Chemistry Reference
In-Depth Information
(a) Contributions to ground-state potential energy 〈
U
(H
2
+
)〉
1
σ
g
- 〈
U
(H)〉
Energy/Ha
1
R
12
s
1
|
V
1
|
s
1
〉
(2
N
1g
2
−
1)
〈
0.4
0.2
Total
2
3
4
5
6
〈
s
2
|
V
1
|
s
2
〉
2
N
1g
2
R
12
/bohr
-0.2
-0.4
〈
s
1
|
V
1
|
s
2
〉
4
N
1g
2
(b) Contributions to first excited-state potential energy 〈
U
(H
2
+
)〉
2
σ
u
- 〈
U
(H)〉
Energy/Ha
1.0
-4
N
2u
2
〈
s
1
|
V
1
|
s
2
〉
1
R
12
0.5
Total
2
3
4
5
6
2
N
2u
2
〈
s
2
|
V
1
|
s
2
〉
R
12
/bohr
-0.5
U
(H
2
+
)
〈
〉
2
σ
u
-
〈
U
(H)
〉
-1.0
Figure A10.9
The various terms in the electron-nuclear potential energy plotted as a func-
tion of internuclear separation R
12
for (a)
H
2
+
in the ground state, with the electron in
|
1
σ
g
+
,
and (b)
H
2
+
in the first excited state, with the electron in
. In each case the internuclear
repulsion energy is also shown, and the solid lines marked 'Total' are estimates for the bond
formation energy at each R
12
value. In these calculations, the decay constant of the basis
functions is fixed at the AO value (
|
2
σ
u
+
ζ
=
1
).
occupied. This occurs because in the antibonding MO the contributions from the integrals
involving only a single s-orbital are both negative and outweigh the unfavourable effect
from the overlap integral. In the antibonding combination the electron density is, on aver-
age, closer to the nuclei because of the node at the bond centre than in the reference atomic
state (Figure A10.3d).
A10.8 The Chemical Bond Formation Energy Based on Rigid Atomic
Orbitals
The above discussion of the potential energy should be unsettling: we have found that
it is the kinetic energy in H
2
+
that stabilizes the chemical bond with the electron in the
ground state, while the potential energy is destabilizing. This seems to contradict the com-
monly proposed picture of the chemical bond, in which the overlap density stabilizes the
