Multipole structure of exchange polarization energy for H 2 + Ion

The exchange polarization energy for the H 2 + ion is expressed as an infinite sum of its angular components. At large internuclear distances R , a particular l ‐component, referred to as induced 2 l ‐ pole exchange energy , behaves asymptotically like\documentclass{article}\pagestyle{empty}\begin{document}$$- \frac{4}{{\left({l + 1} \right)\left({l + 2} \right)\left({l + 3} \right)\left({l + 4} \right)}}Re^{ - R}$$\end{document}For larger R this suggests a rather slow l −4 rate of convergence of the series. However, as contrasted to the analogous expansion for the induction energy the convergence speeds up considerably with decreasing internuclear separation. It is also shown that at sufficiently large R a given induced 2 l ‐pole exchange energy can be computed with a high accuracy using a polarization function obtained with neglect of charge overlap effects. Near the bottom of the van der Waals minimum over 99% of the exchange polarization energy can be produced using this simplified form of the polarization function.