Henrik Szichman

Four mathematical dimensional quantum mechanical studies of tetra-atom systems: State-to-state J=0 probabilities for the H2+OH→H2O+H reaction

This paper presents reactive state-to-state J=0 probabilities for the title system as obtained in a four-mathematical-dimensional quantum mechanical treatment. The present treatment differs from our previous one by the fact that in addition to the three Jacobi radial coordinates also the angular coordinate related to the H2 axis is treated as coordinates. As a result only the Jacobi angle related to the OH axis is treated as a parameter and the final probabilities follow from an integration over this angle (the out-of-plane angle, β, is eliminated by using a β-averaged potential). The calculations yielded final rotational and vibrational distributions that were analyzed and discussed with respect to more accurate (i.e., five- and six-mathematical-dimensional) results.

Quantum mechanical treatment of the H2 + OH ⇔ H + H reactions. Calculations of cross sections and rate constants

Abstract A quantum mechanical study for the reactive HHOH system is reported. Cross sections for the two possible reaction routes, namely the interaction of the two diatoms to form an atom-triatom and the reserved process, i.e. the interaction of an atom-triatom to form two diatoms, were calculated. The numerical treatment was carried out in the reagents arrangement channel only employing negative imaginary potentials and, therefore, transformations of coordinates between different arrangement channels were avoided. To solve the Schrodinger equation we employed the infinite-order sudden approximation which was found to yield relevant results. The calculated cross sections and rate constants were compared with experiment and with other numerical results. In particular the cross sections for the diatom-diatom case were in reasonable agreement with accurate results.

A THREE-DIMENSIONAL QUANTUM MECHANICAL STUDY OF THE NH+NO REACTIONS

In this article is described a three‐dimensional quantum mechanical study within the nonreactive infinite order sudden approximation (IOSA) of the title system. The study was performed using a recently introduced global potential energy surface [J. Chem. Phys. 102, 6696 (1995)]. Integral total cross sections for the two separate products, namely, N2O+H and N2+OH, were calculated as a function of kinetic energy in the range 0.05–0.50 eV. Our main findings are (a) the overall cross sections and the cross sections for N2O+H are only mildly dependent on the energy; (b) the cross sections for N2+OH, in conrast to those for N2O+H, depend on the energy and increase as the energy increases; (c) the yield of N2O+H is about 80–90 % of the total yield, in accordance with experiment; (d) the overall cross sections are about 1 to 3 times smaller than the quasiclassical‐trajectory ones and about 5 to 15 times smaller than the experimental ones.

A four-dimensional quantum mechanical state-to-state study of the H2+C2H→H+C2H2 reaction

A quantum mechanical approach to treat diatom–triatom exchange processes of the type AB+CDE→A+BCDE is presented. The initial nine degree-of-freedom problem is simplified to a reaction having active only five of such degrees of freedom, which emulates a rotating–stretching AB molecule colliding colinearly with a linear CDE molecule. This model is then applied to study the H2+C2H→H+C2H2 reaction. In the present work, the H2 rotations are treated using the infinite-order-sudden-approximation (IOSA) method, whereas the coupled states (CS or jz) approximation is employed to uncouple the total angular momentum J from internal rotations. Thus, a four-dimensional mathematical analysis is performed, which allows the computation of state-to-state reactive probabilities and cross sections. The bending vibrational levels of the acetylene C2H2 molecule are calculated on the basis of a one single degenerate bending expansion, i.e., just one H (the attacked one) is considered to bend, the remainder being frozen. Present...

QUANTUM MECHANICAL CROSS SECTIONS FOR THE ISOTOPIC REACTIONS H+X2O, X=H, D: A COMPARISON WITH EXPERIMENT AND WITH OTHER CALCULATIONS

In this work are presented 3-mathematical-dimensional quantum mechanical energy-dependent cross sections for the two isotopic reactions H+X2O→Products; X=H,D. The results are compared with experiment and with other calculations. The comparison between theory and experiment leads to two contradictory conclusions regarding the application of the Walch–Dunning–Schatz–Elgersma (WDSE) potential energy surface: (a) The WDSE surface seems to adequately describe the abstraction process; (b) however, the WDSE barrier for the exchange process seems to be too high and therefore yields small cross sections in contrast to those found in the experiment.

The application of Toeplitz matrices to scattering problems

This work describes a new approach to treating quantum mechanical scattering problems. It is based on expanding the wave function in terms of an infinite set of localized Gaussian functions and employing the features of a Toeplitz matrix.

A reduced dimensionality QM study of the BO+H2→HBO+H reaction: tunneling in polyatomic reactions

Abstract We report in the present Letter a three-dimensional, quantum mechanical, infinite order sudden approximation (IOSA) study of the H 2 +BO combustion reaction using a recently reported, six-dimensional potential energy surface (PES) for the adiabatic ground electronic state H 2 BO. Total reactive probabilities, cross-sections and rate constants are thus computed. These last ones compare relatively well with the experimental data, the agreement being much more improved with regard to previous quasi-classical trajectories (QCT) predictions. Furthermore, it is found that computed reactive cross-sections by both models compare well only beyond a translational energy of 0.8 eV.