Spin Degeneracy and Wave-Functions for Increased-Valence Structures

15-2 Spin Degeneracy and Wave-Functions for Increased-Valence Structures 

Except for 4-electron 3-centre and 6-electron 4-centre increased-valence structures, all other increased-valence stmctures involve the spin-pairing of three or more odd electrons, i.e. in the increased-valence wave-function, three or more orbitals must be singly-occupied. This may be seen by examination of the increased-valence structures (7) and (8) 

S = S =0 for structure (8). These wave-functions are given by Eqs. (9)-(12), in which we have omitted all doubly-occupied orbitals from the Slater determinants. 

In Eqs. (11) and (12), there are six types of Slater determinants. They generate different spin arrangements for the four singly-occupied orbitals, and lead to the 

Each of the spin structures (9a)-(9f) involves two one-electron A-B and C-D bonds, but they differ in the number of two-electron spin-pairings which can occur between pairs of adjacent atoms. Thus, each of (9a) and (9b) can lead to fractional Y-A, B-C and D-E spin-pairings (9c) and (9d) generate Y-A and D-E spin-pairings, and (9e) and (9f) can only involve B-C spin pairing. We may construct any linear combination of and 2 which generates some Y-A, B-C 

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