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) H_rr = a for all conjugated carbon atoms r

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

i.e if atoms r and s are adjacent

H_rs = 0 otherwise

(iii) S_rs = 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