Chemistry Reference
In-Depth Information
Fragments
f
1
+f
2
+f
3
+
...
+f
N
E
int
D
e
= -
E
int
Cluster
f
1
f
2
f
3
... f
N
Intermolecular Separation
Figure 3
Interaction energies (
E
int
) and dissociation energies (
D
e
) are simply the energy
difference between the cluster and the isolated fragments.
For example, to obtain
E
int
for the HF
CH
3
OH trimer requires four
separate computations:
E
[HF],
E
[H
2
O],
E
[CH
3
OH], as well as the electronic
energy of the cluster. The number of computations can be reduced if some of
the fragments are identical (e.g., HF
H
2
O
H
2
O
HF).
Interaction Energies: Rigid Monomers vs. Fully Optimized Clusters
The interaction energies reported toward the left side of Table 2 for the
HF clusters were calculated with the electronic energies from Table 1 and
Eq. [2] (which reduces to Eq. [1] for these homogeneous HF clusters). A simple
conversion factor was used to convert
E
int
from
E
h
to kilojoule per mole
(1
E
h
5 kJ mol
1
). Step 2 of this tutorial is to calculate the interaction
energies on the left side of Table 2.
Because the RMA had relatively little effect on the electronic energies of
the HF clusters (Table 1), it is not surprising that the approximation has only a
modest effect on the interaction energies (Table 2). For all three clusters, the
magnitude of
E
int
and
E
CP
2625
:
int
decreases slightly when the RMA is employed.
Comparison of the values for
E
int
from the top of Table 2 to those at the bot-
tom reveals that the change does not exceed 3% [
49
:
97 vs.
49
:
13 or 1.7%
for (HF)
3
,
86 or
2.9% for (HF)
5
], which is tolerable for many applications. For systems with
even smaller cluster-induced geometrical perturbations, such as
90
:
53 vs.
88
:
12 or 2.7% for (HF)
4
and
124
:
53 vs.
120
:
-type van
der Waals interactions, the RMA has almost no discernable effect on the inter-
action energies.
93
Note that the RMA must, by definition, decrease the magnitude of the
interaction energy (for variational electronic structure methods). This result
p
