Chemistry Reference
In-Depth Information
Figure 2.23
sp hybrids on nitrogen resulting from the orthogonal transformation
O
of the original basis set of A
1
symmetry. Left, lone pair hybrid l; right, bond hybrid b.
Reprinted fromChemical Physics Letters, 477, Magnasco, V., H ¨ ckel transformation
theory of the hybridization problem in NH
3
. 392-396, Copyright (2009), with
permission from Elsevier
which corresponds to introducing the orthonormal hybrids (Figure 2.23):
0
@
1
A
cos
v
sin
v
0
ð
lbh
z
Þ¼
ð
szh
z
Þ
sin
v
cos
v
0
ð
2
:
234
Þ
0
0
1
where
v
is the hybridization parameter. Putting
v ¼
0 gives the previous
case of no hybridization.
The transformed H
€
uckel matrix has elements:
<
a
l
¼ a
s
cos
2
vþa
p
sin
2
v
a
s
a
p
2
b
lb
¼
sin 2
v
p
ðb
sh
cos
vb
s
h
sin
v
cos
b
lh
¼
gÞ
ð
:
Þ
2
235
:
a
b
¼ a
s
sin
2
vþa
p
cos
2
v
p
ðb
sh
sin
vþb
s
h
cos
v
cos
b
bh
¼
gÞ
a
h
giving the 3
3 transformed secular equation:
a
l
«
lb
b
lh
b
lb
a
b
«
bh
¼
0
ð
2
:
236
Þ
b
lh
b
bh
a
h
«
