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.

到目前为止，已经在两种不同方法的框架内对占据有限空间区域的非局部极性介质的静电势分布和其他电性能进行了计算。其中之一（可以称为“无限制介质近似”，UMA）无视“外部区域”（介电特性与介质的介电特性不同）的存在，即假定介质占据整个空间，因此非局部介电特性在任何地方都与大容量介质相同，而电荷（电场源）被认为是浸没在介质内部，而不会产生空腔或改变其介电特性。另一种方法（通常称为“介电逼近”V和“外部”区域；关于区域V内部的非局部介电函数，即使其空间点在区域边界附近，也假定与体积介质相同。实际的研究提出了一种新颖的通用程序（称为IDA）来解决相同的问题。与DA相似，它也考虑了区域V和外部区域中介电特性的差异。但是，对于空间受限的极性介质的介电特性，假定使用不同的背景关系（“均匀度ansatz”）：其极化起伏的相关函数在空间区域V内的所有点具有相同的形式（与非受限介质的形式相同），即使在其边界附近。介质内部区域V的逆介电函数自动实现相同的属性。对于系统的几个重要几何形状（例如，半空间，球形或圆柱形空腔等），定义为“逆介电方法”（IDA）的结果是，对于任何非局部介电函数，势能和电场分布都可以用简单的解析表达式表示。大量极性介质以及“外部电荷”的任何分布（满足相应的对称条件）。作为第一个应用程序，IDA方法已用于分析球对称系统的电场和电势分布，在该系统中，空腔（模拟“溶质离子”）被非局域介电介质（“极性溶剂”）包围。对于离子电荷的任何球形对称分布（通常位于腔体内部和该区域之外）以及任何介电体，都可以得出这些特性以及静电对溶剂化能量的贡献的分析表达式。空腔内部和空腔外部的极性介质的响应都可以。这些结果与腔体外部的电势分布和离子溶剂化能量均仅由腔体内部的总离子电荷决定，而与该区域中特定的电荷分布无关的一般原理完全吻合。还分析了由于离子电荷渗透到极性介质中而产生的影响。比较了新型IDA方法与UMA和DA程序的电位分布和溶剂化能的结果。已得出IDA方法的实质优势的结论。