method of descending symmetry. If the e
2
g configuration is considered, when we
decrease the symmetry from O h to D 4h , the determination of the spin state becomes
straightforward, and the following configurations are expected
e y
a 1g
b 1g
O h
D 4h
b
2
1g (S = 0), a 1g b 1g (S = 0 and S = 1), a
2
1g (S = 0) which give the terms A 1g (S = 0)
B 1g (S = 0 and S = 1) A 1g (S = 0).
Given the following correlations:
the spin state and the orbital degeneracy can be assigned
Table 3.4 Correlation between the spectroscopic states in different symmetries
O h O T d D 4k
D 2d
C 4u
C 2u
D 3d
D 3
C 2h
A 1g A 1 A 1 A 1g
A 1
A 1
A 1
A 1g
A 1
A g
A 2g A 2 A 2 B 1g
B 1
B 1
A 2
A 2g
A 2
B g
E g E E A 1g + B 1g A 1 + B 1 A 1 + B 1 A 1 + A 2
E g
E
A g + E
T 1g T 1 T 1 A 2g + E g A 2 + E A 2 + E A 2 + B 1 + B 2 A 2g + E g A 2 + E A g + 2
T 2g T 2 T 2 B 2g + E g B 2 + E B 2 + E A 1 + B 1 + B 2 A 1g + E g A 1 + E 2A g +
A 1u A 1 A 2 A 1u
B 1
A 2
A 2
A 1u
A 1
A u
A 2u A 2 A 1 B 1u
A 1
B 2
A 1
A 2u
A 2
B u
E u E E A 1u + B 1u A 1 + B 1 A 2 + B 2 A 1 + A 2
E u
E
A u + E
T 1u T 1 T 2 A 2u + E u B 2 + E A 1 + E A 1 + B 1 + B 2 A 2u + E u A 2 + E A u + 2
T 2u T 2 T 1 B 1u + E u A 2 + E B 1 + E A 2 + B 1 + B 2 A 1u + E u A 1 + E 2A u +
50
3 Perturbation Theory