Chemistry Reference
In-Depth Information
(MP2) or coupled-cluster methods would certainly provide more reliable
results, but they are not appropriate for a tutorial because the computations
become rather time consuming. Furthermore, matching results from correlated
WFT methods can be difficult for users not familiar with the frozen core or
deleted virtual approximations because some software packages correlate all
electrons by default while others exclude core electrons (i.e., adopt the frozen
core approximation) by default. Computations in this work employed spheri-
cal harmonic (5
d
,7
f
, etc.) rather than Cartesian (6
d
,10
f
, etc.) functions,
which gives 32 basis functions per HF monomer.
The geometrical parameters given in the top half of Table 1 for the HF
clusters are from RHF/aug-cc-pVDZ optimizations and have been rounded off
to three significant figures for bond lengths and two significant figures for bond
angles. Although the values differ appreciably from the ''best estimates'' of
Ref. 91, the bond lengths and angles are appropriate for the computational
methods adopted for this tutorial. The electronic energies of these fixed struc-
tures (i.e., single-point energies) listed in Table 1 are from RHF computations
with the aug-cc-pVDZ basis set. Step 1 in this tutorial is to reproduce the RHF/
aug-cc-pVDZ electronic energies in Table 1. Sample input files for several pop-
ular software packages are available online.
92
Rigid Monomer Approximation
Frequently, computational studies of weakly bound clusters employ the
rigid monomer approximation (RMA). The RMA assumes that geometries of
the monomers do not change as they coalesce to form the cluster. Because
the interactions between the fragments of such clusters are, by their very defi-
nition, weak, the electronic structure, and hence the geometry, of the mono-
mers does not change appreciably. This approach can simplify dramatically
theoretical descriptions of the cluster because the intramolecular geometrical
5
a
Table 1
Geometrical Parameters and Electronic Energies of (HF)
n
,
n
¼
1
;
3
Symmetry
R(FF)
R(HF)
y
(HFF)
E
HF
n/a
0.900
n/a
100
:
033816
C
1
v
Fully Optimized Clusters
(HF)
3
C
3
h
2.71
0.910
25
300
:
120482
(HF)
4
C
4
h
2.64
0.915
13
400
:
169746
(HF)
5
C
5
h
2.61
0.916
6.6
500
:
216512
Rigid Monomer Approximation
(HF)
3
C
3
h
2.72
0.900
26
300:120162
(HF)
4
C
4
h
2.65
0.900
13
400
:
168826
(HF)
5
C
5
h
2.63
0.900
7.1
500
:
215113
a
Bond lengths (R) in
˚
, bond angles (
y
) in degrees, and electronic energies (
E
)inE
h
are from
RHF/aug-cc-pVDZ calculations.
