Centre Molecular Orbitals and Pauling 3-Electron Bonds

6-4 3-Centre Molecular Orbitals and Pauling 3-Electron Bonds  

To provide a simple demonstration of this equivalence, it is only necessary to show that the molecular orbital configuration (vpi) (v /2) (q/3) can be expressed 

This is because resonance between the Pauling 3-electron bond and Y A B is equivalent to resonance 

y A B and Y A B. We may write ( Pi) (T2) (T ) 3S v / v /[ v(/ vi/ v /3, in which a and p are the spin wave-functions for electrons with spin quantum numbers of +V2 and -V2, and the odd-electron is assumed to have = + /2. By substituting the linear combinations of atomic orbitals of Eqn. (6-1) into this configuration, and then expanding the configuration as a linear combination of atomic orbital configurations, we obtain Eqn. (6-2) 

---