Calculation of the dipole moment of the carbon-hydrogen bond in methane by the Thomas-Fermi method

Abstract

To compute the dipole moment of the CH bond in methane, the pyramids formed by the planes bisecting the HCH bond angles were taken as elements of symmetry. Each pyramid encloses a carbon-hydrogen bond and the four close-pack to form the methane molecule. To symplify the problem, the pyramid was replaced by a cone of equal volume. The Thomas-Fermi equation was solved for the potential within this cone subject to the appropriate boundary conditions, on the IBM Type 701 electronic data processing machines, using the extrapolated Liebmann method. Boundaries were chosen about each nucleus on which the superposition solution was used. The equation was solved for carbon alone and then for carbon-hydrogen within the cone. The dipole moment was taken as the difference between the two in accordance with views recently expressed by Shull and by Coulson. The value obtained was 2.8D C+H-. The large magnitude is attributed to the poor description of the system by the statistical theory.