D. A. Kohl

Ab initio Hartree–Fock calculation of the elastic electron scattering cross section of sulphur hexafluoride

The ab initio Hartree–Fock calculation of the elastic electron scattering cross section of sulphur hexafluoride is reported. The integrals for the Born scattering amplitudes have been evaluated by a new simple technique, based on Gaussian quadrature. Spherical averaging was performed numerically; different techniques for spherical averaging are discussed. An estimated re structure was used and vibrational effects have been neglected. In order to assess the effect of the basis set on the intensities, calculations have been performed for the nitrogen molecule with six different basis sets. Using these results as a guide, a triple‐zeta basis set, augmented with polarization functions and diffuse functions, was selected for SF6. The results confirm Bartell’s hypothesis that the observed residuals from the independent atom model intensities are due to electronic bonding effects. It is suggested that, for very accurate electron diffraction work, the effect of electron redistribution has to be taken into account...

On an electron diffraction study of the structure of the dibromomethylene radical

The molecular structures of two states of the dibromomethylene radical have been observed by the technique of gas phase electron diffraction. The radicals were produced by the thermal decomposition of tetrabromomethane utilizing an oven nozzle within the scattering chamber. The decomposition resulted in about 60% conversion to dibromomethylenes and lesser amounts of hexabromomethane, tribromomethyl radicals, and molecular bromine. The two structures observed for dibromomethylene were a near linear form, assigned as the triplet state, and a bent form assigned as the singlet state. An average carbon‐bromine bond distance of 1.74 A was observed for both states.

Elastic electron scattering. I. Scattering from diatomic potentials

A method is described for calculating electron scattering cross sections from diatomic molecules. The wave function for the scattered electron is represented by a superposition of atomic scattering functions for the component atoms in the molecule plus correction terms for intramolecular multiple scattering. This formalism is applied to scattering from the nitrogen molecule at incident electron energies of 100 eV to 40 keV. The differential cross sections are consistent with the optical theorem and are smaller than the cross sections calculated in the conventional quasikinematic approximation.

On the calculation of elastic electron scattering cross sections from molecular wavefunctions: CF4 and CH4

Abstract A very efficient method is described for calculating the Born elastic differential scattering cross section with molecular Hartree-Fock wavefunctions. This approach, which is based on Gaussian orbitals, reduces the computational time by about an order of magnitude, and is more stable at high momentum transfer than previous methods. Elastic electron scattering cross sections for CF4 and CH4 were calculated with large basis sets and both curves mimic the shapes of the experimental total cross sections for these molecules.

Electron diffraction study of the thermal decomposition of BrCCl3

The thermal decomposition of bromotrichloromethane was studied in the gas phase by electron diffraction. An oven was incorporated into the sample inlet system of a conventional photographic plate unit to decompose the sample. Three different diffraction patterns were recorded and analyzed. A peak in the radial distribution curve corresponding to a normal carbon‐bromine bond was absent. However, in order to satisfy stoichiometry requirements and to match the areas of all of the peaks, it was necessary to introduce species with an abnormally long carbon‐bromine bond length. For each of the three diffraction patterns, the major components in the scattering volume were found to be mixtures of BrCCl3/BrCCl2/CCl4/CCl3, C2Cl4/C2Cl6, and BrCl/Br2. Except for the C–Br bond, all distances and angles had normal values. A plausible explanation of the lengthening (∼ 0.15 A) of the C–Br bond is that a long‐lived excited state of BrCCl3/BrCCl2 was formed as an intermediate in the reaction.

Molecular Structure of Gaseous d,l‐1,2,3,4‐Diepoxybutane from Electron Diffraction Data

The d,l isomer of 1,2,3,4‐diepoxybutane was studied in the vapor phase by electron diffraction. The following values were found for the bond lengths and bond angles (standard deviations are given in parentheses): r(C–C)ring= 1.463(0.005) A, r(C–C)= 1.521(0.009) A, r(C–O)= 1.439(0.004) A, and ∠CCC= 115.2°. The data were consistent with a single conformation corresponding to a nearly trans configuration for the carbon chain.

H+2 —A full three‐body variational treatment

The eigenstates of the hydrogen molecule ion have been determined by a variational calculation without resorting to the Born–Oppenheimer or adiabatic approximations. A Slater‐type orbital basis in terms of perimetric coordinates was used and the eigenvalues were obtained by diagonalizing a 300×300 matrix. Computational techniques and numerical stability tests are described. Because of the relatively small basis and the large number of bound states, most of the eigenvalues were sensitive to the basis set. With a basis which favored the upper states, 18 bound states were obtained in a single diagonalization vs 20 bound states in the adiabatic approximation. With the best basis for the ground state, the eigenvalues of the six lowest levels were 1 to 3×10−6 a.u. lower than adiabatic calculations and the differences appear to increase with increasing vibrational quantum number.

Elastic electron scattering. II. Scattering from polyatomic potentials

A treatment of intramolecular multiple scattering in diatomic molecules is extended to cover the polyatomic case. The differential cross section is expressed as a sum of two and three atom interactions with the latter depending strongly on the geometrical arrangement. However, an interplay between the multiple scattering amplitudes for each three atom fragment ensures that all symmetry requirements of the entire molecule are satisfied. For illustrative purposes, cross sections for ten keV electrons are calculated for the fragments FF2 and FF3 to demonstrate the detailed character of the multiple scattering corrections.A treatment of intramolecular multiple scattering in diatomic molecules is extended to cover the polyatomic case. The differential cross section is expressed as a sum of two and three atom interactions with the latter depending strongly on the geometrical arrangement. However, an interplay between the multiple scattering amplitudes for each three atom fragment ensures that all symmetry requirements of the entire molecule are satisfied. For illustrative purposes, cross sections for ten keV electrons are calculated for the fragments FF2 and FF3 to demonstrate the detailed character of the multiple scattering corrections.

An electron diffraction investigation of the reaction intermediate in the gas‐phase bromination of ethylene

The addition of bromine to ethylene was studied in the gas phase by electron diffraction. Atomic bromine and an excess of ethylene were mixed just prior to introduction into the scattering region by a dual‐sample inlet system. The atomic bromine was produced from molecular bromine by thermolysis in an oven adjacent to the mixing region. Diffraction patterns recorded at each of three different oven temperatures were analyzed. The radial distribution curve for one pattern had the normal distances attributed to ethylene and bromine plus a Br–Br peak corresponding to the 3Π0+μ state of Br2. The radial distribution curve for a second pattern exhibited a peak at 1.7 A in addition to the ethylene and bromine distances. The radial distribution curve for a third pattern, recorded at the highest oven temperature, again showed the 1.7 A peak and ethylene peaks but no bromine peak. To account for the scattering power and still preserve stoichiometry, it was necessary to assign the 1.7 A peak to a carbon‐bromine pair ...

Basis set dependence of abinitio SCF elastic, Born, electron scattering cross sections for C2H4

The results of ab initio Hartree–Fock calculations of the orientationally averaged, elastic electron scattering cross section of C2H4 with six different basis sets are reported. The averaging and Fourier transform were calculated by the approach of Kohl, Pulay, and Fink. Six different basis sets, ranging from 6‐31G to 6‐311 G4*, were employed in the calculations. The improvement in the calculated Born cross section parallelled the lowering of the energy as the basis was varied. For C2H4, a calculation at the 6‐311G** level provides a good description of the cross section at a modest expenditure of computational time.