Roger L. Wilkins’s research while affiliated with University of Southern California and other places

A summation technique is used to calculate the static dipole electric polarizabilities of molecular hydrogen. The technique requires a complete set of single‐particle Hartree–Fock states. The occupied Hartree–Fock orbitals for molecular hydrogen are bound, and the complementary set of Hartree–Fock orbitals all lie in the continuum. Such a basis set permits one to evaluate the required sums by integrating over the excited states. The uncoupled Hartree–Fock model is used to calculate the zero‐order terms of the components of the polarizability tensor. The first‐order corrections to the components of the polarizability tensor are calculated using double perturbation theory. At the equilibrium internuclear separation, R = 1.4 a 0 , the static parallel dipole polarizability α ‖ and static perpendicular polarizability α ⊥ are 0.941 Å3 and 0.728 Å3, respectively, which compare favorably with the values 0.944 Å3 and 0.677 Å3 calculated by Kolos and Wolniewicz using a variation–perturbation method. The results are also in satisfactory agreement with the experimental values.

Molecular parameters are estimated for the sulfur-fluorine species SF, SF2, SF3, SF5, and S3. A normal-coordinate analysis is performed for SF5 on the basis of a model having D3h symmetry. Recent spectroscopic data for SF4, SF6, S2F2, S2, S8, SOF2, SOF4, and SO2F2, along with the approximate molecular structure data, are used to calculate the thermodynamic functions in the ideal-gas state from 50K to 6000K for thirteen sulfur-fluorine-containing species. Corrections are made to the rigid rotator-harmonic oscillator approximation for anharmonicity only for the diatomic species. Values of the heats of formation at 298.15K are presented for sulfur-fluorine species, along with the relevant references. These thermochemical data and thermodynamic functions are used to calculate the equilibrium composition of a sulfur hexafluoride system. The temperature range is 1000K to 3000K, and the pressure is 1 atm. The results show that the principal sulfur-fluorine species are as follows: SF4 in the temperature range 1000K to 1500K, SF4 and SF3 in the range 1500K to 2000K, and SF2 and SF at temperature above 2000K. (Author)

A Hartree–Fock single‐determinant wavefunction is calculated numerically for the normal state 1 Σ g + of the hydrogen molecule. The one‐electron molecular orbitals in this determinant are expanded up to fourth‐order terms as a product of a series of spherical harmonics and radial wavefunctions about the molecular midpoint of the molecule. The potential field due to the nuclei is expanded in spherical harmonics up to eighth‐order terms and the complete Hartree–Fock equations are set up and solved numerically for the three radial functions occurring in one‐electron molecular orbitals. The numerical technique used to solve the three coupled second‐order differential–integral equations differs from that usually used in atomic calculations. The total numerical energy is −1.13236 a.u. The more accurate Kolos and Roothaan analytic total energy result is −1.13364 a.u.

The cross sections for elasticscattering of low‐energy electrons by molecular hydrogen are calculated by solving numerically the continuum Hartree—Fock equations for an electron moving in the potential field of the neutral homonuclear diatomic hydrogen molecule. Hartree—Fock equations make full allowance for electron exchange. The cross sections for elasticscattering of electrons by molecular hydrogen are calculated with and without the inclusion of electron exchange. The agreement in the exchange approximation with experimental data is very good but disappears completely if exchange is neglected. The method of calculation is based on an expansion of the continuum orbitals up to fourth order as a product of a series of spherical harmonics and radial wavefunctions about the molecular midpoint of the molecule. The potential field of the incident electron due to the nuclei of the neutral molecule is expanded in spherical harmonics up to the eighth order. The continuum orbitals are substituted into the Hartree—Fock equations, integration is performed over angular coordinates, and the resulting infinite set of coupled differential—integral equations is truncated and solved numerically to a self‐consistent solution, by an iterative technique for three radial continuum functions.

In a recent paper Bauer and Wu proposed a model which was self‐consistent for the application of perturbation theory to the problem of calculating the general order of magnitude of cross sections of electron—positive‐molecular‐ion dissociative recombination. In applying their model to the calculation on a hypothetical system of electron capture by molecular hydrogen ions it was necessary to make several approximations, without which it would have been exceedingly difficult to evaluate certain matrix elements. We show here that Monte Carlo methods can be used for evaluating these matrix elements without resorting to approximations other than the model itself. The Monte Carlo method of stratified sampling has been tested successfully on the problem of capture of electrons by molecular hydrogen ions. The dissociative recombination coefficient is found to be of the order of 3×10−8 cm3/sec at room temperature, which is in excellent agreement with reported experimental results.

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Continuous absorption coefficients of chlorine have been calculated at wavelengths between 4000 and 2300 Å for temperatures from 291 to 2400°K. The necessary partial absorption coefficients were calculated on a high-speed electronic digital computer. The resulting total absorption coefficients for chlorine agree well enough with the available experimental data to verify existing theory.