In summary, all of the methods shown in Tables 6.6 - 6.8 give good overall performance for the prediction of radical heats of formation (MADs of 2.1 - 4.5 kJ/mol). For species displaying significant spin contamination, methods based on a UMP2 reference geometry may give heats of formation for radicals that show larger-than-normal deviations from experiment. The RAD procedures give improved performance in such circumstances.

5.BOND DISSOCIATION ENERGIES

Bond dissociation energies (BDEs) provide a measure of both the reactivity of a compound (with respect to homolytic bond rupture) and the stability of the corresponding radical. There have been many theoretical investigations of BDEs for a wide variety of species [36]. In particular, the C–H BDE for a substituted methane is given by the enthalpy change for the reaction:

Bond dissociation energies for a selection of substituted methanes, calculated at a range of levels [23], are compared with experimental values [37] in Tables 6.9 and 6.10. Also listed are mean absolute deviations (MADs) and mean deviations (MDs) from experimental values [e.g. MAD(Exp.)] and from CBS-RAD [e.g. MD(CBS-RAD)].

The results in Table 6.9 show that the high-level procedure generally produces close agreement with experiment, particularly for species with small error bars (< 5 kJ/mol). Several radicals (

to within the given experimental uncertainties. Cyanomethyl and carboxymethyl radicals show the largest deviations between theory and experiment (8.6 and 15.1 kJ/mol, respectively). The mean absolute de-

therefore not easily accessible for the larger systems listed in Tables 6.9 and 6.10. The CBS-RAD procedure, however, demonstrates close agree-

viation is only 3.3 kJ/mol. Therefore, the CBS-RAD method represents a suitable secondary benchmark level for the assessment of the perfor-

ods give acceptable performance. The absolute values of bond dissociation energies obtained from UB3LYP and RMP2 single-point energies are somewhat less satisfactory.

6.RADICAL STABILIZATION ENERGIES

Understanding the stabilizing or destabilizing influence of different substituents on radicals can be particularly important in controlling chemical processes that involve such radicals. Such effects have been studied extensively with electronic structure methods [36].

The radical stabilization energy (RSE) of a substituted methyl radical is generally defined as the difference between the C–H bond dissociation energy in methane and the C–H BDE in the substituted methane

This quantity is equivalent to the enthalpy change for the isodesmic reaction:

Radicals with a positive RSE can therefore be considered stabilized relative to

It is often assumed that there will be substantial cancellation of errors associated with the calculation of stabilization energies via reactions such as (6.2). However, this is not always the case. In particular, it has recently been shown [21, 34] that stabilization energies calculated for the cyanomethyl and cyanovinyl radicals show large variation with level of theory. For these situations, methods such as UMP2 perform very poorly because errors associated with spin contamination in the reactant and product radicals are very different and do not cancel.

Representative radical stabilization energies for the cyanomethyl radical [23, 34, 38] are displayed in Table 6.11. It can be seen that the high-level compound methods all predict RSEs within the narrow range of 31.9 - 37.9 kJ/mol. These values are reasonably close to but slightly lower than the value derived from recent experimental data of 41.74.8 kJ/mol (suggesting that the experimental value may be slightly overestimated). On the other hand, the UMP2/6-311+G(3df,2p) approach gives the wrong sign for the RSE (-5.7 kJ/mol), i.e. it wrongly predicts a slight destabilizing effect for the cyano substituent. This problem arises because of the artificially high energy calculated within the UMP2 approximation for cyanomethyl radical due to spin contamination. Similar

shortcomings are observed (but to a lesser extent) at the UMP4 (8.8 kJ/mol) and PMP2 (22.2 kJ/mol) levels of theory. Methods such as RMP2, UQCISD, UQCISD(T), UCCSD(T) and URCCSD(T) all perform reasonably well for the RSE of cyanomethyl radical.

RSEs for a broader selection of substituted methyl radicals, as well as MADs and MDs from experiment and CBS-RAD values, are presented in Tables 6.12 and 6.13. We noted in the previous section that our highest-level procedure, namely gives accurate BDEs, and this observation carries over to the RSEs calculated at this level. The MAD from experiment for the method is 3.1 kJ/mol. The RSEs tend to be slightly lower than those determined from experimental data [MD(Exp.) of -2.2 kJ/mol].

At the CBS-RAD level of theory, the MAD from experiment is only 2.4 kJ/mol. Here once again, the CBS-RAD procedure tends to give slightly lower RSEs than experiment [MD(Exp.) of -1.9 kJ/mol].