Chemistry Reference
In-Depth Information
framework for thinking about similar problems. To give just one example, the
conventional wisdom about substituent effects in
interactions is that they
are governed by electrostatic terms, as proposed by Hunter and Sanders
156
on
the basis of a very simple mathematical model and experimental data. How-
ever, direct computations on substituted benzene dimers in our labora-
tory
157,158
show that this picture is oversimplified and cannot explain such
phenomena as the greater binding of sandwich phenol-benzene and
toluene-benzene complexes relative to the benzene dimer. Our explanation
of this situation, which is summarized in a recent review,
159
p
-
p
relied heavily
on analysis tools provided by SAPT.
67
Symmetry-adapted perturbation theory is a well-motivated theoretical
approach to compute the individual components of intermolecular interac-
tions, namely, the electrostatic, induction, dispersion, and exchange-repulsion
terms. The approach is a double-perturbation theory that uses a Hartree-Fock
reference, with a Fock operator
F
written as the sum of Fock operators for the
individual molecules. Both the intramolecular correlation potential (
W
) and
the intermolecular interactions (
V
) are treated as perturbations, so that the
Hamiltonian is expressed as
H
¼
F
þ
V
þ
W
½
17
These perturbations may be treated using second-order perturbation theory,
resulting in an approach that is referred to as SAPT2.
67,160
One can also
include certain higher order terms using coupled-cluster techniques, which
yields the full SAPT. The approximate SAPT2 approach is less expensive com-
putationally, but it appears to give good results for qualitative analysis of
intermolecular interactions.
The SAPT energy may be written as
E
HF
int
E
corr
int
E
int
¼
þ
½
18
where
E
HF
int
is the Hartree-Fock component of the energy, which may be bro-
ken down as
E
ð10Þ
E
ð10Þ
E
ð20Þ
ind
E
ð20Þ
E
HF
int
E
HF
ind
¼
elst
þ
exch
þ
resp
þ
exch
-
ind;resp
þ
d
½
19
;
;
resp
The superscripts in Eq. [19] refer to orders in the two perturbations,
V
and
W
,
respectively. The terms denoted ''resp'' refer to the inclusion of higher order
terms via the coupled-perturbed Hartree-Fock equations.
160
The term
E
ð20Þ
exch
is a cross term involving both exchange and induction. The
ind
;
resp
E
HF
ind
term
resp
includes higher order Hartree-Fock induction as well as
exchange-induction contributions.
d
;
