Dielectric Relaxation of Gaussian-smoothed Solutes

The dielectric solvation dynamics of charged solutes is investigated for models with slowly-varying continuous charge densities. We describe the dielectric effects of Gaussian-smoothed ionic and dipolar solutes by assuming a linear response induced in the solvent. Empirical dielectric functions, such as Debye relaxation function, are employed to derive the relaxation time of the considered models. We suggest a mathematical framework incorporating both Gaussian-smoothed and classic models to predict the dielectric and relaxation behavior of dipoles.