210
Chapter 15 Slater Determinants and Wave-Functions for “Increased-Valence” Structures
structure (12), and Eqn. (12) for structure (13); the order of spatial orbitals in each
Slater determinant is y,
ab
*
 , c and d. For the linear combination
1 1
2
2
C
C
    
, 1
2
C
C

near the commencement of the reaction and 2
1
C
C

near its
conclusion.
In Table 15-1, we report the spin degeneracies for the S = 0 and S = ½ spin
wave-functions for “increased-valence” structures with 4-12 electrons.
Table 15-1: Some “increased-valence” structures expressed in terms of their component “threeelectron bonds”. n = number of electrons; u number of unpaired electrons

n
; D = spin degeneracy
for singlet (S = 0 spin) and doublet (S = ½ spin) states.
n
u
n
D
 
A · B
3
1
1
Y A · B



4
2
1
A B · C D




5
3
3
A · B C · D




6
2
1
Y · A B · C D





7
3
2
Y A · B C · D E




 
8
4
2
Y · A B · C D · E




 
9
3
2
Y · A B · C D · E F




  
10
4
2
Y A · B C · D E · F G





  
11
5
5
Y · A B · C D · E F · G





  
12
4
2