An Example The Hartree-Fock Wave Function of Butadiene

3 An Example The Hartree—Fock Wave Function of Butadiene 

The MOs of butadiene are listed in Table 4.1. At the Hartree—Fock level, only the two first MOs are occupied, and the wave function reads  

In the second way, one can decide that all determinants will have their spins arranged in alternated order, that is, a, (3, a, etc., in which case the spin-coupling is characterized by permutations of the AOs. In such a case, the coefficients of the AO-determinants are all positive for a singlet state. Both methods are strictly equivalent, and the first one is generally employed in this book. However, the method of half-determinants is easier to apply with the second convention, which will be used in this section. Accordingly, the VB functions for structures 6 and 7 can be rewritten as in Equation 4.17 and 4.18  

In Equations 4.16-4.18, Ni and N2 are normalization constants that can be calculated exactly by using Equation 3.15 in Section 3.2, knowing the overlaps between AOs. We may, however, skip this calculation for the sake of simplicity. Indeed, given that the AO-determinants in Equations 4.17 and 4.18 all differ from one another by replacements of at least two orbitals, their 

TABLE 4.2 Coefficients of the AO-Half-Determinants in the Expansion of the Hartree Fock Wave Function of Butadiene 

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