Essentials of Computational Chemistry

368 10 THERMODYNAMIC PROPERTIES
Energy units
0.0
Computed ∆E
+ZPVE
Computed ∆H 0
+(H 298 − H 0)
Computed ∆H 298
+(H 298 − H 0 ) −298S˚ 298
−298S˚ 298
∆H o f,0 ∆H o f,298 ∆G o f,298
Elemental standard states
Computed ∆G o 298
molecular
calculations
spin-orbit
corrected
atomic
calculations
atomic
experimental
data
Figure 10.1 Graphical illustration of the procedure for predicting enthalpies and free energies of
formation from computation
we would slide the entire inset region down until the computed H298 and experimental
H o
f,298 bars for the atoms overlapped; then, the position of the molecular H298 would be
the predicted value for the molecular H o
f,298
. (Note that, for ease of illustration, all molec-
ular energies are shown here as higher than the corresponding atomic energies, but this is
certainly not a requirement, and negative molecular heats and free energies of formation are
common.) Thus, a theoretical level is chosen for the computation of the electronic energies
of the molecule and its constituent atoms. Either the same or potentially a different level of
theory is chosen for the calculation of the thermal contributions to the enthalpy and entropy.
The difference between the computed quantities for the molecule and its constituent atoms
is then added to the experimental quantity associated with the atoms to determine the final
theoretical value.
The three quantities that are most routinely employed in practice are the 0 K enthalpy
of formation, the 298 K enthalpy of formation, and the 298 K free energy of formation.
Enthalpies of formation are also commonly known as heats of formation. The values of
these quantities for most of the elements in the first two rows of the periodic table are
provided in Table 10.2. Also listed in the table are the spin–orbit corrections for atoms
having P ground states. Experimental data refer to the lower energy spin–orbit state, but
calculations that do not include a (relativistic) spin–orbit operator in the Hamiltonian fail
to account for the energy lowering associated with this coupling. To make the experimental
and computational levels for the atoms consistent with one another (see Figure 10.1) the
spin–orbit correction must be added to theoretical atomic energies.
A technical point associated with Figure 10.1 bears mention. If one overlaps the computed
and experimental atomic values for any one quantity, there is no guarantee (and indeed it is