Computational Chemistry

unsatisfactory for the reaction of ozone with ethyne and ethene, and CBS-QB3 was
singled out for special cautioning; the reaction did yield to a kind of extrapolation
method, the “reference focal point approach” [ 219 ]. Ozone is, of course, a problem
molecule (Section 5.5.1), and CBS-QB3 worked well for other cycloadditions [ 193 ].
The results of the calculations are summarized in Table5.11(calculated from the
data in Table5.12). For each of the four computational levels, the free energy of
activation was used to calculate the rate constant and halflife using Eq. (5.197/
5.198). Table5.11reveals the usefulness of this simple way of calculating unim-
olecular reaction rates. All four methods yield for each reaction approximately
the same activation free energy: for CH 3 NC!CH 3 CN, ca. 160 kJ mol#^1 , for
CH 2 ¼CHOH!CH 3 CHO, ca. 235 kJ mol#^1 , and for cyclopropylidene!allene,
ca. 20 kJ mol#^1. The qualitative, and even semiquantitative, predictions for the
stability of each compound are the same for all four methods: for CH 3 NC, a halflife
of ca. 10^15 –10^16 s, for CH 2 ¼CHOH a halflife of ca. 10^26 –10^29 s, and for cyclopro-
pylidene, a halflife of ca. 10#^10 # 10 #^9 s. Note however, that using Eq. (5.197), a

Table 5.12 Free energies of reactant and transition state (hartrees) and free energy of activation
DG{(hartrees/kJ mol#^1 ) by four methods; hartrees were converted to kJ mol#^1 by multiplying by
2,626. The rate constants and halflives calculated from these values are given in Table5.11
Reaction MP2/6–31G B3LYP/6–31G G3(MP2) CBS-QB3
CH 3 NC!CH 3 CN #132.26990 #132.69425 #132.53125 #132.51216
#132.20547 #132.63289 #132.47102 #132.45098
DG{0.06443/ DG{0.06136/ DG{0.06023/ DG{0.06118/
169.2 161.1 158.2 160.7
CH 2 ¼CHOH!
CH 3 CHO

#153.28714 #153.77339 #153.60839 #153.59006
#153.19837 #153.68802 #153.51725 #153.49883
DG{0.08877/ DG{0.08537/ DG{0.09114/ DG{0.09123/
233.1 224.2 239.3 239.6
Cyclopropylidene
!allene

#116.09212 #116.51746 #116.35895 #116.33697

#116.08301 #116.50839 #116.35211 #116.32789

DG{0.00911/ DG{0.00907/ DG{0.00684/ DG{0.00908/

23.9 23.8 18.0 23.8

Table 5.11 Calculated (298 K) rate constantskr(s#^1 ) and halflivest1/2(s) fromkr¼(kBT/h)eDG/RT/
kr¼(6.22' 1012 )e#DG{/2.478(Eqs. (5.197/5.198)) andt1/2¼ln2/kr¼0.693/kr, using free energies
of activationDG{(kJ mol#^1 ) from four methods. The free energies of reactants and transition states
that were used to calculate the free energies of activation are given in Table5.12
Reaction MP2/6–31G B3LYP/6–31G* G3(MP2) CBS-QB3
CH 3 NC!CH 3 CN kr1.50' 10 #^17 kr3.63' 10 #^16 kr1.17' 10 #^15 kr4.26' 10 #^16
t1/24.6' 1016 t1/21.9' 1015 t1/25.9' 1014 t1/21.6' 1015
DG{169.2 DG{161.1 DG{158.2 DG{160.7
CH 2 ¼CHOH!
CH 3 CHO

kr8.72' 10 #^29 kr3.17' 10 #^27 kr7.15' 10 #^30 kr6.33' 10 #^30
t1/27.95' 1027 t1/22.2' 1026 t1/29.7' 1028 t1/21.1' 1029
DG{233.1 DG{224.2 DG{239.3 DG{239.6
Cyclopropylidene
!allene

kr4.03' 108 kr4.19' 108 kr4.36' 109 kr4.19' 108

t1/22.5' 10 #^9 t1/22.4' 10 #^9 t1/21.6' 10 #^10 t1/22.4' 10 #^9

DG{23.9 DG{23.8 DG{18.0 DG{23.8

5.5 Applications of the Ab initio Method 327