从分子动力学轨迹估计位置依赖和各向异性扩散张量：现有方法与未来展望
Estimating position-dependent and anisotropic diffusivity tensors from molecular dynamics trajectories: Existing methods and future outlook
AI总结：
本文综述了从分子动力学轨迹估计位置依赖和各向异性扩散张量的多种方法，包括启发式扩展、核方法、贝叶斯方法等，并展望了未来挑战与机遇。
摘要：
限制可以显著改变材料的物理化学性质，通过打破平移各向同性并使所有物理性质变得位置依赖。分子动力学（MD）模拟已被证明在表征这种空间异质性和探测限制对材料性质的影响方面具有重要作用。对于静态性质，这是一个直接的任务，可以通过简单的空间分箱来实现。然而，这种方法不能直接应用于输运系数，因为缺乏用于在体相中计算这些系数的自相关的自然扩展。这一挑战的主要例子是扩散率，在体相中，可以从满足福克-普朗克方程的粒子迁移率统计中轻松估计。然而，在限制条件下，这些统计将遵循斯莫卢霍夫斯基方程，该方程缺乏闭合形式的解析解。这篇简短的综述探讨了从MD模拟估计扩散张量剖面的丰富历史，并讨论了为此目的开发的各种近似方法和算法。除了讨论体相方法的启发式扩展外，我们概述了更严格的算法，包括基于核的方法、贝叶斯方法和算子离散化技术。此外，我们概述了基于对示踪粒子施加偏置势或约束的方法。最后，我们讨论了从平均首次通过时间或通勤概率剖面估计扩散率的方法，这一概念框架最初是在计算化学和生物学中描述稀有事件的集体变量空间的背景下开发的。总之，本文提供了从MD轨迹估计扩散率的多种方法的简明调查，强调了该领域的挑战和机遇。
英文摘要：
Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in characterizing such spatial heterogeneities and probing the impact of confinement on materials' properties. For static properties, this is a straightforward task and can be achieved via simple spatial binning. Such an approach, however, cannot be readily applied to transport coefficients due to lack of natural extensions of autocorrelations used for their calculation in the bulk. The prime example of this challenge is diffusivity, which, in the bulk, can be readily estimated from the particles' mobility statistics, which satisfy the Fokker-Planck equation. Under confinement, however, such statistics will follow the Smoluchowski equation, which lacks a closed-form analytical solution. This brief review explores the rich history of estimating profiles of the diffusivity tensor from MD simulations and discusses various approximate methods and algorithms developed for this purpose. Beside discussing heuristic extensions of bulk methods, we overview more rigorous algorithms, including kernel-based methods, Bayesian approaches, and operator discretization techniques. Additionally, we outline methods based on applying biasing potentials or imposing constraints on tracer particles. Finally, we discuss approaches that estimate diffusivity from mean first passage time or committor probability profiles, a conceptual framework originally developed in the context of collective variable spaces describing rare events in computational chemistry and biology. In summary, this paper offers a concise survey of diverse approaches for estimating diffusivity from MD trajectories, highlighting challenges and opportunities in this area.
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