Basis set effect at the Hartree Fock level

Figure 11.1 shows the bond dissociation curves at the HF level with the STO-3G, 3-21G, 6-31G(d,p), cc-pVDZ and cc-pVQZ basis sets.

The total energy drops considerably upon going from the STO-3G to the 3-21G and again to the 6-31G(d,p) basis. This is primarily due to the improved description of the oxygen 1s-orbital. The two different types of DZP basis sets, 6-31G(d,p) and cc-pVDZ, give very similar results, and the improvement upon going to the cc-pVQZ basis is relatively minor.

More important than the total energy is the shape of the curve, i.e. the energy relative to the equilibrium value which is shown in Figure 11.2.

The minimal STO-3G basis increases much more steeply than the other basis sets, while the 3-21G is slightly too low in the AR range of 0.3-1.3A. Considering that the STO-3G and 3-21G basis set have the same number of primitive GTOs (Section 5.4.1), it is clear that uncontraction of the valence orbitals greatly improves the flexibility. The 6-31G(d,p), cc-pVDZ and cc-pVQZ basis sets give essentially identical curves, i.e. improvement of the basis set beyond DZP has a very minor effect at the HF level. Note also that the total energy for the 6-31G(d,p) basis is ~0.05au (~130kJ/mol, Figure 11.1) above the HF limit, but this error is constant to within a few kJ/mol over the whole range.

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