Exchange interaction energy between two one-active electron atoms at large distances

Developed formulas for the exchange interaction energy between two neutral one-active electron atoms interacting at large distances R are presented in terms of known basic integrals obtained from an asymptotic method for the alkali dimers M₂ dissociating to M(ns) + M(ns), M(n′l) + M(n′l), l = 0, …, 3 and M (np) + M(np). Detailed illustrative numerical results are displayed for the molecular states of Na₂ dissociating to the limit Na(3s) + Na(3p). Comparisons with very accurate ab initio results as well as with some available experimental data show that accurate potential energy curves for these excited states may be obtained in a very large range of internuclear distances by connecting ab initio curves for small and intermediate values of R with long-range curves obtained as the sum of usual multipolar Coulombic energy and asymptotic exchange energy.