SCF, IEPA-PNO, CEPA-PNO, and PNO-CI calculations have been performed for the molecules N2 and F2 at their experimental equilibrium distances with two basis sets, a "small" basis that contains one d set per atom and a "standard" basis with two d sets and one f set. Potential curves of these molecules are calculated with the small basis sets. The molecules C2H2 and C2H4 are calculated with the small basis (which contains additionally one p set on H) and with a "hydrocarbon" basis that is smaller in the s,p part, but includes the same polarization functions. For C2H6 in both its staggered and eclipsed forms only the hydrocarbon basis is used. The computed correlation energies are analyzed in terms of quantities defined in Part I, in particular, in terms of the IEPA pair correlation energies ∈μIEPA and the error ΔEIEPA of the IEPA energy. A comparison is made between the results in the canonical and the localized representations and a partially localized description in which the σ-π separation is preserved. The IEPA error is rather large for all of these molecules, especially for N2. The IEPA error in the localized representation changes smoothly in the series C2H2 to C2H6; whereas in the canonical representation it varies by almost two orders of magnitude. A new geometry optimization for staggered and eclipsed ethane is carried out, since previous optimizations turned out to be unsatisfactory. Correlation, however, does not affect the geometries significantly; its effect on the rotational barrier is very small. For N 2 and F2 in the neighborhood of the equilibrium distances the CEPA potential curves turn out to be very close to the exact ones (and yield good equilibrium distances and force constants); whereas the PNO-CI curves (and, of course, more so the SCF and IEPA curves) are unacceptable. At large internuclear distances, where the weight of the leading determinant in the full wavefunction becomes smaller than ∼0.8 the CEPA curve is unsatisfactory.