Isolated, total electrostatic potential

Fig. 11. The total electrostatic potential for an HMX molecule isolated from the crystal structure in the N(l), 0(1), 0(2) plane. Contour intervals are +0.01 eA-1 (solid line), -0.01 eA-1 (dotted line), and zero (dashed line).

For an isolated system there are no external influences so the first term of Equation A4 is zero. The effective pair potential is a function of the pair separation = r, — r jl and is constructed in such a way as to include the true pair potential and average effects of higher order terms it often includes also electrostatic and dipolar effects. The total potential energy of the system is then a sum over all distinct pairs of particles... 

In electrostatics, for example, the capacitance C is the total charge Q, required to raise the potential ( )e of an isolated body to the electrical potential V and the relationship between them is (e.g., Greenspan [27], Morse and Feshbach [68,69], Smythe [98], and Stratton [111])... 

The basic derivations of the van der Waals forces is based on isolated atoms and molecules. However, in many particle calculations or in the condensed state major difficulties arise in calculating the net potential over all possible interactions. The Debye interaction, for example is non additive so that a simple integration of Equation (4.27) over all units will not provide the total dipole-induced dipole interaction. A similar problem is encountered with the dipole-dipole interactions which depend not only on the simple electrostatic interaction analysis, but must include the relative spatial orientation of each interacting pair of dipoles. Additionally, in the condensed state, the calculation must include an average of all rotational motion. In simple electrolyte solutions, the (approximately) symmetric point charge ionic interactions can be handled in terms of a dielectric. The problem of van der Waals forces can, in principle, be approached similarly, however, the mathematical complexity of a complete analysis makes the Keesom force, like the Debye interaction, effectively nonadditive. 

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