化学环境的表现
On representing chemical environments
摘要：
我们回顾了最近发表的一些方法来表示原子邻域环境，并分析了他们的相对优点，在他们的忠实性和适用性拟合势能面。这种表示（有时称为描述符）必须具有的关键性质是相对于移动原子的可微性，以及物理学基本对称性的不变性：旋转，反射，平移和同种原子的排列。我们表明，某些广泛使用的描述符，最初看起来很不同的是一个一般的方法，其中一组有限的基函数与角波数增加被用来扩大原子邻域密度函数的具体情况。使用的例子系统的小集群，我们定量地表明，这种扩展需要进行到越来越高的波数的邻居的数量增加，以获得一个忠实的表示，和变量的描述符收敛在非常不同的速度。我们还提出了一个全新的方法，称为平滑重叠的原子位置（SOAP），回避这些困难，直接定义任何两个邻域环境之间的相似性，并表明它仍然是紧密相连的不变描述符。我们测试的性能，通过拟合模型的小硅团簇和大块晶体的势能面的各种表示。
英文摘要：
We review some recently published methods to represent atomic neighbourhood environments, and analyse their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms, and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighbourhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbours increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether new approach, called Smooth Overlap of Atomic Positions (SOAP), that sidesteps these difficulties by directly defining the similarity between any two neighbourhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.
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