Chemistry Reference
In-Depth Information
or, by expanding the determinants:
<
:
að
s
1
Það
s
2
Þ
1
2
a
ð
r
1
Þ
b
ð
r
2
Þ
b
ð
r
1
Þ
a
ð
r
2
Þ
2
2S
2
p
½
að
s
1
Þbð
s
2
Þþbð
s
1
Það
s
2
Þ
3
u
Þ¼
p
Yð
HL
;
S
bð
s
1
Þbð
s
2
Þ
32
0
Þ
ð
9
:
The quantum mechanical exchange-overlap component of the inter-
action energy for the triplet is now
u
Þ¼
S
ð
ab
Sa
2
j
V
B
Þþð
ba
Sb
2
j
V
A
Þ
ð
ab
j
ab
Þ
S
2
ð
a
2
j
b
2
Þ
D
E
exch-ov
3
ð
S
1
S
2
1
S
2
ð
9
:
33
Þ
and is repulsive for any value of R (a scattering state, left bottom part of
Figure 9.2). At the rather large internuclear distance of about 8a
0
we
observe the formation of a rather flat van der Waals (VdW) minimum of
20
10
6
E
h
, due to the prevalence of theweakLondon attractive forces
(Chapter 11) over this weak triplet repulsion. The appearance of this weak
VdWbond is depicted qualitatively in the right bottom part of Figure 9.2,
which refers to large internuclear distances.
4
It should be noted that,
3
u
at variance with the ground state,
Yð
MO
;
S
Þ
now coincides with
3
u
Yð
HL
;
S
Þ
.
9.3 THE ORIGIN OF THE CHEMICAL BOND
The HL theory of the chemical bond in H
2
can be considered as the first
approximation including exchange in an RS perturbation expansion of
the interatomic energy (see Chapters 10 and 11). In a VB calculation,
variational optimization of the orbital exponent c
0
of a simple STO basis
is tantamount to including in first order a large part of the spherical
distortion, so giving a fairly good description of the quantum exchange-
overlap component of the interaction that is dominant in the bond region
(Magnasco, 2007).
4
Note in the figure the change in the energy scale for chemical (top, 10
3
E
h
) and VdW (bottom,
10
6
E
h
) bonds, meaning that the latter are 1000 times smaller in their order of magnitude.
