First we note that the high-accuracy (G3(MP2), CBS-QB3, and CBS-APNO;
Section 5.5.2.2b) values are close to the reported measured reaction enthalpies,
with two qualifications: the highly accurate CBS-APNO method (mean absolute
deviation from experiment, 2.2 kJ mol"^1 )[ 83 ] was not applicable to the H 2 þCl 2
reaction because of its inability to treat Cl, and this method indicates that the
reaction enthalpy of the 2H 2 þO 2 reaction is closer to"477 kJ than to the
reported"484 kJ mol"^1. We will judge the functional/basis set combinations by
comparison with values of"184 (H 2 þCl 2 ) and ca."480 kJ mol"^1 (2H 2 þO 2 ).
In all cases the 6-311þþG(2df,2p) basis performs better, usually dramatically
so, than the 6-31G Only M06 gives reasonably good results for both reactions
("180 cf."184 and"490 cf. ca."480 kJ mol"^1 ), with the 6-311þþG(2df,2p) basis
set. Even with the bigger basis, TPSS performs poorly. These calculations show that
contrary to what might be inferred from [ 38 , 58 ], the 6-31G basis cannot be used for
generalthermochemistry with any of these functionals. For certain classes of
reactions, however, 6-31G* may be acceptable, e.g. the Diels-Alder reaction [ 84 ],
and bond dissociation (Table7.3). Only tests with model systems can show if a
particular basis can be expected to be satisfactory for the desired purpose.
There are many studies in the literature of the ability of DFT to handle molecular
thermodynamics (thermochemistry). Martell et al. tested six functionals on 44
atomization energies and six reactions and concluded that the best atomization
energies were obtained with hybrid functionals, but slightly better reaction enthal-
pies were obtained with non-hybrid ones [ 85 ]. St-Amant et al. found that gradient-
corrected functionals gave good geometries and energies for conformers; the
dihedrals were on average within 4of experiment and the relative energies were
nearly as accurate as those from MP2 [ 52 ]. Scheiner et al. found that, as for
geometries, Becke’s original three-parameter function (also called ACM, adiabatic
Table 7.4 Reaction enthalpies (kJ mol"^1 ), calculated with three functionals and two basis sets,
6-31G and 6-311++G(2df, 2p), and with three high-accuracy methods (but CBS-APNO is unable
to handle Cl species). The calculated reaction enthalpies follow from the calculated 298 K product
enthalpies minus the reactant enthalpies
Method Reaction
H 2 þCl 2 !2 HCl H 2 þO 2 !2H 2 O
B3LYP
6-31G " 169 " 344
6-311++G(2df, 2p) " 182 " 447
M06
6-31G " 171 " 401
6-311++G(2df, 2p) " 180 " 490
TPSS
6-31G "152.5 " 295
6-311++G(2df, 2p) " 162 " 393
G3(MP2) " 184 " 479
CBS-QB3 " 182 " 474
CBS-APNO Unavailable " 477
Experimenta " 184 " 484
aExperimental heats of formation of HCl and H
2 O: [^82 ].
7.3 Applications of Density Functional Theory 479