Abstract
The exchange-splitting energy of the lowest gerade and ungerade states of the 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-Schrödinger perturbation theory (the polarization expansion). Our calculations show that very accurate values of 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-Schrödinger perturbation theory, one correctly obtains only the first four terms in the asymptotic expansion of the exchange-splitting energy.
- Received 10 May 2014
DOI:https://doi.org/10.1103/PhysRevA.90.022506
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