The calculation of exchange forces: General results and specific models

In order to clarify questions about the calculation of the exchange energy of a homonuclear molecular ion, an analysis is carried out of a model problem consisting of the one-dimensional limit of H2+. It is demonstrated that the use of the infinite polarization expansion for the localized wave function in the Holstein–Herring formula yields an approximate exchange energy which at large internuclear distances R has the correct leading behavior to O(e−R) and is close to but not equal to the exact exchange energy. The extension to the n-dimensional double-well problem is presented.