Potential-energy surfaces Attractive

Here, the first term is the kinetic energy of the electrons only. The second term is the attraction of electrons to nuclei. The third term is the repulsion between electrons. The repulsion between nuclei is added onto the energy at the end of the calculation. The motion of nuclei can be described by considering this entire formulation to be a potential energy surface on which nuclei move. 

Figure 6.3. Schematic potential energy curve describing the interactions between colloidal particles. The overall potential is a sum of an electrostatic repulsive term which arises due to any charged groups on the surface of the particle and the attractive van der Waals term.

This type of fully local potential has some limited use, e.g., to consider adsorption in a slowly varying external potential. It fails, however, to describe the most important phenomena such as surface tension and adsorption at most types of interfaces. These phenomena reflect in a fundamental way the nonlocal interactions in the fluid. The most obvious nonlocality of the free energy arises due to the range of the attractive or soft interactions represented by the second term in the equation of state, —The corresponding potential energy can be obtained by the functional... 

Schematic forms of the curves of interaction energies (electrostatic repulsion Vr, van der Waals attraction Va, and total (net) interaction Vj) as a function of the distance of surface separation. Summing up repulsive (conventionally considered positive) and attractive energies (considered negative) gives the total energy of interaction. Electrolyte concentration cs is smaller than cj. At very small distances a repulsion between the electronic clouds (Born repulsion) becomes effective. Thus, at the distance of closest approach, a deep potential energy minimum reflecting particle aggregation occurs. A shallow so-called secondary minimum may cause a kind of aggregation that is easily counteracted by stirring.

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