Asymptotic exchange energies for H₂

An analytical approximation of the asymptotic exchange energy of two interacting hydrogen atoms is obtained. This approximation depends only on functions of the internuclear distance R, which remain bounded as R→ and is derived using the Herring-Holstein surface-integral technique. It is found that, for large R, the exchange energy is O(R3exp(-2R)) in contrast to earlier approximations of O(R2.5exp(-2R)). Our result is similar to the classic Heitler-London expression without the unphysical term O(R3ln(R)exp(-2R)).