Results for molecules

Since application of electron correlation methods more elaborate than CCSD(T) would be well-nigh impossible for molecules of practical size, we have restricted ourselves to W[Q5;Q5;TQ5] and W[TQ5;TQ5;TQ5].

Inner-shell correlation contribution, as well as scalar relativistic corrections, were initially computed with the largest basis sets practicable -Ñ in most cases ACV5Z or MTavqz (see Table IV for details).

From a prerelease version of a re-evaluation of the experimental data in the G2/G3 set at the National Institute for Standards and Technology (NIST)[65], we have selected 28 first-and second-row molecules which satisfy the following criteria: (a) the uncertainty in the experimental total atomization energy TAE is on the order of 0.25 kcal/mol or better; (b) the molecules are not known to exhibit severe multireference effects; (c) anharmonic vibrational zero-point energies are available from either experiment or high-level ab initio calculations (see footnotes to Table IV for details).

Geometries were optimized at the CCSD(T)/VQZ+1 level, and to all second-row atoms a complement of two tight d and one tight f function were added in every basis set to ensure saturation in inner-shell polarization effects. In all cases, the exponents were derived as even-tempered series $\alpha\beta^n$ with $\beta=3.0$ and $\alpha$ the highest exponent already present for that angular momentum.

Computed (W[Q5;Q5;TQ5]) and observed results are compared in Table IV. The excellent agreement between theory and experiment is immediately apparent: in many cases, the computed results fall within the already quite narrow experimental error bars. Over the entire sample of molecules, the mean absolute error is 0.24 kcal/mol, with the largest errors being about 0.6 kcal/mol (O₂ and F₂). Restricting our sample to first-row molecules only, we find a mean absolute error of 0.24 kcal/mol, which however gets reduced to 0.17 kcal/mol (maximum error 0.39 kcal/mol for N₂) upon elimination of F₂, NO, and O₂ as having known appreciable nondynamical correlation effects. Over the subset of second-row molecules in our sample MAE is 0.23 kcal/mol (maximum error 0.44 kcal/mol for H₂S); upon elimination of H₂S and SO₂ this is lowered to 0.20 kcal/mol.

It should be noted that these MAEs are comparable to those found by Martin and Taylor[14] for a sample of first-row molecules, yet unlike their study no correction for N-containing bonds is required here.

The possibility that the errors in F₂, NO, and O₂ are actually due to residual basis set incompleteness and/or that the excellent agreement with experiment for the other molecules is actually due to an error compensation involving deficiencies in the predicted basis set limit, was examined by carrying out W[56;56;Q56] calculations for H₂O, F₂, NO, O₂, N₂, HF, and CO. As seen in Table V, the predicted basis set limits do not differ materially from their W[Q5;Q5;TQ5] counterparts, strongly suggesting that the latter expression in fact does reach the basis set limit and that the residual errors are largely due to imperfections in the CCSD(T) method.

While molecules liable to exhibit such errors are readily identifiable from inspection of the largest coupled cluster amplitudes or evaluation of the ${\cal T}_1$ diagnostic[66], an even simpler criterion is apparently offered by the ratio TAE[SCF]/TAE[SCF+val.corr.]. In ``well-behaved'' molecules such as CH₄ and H₂O, the SCF component makes up upwards of two-thirds of the binding energy, while in NO and in O₂ it makes up no more than a third and a fifth, respectively, of the total and F₂ is actually metastable towards dissociation at the SCF level. While for some molecules of this variety we actually obtain excellent results (e.g. ClF), this may be due to error compensation or to the binding energies being fairly small to begin with.

Further inspection of Table IV reveals that some of the `negligible' contributions are in fact quite significant at the present precision level: for instance, Darwin and mass-velocity contributions in SO₂ amount to -0.71 kcal/mol (for SiF₄ a somewhat extravagant -1.88 kcal/mol was found[8]), while atomic spin-orbit splitting in such compounds as Cl₂, ClF, and SO₂ amounts to -1.68, -1.23, and -1.01 kcal/mol, respectively. Inner-shell correlation contributions of 2.36 (C₂H₄), 2.44 (C₂H₂), 1.68 (OCS), and 1.76 (ClCN) kcal/mol speak for themselves; interestingly (as noted previously[23,50]), these effects on the whole do not seem to be more important in second-row than in first-row compounds.

Finally, we shall compare the performance of W[TQ5;TQ5;TQ5] and W[Q5;Q5;TQ5] (Table VI). In general, the results with the three-point valence correlation extrapolation are at best of the same quality as those with the two-point valence correlation extrapolation and in many cases agree less well with experiment. We therefor will use the two-point extrapolation exclusively henceforth.