we need to find approximate solutions of the non-relativistic time-independent Schrödinger equation for our basic cluster where we treat all the electrons with quantum mechanics.

where

H = - kinetic energy of the e^{-} - kinetic energy of the nuclei - colomb attraction between nuclei and e^{-} + electronic repulsion + nuclear repulsion.

We know that nucleus are much heavier than electrons and so they move more slowly than electrons. hence, to a good approximation, one can consider the electrons in a molecule to be moving in the field of fixed nuclei.

We can then write the following hamitonian which correspond to the electronic hamiltonian that consider only the motion of electrons.

The total energy can then be express as follow :