PNO–CI (pair natural orbital configuration interaction) and CEPA–PNO (coupled electron pair approximation with pair natural orbitals) calculations of molecular systems. II. The molecules BeH2, BH, BH3, CH4, CH−3, NH3 (planar and pyramidal), H2O, OH+3, HF and the Ne atom

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Abstract
PNO−CI and CEPA−PNO calculations are performed in a systematic way for the molecules BeH2, BH, BH3, CH4, CH−3, NH3, H2O, H3O+, HF, and the neon atom. Two types of Gaussian basis sets are used: the ’’small basis,’’ which contains one set of polarization functions on the heavy atom and one on the hydrogen atoms, and the ’’standard basis,’’ which contains two d and one f set on the heavy atom and two p sets on the hydrogen atoms. For neon, in addition, a ’’large’’ basis is used. The improvement of the energy due to the different polarization functions is discussed in detail. The computed correlation energies are analyzed in terms of quantities defined in Paper I, in particular, in terms of the IEPA (independent electron pair) correlation energies EIEPAμ and the error ΔEIEPA of the IEPA approximation. The pair interaction contributions ΔEμν to EIEPA are usually smaller in absolute value in the localized than in the canonical representation. In the canonical description ΔEμν values of either sign occur so that because of a partial cancellation, ΔEIEPA is usually smaller in absolute value than for localized pairs where almost all ΔEμν are positive. Nevertheless the localized representation turns out to be generally preferable, mainly because it is more economical. The correlation energies accounted for in calculations that give rigorous upper bonds are in the order of ?85% of the exact correlation energies for the standard basis sets and ?70% as obtained with the small basis sets. The force constants and equilibrium geometries of BH, BeH2, and NH3 are calculated using the small basis sets. The role of the correlation energy for the inversion barrier of NH3 (and the isoelectronic species CH3− and OH3+) is discussed in detail.