Extended Huckel Theory—Whelands Method

One restriction imposed by Huckel theory that is rather easy to release is that of zero overlap for nearest-neighbor interactions. One can retain a — as the diagonal elements in the secular matrix and replace p by p — EjS as nearest-neighbor elements where S is the overlap integral. Now, 

By analogy to the substitution x = a — E/ m the section on the secular matrix in Chapter 6, we can make the substitution 

Millikan has shown that the overlap integral for hydrogen-like p orbitals in linear hydrocarbons is about 0.27 (Millikan, 1949). 

What is the energy separation E2 — E of the bonding and antibonding orbitals in ethylene, assuming that the overlap integral S is 0.27  

The separation is 2.16P, which, considering all the approximations already made, is not greatly different from the separation we found ignoring overlap. 

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