and considering the character table of the irreducible representations of the D ∞h
group
D 1h E
C
u
1
r v
i
S
u
1
C 2v
P þ
g
1
1
1
1
1
1
P þ
u
1
1
1 À1
À1
À1
P g
2 2 cos u 0
2 À2 cos u 0
P u
2 2 cos u 0 À2 2cosu
0
the base of six p atomic orbitals allows to build the following symmetry orbitals reported
in a general Scheme 2.1 with the s-based atomic orbitals where the number before the
symmetry orbital indicates the progression of orbitals of analogous symmetry.
/ 3r
þ
g
¼ 2p zA þ 2p zB
ð
Þ
/ 3r
þ
g
¼ 2p zA À 2p zB
ð
Þ
/ 1p u ¼ 2p xA À 2p xB
ð
Þ: 2p yA þ 2p yB
/ 1p u ¼ 2p xA À 2p xB
ð
Þ: 2p yA À 2p yB
E
2p
1л g
1л υ
2s
(a)
(b)
3σ υ
+
2σ υ
+
3σ g
+
2σ g
+
Scheme 2.1 General energy trend for the first row biatomic molecules
2.1 Homonuclear Diatomic Molecules A-A of the Periodic Table First …
27
group
D 1h E
C
u
1
r v
i
S
u
1
C 2v
P þ
g
1
1
1
1
1
1
P þ
u
1
1
1 À1
À1
À1
P g
2 2 cos u 0
2 À2 cos u 0
P u
2 2 cos u 0 À2 2cosu
0
the base of six p atomic orbitals allows to build the following symmetry orbitals reported
in a general Scheme 2.1 with the s-based atomic orbitals where the number before the
symmetry orbital indicates the progression of orbitals of analogous symmetry.
/ 3r
þ
g
¼ 2p zA þ 2p zB
ð
Þ
/ 3r
þ
g
¼ 2p zA À 2p zB
ð
Þ
/ 1p u ¼ 2p xA À 2p xB
ð
Þ: 2p yA þ 2p yB
/ 1p u ¼ 2p xA À 2p xB
ð
Þ: 2p yA À 2p yB
E
2p
1л g
1л υ
2s
(a)
(b)
3σ υ
+
2σ υ
+
3σ g
+
2σ g
+
Scheme 2.1 General energy trend for the first row biatomic molecules
2.1 Homonuclear Diatomic Molecules A-A of the Periodic Table First …
27