18
1 Basic Concepts
Fig. 1.5 Branching diagram
for two-by-two electron
incorporations. Gray solid
lines represent singlet
coupled additions. The other
lines represent triplet
additions with S = S ′ − 1
(black dashed), S = S ′ (gray
dashed)andS = S ′ + 1
(black solid)
1
1
3
9
5
5
7
2
1
1
1
14
20
28
1
0
2
3
4
24
68
N
S
• case 2: Triplet incorporation (black solid lines); S = S ′ + 1
Ψ(N , S, M S ) =
{(S + M S )(S + M S − 1)}
1
2 Ψ(N − 2, S − 1, M S − 1)Φ b
+{ 2(S + M S )(S − M S )}
1
2 Ψ(N − 2, S − 1, M S )Φ c
+{ (S − M S )(S − M S − 1)}
1
2 Ψ(N − 2, S − 1, M S + 1)Φ d
×[ 2S(2S − 1)]
−
1
2
(1.53)
• case 3: Triplet incorporation (gray dashed lines); S = S ′
Ψ(N , S, M S ) =
−{(S + M S )(S − M S + 1)}
1
2 Ψ(N − 2, S, M S − 1)Φ b
+
√
2M S Ψ(N − 2, S, M S )Φ c
+{ (S − M S )(S + M S + 1)}
1
2 Ψ(N − 2, S, M S + 1)Φ d
×[ 2S(S + 1)]
−
1
2
(1.54)