A self-consistent field for methane and its applications

Abstract

An approximate self-consistent field for methane has been obtained by first averaging the proton distribution over all orientations so as to obtain a spherically symmetrical field due to all the nuclei. The eight-electron problem then presented was solved by the usual self-consistent field method without exchange. Rapid convergence to self-consistency was found by using as initial approximations the charge distributions given by Coulson for the two-quantum orbitals of the tetrahedral system, averaged over all orientations. The self-consistent wave functions are used to calculate the charge distribution, energy, diamagnetic susceptibility and polarizability of the molecule and also the van der Waals forces between two molecules. The scattering of slow electrons by the self-consistent field obtained is also investigated in detail and compared with observations of total collision areas and angular distributions for methane. The observed similarity of behaviour between argon and methane in scattering slow electrons is reproduced by the theory provided the same approximation of using the self-consistent field without exchange is employed for each. Comparison of observed and calculated values of the quantities investigated indicate that the methane field is little less satisfactory than the corresponding fields for atoms.