with and without the use of electron correlation methods, for processes involving
homolytic cleavage, are discussed further inSection 5.5.2.
There are basically three approaches to dealing with electron correlation:
explicit use of the interelectronic distances as variables in the Schr€odinger equation,
treatment of the real molecule as a perturbed Hartree–Fock system, and explicit
inclusion in the wavefunction of electronic configurations other than the ground-
state one. Using interelectronic distances explicitly quickly seems to become
mathematically intractable and is currently limited to atoms and molecules that
are very small [ 83 ]. The other two methods are general and very important: the
perturbation approach is used in the very popular Møller–Plesset^4 methods, and the
use of higher electronic configurations in the wavefunction forms the basis of
configuration interaction, which in various forms is employed in some of the
most advanced ab initio methods currently used for dealing with electron correla-
tion. A powerful method that is becoming increasingly popular and incorporates
mathematical features of the perturbation and higher-electronic-state methods, the
coupled-cluster approach, is also described.
5.4.2 The Møller–Plesset Approach to Electron Correlation..........
The Møller–Plesset (MP) treatment of electron correlation [ 84 ] is based on pertur-
bation theory, a very general approach used in physics to treat complex systems
[ 85 ]; this particular approach was described by Møller and Plesset in 1934 [ 86 ] and
developed into a practical molecular computational method by Binkley and Pople
[ 87 ] in 1975. The basic idea behind perturbation theory is that if we know how to
treat a simple (often idealized) system then a more complex (and often more
realistic) version of this system, if it is not too different, can be treated mathemati-
cally as an altered (perturbed) version of the simple one. Møller–Plesset calcula-
tions are denoted as MP, MPPT (Møller–Plesset perturbation theory) or MBPT
(many-body perturbation theory) calculations. The derivation of the Møller–Plesset
method [ 88 ] is somewhat involved, and only the flavor of the approach will be
given here. There is a hierarchy of MP energy levels: MP0, MP1 (these first two
designations are not actually used), MP2, etc...., which successively account more
thoroughly for interelectronic repulsion.
“MP0” would use the electronic energy obtained by simply summing the
Hartree–Fock one-electron energies (Section 5.2.3.6.4, Eq.5.84). This ignores
interelectronic repulsion except for refusing to allow more than two electrons in
the same spatial MO. “MP1” corresponds to MP0 corrected with the Coulomb and
exchange integralsJandK(Eqs.5.85and5.90), i.e. MP1 is just the Hartree–Fock
energy. As we have seen, this handles interelectronic repulsion in an average way.
(^4) Møller–Plesset: the Norwegian letter ø is pronounced like Frencheuor Germano€.
5.4 Post-Hartree–Fock Calculations: Electron Correlation 261