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8.REACTION ENTHALPIES

The addition of radicals to alkenes is used to assess the performance of various levels of theory in the prediction of radical reaction enthalpies. Results for the addition of methyl radical to ethylene (Table 6.24) [41] show that the higher-level methods perform well in predicting the reaction enthalpy; values range from -105.6 to -111.5 kJ/mol compared with the corrected experimental value of -113.1 kJ/mol. The AM1 method greatly overestimates the exothermicity while the UB3LYP/6- 311+G(3df,2p) level of theory, which performs well for the reaction barrier, significantly underestimates the exothermicity. The RB3LYP values

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are very similar to their UB3LYP counterparts for each of the selected basis sets.

Very few directly measured experimental enthalpies are available for methyl radical additions to substituted ethylenes. Reaction enthalpies are therefore normally estimated from other known thermochemical quantities (e.g. C–H BDEs), which often have considerable uncertainties [3], and the derivation generally involves the use of additivity approximations [42, 45]. Therefore, theory may be able to provide more accurate values for these enthalpies. Tables 6.25 and 6.26 present reaction enthalpies determined at several levels of theory and compared with the experimental estimates.

At the UB3LYP level of theory, the MADs range from 8.8 kJ/mol for the 6-31G(d) basis set to 11.7 kJ/mol for the 6-311+G(3df,2p) basis set. Interestingly, the UB3LYP/6-31G(d) level of theory generally over-

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estimates the exothermicity (MD of -8.8 kJ/mol) while the UB3LYP functional used in conjunction with larger basis sets underestimates the experimental exothermicities. The CBS-RAD method gives the best performance with an MAD of 4.7 kJ/mol. The G3(MP2)-RAD method (MAD of 6.1 kJ/mol) performs somewhat better than the UB3LYP functional but also tends to underestimate the exothermicity (MD of 5.7 kJ/mol). In all cases the correlation with experiment is quite good ( spanning the range of 0.87 - 0.91).

9.CONCLUDING REMARKS

The amount of experimental information available regarding the thermochemistry of radicals is limited because of the inherent instability of such species. Therefore, theory has a potentially useful complementary role to play. However, the theoretical determination of radical thermochemistry is not without its own difficulties, and thus a careful assessment of accuracy needs to be carried out before theoretical procedures can be used routinely in this area. Steps in this direction are described in this chapter.

An important general conclusion is that unrestricted procedures such as UMP2 may perform poorly in the case of radicals for which there is significant spin contamination in the underlying UHF wavefunction. Under such circumstances, it is safest to avoid the use of the UHF and UMP2 approximations entirely. The B3LYP procedure appears to be much less sensitive to spin contamination. It is recommended in place of the UHF and UMP2 methods for geometry and frequency predictions in cases where the still more reliable CCSD(T) procedure is not feasible.

High-level compound methods such as Gn, CBS, and generally perform well in describing radical thermochemistry. However, the reliability of the standard Gn and CBS procedures for radical thermochemistry may generally be improved through modifications (designated RAD) that involve UB3LYP instead of UHF or UMP2 geometries and/or frequencies, RMP2 in place of UMP2 in the additivity steps (of Gn), and CCSD(T) in place of QCISD(T) as the ultimate correlation level. The modified procedures generally perform well in the test cases examined, which include the calculation of heats of formation, bond dissociation energies, radical stabilization energies, and barriers and reaction enthalpies for radical addition reactions.

The B3LYP procedure, while not as reliable for thermochemistry as its higher-level counterparts, is much less expensive computationally and is generally a reasonable cost-effective alternative.

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