基于Ewald求和多极展开的结晶集体变量
Collective Variables Based on Multipole Expansion of Ewald Summation for Crystallization
AI总结：
本文提出基于Ewald求和多极展开的集体变量框架，通过球谐函数投影编码平移与取向有序，实现结晶模拟中高保真且可转移的晶体结构预测。
摘要：
结晶是一种基本的相变过程，控制着自然和工业环境中材料的形成，涉及从无序相自发涌现出长程结构有序。这种长程周期性包含空间和分子取向有序。结晶的分子动力学（MD）模拟需要能够准确区分这种长程周期性的集体变量（CVs）。现有的基于局部描述符（如键取向序）的CVs在不同晶体结构间往往缺乏可转移性。为解决这一问题，我们提出了一个统一的CV框架，该框架源自Ewald求和多极展开：一种连接X射线衍射（XRD）原理与MD中静电能量计算的数学形式体系。通过将原子构型投影到球谐函数基（对角度函数表示完备）上，我们的CV实现了对平移和取向有序的高保真编码。元动力学模拟表明，该CV能够驱动对已知晶体多晶型路径的高效采样，并能在即使没有晶体结构的情况下预测稳定相。该方法展现出作为从头晶体结构预测可转移平台的潜力。
英文摘要：
Crystallization, a fundamental phase transition process governing material formation in natural and industrial contexts, involves the spontaneous emergence of long-range structural order from disordered phases. This long-range periodicity involves spatial and molecular orientation order. Molecular dynamics (MD) simulations of crystallization require collective variables (CVs) that accurately distinguish this long-\range periodicity. Existing CVs based on local descriptors (e.g., bond-orientational order) often lack transferability across crystal structures. To address this, we propose a unified CV framework derived from the multipole expansion of Ewald summation: a mathematical formalism bridging X-ray diffraction (XRD) principles and electrostatic energy computation in MD. By projecting atomic configurations onto a basis of spherical harmonics (complete for angular function representation), our CV achieves high-fidelity encoding of both translational and orientational order. Metadynamics simulations demonstrate that this CV drives efficient sampling of polymorphic pathways for known crystals and predicts stable phases even without crystal structures. This approach shows potential as a transferable platform for ab initio crystal structure prediction.
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