extensive calculations that such HF/3–21G and HF/6–31G energy differences
generally give only a rough indication of energy changes. Much better results are
obtained from MP2/6–31G calculations on MP2/6–31G*, HF/3–21G or even
semiempirical AM1 geometries, and it is well worth consulting the book by
Hehre for details [ 154 ]. We shall see in Section 5.5.2.2b that itispossible to obtain
good relative energies “directly”.
To get from relatively low-level calculations the best energy changes, one can
utilizeisodesmic reactions(Greek: “same bond”, i.e. similar bonding on both sides
of the equation). These are reactions in which the number of each kind of bond and
lone pair is conserved. For example
NH 3 þCH 3 NHþ 3 !NHþ 4 þCH 3 NH 2 ð 5 : 187 Þand
CH 2 F 2 þCH 4 !CH 3 FþCH 3 F ð 5 : 188 Þare isodesmic reactions; the first one has on each side six N–H bonds, three C–H
bonds, one C–N bond and one nitrogen lone pair, and the second has on each side
six C–H and two C–F bonds. The reaction
H 3 C#CH 3 þH 2 !2CH 4 ð 5 : 189 Þis, strictly speaking, not isodesmic, since although it has the same number of bonds,
even the same number of single bonds, on both sides: there are six C–H, one C–C,
and two H–H bonds on one side and eight C–H bonds on the other. Note that an
isodesmic reaction does not have to beexperimentallyrealizable: it is an artifice to
obtain a reasonably accurate energy difference by ensuring that as far as possible
errors due to limitations of basis sets and treatment of electron correlation cancel.
This will happen to the extent that particular errors are associated with particular
structural features; electron correlation effects are thought to be especially impor-
tant in calculating energy differences, and such effects tend to cancel when the
number of electron pairs of each kind is conserved. The concept and the name
appear first in a 1970 paper by Hehre et al., where the method was introduced to
calculate enthalpy changes for complete hydrogenation of molecules using the
small basis sets then available [ 155 ], and the approach was applied to many kinds
of reaction in the classic book by Hehre, Pople, Radom and Schleyer [ 1 g]. The
purpose of such reactions is to calculate stabilization or destabilization energies
that can be ascribed to factors like aromaticity [ 156 ], strain [ 157 ], or replacement
of one group by another, say H by F [ 158 ]. In attempts to focus on these factors
and exclude the beside-the-point effect of different bond strengths, a hierarchy of
increasingly finicky reactions grew up, and the nomenclature for isodesmic-type
304 5 Ab initio Calculations