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The Rayleigh–Schrödinger (polarization) perturbation theory without symmetrization is used to calculate the exchange energy of H+2 through the surface integral of Holstein–Herring. It is mathematically proven that the exchange energy series so obtained is exact in the same sense as Herring’s result is exact. It is shown that the contributions to the leading term of the exchange energy series from all orders of polarized wave functions can be calculated exactly. Furthermore, it is explicitly demonstrated that the sum of these contributions converges to the exact value. The rate of convergence is relatively fast. With the first four orders of wave function, virtually 100% of the asymptotic exchange energy is recovered. With the present theory, terms other than the leading one can also be calculated systematically. This is demonstrated by the calculation of the first three terms of the exchange energy series from the first- and second-order wave functions.
Tang et al. (Sat,) studied this question.