G3/B3LYP

Figure 3.4 Effect of inclusion of higher level corrections on the mean absolute deviations of G3, B3LYP, and BLYP methods for the enthalpies of formation in the G3/99 test set.

G3//B3LYP [27], its performance was very similar to that of G3 theory though it may be useful in cases where the MP2 theory is deficient for geometries. Another variation involves the use of CCSD(T)/6-31G(d) instead of QCISD(T)/6-31G(d) to evaluate the contribution of higher order correlation effects. The resulting G3(CCSD) method [28] has an accuracy very similar to that of G3 theory and may be useful in cases where the QCISD(T) method is not available or deficient. 

G3//B3LYP (also called G3B3 or G3B) is a modification of G3 that uses geometries and zero-point vibrational energies found from B3LYP/6-31G calculations instead of from MP2/6-31G and HF/6-31G calculations [A. G. Baboul, J. Chem. Phys., 110,7650 (1999)]. G3//B3LYP is faster than G3 and just as accurate as G3. 

There is a significant increase in deviations of the data obtained with DFT methods for the heats of formation in the new G3-3 subset. The B3LYP and BLYP mean absolute deviations for the G3-3 subset are about two times larger than that in the G2/97 test set (8.21 kcal/mol vs. 3.08 kcal/mol and 13.32 kcal/mol vs. 7.25 kcal/mol, respectively). 

Figure 3.3 Mean absolute deviations for G3, G3S, and B3LYP as a function of the average number of electron pairs in the G2-1, G2-2, and G3-3 subsets (enthalpies of formation only).

The mean absolute deviations of LDA method are much larger (216.5 kcal/mol vs. 91.9 kcal/mol). The increase in the deviations is largest for the hydrocarbons and their substituted derivatives. For B3LYP, the mean absolute deviations increase from 2.92 kcal/mol (G2/97) to 9.64 kcal/mol (G3-3 subset) for the hydrocarbons, and from 2.22 kcal/mol (G2/97) to 7.15 kcal/mol (G3-3 subset) for substituted hydrocarbons. The B3LYP mean absolute deviation for the non-hydrogen species increases from 5.15 kcal/mol to 10.99 kcal/mol. An example of the increase in error with molecular size is evident from comparison of results for propane and n-octane. The B3LYP enthalpy deviates from experiment by -1.46 kcal/mol for propane and -14.04 kcal/mol for n-octane. The G3 deviations for these cases are only 0.33 kcal/mol and 0.88 kcal/mol, respectively. The error per bond in G3 theory is about 0.035 for both propane and n-octane, whereas for B3LYP it is 0.146 and 0.51 kcal/mol, respectively. 

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. 

A high-level ab initio study of related reactions of alkyl nitrates (RO—NO2) at the G3 and B3LYP/6-311-I— -G(d,p) levels has revisited the reactions of alkyl peroxy radicals (ROO") with nitric oxide. Activation barriers for the isomerization of RO—ONO to RO—NO2 were found to be too high to account for the formation of alkyl nitrates... 

Calculated relative energies for a small selection of structural isomers are compared with experimental values and with the results of G3 calculations in Table 6-11. These have been drawn from a much more extensive set of comparisons found in Appendix A6 (Tables A6-24 to A6-31). Mean absolute errors from the full set of comparisons are collected in Table 6-12, and a series of graphical comparisons involving Hartree-Fock, EDF1, B3LYP and MP2 models... 

Bond separation energies from Hartree-Fock models with STO-3G, 3-2IG, 6-3IG and 6-311+G basis sets, local density models, BP, BLYP, EDFl and B3LYP density functional models and MP2 models all with 6-3IG and 6-311+G basis sets and MNDO, AMI and PM3 semi-empirical models are compared with values based on G3 energies and on experimental thermochemical data in Table 6-13. These have been abstracted from a much larger collection found in Appendix A (Tables A6-36 to A6-43). A summary of mean absolute deviations from G3 values in calculated bond separation energies (based on the full data set) is provided in Table 6-14. 

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