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specting the group energy differences. In contrast, as shown in Fig. 3.5, the error per bond remains constant at about 0.04 kcal/mol for G3 theory. Isodesmic or homodesmotic schemes may be necessary for improving the accuracy of B3LYP results for such large molecules [66, 67].

7.CONCLUDING REMARKS

G3 theory is a general predictive procedure for thermochemical calculations of molecules containing firstand second-row atoms. It has been recently extended to molecules containing third-row non-transition elements. While being computationally more efficient, it constitutes a significant improvement in accuracy over G2 theory. Overall, G3 theory has a mean absolute deviation of 1.07 kcal/mol for the G3/99 test set compared to 1.01 kcal/mol for the G2/97 test set. G3 theory does about as well for the larger hydrocarbons and substituted hydrocarbons in the expanded test set as it does for those in the G2/97 test. However, it does poorly for some of the new and larger non-hydrogen systems in the G3/99 test set such as and which have errors of 6 - 7 kcal/mol. Part of the source of errors in the G3 results for the non-hydrogen species is traced to the MP2(fu)/6-31G* geometries used in G3 theory. The use of experimental geometries reduces the deviations in those molecules, but they still remain around 3 - 4 kcal/mol. The G3 variants that are based on reduced perturbation orders, G3(MP2) and G3(MP3), perform in a similar manner.

. G3 theory based on multiplicative scaling of the energy terms (G3S) instead of the additive higher-level correction has a mean absolute deviation of 1.08 for the G3/99 test set, an increase from 0.99 for the G2/97 test set. As in the case of G3 theory, the increase is largely due to the new non-hydrogen species in the test set. However, systems such as the highly strained molecule perform poorly with the scaled methods.

. G3X theory corrects for most of the shortcomings of G3 theory for larger molecules. It includes better geometries as well as g polarization functions on second-row atoms to correct for the deficiencies of G3 theory for hypervalent molecules. G3X theory gives significantly better agreement with experiment for the G3/99 test set of 376 energies. Overall, the mean absolute deviation from experiment decreases from 1.07 kcal/mol (G3) to 0.95 kcal/mol (G3X). The largest improvement occurs for non-hydrogens for which the mean absolute deviation from experiment decreases from 2.11 to 1.49 kcal/mol. G3X has a mean absolute deviation of 0.88 kcal/mol for the 222 enthalpies of formation in the G3/99 test set. Unlike G3 theory, G3X does not decrease in accu-

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racy for the larger molecules added to the G2/97 test set to form the G3/99 test set. The related G3SX methods have the advantage of being suitable for studies of potential energy surfaces.

The density functional methods assessed in this study (B3LYP, BLYP, and LDA) all perform much worse for the enthalpies of formation of the larger molecules in the G3/99 set. This is due to a cumulative effect in the errors for the larger molecules in this test set. The errors are found to be approximately proportional to the number of pairs of electrons in the molecules but the methods are not improved significantly when a higher-level correction such as that used in G2 or G3 theory is added the DFT methods. Further correction schemes may be necessary to improve the performance of density functional methods for large molecules.

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