Using a projected integral expansion technique, the energy of a molecule calculated at the SCF level is expressed approximately but to a good accuracy as a sum of atomic and diatomic contributions, the computation of which requires the use of one- and two-center integrals only. The decomposition is exact for diatomic molecules, while the three- and four-center effects are compressed into one- and two-center ones as much as it is possible by performing appropriate projections. The proposed scheme is devised to perform a posteriori analysis of the wave functions obtained in the actual SCF calculations: the energy components obtained permit one to identify the different chemically relevant interactions in a molecule and give a useful tool for interpretations and perhaps predictions.