Comparison between molecular orbital and surface integral calculations of the exchange energy for the homonuclear dimer ions He-2(+), Li-2(+) and Be-2(+)

The exchange energy, defined as half of the energy splitting of the gerade and ungerade states of a molecular ion, is investigated by molecular orbital calculations and by the surface integral method. Numerical results of He-2(+), Li-2(+), and Be-2(+) are obtained through restricted Hartree-Fock, unrestricted Hartree-Fock and localized Heitler-London type calculations. The results of the surface integral method are analytical expressions which depend only on the ionization energy. While the approaches are completely different, the results are generally in good agreement. Discrepancies are highlighted with the hope of promoting further interplay of these complementary methods. (C) 1995 American Institute of Physics.