The van der Waals Interaction of Hydrogen Atoms

Abstract

The van der Waals interaction energy of two hydrogen atoms at large internuclear distances is discussed by the use of a linear variation function. By including in the variation function, in addition to the unperturbed wave function, 26 terms for the dipole-dipole interaction, 17 for the dipole-quadrupole interaction, and 26 for the quadrupole-quadrupole interaction, the interaction energy is evaluated as ${W}^{\ensuremath{'}\ensuremath{'}}=\ensuremath{-}\frac{6.49903{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{6}}\ensuremath{-}\frac{124.399{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{8}}\ensuremath{-}\frac{1135.21{e}^{2}}{{a}_{0}{\ensuremath{\rho}}^{10}}\ensuremath{-}\ensuremath{\cdots},$ in which $\ensuremath{\rho}=\frac{R}{{a}_{0}}$, with $R$ the internuclear distance. Some properties of the functions ${F}_{\ensuremath{\nu}\ensuremath{\lambda}\ensuremath{\mu}}(\ensuremath{\xi},\ensuremath{\vartheta},\ensuremath{\phi})$, which are orthogonal for the volume element $\ensuremath{\xi}d\ensuremath{\xi}sin\ensuremath{\theta}d\ensuremath{\theta}d\ensuremath{\phi}$, are discussed, and their usefulness in atomic problems is pointed out.