Molecular Orbitals and the Linear Combination of Atomic Orbitals (LCAO) Approximation

To find electronic wavefunctions of molecules, usually the problem is broken down to simplify it.

The overall wavefunction (Y) is treated as a product of molecular orbitals (y):

Y = |y₁y₂y₃….y_n|

Each MO is a wavefunction for one electron, and each MO spreads over the whole molecule.

We will see that individual MOs can tell us a lot about molecular behaviour.

In the linear combination of atomic orbitals (LCAO) approximation, each MO is treated as being made up of the AOs of the atoms in the molecule.

To find the MOs, we need to find the coefficients which appear in the linear combination, by the variational method.

Consider a molecular orbital which is written as a linear combination of atomic orbitals:

(4)

where

y is the molecular orbital

and

f₁ etc. are the atomic orbitals centred on the different atoms.

y is our approximate wavefunction. We will substitute it into eq.2 above and use the variational method to determine the molecular orbital coefficients c₁ etc.

An example of the LCAO-MO method