P þ
g ¼ u 1 þ u 2 (bonding) and
P þ
u ¼ u 1 À u 2 (antibonding), in the following
energy scheme
(bonding)
(antibonding)
ϕ
ϕ
ϕ
u
g
ϕ
ϕ
ϕ
2.1 Homonuclear Diatomic Molecules A-A of the Periodic
Table First Row
We assume the following base of atomic orbitals.
For the 2s orbitals
u 1 ¼ 2s A u 2 ¼ 2s B leads to
P þ
g ¼ u 1 þ u 2 (bonding)
P þ
u ¼ u 1 À u 2 (antibonding)
For the 2p orbitals u
A
1 ¼ 2p x u
A
2 ¼ 2p y u
A
3 ¼ 2p z ; u
B
4 ¼ 2p x u
B
5 ¼ 2p y u
B
6 ¼ 2p z
D 1h E
C
u
1
r v i S
u
1 C 2v
v t
6 2þ 4 cos u 2 0 0
0
v t indicates the total representation of the base containing the six p orbitals.
Looking at the character tables of the linear groups C 1v and D 1h
26
2 Symmetry Orbitals for Different Bis and Polyatomic Molecules