Manchester Institute of Biotechnology, 131 Princess Street, Manchester, M1 7DN, United Kingdom.
J Comput Chem. 2013 Aug 5;34(21):1850-61. doi: 10.1002/jcc.23333. Epub 2013 May 29.
We propose a generic method to model polarization in the context of high-rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc-1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds ("1, 4 and higher" interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom-atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol(-1).
我们提出了一种在高阶多极静电学背景下建模极化的通用方法。该方法涉及机器学习技术克里金法，这里用于捕获给定原子的原子多极矩对该原子周围原子位置变化的响应。原子是具有尖锐边界的可变形盒子，它们不重叠且占据空间。该方法应用于组氨酸，在使用 B3LYP/apc-1 水平下其 24 个局部能量极小值中的每一个的正常模式对 600 个几何形状进行变形后，在 600 个几何形状上进行训练后，它能够预测未见构型的原子多极矩（高达十六极）。通过计算具有预测的矩的原子与周围原子（具有精确的矩）之间的库仑能来评估预测的质量。仅包括原子之间的相互作用，这些原子之间的距离为三个或更多键（“1、4 和更高”相互作用）。将此能量与具有相同环境的具有精确多极矩的中心原子相互作用的能量进行比较。对于组氨酸的 29 个中心原子中的每一个，对于 539 个测试构型中的 80%（在训练集之外），将这 328 个原子-原子相互作用的总能量偏差小于 1 kcal mol(-1)。
