Empirical MO methods
Explanation of the empirical MO approach
Empirical methods are differentiated from semi-empirical methods in general by the choice of Hamiltonian operator. Empirical methods use a Hamiltonian which is simply a sum of one-electron terms. The two-electron electron repulsion term is in effect averaged into the one-electron terms. In contrast, semi-empirical methods use the correct Hamiltonian with both one- and two-electron terms. In both cases the resulting integrals that arise from the terms in the Hamiltonian are often approximated, neglected or fitted to experimental data.
All the methods we will discuss, both empirical and semi-empirical, use the molecular orbital single determinant method, although, in general, this is not a restriction. The PCILO (perturbative configuration interaction using localised orbitals) method, for example, uses an approach which goes beyond the molecular orbital approach while still using the same approximations as other semi-empirical methods.
The Hückel method
The earliest empirical method is the Hückel method which is applicable to planar aromatic or conjugated systems. In fact, the Hückel method, in 1930, was the first application of quantum mechanics to a polyatomic system.
The earliest and simplest method is restricted to hydrocarbons and we will start with that approach.
Later the method was extended to include so-called heteroatoms (i.e. not carbon) in order to study heterocyclic aromatic systems.
The Hückel method calculates the π electron molecular orbitals only. This is often described by the term σ-π separability. Another term that is often used is the π electron approximation.
Now we can start looking at Hückel approximations in detail and then do some actual calculations.