Correlation Energy

Each electron is coupled to all the others through a mean field, the Hartree and exchange potential generated by all the other electrons. This mean field describes the behavior of an electron in the average field of the remaining electrons. Therefore, in the HF approach, all information concerning pair and higher order correlations is lost. In accordance with the variational principle, the effect of neglecting these contributions is to raise the energy above the exact energy. The correlation energy is then usually defined as the difference between the exact (non-relativistic) energy and the HF energy. The success of the HFA often depends upon a cancellation of the correlation energies when going from one system to another. However, it is impossible to predict when this cancellation will take place. Therefore, it would be useful to go beyond the HFA to an approach that provides some estimate of the correlation energy.