THE INTERACTION POTENTIAL OF H-2(+) CALCULATED FROM THE EXACT 1ST-ORDER WAVE-FUNCTION OF THE POLARIZATION PERTURBATION-THEORY

The interaction potential of the H-2+ molecular ion is calculated with the exact first order wave function of the unsymmetrized Rayleigh-Schrodinger perturbation theory. An earlier asymptotic theory for the exchange energy based on the Holstein-Herring surface integral is extended to small distances by including the denominator of the expression. This exchange energy is modulated by the overlap integrals and combined with the polarization energy in the prescribed way of the generalized Heitler-London theory to give the ground state energy. Every term is evaluated analytically. The results are compared with the exact values of the potential and they agree to better than 5% over the entire range of distances from zero to infinity.