The Hückel Molecular Orbital Method

 

In general the calculation of all the matrix elements is not straightforward. 

 

The Hückel method makes some severe approximations as to the values of the Hamiltonian and the overlap matrix elements:

Hückel Approximations:

 

(i)    Hrr = a for all conjugated carbon atoms r

(ii)   Hrs = b for any conjugated carbon link r-s,

                        i.e if atoms r and s are adjacent

        Hrs = 0 otherwise

(iii)  Srs = 0 for r ¹ s, i.e. zero overlap for r ¹ s.

 

 

·       a is often referred to as a 'Coulomb integral'. 

·       Use of equation (3) shows that a is the atomic 2p energy. 

·       b is often referred to as the 'resonance integral' or 'bond integral' since the value of   b determines the strength of the bonding interactions. 

·       Both a and b are NEGATIVE. 

 

The Hückel approximations applied to ethene