in several program suites. Ventura et al. found DFT to be better than CCSD(T)
(a high-level ab initio method, Section 5.4.3) for studying the thermochemistry of
compounds with the O–F bond [ 89 ].
Regarding the application of functionals to thermochemistry, more recent refer-
ences than those in the preceding paragraph (which run from 1993 to 2000) are
three thorough compilations [ 44 – 46 ] (all 2007). References [ 44 , 45 ] give the
impression that for best results one should select a functional based on quite specific
requirements. Reference [ 46 ] indicates that of the functionals we have considered
(M06 and the related M05 were not examined there), with Pople basis sets TPSS
with 6-31G, 6-31+G or 6-31++G gives among the smallest average heat of
formation (Figs. 10 and 11) errors: ca. 5 kcal mol"^1 , ca. 20 kJ mol"^1 , and these
values were similar with Dunning basis sets. This is surprising in view of the poor
performance of TPSS with the H 2 /Cl 2 and H 2 /O 2 reactions (Table7.4). B3LYP
gave similar heat of formation errors (ca. 20 kJ mol"^1 ) with 6-31G but capri-
ciously ca. 60 kJ mol"^1 with 6-31+G or 6-31++G, and with the biggest Dunning
basis its error was ca. 20 kJ mol"^1. There is a lack of regularity in the thermochem-
ical results from DFT calculations, and a user would do well to first explore
results from model systems related to the particular project at hand. Reliably
accurate thermochemistry still requires some largely (these incorporate empirical
corrections and sometimes DFT optimizations) ab initio high-accuracy method
(Section 5.5.2.2b).
7.3.2.2b Kinetics
Consider the reaction profiles in Fig.7.2. Analogously for geometries in Sec-
tion7.3.1, for energies we first content ourselves with some simple comparisons,
because a reliable experimental barrier is available only for the CH 3 NC reaction
(the measured activation energy for HNC!HCN may represent a wall-catalyzed
process), and experimental reaction free energies are available only for the
H 2 C¼CHOH and HNC reactions (but the HNC value of"42 kJ mol"^1 versus
the value of"59 kJ mol"^1 by the normally reliable G3(MP2) method casts doubt on
the accuracy of the former enthalpy); see [ 70 ]. However, for all these reactions the
qualitative situation is known: ethenol, HNC and CH 3 NC are much less stable than
their isomers CH 3 CHO, HCN, and CH 3 CN and the barriers inhibit the uncatalyzed
isomerization at room temperature (the threshold barrier for room temperature
stability is ca. 100 kJ mol"^1 ); cyclopropylidene has never been observed and a
reasonable inference is that it isomerizes rapidly (perhaps even at 77 K) and
essentially completely to allene. The energies in Fig.7.2are simply 0 K energy
differences with ZPE correction – inChapter 5, in connection with Fig. 5.21, we
saw that for these reactions the 0 and 298 K energies (activation energies, enthal-
pies, free energies) are very similar. Even with this modest (6-31G*; compare the
discussion in Section7.3.1for Fig.7.3and the effect of bigger basis sets on
geometry) basis set all the results are in qualitative agreement with experiment.
7.3 Applications of Density Functional Theory 481