Generalized Heitler-London Theory for H₃: A Comparison of the Surface Integral Method with Perturbation Theory

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The generalized Heitler-London (GHL) theory provides a straightforward way to express the potential energy surface of H₃ in terms of Coulomb and exchange energies which can be calculated either by perturbation theory or using the surface integral method (SIM). By applying the Rayleigh-Schroedinger perturbation theory, GHL theory for the quartet spin state of H₃ is shown to yield results equivalent to the symmetrized Rayleigh-Schroedinger version of symmetry adapted perturbation theory (SAPT). This equivalence allows a comparison with the corresponding results obtained by the surface integral method. The surface integral result calculated with a product of atomic wave functions is found to have certain advantages over the perturbation approach.