Chemistry Reference
In-Depth Information
Table 3
Unique Many-Body Electronic Energies
(in
E
h
)
for
(HF)
n
,
n
¼
3
5
Computed at the RHF/aug-cc-pVDZ Level
E
½
f
i
f
j
E
½
f
i
f
k
E
½
f
i
f
j
f
k
E
½
f
i
f
j
f
l
E
½
f
i
f
j
f
k
f
l
Fully Optimized Clusters
a
Þ
3
b
ð
HF
200
:
072923
—
—
—
—
Þ
4
b
ð
HF
200
:
072748
200
:
069328
300
:
116161
—
—
Þ
5
b
ð
HF
200
:
072425
200
:
068570
300
:
115003
300
:
109494
400
:
160289
Rigid Monomer Approximation
c
Þ
3
b
ð
HF
200
:
073038
—
—
—
—
Þ
4
b
ð
HF
200
:
073100
200
:
069755
300
:
116246
—
—
Þ
5
b
ð
HF
200
:
072990
200
:
069093
300
:
115406
300
:
110113
400
:
160256
a
See Tables 1 and 2 for 1-body energies.
b
See Table 1 for the full
n
-body energies for
ð
HF
Þ
n
.
c
See Table 1 for 1-body energy.
CP-corrected many-body decomposition. However, that would increase the
time of the computations for this tutorial substantially.
The monomer energies from Tables 1 and 2 have been used to determine
the
E
DIST
values (Eq. [12]) shown in Table 4. (Again, a conversion factor of
1
E
h
5 kJmol
1
has been adopted.) For these symmetric cyclic
2625
:
ð
HF
Þ
n
HF
(
n
.
The many-body interaction energy can then be calculated from
E
int
and
E
DIST
via Eq. [17]. Recall that within the RMA,
E
DIST
¼
¼
3
5) clusters,
E
DIST
is simply
n
ð
E
½
E
½
HF
Þ ¼
n
ð
E
RLX
Þ
0 so that in the bottom
half of Table 4
E
many
-
body
int
is the same as
E
int
.
The 2-body through 5-body contributions to the many-body interaction
energy shown in Table 4 are relatively simple to compute because there are
only a few symmetry-unique terms. As mentioned earlier, there exist at most
two unique 2-body energies [in (HF)
4
and (HF)
5
] and two unique 3-body energies
[in (HF)
5
]. Furthermore, all monomers in a given cluster are identical, and the cor-
responding energies can be obtained from Table 2 (
E
HF
¼
monomer basis
cluster geom
½
E
½
HF
).
Table 4
Many-Body Decomposition of
E
int
for (HF)
n
,
n
¼ 3 5
a
E
dist
E
many
-
body
int
E
nonadd
E
2
E
3
E
4
E
5
d
Fully Optimized Clusters
(HF)
3
þ
0
:
96
50
:
93
43
:
58
7
:
34
—
—
7
:
34
(HF)
4
þ
2
:
87
93
:
40
71
:
23
20
:
65
1
:
51
—
22
:
17
(HF)
5
þ
4
:
08
128
:
61
91
:
52
33
:
43
3
:
38
0
:
27
37
:
08
Rigid Monomer Approximation
(HF)
3
—
49
:
13
42
:
58
6
:
55
—
—
6
:
55
(HF)
4
—
88
:
12
68
:
56
18
:
27
1
:
28
—
19
:
55
(HF)
5
—
120
:
86
89
:
51
28
:
45
2
:
66
0
:
24
31
:
35
a
All values were computed at the RHF/aug-cc-pVDZ level and are reported in kJ mol
1
.
