On the Approximate Treatment of Exchange Symmetry in Second-Order Interaction Energies

The second‐order energy expression from Hirschfelder–Silbey perturbation theory is rewritten in a form which facilitates a comparison with the conventional Rayleigh–Schrödinger theory. It is shown that the approximate procedure used by McQuarrie and Hirschfelder to evaluate the second‐order energy for the ${\text{1sσ}}_g$ and ${\text{2pσ}}_u$ states of H₂⁺ is equivalent to approximating the first‐order Rayleigh–Schrödinger function by a symmetry‐projected combination of unsymmetric polarization functions. The addition of a correction term to the values calculated by McQuarrie and Hirschfelder leads to substantial improvement of their results.