Uniformity ansatz for inverse dielectric function of spatially restricted nonlocal polar medium as a novel approach for calculation of electric characteristics of ion-solvent system

Till now, calculation of the electrostatic potential distribution and other electric properties of a nonlocal polar medium occupying a restricted spatial region has been carried out within the framework of two different approaches. One of them (which may be called ``unrestricted medium approximation'', UMA) disregards the existence of ``external region'' (where dielectric properties are different from those of the medium), i.e. it assumes that the medium occupies the whole space so that its nonlocal dielectric properties are everywhere identical to those of the bulk medium while the charges (sources of the electric field) are considered as immersed inside the medium, without creating cavities or modifying its dielectric properties. Another approach (usually called ``dielectric approximation'', DA) takes into account the difference of dielectric properties between the region occupied by the medium, V, and an ``external'' region; as for the nonlocal dielectric function inside region V it is assumed to be identical to that of the bulk medium, even for its spatial points near the boundary of the region. The actual study has proposed a novel general procedure (called IDA) for solving the same problem. Similar to the DA one, it also takes into account the difference of dielectric properties in region V and external region(s). However, a different background relation (''uniformity ansatz'') is assumed for dielectric properties of the spatially restricted polar medium: its correlation function of polarization fluctuations has the same form (identical to that for the unrestricted medium) in all points inside spatial region V, even in the vicinity of its boundary. The same property is automatically fulfilled for the inverse dielectric function of the medium inside region V. For several important geometries of the system (e.g. half-space, spherical or cylindrical cavity, etc.) thus defined ``the inverse dielectric approach'' (IDA) results in simple analytical expressions for the potential and electric field distributions for any nonlocal dielectric function of the bulk polar medium as well as for any distribution of ``external charges'' (satisfying to the corresponding symmetry conditions). As the first application, the IDA approach has been used for analysis of the electric field and potential distributions for the spherically symmetrical system where a cavity (imitating a ``solute ion'') is surrounded by a nonlocal dielectric medium (''polar solvent''). Analytical expressions for these characteristics as well as for the electrostatic contribution to the solvation energy have been derived for any spherically symmetrical distribution of the ionic charge (which may be located in the general case both inside the cavity and outside this region) and for any dielectric responses both inside the cavity and of the polar medium outside the cavity. These results are in perfect agreement with the general principles that both the potential distribution outside the cavity and the ion solvation energy are determined only by the total ionic charge inside the cavity while they are independent of the particular charge distribution in this region. Effects due to the ionic charge penetration into the polar medium are also analyzed. Results for the potential distribution and solvation energy are compared for the novel IDA approach with those for the UMA and for the DA procedures. Conclusion on substantial advantages of the IDA method has been made.