3.1 Single-point Calculations

Using the methods described in Section 2, single-point calculations were done for various diatomic systems in the vicinity of the equilibrium geometry using basis sets of varying sizes. In the table below we compare the relative quality of full core and frozen core results with the validity of criterion (8) averaged over the different basis sets. For each molecule except Hydrogen we refer to two tables, the first for full core and the second for frozen core data.

System	Table	Criterion (8)	Errors wrt. CCSD(T)
B2	1, 2	not satisfied	large
BH	3, 4	well satisfied	small
C2	5, 6	not satisfied	large
F2	7, 8	satisfied	acceptable
H2	9	well satified	small
HF	10, 11	well satified	small
N2	12, 13	sometimes satisfied	acceptable or large
NH2 -	14, 15	sometimes satisfied	acceptable or large
OH-	16, 17	mostly satisfied	small or acceptable

From the data presented in these tables, the following conclusions may be drawn

• Criterion (8) gives good guidance, for which system and with which basis set the perturbation-derived methods yield good or acceptable errors wrt. to CCSD(T) calculations with the same basis set that are more expensive than MP4 calculations. It also seems to help to identify cases like N₂ for which single-reference methods are problematic.
• The $\Pi$2 estimator produces in many cases the best energies. This holds especially for basis sets of double zeta and valence double zeta quality. Adding polarization functions is not always improving the (relative) performance.
• For basis sets containing diffuse functions, the F4 estimator seems to be preferable to the $\Pi$2 estimator.

These conclusions seem to be valid for both frozen core and full core calculations.