benzaldehyde and methyl radical products. Figure 1 shows some key distances associated with
the two structures. We then performed single-point calculations using the CBS-QB3 composite
approach,
47
which is capable of predicting fairly accurate barrier heights. This procedure
provided our benchmark, electronic energy barrier height of 13.1 kcal/mol. Using unadorned
B3LYP/6-31+G(2d,2p) we obtain a barrier height of 11.7 kcal/mol, which is 1.4 kcal/mol too low.
This value remains unchanged when pair-wise correction schemes for dispersion are employed
because the bond changes involved in TS structure formation are below the cut-off distances
usually employed in such schemes. On the other hand, the DCPs published in reference 19, as
mentioned above, give a barrier height of 20.8 kcal/mol, which is 7.9 kcal/mol too high. Utilizing
the carbon DCP given in Table 1, along with the H- and O-DCP of reference 19, gives a barrier
height of 14.8 kcal/mol, which is too high by 1.7 kcal/mol. We reiterate that this latter result
was achieved by simply guiding the C-DCP optimization toward smaller magnitude coefficients
for Gaussian-type functions as described above and not by inclusion of the cumyloxyl radical
and its
β
-scission transition state in the optimization process.
On the basis of the results for the
β
-scission barrier height, it is clear that our hypothesis
that the C-DCPs from reference 19 over-stabilize the cumyloxyl radical relative to the
β
-scission
transition state compared to both unadorned B3LYP and to CBS-QB3 is correct. The C-DCPs
optimized in this work do appear to offer some preferential stabilization of the transition state,
but to an extent that the predicted barrier height has an error that is on par with that given by
B3LYP without DCPs.
Application of Dispersion-Correcting Potentials to Intermolecular Non-covalently Interacting
Systems
In Tables 2-5, we illustrate the performance of the C-DCPs of the present work, along
with the H, N, and O DCPs taken from reference 19, with respect to the treatment of non-
10
covalently bound (nominally) dimer systems. Table 2 lists the high-level BEs of the S66 set along
with the signed errors of the calculated BEs using the B3LYP-DCP/6-31+G(2d,2p) approach, and
shows that the DCPs perform quite well. In general, the non-CP DCPs give a slight over-binding
(mean signed error, MSE, = 0.09 kcal/mol) of the H-bonded dimers and a slight under-binding in
dispersion-bound dimers (MSE = -0.05 kcal/mol). The dimers in the set that is characterized as
interacting via mixed forces have an MSE = -0.03 kcal/mol.
Table 2
. Signed errors in binding energies (SE) calculated for the non-covalently bonded dimers of the
S66 benchmark set using B3LYP/6-31+G(2d,2p) with dispersion-correcting potentials
without (Non-CP)
counterpoise corrections. The data are ordered according to interaction type, with performance
statistics provided for data in each section. Overall performance statistics for the entire S66 set are
provided at the bottom of the Table. All data are in kcal/mol except percent values.
