Hu Yunfeng, Ounkham Phonemany, Marsalek Ondrej, Markland Thomas E, Krishmoorthy Bala, Clark Aurora E
Department of Mathematics and Statistics, Washington State University, Pullman, WA, United States.
Department of Chemistry, Washington State University, Pullman, WA, United States.
Front Chem. 2021 Mar 5;9:624937. doi: 10.3389/fchem.2021.624937. eCollection 2021.
Nuclear quantum effects (NQEs) are known to impact a number of features associated with chemical reactivity and physicochemical properties, particularly for light atoms and at low temperatures. In the imaginary time path integral formalism, each atom is mapped onto a "ring polymer" whose spread is related to the quantum mechanical uncertainty in the particle's position, i.e., its thermal wavelength. A number of metrics have previously been used to investigate and characterize this spread and explain effects arising from quantum delocalization, zero-point energy, and tunneling. Many of these shape metrics consider just the instantaneous structure of the ring polymers. However, given the significant interest in methods such as centroid molecular dynamics and ring polymer molecular dynamics that link the molecular dynamics of these ring polymers to real time properties, there exists significant opportunity to exploit metrics that also allow for the study of the fluctuations of the atom delocalization in time. Here we consider the ring polymer delocalization from the perspective of computational topology, specifically persistent homology, which describes the 3-dimensional arrangement of point cloud data, (i.e. atomic positions). We employ the Betti sequence probability distribution to define the ensemble of shapes adopted by the ring polymer. The Wasserstein distances of Betti sequences adjacent in time are used to characterize fluctuations in shape, where the Fourier transform and associated principal components provides added information differentiating atoms with different NQEs based on their dynamic properties. We demonstrate this methodology on two representative systems, a glassy system consisting of two atom types with dramatically different de Broglie thermal wavelengths, and ab initio molecular dynamics simulation of an aqueous 4 M HCl solution where the H-atoms are differentiated based on their participation in proton transfer reactions.
核量子效应（NQEs）已知会影响许多与化学反应性和物理化学性质相关的特征，特别是对于轻原子和在低温下。在虚时路径积分形式中，每个原子被映射到一个“环聚合物”上，其展宽与粒子位置的量子力学不确定性有关，即其热波长。此前已经使用了许多指标来研究和表征这种展宽，并解释由量子离域、零点能和隧穿引起的效应。许多这些形状指标只考虑环聚合物的瞬时结构。然而，鉴于人们对诸如质心分子动力学和环聚合物分子动力学等将这些环聚合物的分子动力学与实时性质联系起来的方法有着浓厚兴趣，存在着利用能够研究原子离域随时间波动的指标的重大机会。在这里，我们从计算拓扑学的角度，特别是持久同调的角度来考虑环聚合物离域，持久同调描述了点云数据（即原子位置）的三维排列。我们使用贝蒂序列概率分布来定义环聚合物所采用的形状集合。相邻时间的贝蒂序列的瓦瑟斯坦距离用于表征形状的波动，其中傅里叶变换和相关的主成分提供了基于动态性质区分具有不同核量子效应的原子的附加信息。我们在两个代表性系统上展示了这种方法，一个由两种具有截然不同德布罗意热波长的原子类型组成的玻璃态系统，以及对4M盐酸水溶液的从头算分子动力学模拟，其中氢原子根据它们参与质子转移反应的情况进行区分。
