Even with the application of the Hartree-Fock and LCAO approximations to generate the Roothaan-Hall equations, we do not have a set of equations that can be solved analytically.

Instead, we conduct an iterative procedure, in which each molecular orbital is evaluated under the influence of an average potential field from the other electrons.

• The derived MO then contributes to the field used for the next MO, and the process repeats until it is internally consistent within specified limitations.

• This approximation is referred to as the self consistent field, or SCF, procedure.

The total Hartree-Fock energy then is given by:

The four terms are defined as follows:

• Nuclear term

  

• Core term

  

• Coulomb term

  

• Exchange term

  

Computations based on the approximations discussed here give quite good structures for molecules containing Main Group elements. However, even in the limit of a complete basis set, the Hartree-Fock energy is not equal to the experimental energy of a molecule, largely because of the error introduced by using the SCF model.