experiment [ 80 ]). Althoughfrequenciesmust be calculated with the same method
(HF, MP2, etc.) and basis set as were used for the geometry optimization,ZPEs
from a particular method/basis may legitimately be used to correct energies
obtained with another method/basis. The only calculations that give reasonable
agreement with the experimental ethane C–C dissociation energy (reported at
377 kJ mol#^1 [ 81 ]) are the correlated (MP2) ones, 370 and 363 kJ mol#^1 with
different basis sets; because of error in the experimental value the two MP2 results
may be equally good. The Hartree–Fock values (248 and 232 kJ mol#^1 ) are very
poor, even (especially!) when the very large 6–311þþG(3df,3p2d) basis is used.
Accurate calculation of reaction energies is now usually done with one of the
multistep methods like G3 or a CBS method (Section 5.5.2.2b).
This inability of Hartree–Fock calculations to model correctly homolytic bond
dissociation is commonly illustrated by curves of the change in energy as a bond is
stretched, e.g. Fig.5.19. The phenomenon is discussed in detail in numerous
expositions of electron correlation [ 82 ]. Suffice it to say here that representing the
wavefunction as one determinant (or a few), as is done in Hartree–Fock theory, does
not permit correct homolytic dissociation to two radicals because while the reactant
(e.g. H 2 ) is a closed-shell species that can (usually) be represented well by one
determinant made up of paired electrons in the occupied MOs, the products are two
radicals, each with an unpaired electron. Ways of obtaining satisfactory energies,
(^01234)
200
400
600
800
1000
HF / 6-31G
MP2 / 6-31G
H H distance, Å
energy (relative
to equilibrium bond
length energy)
kJ mol–1
Fig. 5.19 Dissociation curves (change in energy as the bond is stretched) for H 2 , from HF/6–31G
and MP2/6–31G calculations. The equilibrium bond lengths are reasonable (HF/6–31G, 0.730;
MP2/6–31G, 0.737 (cf. experimental, 0.742), but only the MP2 curve approximates the actual
dissociation behavior of the molecule
260 5 Ab initio Calculations