Most empirical force fields use atom-centered point charges (PCs) to represent the electrostatic potential (ESP) around molecules. While such PC models are computationally efficient, they are unable to capture anisotropic electronic features, such as $\sigma$ holes or lone pairs. These features are better described using atomic multipole (MTP) moments, which significantly improve the quality of the resulting ESP. However, the improvement comes at the expense of a considerably increased computational complexity and cost for calculating the interaction energies and forces. In the present work, a novel minimal distributed charge model (MDCM) based on off-centered point charges is presented and the quality of the resulting ESP is compared to the performance of MTPs and atom-centered PC models for several test molecules. All three models are fitted using the same algorithm based on differential evolution, which is available as a Fortran90 program from the authors upon request. We show that the MDCM is capable of approximating the reference ab initio ESP with an accuracy as good as, or better than, MTPs without the need for computationally expensive higher order multipoles. Further it is demonstrated that the MDCM is numerically stable in molecular dynamics simulations and is able to reproduce electrostatic interaction energies and thermodynamic quantities with the same accuracy as MTPs at reduced computational cost.

中文翻译：

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最小的分布电荷：多极质量，但以点电荷静电为代价

大多数经验力场使用原子中心点电荷（PC）来表示分子周围的静电势（ESP）。尽管此类PC模型在计算上非常有效，但它们无法捕获各向异性的电子特征，例如$\sigma$洞或孤对。使用原子多极（MTP）矩可以更好地描述这些功能，从而显着提高生成的ESP的质量。然而，这种改进是以显着增加的计算复杂度和用于计算相互作用能和力的成本为代价的。在本工作中，提出了一种基于偏心点电荷的新型最小分布电荷模型（MDCM），并将所得ESP的质量与MTP和原子中心PC模型的性能进行了比较。这三种模型都使用基于差异进化的相同算法进行拟合，作者可以根据要求将其作为Fortran90程序使用。我们证明了MDCM能够近似参考从头算起具有与MTP相同或更好的精度的ESP，而无需计算上昂贵的高阶多极子。进一步证明，MDCM在分子动力学模拟中在数值上是稳定的，并且能够以降低的计算成本以与MTP相同的精度重现静电相互作用能和热力学量。