The Hückel Molecular Orbital Method
All the matrix elements – i.e. all the energies (integrals) Hrs
and the overlap integrals Srs for all the atomic orbitals r,
s…etc. – would need to be calculated
i.e. a lot of very
difficult calculations!
In
modern molecular orbital calculations, these would be calculated with a
computer.
Before computers, approximate methods had to be used, in which
values of these integrals were guessed.
Hückel MO Theory is an
important and useful approximate method of this type.
The Hückel
method makes some sweeping and surprising approximations for 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'.
· a is the atomic 2p energy (show this by looking at the
equation for the expectation value, i.e. the energy Hrr)
· 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
energies.