In lieu in a full repertoire of experimental results, for a quantitative comparison of
the effect on these four reactions of varying basis set size with the B3LYP, M06 and
TPSS functionals, the CBS-QB3 barriers and reaction energies were calculated
(Table7.6). Reservations have been expressed about the reliability of such methods
for barriers, because they are parameterized for thermodynamics, and specifically
one might wonder about the effect of changes of the number of paired spins along the
reaction coordinate [ 90 ]. Nevertheless, despite a caveat [ 91 ] the CBS-QB3 method
has been explicitly recommended for barriers [ 92 , 93 ]. We shall assume that as well
as the reaction energies, the CBS-QB3 barriers also are reliable for these four
reactions. Comparison of the values in Table7.6(CBS-QB3) and those in Table7.7
(B3LYP, M06 and TPSS functionals and 6-31G*, 6-311þG* and 6-311þþG
(2df,2p) basis sets) reveals the effect on barriers and reaction energies of increasing
basis set size with the three functionals. Table7.7also extends the information in
Fig.7.3for relative energies, shown in the Figure only for B3LYP, to M06 and
TPSS, and may be also be compared with Table 5.11, which shows free energies of
activation for the H 2 C¼CHOH, CH 3 NC and cyclopropylidene reactions, using
MP2/6-31G, B3LYP/6-31G*, G3(MP2), and CBS-QB3. The values in Tables7.6
and7.7are 298 K relative free energies, while as discussed above those in Figs. 7.2
and7.3are the very similar (for these reactions) relative ZPE-corrected 0 K energies.
Table 7.7 Barriers and reaction energies (relative energies for reactant, transition state, product)
calculated for the B3LYP, M06, and TPSS functionals using the 6-31G*, 6-311þG**, and
6-311þþG(2df,2p) basis sets (shown respectively from top to bottom line). The barrier is the
free energy of activation at 298 K and the reaction energy is the free energy of reaction at 298 K, in
kJ mol"^1. Cf. Table7.6and Table 5.11
Functional Reaction (cf. Table7.6)
H 2 C¼CHOH HNC CH 3 NC Cyclopropylidene
B3LYP 0, 224,"67.9 0, 123,"67.0 0, 161,"99.9 0, 23.6," 282
0, 231,"47.8 0, 123,"58.2 0, 158,"99.7 0, 17.8," 286
0, 232,"45.0 0, 124,"56.2 0, 160,"97.5 0, 16.4," 289
M06 0, 218,"69.5 0, 125,"58.5 0, 160,"97.1 0, 45.2," 246
0, 223,"52.5 0, 125,"53.8 0, 160,"97.7 0, 40.1," 251
0, 224,"50.0 0, 127,"50.7 0, 163,"93.3 0, 40.3," 253
TPSS 0, 205,"70.5 0, 119,"70.5 0, 151,"97.9 0, 19.7," 274
0, 211,"52.5 0, 118,"63.7 0, 147,"98.9 0, 15.5," 276
0, 212,"50.2 0, 118,"62.0 0, 149,"96.8 0, 13.7," 280
Table 7.6Barriers and reaction energies calculated by CBS-QB3, for comparison with the DFT
and MP2 results in Figs.7.2and7.3and Table7.7. The barrier is the free energy of activation at
298 K and the reaction energy is the free energy of reaction at 298 K, in kJ mol"^1. Cf. Table 5.11
Reaction Barrier Reaction energy
CH 2 ¼CHOH!CH 3 CHO 240 "45.6
HNC!HCN 125 "58.5
CH 3 NC!CH 3 CN 161 "98.6
Cyclopropylidene!allene 23.8 " 279
482 7 Density Functional Calculations