标题： 通过包含长程库仑相互作用的机器学习势能对水的介电常数的模拟 显示英文标题

标题： Simulations of dielectric permittivity of water by Machine Learned Potentials with long-range Coulombic interactions

摘要： 液体水的介电常数是一个基本性质，它决定了其在众多物理、生物和化学过程中的独特行为。 在机器学习框架中，我们提出了一种统一的方法来计算水的介电常数，并系统地结合了各种电边界条件。 我们的方法使用了一个基于混合密度泛函理论计算数据训练的包含长程作用的深度势能。 介电响应通过一个辅助深度神经网络进行评估，该网络预测最大局部化Wannier函数的中心。 我们研究了三种类型的电边界条件——金属、绝缘和Kirkwood-Frohlich——以评估它们对关联偶极涨落和介电弛豫动力学的影响。 特别是，我们在每种边界条件下展示了一种计算Kirkwood关联因子、关联长度和介电常数的一致性方法，其中长程静电作用起着关键作用。 这项工作建立了一个稳健且可推广的机器学习框架，用于在多种静电环境中模拟极性液体的介电特性。 显示英文摘要

摘要： The dielectric permittivity of liquid water is a fundamental property that underlies its distinctive behaviors in numerious physical, biological, and chemical processes. Within a machine learning framework, we present a unified approach to compute the dielectric permittivity of water, systematically incorporating various electric boundary conditions. Our method employs a long-range-inclusive deep potential trained on data from hybrid density functional theory calculations. Dielectric response is evaluated using an auxiliary deep neural network that predicts the centers of maximally localized Wannier functions. We investigate three types of electric boundary conditions--metallic, insulating, and Kirkwood-Frohlich--to assess their influence on correlated dipole fluctuations and dielectric relaxation dynamics. In particular, we demonstrate a consistent methodology for computing the Kirkwood correlation factor, correlation length, and dielectric permittivity under each boundary condition, where long-range electrostatics play a critical role. This work establishes a robust and generalizable machine-learning framework for modeling the dielectric properties of polar liquids under diverse electrostatic environments.