Huckel molecular orbital method determinant

H was the matrix-component of the Hiickel effective-Hamiltonian operator, effective between two basis atomic-orbitals, 4>r and 4>s, Srs was the overlap integral between 4>r and s, and H was set equal to a, H to / . This is how we developed the simple HMO-approach in Chapter Two. What Roothaan did was to show that a formally similar determinant is obtained in a full treatment of the re-electrons, but that it involves a somewhat more complicated expression for the matrix-elements, H . Furthermore, he showed that this more-complicated expression somehow had to take into account interactions between any one re-electron and all the other re-electrons. We do not go into the details of this here, except to say that, in order to find the LCAO-MO coefficients for one molecular orbital, it is necessary to know all the others, because all the others appear in the expressions for the equivalent terms, Hrs. This is a very familiar situation which mathematicians have long known how to deal with and which we encountered during our discussion of the self-consistent" Huckel-methods in 7.2—7.5 it is necessary to use an iterative scheme. An initial guess is made of all the orbitals except one and these are used to calculate the H -terms for the one orbital which has not yet... 

The molecular orbitals obtained by the Huckel method are delocalized over the molecule, and are used in a Slater determinant to build the reference wave function i Pref) of our Hiickel-Lewis family of methods. Hence, for ethylene = l tSl and for a four-7t-electron molecule likeacrolein, it reads Thus, we... 

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