Chemistry Reference
In-Depth Information
parameters are fixed. For example, by employing the RMA, geometry optimi-
zations of weakly bound clusters need only consider the interfragment degrees
of freedom. For a system as simple as (H
2
O)
2
, the RMA already reduces the
full 12-dimensional problem to a more tractable 6-dimensional intermolecular
potential energy hypersurface.
This approximation is typically valid for clusters held together by hydro-
gen bonds or van der Waals forces because the geometrical distortions tend to
be modest and do not qualitatively change the structure of the monomers. As
can be seen in bottom half of Table 1, fixing the intramolecular R(HF) distance
at 0.900
˚
for the HF trimer, tetramer, and pentamer has relatively little effect
on the optimized interfragment parameters [R(FF) changes by no more than
0.02
˚
(HFF) by less than a degree]. This constraint also has relatively
little effect on the electronic energies of (HF)
3
, (HF)
4
, and (HF)
5
, which
increase by only
and
y
1mE
h
on average.
These limited results demonstrate that the RMA can be accurate even for
relatively strong hydrogen bonds, which can induce some of the largest geome-
trical distortions in weakly bound molecular clusters. The effect of the RMA
on interaction energies will be discussed next. However, the RMA can break
down if large qualitative geometrical changes occurs as the complex forms
(e.g., conformational changes or isomerization).
Supermolecular Dissociation and Interaction Energies
Within the supermolecule approach, the dissociation energy
ð
D
e
Þ
or inter-
action energy
of a cluster is obtained by calculating the energy difference
between the cluster and the noninteracting fragments. This energy difference is
depicted in Figure 3. Note that
D
e
and
E
int
are essentially the same quantity. The
only significant difference is the sign
ð
E
int
Þ
. A more subtle, technical dis-
tinction is that the term
dissociation energy
should be applied only to minima on
the potential energy surface (PES) while
interaction energies
are more general
and can describe any point on the surface.
When using a size-consistent method, the dissociation of homogeneous sys-
tem such as
ð
D
e
¼
E
int
Þ
n
HF] can be deter-
mined by computing the energy of the cluster and the energy of the monomer:
ð
HF
Þ
n
into
n
identical HF monomers [
ð
HF
Þ
n
!
E
int
¼
E
½ð
HF
Þ
n
nE
½
HF
½
1
In the more general case of a heterogeneous cluster composed of
N
frag-
ments (
f
1
f
2
f
3
...
f
N
!
f
1
þ
f
2
þ
f
3
þþ
f
N
), up to
N
þ
1 computations need
to be performed to determine
E
int
or
D
e
:
E
int
¼
E
½
f
1
f
2
f
3
...
f
N
E
½
f
1
E
½
f
2
E
½
f
3
E
½
f
N
X
N
¼
E
½
f
1
f
2
f
3
...
f
N
E
½
f
i
½
2
i
¼1
