Electrostatics of charged dielectric spheres with application to biological systems. III. Rigorous ionic screening at the Debye-Hückel level,Physical Review E

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Electrostatics of charged dielectric spheres with application to biological systems. III. Rigorous ionic screening at the Debye-Hückel level
Physical Review E ( IF 2.2 ) Pub Date : 2020-11-06 , DOI: 10.1103/physreve.102.052404
Yi-Kuo Yu ₁

Affiliation

The unequivocal role of electrostatic forces in biological (and colloidal) systems underscores the importance of attaining accurate and rapid calculations of electrostatic forces if one wishes to faithfully simulate the electrostatic aspect of a biological system. This paper makes significant progress toward this aspect as it rigorously incorporates ionic screening at the Debye-Hückel level for an electrolyte system containing dielectric spheres of finite radii. We investigated earlier this system without mobile ions via a surface charge method. However, the need for computing a large number of Wigner rotation matrix elements per configuration can significantly slow down the numerical calculations. This difficulty was recently overcome by our Wigner-matrix-free formalism. Unfortunately, in that method ions can only be included individually, making it impractical to investigate, for example, ionic screening in a system modeled by charged dielectric spheres immersed in a solution of mobile ions. Here, we overcome this difficulty by extending the surface charge method to treat ions implicitly. Previous treatments of charged dielectric spheres in a solution of mobile ions did not emphasize the energy reciprocity of electrostatics and are largely limited to a few spheres and/or special symmetries. Our new formalism respects reciprocity and accommodates arbitrarily many dielectric spheres of different dielectric constants and sizes while being rigorous at the Debye-Hückel level. The differences, and the relationship, between our new implicit ion treatment and our previous ion-free (or explicit ion) approach are described. A closed form for the electrostatic energy with implicit ions is also provided. This new formalism speeds up the computation of the electrostatic energy in the presence of ions, and accommodates permanent and induced multipoles that are very important when the polarization effect needs to be correctly included. We also mention how the proposed method can be transformed to a numerical method for use with arbitrary nonspherical surfaces.

中文翻译：

带电介电球的静电及其在生物系统中的应用。三．Debye-Hückel 级别的严格离子筛选

静电力在生物（和胶体）系统中的明确作用强调了如果希望忠实地模拟生物系统的静电方面，则获得准确和快速的静电力计算的重要性。本文在这方面取得了重大进展，因为它严格地将德拜-休克尔水平的离子筛选纳入包含有限半径介电球的电解质系统。我们之前通过表面电荷方法研究了这个没有移动离子的系统。然而，每个配置需要计算大量维格纳旋转矩阵元素会显着减慢数值计算速度。这个困难最近被我们的无维格纳矩阵形式主义克服了。不幸的是，在该方法中只能单独包含离子，这使得研究例如由浸入移动离子溶液中的带电介电球建模的系统中的离子筛选是不切实际的。在这里，我们通过扩展表面电荷方法来隐式处理离子来克服这个困难。先前对移动离子溶液中的带电介电球的处理并没有强调静电的能量互易性，并且很大程度上仅限于少数球体和/或特殊的对称性。我们的新形式主义尊重互易性，并容纳任意多个不同介电常数和尺寸的介电球，同时严格遵守德拜-休克尔水平。描述了我们新的隐式离子处理和之前的无离子（或显式离子）方法之间的差异和关系。还提供了隐式离子静电能的封闭形式。这种新的形式加速了存在离子时静电能的计算，并适应永久和感应多极，这在需要正确包含极化效应时非常重要。我们还提到如何将所提出的方法转换为用于任意非球面的数值方法。

更新日期：2020-11-06

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