Linear combination of atomic orbitals

It was introduced in 1929 by Sir John Lennard-Jones with the description of bonding in the diatomic molecules of the first main row of the periodic table, but had been used earlier by Linus Pauling for H2+.

By minimizing the total energy of the system, an appropriate set of coefficients of the linear combinations is determined.

However, since the development of computational chemistry, the LCAO method often refers not to an actual optimization of the wave function but to a qualitative discussion which is very useful for predicting and rationalizing results obtained via more modern methods.

In this case, the shape of the molecular orbitals and their respective energies are deduced approximately from comparing the energies of the atomic orbitals of the individual atoms (or molecular fragments) and applying some recipes known as level repulsion and the like.

The graphs that are plotted to make this discussion clearer are called correlation diagrams.

The required atomic orbital energies can come from calculations or directly from experiment via Koopmans' theorem.

Molecular orbital diagrams provide simple qualitative LCAO treatment.