available may replace G3(MP2). Within these confines, the question will then be
whether to use G3(MP2) or CBS-QB3. Which one, if either, has the edge can be
found only by comparing calculations with experiment for the property or reaction
of interest. Here are a few examples of studies using these methods. Pokon et al.
compared CBS-QB3, CBS-APNO, and G3 (this latter being presumably similar to
G3(MP2) for such calculations) for the enthalpies and free energies of gas-phase
deprotonation reactions and found that “The combination of high accuracy and
relatively low computational cost makes the CBS-QB3 method the best choice of
the three” (all three gave a mean absolute deviation from experiment of about 1 kcal
mol#^1 , i.e. about 4 kJ mol#^1 )[ 190 ]. Bond compared G2, G2(MP2), G3, G3(MP2),
G3(B3), G3(MP2B3), CBS-QB3, and DFT for the calculation of enthalpies and free
energies of formation of nearly 300 organic compounds and found G3 to be best with
G3(MP2) somewhat worse; CBS-QB3 was also accurate but more limited in the size
of molecules it could handle [ 191 ]. The mean absolute deviations for those three
methods using an isodesmic reaction (see Section 5.5.2.2c) were (kJ mol#^1 ):
Enthalpy Free energy
G3 3.1 3.7
G3(MP2) 3.2 4.1
CBS-QB3 4.5 5.6Other work by Bond also showed little difference between enthalpies of forma-
tion by isodesmic-type reactions from the G3 and the G3(MP2) methods [ 192 ].
Ess and Houk found CBS-QB3 to be satisfactory for the activation enthalpies of
pericyclic reactions [ 193 ], which is noteworthy because the high-accuracy methods
we are discussing were designed to give good results for thermodynamics, not
kinetics; the problem here lies in the parameterization, particularly for paired and
unpaired spins, the number of which might alter along a reaction coordinate [ 194 ].
In fact, CBS-QB3 has been explicitly stated to be suitable for activation energies
[ 186 ]. An indication of the speed and size capacities of G3(MP2) and CBS-4M,
CBS-QB3, and CBS-APNO is given by Table5.10.
5.5.2.2c Thermodynamics; Calculating Heats of Formation
The heat of formation (enthalpy of formation) of a compound is an important
thermodynamic quantity, because a table of heats of formation of a limited number
of compounds enables one to calculate the heats of reaction (reaction enthalpies) of
a great many processes, that is, how exothermic or endothermic these reactions are.
The heat of formation (enthalpy of formation) of a compound at a specified
temperatureTis defined [ 195 ] as the standard heat of reaction (standard reaction
enthalpy) for formation of the compound atTfrom its elements in their standard
states (their reference states). By the standard state of an element we mean the
thermodynamically stablest state at 10^5 Pa (standard pressure, about normal atmo-
spheric pressure), at the specified temperature (the exception is phosphorus, for
5.5 Applications of the Ab initio Method 313