Outer repulsion energy

The total energy of repulsion between charge cloud 2 and electron 1 at r is the sum of inner and outer repulsive energies. But electron 1 is not always at r. Therefore, we must finally integrate over all positions of electron 1, weighted by the frequency of their occurrence ... 

The same pattern of finding the Lewis structure and then matching it to a geometry that minimizes the repulsive energy of bonding electrons is followed through steric numbers 4, 5, 6, 7, and 8 where the outer atoms are identical in each molecule, as shown in Figure 3.8. 

The corresponding overlap volume is the sum of the elementary volumes of all space pixels in which the electron density of both molecules is above a given threshold. The case is illustrated in Table 1.5 for the succinic anhydride crystal. As expected, the overlap integral correlates with the distance between molecular centers of mass. Coherently with the results shown in Table 1.4, the overlap volumes are non-zero only if the electron density threshold is less than 0.02 e A . In Section 12.2 it will be shown that the overlap integral correlates with the repulsion energy between neighbor molecules, and that the outer electrons play a crucial role in defining the details of the directional intermolecular interaction in crystals. 

The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... 

---