Essentials of Computational Chemistry

15.6 CASE STUDY: ISOMERIZATION OF PROPYLENE OXIDE 545
point. They then carried out IRC calculations to verify that the TS structure connected in
one direction to the desired product and in the other direction to propylene oxide.
For the isomerizations to allyl alcohol, propanal, and acetone, they found concerted
TS structures that represented the only barrier between reactant and product, and these
structures were predicted to have stable, closed-shell singlet wave functions. However, for
the isomerization to methyl vinyl ether, a pathway involving three TS structures and two
intermediates was identified, with several stationary points having a high degree of biradical
character. To deal with this problem, they used a broken-symmetry SCF procedure (see
Section 8.5.3). Another multistep pathway involving a carbene intermediate was also found
for the isomerization of propylene oxide to methyl vinyl ether, but Dubnikova and Lifshitz
assigned it as being kinetically unimportant based on significantly higher TS energies than
those found for the first pathway.
While the B3LYP/cc-pVDZ level was judged to be a good choice for locating stationary
points, it was not expected to be quantitatively useful in computing activation enthalpies.
For this purpose, single-point CCSD(T)/cc-pVDZ calculations were carried out. Dubnikova
and Lifshitz are not clear on what, if any, special precautions were taken with the biradical
species (i.e., were single-reference HF wave functions somehow generated, or were mixedstate
UHF reference wave functions used?) The potential energies were combined with the
ZPVEs and thermal enthalpic contributions calculated from scaled B3LYP frequency calculations
to determine absolute H values for all species. Absolute entropies S were computed
from the B3LYP geometries and scaled vibrational frequencies. The energies for several
of the stationary points relative to propylene oxide varied by as much as 4 kcal mol −1
comparing CCSD(T) to B3LYP. Although it is not a priori obvious which might be expected
to do better, the general rule that B3LYP somewhat underestimates barrier heights compared
to CCSD(T) suggests the latter will be of greatest utility.
With all activation parameters in hand, Dubnikova and Lifshitz convert them to A and
Ea of the Arrhenius equation (Eqs. (15.30)–(15.32)) to compare to measured values; the
data are provided in Table 15.2. In the case of the rearrangement to methyl vinyl ether, the
data for the highest energy TS structure along the path were used. It is interesting to note
that the comparison of the rate constants derived from the activation parameters at some
particular temperature – 1000 K is shown in Table 15.2 – appears more favorable than a
direct comparison of the activation parameters themselves. This occurs because in every
case the error in activation energy is compensated for by an error in the pre-exponential
factor. That is, if the activation energy is predicted to be too high, which would predict too
Table 15.2 Predicted and measured activation parameters for unimolecular rearrangements of
propylene oxide
Product Source A (sec −1 ) Ea (kcal mol −1 ) k1000 (sec −1 )
Allyl alcohol Experiment 7.9 × 10 12 57.1 2.7
Theory 2.2 × 10 13 60.2 1.6
Methyl vinyl ether Experiment 3.2 × 10 13 58.8 4.7
Theory 1.3 × 10 14 59.3 14.9
Propanal Experiment 2.5 × 10 14 58.5 42.8
Theory 3.5 × 10 13 54.4 47.0
Acetone Experiment 1.7 × 10 14 60.7 9.6
Theory 1.1 × 10 14 54.2 163.3