Asymptotic Exchange Coupling of Two Hydrogen Atoms

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=-1. 641R^5{2}e^-2R+O (R^2e^-2R), where J is in atomic units (2Ry) and R is in Bohr units.