Ca+HF: The anatomy of a chemical insertion reaction

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Abstract
A comprehensive first principles theoretical investigation of the gas phase reaction Ca+HF→CaF+H is reported. The overall study involves three distinct elements: (a) generation of an accurate ab initio potential energy surface for the ground electronic state of the Ca–F–H system, (b) careful fitting of the computed surface to an analytical form suitable for three‐dimensional reactive scattering calculations, and (c) execution of classical trajectory calculations for Ca+HF collisions using the fitted potential surface. Ab initio potential energy calculations were performed for 175 Ca–F–H geometries using an MCSCF‐CI method with a large Gaussian orbital basis set. The error in the computed endothermicity for the reaction of Ca and HF is less than 1 kcal/mol and the errors in the computed saddle point energies are believed to be less than 3 kcal/mol. The potential energy surface is dominated by a deep well corresponding to a stable linear H–Ca–F intermediate with an extremely small bending force constant. The calculations clearly demonstrate that the preferred geometry for Ca attack on HF is markedly noncollinear. The saddle point for both fluorine exchange reaction and insertion into the H–Ca–F well occurs for a Ca–F–H angle of 75° and has an energy of 16.1 kcal/mol relative to Ca+HF. The energy barrier for collinear reaction, 30.0 kcal/mol, is nearly twice as high. The analytical representation of the ab initio potential energy surface is based on a polynomial expansion in the three diatomic bond lengths that reproduces the values of the computed energies to within a root mean square deviation of 1.2 kcal/mol and reduces to the appropriate diatomic potentials in the asymptotic limits. Classical trajectory calculations for Ca+HF(v=1) utilizing the fitted surface establish the fact that the H–Ca–F potential well dominates the collision dynamics thus qualifying Ca+HF as a bona fide example of a chemical insertion reaction. Because of the extensive sampling of the H–Ca–F well, many trajectories formed rather long‐lived intermediate complexes before reaching diatomic end products. A significant number of these trajectories were not converged with respect to changes in the integration time step. Despite uncertainties associated with the ultimate fates of the nonconverged trajectories, the results obtained support a number of generalizations relating to microscopic features of Ca+HF collisions. Among these are: (1) at fixed total collision energy, excitation of HF to v=1 is much more effective in promoting reaction than is placing the corresponding amount of energy in Ca,HF translation, (2) at fixed initial translational energy, reaction cross sections increase with increasing HF rotational quantum number J, (3) for trajectories which enter the H–Ca–F well, escape to form products is favored by increasing initial HF rotation and escape back to reactants is favored by increasing the initial relative translational energy, and (4) the CaF fractional product energy disposals are remarkably independent of initial collision conditions. These conclusions are compatible with the observation that significant intermode vibrational energy transfer does not occur in the H–Ca–F intermediate on the collision time scale (1–2 ps).