Benzene as a Stress Test of the Method

As an illustrative example of stress-testing W1 and W2 theory, we shall consider the benzene molecule. The most accurate calculation we were able to carry out is at the W2h level the rate-determining step was the direct CCSD/cc-pV5Z calculation (30 electrons correlated, 876 basis functions, carried out in the D h subgroup of DGh) which took nearly two weeks on an Alpha EV67/667 MHz CPU. Relevant results are collected in Table 2.5. 

Secondly, let us consider the gaps bridged by the extrapolations. For the SCF component, that gap is a very reasonable 0.3 kcal/mol (0.03 %), but for the CCSD valence correlation component this rises to 5 kcal/mol (1.7 %) while for the connected triple excitations contribution it amounts to 1 kcal/mol (3.7 % - note however that a smaller basis set is being used than for CCSD). It is clear that the extrapolations are indispensable to obtain even a useful result, let alone an accurate one, even with such large basis sets. 

Inner-shell correlation, at 7 kcal/mol, is of quite nontrivial importance, but even scalar relativistic effects (at 1 kcal/mol) cannot be ig- 

Reference geometry B3LYP/cc-pVTZ CCSD(T)/cc-pVQZ 

As for the difference of about 0.4 kcal/mol between the old-style and new-style SCF extrapolations in Wlh and W1 theories, comparison with the W2h SCF limits clearly suggests the new-style extrapolation to be the more reliable one. (The two extrapolations yield basically the same result in W2h.) This should not be seen as an indication that the Eoo + A/L5 formula is somehow better founded theoretically, but rather as an example of why reliance on (aug-)cc-pVDZ data should be avoided if at all possible. Users who prefer the geometric extrapolation for the SCF component could consider carrying out a direct SCF calculation in the extra large (i.e. V5Z) basis set and applying the Eoo + A/BL extrapolation to the medium , large , and extra large SCF data. 

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