Asymptotic Exchange Coupling of Two Hydrogen Atoms

Abstract

The energy difference $2J$ between the lowest singlet and triplet states of the hydrogen molecules measures the exchange coupling of the spins of the two atoms. It is known that the Heitler-London expression for $2J$ is inaccurate, even at large interatomic distances $R$, because it takes inadequate account of the mutual avoidance of the exchanging electrons. Gor'kov and Pitaevski have recently shown that the leading term in the expression for $2J$ at large $R$ can be evaluated exactly. The procedure involves treating the interaction of the two atoms as a perturbation on a product of single-atom wave functions. However, their final result differs by a numerical factor, and in the remainder term, from that of an independent though basically identical calculation of ours. It is shown here that the correct result is: $2J=\ensuremath{-}1.641{R}^{\frac{5}{2}}{e}^{\ensuremath{-}2R}+O({R}^{2}{e}^{\ensuremath{-}2R})$, where $J$ is in atomic units (2Ry) and $R$ is in Bohr units.