Computational Chemistry

single-point and optimized energies of butanone are#231.68593 and#231.68818 h,
a difference of 0.00225 h (2.3 mh) or 6 kJ mol#^1 , not large bearing in mind that
special high-accuracy calculations (Section 5.5.2.2) are needed to reliably get
relative energies to within, say, 10 kJ mol#^1. Single-point calculations would also
giverelativeenergies similar to those from the use of optimized correlated geome-
tries if the incremental deviations from the optimized-geometry energies were
about the same for the two species being compared (e.g. reactant and TS for an
activation energy, reactant and product for a reaction energy).
The method can occasionally give not just quantitatively, but qualitatively
wrong results. The HF and correlated surfaces may have different curvatures: for
example a minimum on one surface may be a transition state or may not exist (may

E‡MP2

0 geometry

MP2

HF

GTS, MP2

GTS, HF

single-point

calculation

single-point

calculation

absolute ab

initio energy

(negative)

Gmin, MP

Gmin, HF

E‡HF

Fig. 5.20 Hartree–Fock and MP2 (or other correlated) potential energy surfaces. “Absolute” (as
distinct from relative) ab initio energies are negative, and correlated energies are lower (more
negative) than Hartree–Fock energies. The geometries of the minima and the transition states are
designated Gminand GTS. Activation energies are denoted byE{. HF activation energies are, as
shown, usually bigger than MP2. In this diagram a single-point MP2 calculation on a stationary
point at the HF geometry gives the same energy as would be obtained by optimizing the species at
the MP2 level; this is often true, but single-point MP2 relative energies would be similar to
optimized-MP2 relative energies even if it were not so, provided the incremental energy change
were about the same for the two species being compared (e.g. reactant and TS for an activation
energy, reactant and product for a reaction energy)

266 5 Ab initio Calculations