Asymptotics of the exchange-splitting energy for a diatomic molecular ion from a volume-integral formula of symmetry-adapted perturbation theory

The exchange-splitting energy J of the lowest gerade and ungerade states of the H-2(+) molecular ion was calculated using a volume integral expression of symmetry-adapted perturbation theory and standard basis set techniques of quantum chemistry. The performance of the proposed expression was compared to the well-known surface-integral formula. Both formulas involve the primitive function, which we calculated employing either the Hirschfelder-Silbey perturbation theory or the conventional Rayleigh-Schrodinger perturbation theory (the polarization expansion). Our calculations show that very accurate values of J can be obtained using the proposed volume-integral formula. When the Hirschfelder-Silbey primitive function is used in both formulas the volume formula gives much more accurate results than the surface-integral expression. We also show that using the volume-integral formula with the primitive function approximated by Rayleigh-Schrodinger perturbation theory, one correctly obtains only the first four terms in the asymptotic expansion of the exchange-splitting energy.