Valence Bond Wave Functions with Fragment Orbitals

3 Valence Bond Wave Functions with Fragment Orbitals 

4 Writing Valence Bond Wave Functions Beyond the 2e/2c Case 

Denoting the tt AOs of the C1-C4 carbons by a,b,c, and d, respectively, the fully covalent VB wave function for the tt system of butadiene displays two singlet couplings one between a and b, and one between c and d. It follows that the wave function can be expressed in the form of Equation 3.8, as a product of the bond wave functions. 

Upon expansion of the product, one gets a sum of four determinants as in Equation 3.9. 

The product of bond wave functions in Equation 3.8, involves so-called perfect pairing, whereby we take the Lewis structure of the molecule, represent each bond by a HL bond, and finally express the full wave function as a product of all these pair-bond wave functions. As a rule, such a perfectly paired polyelectronic VB wave function having n bond pairs will be described by 2 determinants, displaying all the possible 2x2 spin permutations between the orbitals that are singlet coupled. 

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