Essentials of Computational Chemistry

374 10 THERMODYNAMIC PROPERTIES
generally not isogyric, and this is an important factor in the large change in correlation
energy associated with atomization.
Note that the above discussion can be rephrased in a very transparent way: a good
isodesmic equation should predict a near-zero heat of reaction. The larger the predicted
change in enthalpy, the greater the chance that lower levels of theory will fail to accurately
account for energetic differences between dissimilar bonds. Note that just because a reaction
does predict an overall enthalpy change near zero does not necessarily imply that the bonds
on both sides are similar – large changes in one type may be offset by similarly large
changes in another type – thus a near-zero heat of reaction is a necessary but not sufficient
condition for an ideal isodesmic equation (for a mathematically more sophisticated approach
to employing various isodesmic reactions, see Fishtik, Datta, and Liebman 2003).
These points are illustrated in more detail for the case of singlet p-benzyne, which has
already been the subject of some discussion in preceding chapters. Consider the following
three isodesmic reactions that might be used to determine its heat of formation:
H
H
H
H
H
+
2 CH 4 +
H
H
•
H
H H
H
H H
H
•
•
H
H H
H
+
•
H
•
H H
•
H
H
H
H H + (10.41)
•
2 CH 3 +
H
H
H H
H
H
H
H H
H
H
•
H
H H
H
(10.42)
2 (10.43)
The issue of isogyricity is a bit tricky in this instance, since p-benzyne is a ground-state
singlet, but the coupling between the highest energy pair of electrons is very small. Table 10.3
indicates the heats of reaction computed for each of Eqs. (10.41)–(10.43) and the heats of
formation determined for p-benzyne (using Eq. (10.37) and the experimentally available data
for the methyl radical, methane, acetylene, ethylene, the phenyl radical, and benzene) at the
CASPT2 and CCSD(T) levels; in each case, the equivalent of a basis set roughly triple-ζ
in quality was used. Note that Eq. (10.43) is predicted to be the most nearly thermoneutral
(which seems intuitively reasonable) and using it both levels of theory make predictions
within the experimental error for H o
f,298 (p-benzyne). Equation (10.41) is predicted to be
highly exothermic, because the r.h.s. has an extra π bond in acetylene compared to ethylene,