Essentials of Computational Chemistry

10.5 TECHNICAL CAVEATS 375
Table 10.3 Predicted heats of reaction and p-benzyne heats of formation
(kcal mol −1 ) using isodesmic Eqs. (10.41)–(10.43)
Isodesmic equation
Theory Quantity (10.41) (10.42) (10.43) Experiment
CASPT2 H o
rxn,298 −68.1 −10.8 4.4
H o
f,298 129.6 136.1 138.2 138.0 ± 1.0
CCSD(T) H o
rxn,298 −76.0 −15.1 5.4
H o
f,298 137.5 140.5 137.2 138.0 ± 1.0
and this degrades the performance of CASPT2. The CCSD(T) level, on the other hand,
captures enough correlation energy (or enjoys some fortuitous cancellation of errors) that
this equation gives an accurate heat of formation as well. Finally, Eq. (10.42), which involves
exchanging aromatic C–H bonds for sp 3 C–H bonds causes both levels of theory to fall
outside the experimental error bars by about 1 kcal mol −1 .
10.5 Technical Caveats
10.5.1 Semiempirical Heats of Formation
Recall that semiempirical methods were parameterized in such a way that the computed
electronic energies were equated with heats of formation, not computed enthalpies. Thus,
when a semiempirical electronic structure program reports a 298 K heat of formation for
AM1, for instance, the reported value derives from adding the atomization energy E to
the experimental 298 K heats of formation of the atoms. Inspection of Figure 10.1 indicates
that this will differ from the rigid-rotor-harmonic-oscillator computed result by ZPVE and
the differential thermal contributions to the enthalpy of the molecule compared to the atoms.
As a result, the ‘correct’ way to compute a heat of formation with a semiempirical
Hamiltonian is somewhat ambiguous. Since experimental data were used to optimize the
parameters, the ZPVE and differential thermal contributions have been absorbed into the
semiempirical parameters, so one is not necessarily improving things by adding these
quantities post facto. On the other hand, to the extent ZPVE and thermal contributions
are included in the parameters, it is in a very average way, and by no means consistent
with rigorous statistical mechanics. In the end, individual investigators must decide for
themselves, on the basis of what they are studying, whether to compute thermodynamic
variables at the semiempirical level or simply to accept the electronic energies as having the
status of enthalpies.
10.5.2 Low-frequency Motions
In the limit of a particular vibration going to zero, we see from Eq. (10.1) that it ceases to
contribute to the zero-point vibrational energy. However, it is less obvious what happens to