We have studied the reactions of T+CH4 and T+CD4, treating these as six distinct particles, using a variety of potential energy surfaces subject to the restriction that only one methane hydrogen at a time is reactive. Our principal findings are: (1) This trial assumption about the potential is unjustified. Substitution (products CH3T+H and CD3T+D) involves strong interactions between at least four atoms. (2) There were no inertial isotope effects of any kind when CH4 was replaced by CD4. (3) From (2) and the details of the trajectories, there is suggestive but not conclusive evidence that substitution in CH4 proceeds by Walden inversion. (4) Abstraction (products CH3+HT and CD3+DT) is direct and concerted and occurs at relatively low energy. In our calculations it had a maximum cross section of 3.5 Å2 for a reactant translation energy of 65 kcal. At sufficiently high energy it is a stripping reaction. (5) About half the abstraction product energy is translational; the remainder appears as internal energy of both HT and CH3. When substitution occurs as a three-centered process, it deposits about 70 kcal in CH3T. Fragmentation is an important process above 100-kcal reactant energy.
Previously obtained Monte Carlo rate constants for unimolecular decomposition of model molecules [J. Chem. Phys. 40, 1946 (1964)] are compared with the predictions of a modified version of the Rice-Ramsperger-Kassel-Marcus theory. The principal modification is an unambiguous method of specification of the critical value of the reaction coordinate. Anharmonicity corrections are accurately calculated, and an improved way of treating rotational state densities, closely related to that of Marcus [J. Chem. Phys. 43, 2658 (1965)], is used. The agreement between theory and Monte Carlo results is drastically improved; remaining deviations are about ± 50% for bent molecules and undetectable (within 20%) for linear ones.
The widespread availability of computers and sophisticated calculators has encouraged chemists to succumb to the lure of "significance" and to use the method of least-squares for routine data analyses. Unfortunately, incorrect application of the method or injudicious interpretation of the results may be worse than old-fashioned eyeball-and-ruler estimations of straight lines. Few elementary expositions of least-squares discuss such crucial topics as proper weighting of the observations, estimation of errors, or establishment of confidence limits for parameters. Textbooks which deal adequately with these subjects are often too formidable for quick reference. This paper is intended to occupy the middle ground between oversimplification and forbidding abstrusity by outlining some common applications of the method of linear leastsquares and examining the statistical significance of the results.
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 I kcallmol and the errors in the computed saddle point energies are believed to be less than 3 kcallmol. 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 kcallmol relative to Ca + HF. The energy barrier for collinear reaction, 30.0 kcallmol, 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 kcallmol 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 = I 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 i...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.