reactions spun out of control. One encounters the terms homodesmotic, hyperhomo-
desmotic, semihomodesmotic, quasihomodesmotic, homomolecular homodesmotic,
isogeitonic, and isoplesiotic, to cite some. To “expose the widespread confusion
over such classes of equations” and bring order and rigor to what might well be
called a chaotic proliferation (to borrow a term [ 68 ]), Wheeler, Houk, Schleyer and
Allen extensively reviewed the subject and made recommendations [ 159 ]. Here we
can sidestep technicalities and the menagerie of terms and simply call this general
class of reactions isodesmic. We shall look at examples of two applications of
isodesmic reactions, namely, calculation of:strain energy, and ofaromatic stabili-
zation energy(ASA), which measures stabilization by aromaticity or destabiliza-
tion by its opposite, antiaromaticity. We can take the ASA as being the time-
honored resonance energy, RE.
Strain energy. Molecular strain is a concept nicely grasped by trying to build
with rigid plastic components a model of a molecule with small angles, like
cyclopropane, and noting that the bonds break. This old concept of angle strain
[ 160 ] has been expanded to encompass torsional and steric strain [ 161 ]. We’ll
consider two examples of angle strain, that in cyclopropane and that in norbornane.
We (conceptually) open cyclopropane to propane by using two Hs from two ethanes
and join the resulting ethyl groups to make butane; we use ethane rather than
methane to effect cleavage because with ethane the bond we make, in butane, and
the bond we break, in cyclopropane, are formally quite similar, in contrast to ethane
cf. cyclopropane. Following Khoury et al. [ 157 ] we use B3LYP/6–31G* (a DFT
method,Chapter 7) energies/geometries without ZPE; this energy is shown under
each species:
H 3 C H 3 C–117.89525–79.83002–119.14423–158.45804CH 3 CH 3Release of strain must correspond to an exothermic process and we take strain
energy as being positive, so the strain energy is the energy of the reactants minus
that of the products:
SE(cyclopropane)¼[#117.89525þ2(#79.83002)]#[#119.14423#158.45804]
¼#277.55529þ277.60227¼0.04698¼123 kJ mol#^1We’ve converted atomic units (hartrees) to kJ mol#^1 by multiplying by 2,626.
Khoury et al. report a value of 121 kJ mol#^1 (29.0 kcal mol#^1 ), similar to the
experimental (115 kJ mol#^1 ) and to other calculated values, which they cite.
5.5 Applications of the Ab initio Method 305