The Huckel Coefficient Matrix

The matrix elements ot — Ej and p are not variables in the minimization procedure they are constants of the secular equations with units of energy. Note that all elements in the matrix and vector are real numbers. The vector is the set of coefficients for one eigenfunction corresponding to one eigenvalue, Ej. From Eq. (7-24), 

But Eq. (7-28) is the same mathematical operation that we used to obtain the diagonalized matrix of the eigenvalues. 

Let us look at the Mathcad output for a Huckel matrix in more detail. We select the matrix for ethylene to preserve simplicity. 

In the Mathcad calculation of eigenvalues and eigenvectors of the Huckel matrix for ethylene (j g), the eigenvalues are given in the order upper followed by lower. The matr ix E for this order is 

In a logical sequence, we might expect to try a solution for propene 

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