ALBERT

Notes: 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 isbased 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).

Notes: We have examined the structure, torsional potentials, vibrational spectra, and harmonic force fields for the s-cis and s-trans isomers of methacryloyl fluoride with the aim of understanding some of the conformational properties of these molecules and their relationship to macroscopic polymer properties. The calculations have been performed at the SCF level with a split valence basis set. We find the structure to be in reasonably good agreement with experiment and as expected find the structural variations between the two isomers to be slight. However, we do suggest a reexamination of the carbonyl geometry in light of our studies. Our calculations show the energy difference between the s-cis and the s-trans isomers to be less than 1 kcal/mol at both the split valence and the split valence polarized levels, favoring the s-trans form. An examination of the torsional potential reveals that a rigid rotor approximation provides an adequate description of the motion of either the methyl group, or of the COF moiety. For the methyl group we find a barrier of 1.5 kcal/mol, with the preferred conformation having the hydrogen atom eclipsed with respect to the carbon–carbon double bond. Our best calculations show that the torsional barrier to interconvert the s-trans to the s-cis form is 7.0 kcal/mol, somewhat higher than the recent experimental values of 6.5 and 5.1 kcal/mol. This study also points out the need to include the difference in zero point energies between reactants and the transition state when evaluating torsional potentials. Our calculated vibrational spectra show the similarities and differences between these two isomers, and suggest areas where the assignments should be further examined. In particular, we suggest that some of the low frequency torsional modes deserve further scrutiny. A fit of our data to a three term Fourier series shows that we are able to reproduce the experimentally derived barrier, even though a direct determination shows that the predicted barrier lies higher.

Notes: [Auszug] Nucleons and other subnuclear particles seem to be composed of more fundamental objects, the quarks, but bombardment of nucleons at increasing energy has failed to liberate quarks from the interior of nucleons. This has led to the development of theories in which quarks are of necessity permanently ...

Notes: Abstract. In 1997 Diakonov, Petrov, and Polyakov, calculated the width of the exotic baryon that they called $\Theta^{ + }$ . The prediction, $\Gamma(\Theta^{ + })\lesssim 15$ MeV, has received considerable attention, especially in light of the narrowness of the experimentally reported $\Theta^{ + }$ resonance. However, there is an arithmetic error in their work: when corrected, the width estimate quoted in that paper should have been $\lesssim 30$ MeV.