modes show significant inverse KIEs, while those of the reactive OH and NH vibrations show both inverse and normal effects. Such effects can be explained by examining changes in the zero-point energies of these modes. The adherence of the HH/HD/DD rates to the rule of the geometric mean is also examined.

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