Computational Chemistry

DH-f0ðCH 3 OHÞ¼DH-f0ðCH 4 ÞþDHf0-ðH 2 OÞþDEisodesmic ð 5 : 196 Þ

whereDEisodesmic¼DEtotal0KðCH 3 OHþH 2 Þ#DEtotal0KðCH 4 þH 2 OÞ
Using G2 values (for comparison with the atomization and the formation
methods):

DEisodesmic¼ð# 115 : 53490 # 1 : 16636 Þ#ð# 40 : 41090 # 76 : 33205 Þh

¼# 116 : 70126 þ 116 :74295 h¼ 0 :04169 h

With this and the experimental 0 K heats of formation of CH 4 and H 2 O[ 197 ]:

DHf0-ðCH 3 OHÞ¼# 66 : 8 # 238 : 92 þ 0 : 04169 ' 2625 :5 kJ mol#^1

¼# 196 :3 kJ mol#^1 :

This is very close to our atomization heat of formation value above (#195.7 kJ
mol#^1 ).
Of the three approaches to calculating heats of formation (atomization, forma-
tion and isodesmic), the atomization has been recommended over the formation
[ 197 ]. However, the isodesmic method with carefully-chosen reactions should be at
least as accurate because of the ability of isodesmic processes to compensate for
basis set and correlation deficiencies (Section 5.5.2.2a). For the calculation of free
energies of formation, which is methodically related to enthalpies of formation but
includes entropies, Bond found in his study of nearly 300 organic compounds that
a kind of isodesmic reaction method gave considerably smaller errors than did
the atomization method: for G3(MP2), 4.1 versus 17.3 kJ mol#^1 , for CBS-QB3,
5.6 versus 13.1 kJ mol#^1 [ 191 ]. In a related paper, these studies were said to be
the “first comprehensive review of computational methodologies used to compute
free energies” [ 192 ]. The atomization approach to enthalpies and free energies
of formation is conceptually the most straightforward, but requires a good high-
accuracy method (CBS-APNO would be very suitable were it not for its size
limitations) because dissociating a molecule into its atoms makes drastic demands
on the accurate treatment of correlation energy. A nice feature of the atomization
method is that, unlike the use of isodesmic reactions, it is amodel chemistry; a term
apparently first used by Pople to denote a sharply-defined procedure that does not
require choosing among various possibilities (like different isodesmic schemes) and
which will thus not vary from one worker to another [ 200 ]. For a collection of
various approaches to calculating heats of formation see [ 201 ].
Note that these calculations of the heat of formation of methanol are notpurely
ab initio (quite apart from the empirical correction terms in the multistep high-
accuracy methods), since they required experimental values of either the heat of
atomization of graphite (atomization and formation methods) or the heat of forma-
tion of methane (formation method). The inclusion of experimental values makes
the calculation of heat of formation with the aid of ab initio methods asemiempiri-
calprocedure (do not confuse the term as used here with semiempirical programs

320 5 Ab initio Calculations