Angle-averaged potentials

Derive the expressions for the angle-averaged potential energy of interaction bet>veen an ion and a dipole given by Eqs. (7-7) and (7-8) from Eq. (7-6) and the Boltzmann expression for the equilibrium energy distribution. 

The second approach to extending the molecular corresponding-states principle to non-spherical molecules was suggested by the work on angle-averaged potentials by Rushbrooke, Pople and Cook and Rowlinson. For example, if the spherical portion of the potential of an axial dipolar molecule can be represented by the Lennard-Jones (12-6) model with... 

Figure 4.40. A plot of the ratio n) C/P)/ n) C) versus log W for reaction pairs interacting via the angle-averaged dipole-dipole potential for the three square-planar lattice systems 3 x 3 (A = 9), 7 x 7 (A = 49), and 21 x 21 (A = 441).

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