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f, χ(r) = (∈(r) - 1)/(4π) is the real-space susceptibility, and the brackets on the right denote the usual product between (square-integrable) functions. This derivation assumes the solute-solvent interface has a finite width and the dielectric constant ∈(r) is a smooth function of position; if desired, one can now make the interface width go to zero and transform the expressions accordingly, in which case the induced surface charge appears.
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To perform the interpolation, we assume the relaxation free energy for charge insertion into a homogeneous medium depends on the dielectric constant ∈ through a term A(1 - 1/∈), and the constant A is fitted to the step 2a data in Table 2.
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