An accurate three‐dimensional potential energy surface for H3 has been obtained by the configuration interaction (CI) method. The calculated energies, for 156 nuclear configurations, with the energy of the saddle point taken to be zero, are believed to lie within 0.1 kcal/mole of the exact clamped‐nuclei limit. The CI calculations used an extended one‐particle basis set of 4 s‐type, 3 p‐type, and 1 d‐type contracted Gaussian functions, and a nearly complete n‐particle basis set. In order to solve the large secular problem, the direct CI method was adapted to the problem of complete CI for three valence electrons. The properties of the accurate H3 potential surface were used to evaluate ab initio and semiempirical methods for potential surface calculations, with emphasis on their applications to other exchange reactions.

An accurate three‐dimensional potential energy surface for H3

Liu and Siegbahn’s recent calculations on the potential energy surface start for H+H2 provide us with the most accurately known potential energy surface for any chemical reaction. We have made an accurate least‐squares fit to this surface which satisfies several criteria for use in scattering calculations, including essentially exact agreement with all saddle point properties and being reasonably compact. With eight nonlinear parameters and 15 linear parameters we fit all 267 ab initio points with a root‐mean‐square error of 0.17 kcal/mol and a maximum absolute deviation of 0.55 kcal/mol. The spherical average of the interaction potential is in good agreement with the recent experimental estimate of Gengenbach, Hahn, and Toennies.

Functional representation of Liu and Siegbahn’s accurate ab initio potential energy calculations for H+H2

elsepa—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules

Accurate three‐dimensional reactive and nonreactive quantum mechanical cross sections for the H+H_2 exchange reaction on the Porter–Karplus potential energy surface are presented. Tests of convergence in the calculations indicate an accuracy of better than 5% for most of the results in the energy range considered (0.3 to 0.7 eV total energy). The reactive differential cross sections are exclusively backward peaked, with peak widths increasing monotonically from about 32° at 0.4 eV to 51° at 0.7 eV. Nonreactive inelastic differential cross sections show backwards to sidewards peaking, while elastic ones are strongly forward peaked with a nearly monotonic decrease with increasing scattering angle. Some oscillations due to interferences between the direct and exchange amplitudes are obtained in the para‐to‐para and ortho‐to‐ortho antisymmetrized cross sections above the effective threshold for reaction. Nonreactive collisions do not show a tendency to satisfy a "j_z‐conserving" selection rule. The reactive cross sections show significant rotational angular momentum polarization with the m_j=m′_j=0 transition dominating for low reagent rotational quantum number j. In constrast, the degeneracy averaged rotational distributions can be fitted to statistical temperaturelike expressions to a high degree of accuracy. The integral cross sections have an effective threshold total energy of about 0.55 eV, and differences between this quantity and the corresponding 1D and 2D results can largely be interpreted as resulting from bending motions in the transition state. In comparing these results with those of previous approximate dynamical calculations, we find best overall agreement between our reactive integral and differential cross sections and the quasiclassical ones of Karplus, Porter, and Sharma [J. Chem. Phys. 43, 3259 (1965)], at energies above the quasiclassical effective thresholds. This results in the near equality of the quantum and quasiclassical thermal rate constants at 600 K. At lower temperatures, however, the effects of tunneling become very important with the quantum rate constant achieving a value larger than the quasiclassical one by a factor of 3.2 at 300 K and 18 at 200 K.

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Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H+H2

A new computational model has been created to describe the interaction of auroral electrons with the atmosphere. For electrons of energy greater than 500 eV, continuous energy losses and small angle deflections are combined in a Fokker-Planck diffusion equation that computes energy spectrums over all pitch angles throughout the atmosphere. These fluxes are then used to determine the rates of secondary electron and degraded (E < 500 eV) primary electron production at all heights. This information is used to compute upward and downward hemispherical fluxes in the energy range 0–500 eV, taking into account discrete energy losses, large angle scattering, and particle transport along magnetic field lines. The model has been used to compute energy spectrums, ionization rates, backscatter ratios, and optical emissions associated with different incident electron spectrums. For monoenergetic electrons of energy 2 keV and above the results obtained agree well with the work of Rees (1969) and Rees and Maeda (1973). At lower energies the effects of transport and elastic collisions become progressively more important, and the present results differ significantly both from the Rees and Maeda results and from those obtained from the ideas of energy degradation. Finally, spectrums typical of the nighttime auroral oval and daytime polar cusp are used to obtain the altitude dependent fluxes, ionization rates, and optical emissions.

A new model for the interaction of auroral electrons with the atmosphere: Spectral degradation, backscatter, optical emission, and ionization

Theoretical electron scattering amplitudes and spin polarizations: Selected targets, electron energies 100 to 1500 eV*

A new H3 potential energy surface and its implications for chemical reaction

On the term-wise analysis of the glauber eikonal series

Exchange in the hydrogen atom–molecule reaction is investigated via classical collinear dynamics on the Yates–Lester potential energy surface. A threshold kinetic energy of 6.4762 kcal/mole (0.2808 eV) is determined. Exchange probabilities are found to be, in general, slightly less than those obtained using the energy surface of Shavitt, Stevens, Minn, and Karplus. Energy banding is observed and discontinuities in the transition region are attributed to snarled trajectories. Reaction probabilities for all possible combinations of H, D, and T are determined. Isotopic variations in reaction probability are explained in terms of the mass‐dependent skew of the potential surface and differences in zero‐point vibrational energy.

Albert C. Yates

Papers

Theoretical electron scattering amplitudes and spin polarizations: Selected targets, electron energies 100 to 1500 eV*

A new H3 potential energy surface and its implications for chemical reaction

On the term-wise analysis of the glauber eikonal series

Collinear classical dynamics on a chemically accurate H+H2 potential energy surface

On the reduction of the glauber exchange amplitude