Exact calculation of exchange polarization energy for H ion

The exchange polarization energy and higher‐order exchange corrections arising in the second order of the Murrell‐Shaw and Musher‐Amos ( MS ‐ MA ) theory are evaluated analytically for the hydrogen molecule ion. At large internuclear distances the second‐order exchange energy predicted by MS ‐ MA theory behaves like {article}{empty}{document}- 118Re- R{document} . It represents only 80% of the difference between the exact result of Holstein and the asymptotic value of the first‐order exchange energy. The same result holds for the case of Hirschfelder‐van der Avoird ( HAV ) and Hirschfelder‐Silbey ( HS ) theories.