Chemistry Reference
In-Depth Information
Table 2
Interaction Energies of (HF)
n
,
n
¼
3
5 Computed at the RHF/aug-cc-pVDZ
Level with (
E
CP
int
) and without (
E
int
) a Counterpoise Correction
a
E
int
b
cluster basis
cluster geom
monomer basis
cluster geom
c
E
½
HF
E
½
HF
E
CP
int
Fully Optimized Clusters
(HF)
3
49
:
97
100
:
034072
100
:
033695
47
:
00
(HF)
4
90
:
53
100
:
034030
100
:
033543
85
:
41
(HF)
5
124
:
53
100
:
034011
100
:
033506
117
:
90
Rigid Monomer Approximation
(HF)
3
49
:
13
100
:
034175
d
46
:
30
(HF)
4
88
:
12
100
:
034287
d
83
:
17
61
a
The monomer electronic energies for the counterpoise correction are also listed (
E
120
:
86
100
:
034292
114
:
(HF)
5
d
½
HF
).
Electronic energies are in E
h
, and the interaction energies are in kJ mol
1
.
b
Obtained via application of Eq. [1] or [2] to energies in Table 1.
c
Obtained via application of Eq. [7] or [8] to energies in Tables 1 and 2.
d
Equal to monomer energy from Table 1 which implies
E
RLX
¼
0 in Eq. [7].
is readily illustrated with Figure 3. Although the RMA does not affect the
asymptote associated with the noninteracting fragments, it does shift the bot-
tom of the well up because the cluster is not allowed to reach its optimal geo-
metry, which necessarily decreases the magnitude of
E
int
and
D
e
.
Counterpoise Corrections for Basis Set Superposition Error
The procedure outlined in Eq. [2] introduces an inconsistency when
small, finite basis sets are used. Effectively, the monomers are using a larger
basis set when the computation is performed on the cluster than when the
computation is performed on the isolated monomer fragment. In the cluster
calculation, monomer A can utilize the basis functions on monomers B, C,
etc. When the computation is performed on the isolated monomer A, those
basis functions are no longer available. This inconsistency was noted as early
as 1968
94
and later termed basis set superposition error (BSSE).
95
A tutorial
covering the theory and practice of basis set superposition errors has appeared
earlier in this topic series.
96
The most common procedure to correct for BSSE
is the counterpoise (CP) procedure developed independently by Jansen and
Ros in 1969
97
and Boys and Bernardi in 1970.
98
BSSE and CP corrections
are discussed in greater detail below, and this portion of the tutorial merely
demonstrates how to perform the necessary computations. Before proceeding,
however, it is worth noting that BSSE is not limited to weakly interacting sys-
tems. It is a concern in any type of dissociation process (such as breaking a
covalent bond) where the energies of fragments are compared to those of
the whole system.
