Chemistry Reference
In-Depth Information
In this part of the tutorial, the standard Boys-Bernardi CP correction is
applied to the interaction energies of the HF clusters in Figure 2 using the geo-
metrical parameters in Table 1. Unfortunately, these corrections call for some
rather hideous notation that denotes both the geometry and the basis set
employed for computations on the monomers. The basic goal of the CP cor-
rection is to compute the energy of the monomer in the basis set of the cluster
ð
cluster basis
monomer geom
. This is readily accomplished within the rigid monomer
approximation because the geometry of the monomer is the same in the com-
plex as in the isolated fragment
E
½
HF
Þ
cluster basis
monomer geom
cluster basis
cluster geom
ð
E
½
HF
¼
E
½
HF
Þ
, and the
CP-corrected interaction energy within the RMA is simply
E
CP;RMA
int
cluster basis
cluster geom
¼
E
½ð
HF
Þ
n
nE
½
HF
½
3
Again, this expression for the HF clusters can readily be generalized for the
case of a heterogeneous cluster composed of
N
fragments:
X
N
E
CP;RMA
int
cluster basis
cluster geom
¼
E
½
f
1
f
2
f
3
...
f
N
E
½
f
i
½
4
i
¼
1
Let us use (HF)
3
in Figure 2 to illustrate the procedure. To perform a
CP correction on the bottom HF unit in the trimer, the computations must
place H and F basis functions, but not nuclei or electrons, at the appropriate
coordinates of the other HF monomers at the top of the figure. In most com-
putational chemistry programs this is accomplished with the use of ghost
atoms or ghost orbitals. (Note, dummy atoms are also used to designate
coordinates where nuclei are not present, but dummy atoms do not place
basis functions at those locations.) Frequently, the input file for the CP-
corrected monomer computation is created by modifying the input file
from a cluster calculation such that the charges of all atoms are set to zero
(i.e., the ghost atoms) except those in the monomer of interest. Because each
computational chemistry software programhasitsownsetofkeywordsfor
the specification of ghost atoms and nuclear charge, some sample input files
for the CP corrections to the
ð
HF
Þ
n
interaction energies are available
online.
92
When the monomers are allowed to relax as the complex forms, the
procedure becomes a bit more complicated because there is no straightfor-
ward, consistent manner by which a computation on the optimized mono-
mer can be performed in the basis set of the cluster. Consequently,
E
cluster basis
cluster geom
when the RMA is not employed. In
other words, the energy of the monomer in the cluster basis set is too
high (too positive) because the monomer is not at its optimal geometry.
This overestimation of the monomer energy can be corrected easily by
cluster basis
monomer geom
½
HF
6¼
E
½
HF
