Charging a Spherical Particle

V is the electrostatic potential created by the solvent that acts on the charge in the center of the cavity. Recalling (2.30), the second-order perturbation theory yields 

If water is considered a homogeneous dipolar liquid, (V)0 = 0 and the expression for the free energy change further simplifies to 

This result implies that AA should be a quadratic function of the ionic charge. This is exactly what is predicted by the Bom model, in which the ion is a spherical particle of radius a and the solvent is represented as a dielectric continuum characterized by a dielectric constant e [1] 

It is instructive to compare these predictions with the results of computer simulations. This comparison, however, requires care. In practice, the computed values of A A exhibit considerable system-size dependence, i.e., they vary with the size of the simulation box. This is because charge-dipole interactions between the solute and 

We note that accurate values of AA for larger values of q - e.g., q= 1 - cannot be obtained from single-step FEP calculations. Instead, a series of calculations, in which q is progressively changed from zero to its final value, need to be performed. This approach is discussed in Sect. 2.6. 

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