CBS-RAD method

Unfortunately, WE is a computationally expensive procedure and therefore not easily accessible for the larger systems listed in Tables 6.9 and 6.10. The CBS-RAD procedure, however, demonstrates close agreement with WE. For example, the mean absolute deviation between the WE and CBS-RAD BDEs is 1.6 kJ/mol while the largest absolute deviation is only 3.3 kJ/mol. Therefore, the CBS-RAD method represents a suitable secondary benchmark level for the assessment of the perfor-... 

Clearly, the Wl and CBS-RAD methods give quite accurate BDEs for substituted methanes while the G3(MP2)-RAD and RB3LYP meth-... 

Calculated barriers for a selection of cyanomethyl radical additions are presented in Tables 6.19 and 6.20. The CBS-RAD method performs particularly well (MAD of 1.3 kJ/mol) for the selected cyanomethyl radical additions. However, the other levels of theory show somewhat larger mean absolute deviations (5.9 - 14.8 kJ/mol). With the exception of CBS-RAD (MD of -0.9 kJ/mol), all levels give higher barriers than those observed experimentally (MD of +5.9 to +14.8 kJ/mol). The correlation with experiment (R2 = 0.76 - 0.85) is somewhat poorer than that for the methyl and hydroxymethyl radical additions (Tables 6.15 - 6.18). 

For example, the UMP2 level of theory performs poorly, the RB3LYP approach predicts higher (by ca. 5-6 kJ/mol) barriers than its UB3LYP counterpart, and the G3(MP2)-RAD level of theory gives a higher barrier than the CBS-RAD method. One noticeable difference is the absence of a significant basis-set effect in the DFT calculations on the intramolecular addition. 

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 Wl, gives accurate BDEs, and this observation carries over to the RSEs calculated at this level. The MAD from experiment for the Wl method is 3.1 kJ/mol. The Wl RSEs tend to be slightly lower than those determined from experimental data [MD(Exp.) of -2.2 kJ/mol]. 

Barriers and enthalpies are very sensitive to the level of theory. Where possible, high level composite procedures should be used for the prediction of absolute reaction barriers and enthalpies, and of these methods the RAD variants of G3 provide the best approximations to the higher level Wn methods (when the latter cannot be afforded) (37). It should also be noted that the (empirically based) spin-correction term in the CBS-type methods appears to be introducing a considerable error to the predicted reaction barriers for these reactions and, imtil this is revised, these methods should perhaps be avoided for these reactions (37). 

The acid and base values of the surface functional groups of the samples were determined by Boehm s titration method [50]. To determine the acid value, O.lg of the sample was added to 100 ml of 0.1 M NaOH solution and the mixture was shaken for 24 h. The solution was then filtered through a membrane filter (pore size = 0.24 pm, nylon) and titrated with 0.1 M HCl. Likewise, the base value was determined by the reverse titration of the acid value. The specific surface areas (Sbet. [51]) of the samples were determined by gas adsorption. Physical adsorption of gases was used to characterize the CBs support, and the adsorbate used was N2 at 77 K with automated adsorption apparatus (Micromeritics, ASAP 2400). Prior to adsorption measurements, the samples were outgassed at 298 K for 6 h to obtain a residual pressure of less than 10 torr in high vacuum. To analyze the functional groups of CBs, the treated CBs were subjected to infrared (IR) spectroscopy (FTS-165 spectrometer, Bio-Rad Co.). 

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