On representing chemical environments
On representing chemical environments
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DOI：
10.1103/physrevb.87.184115
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发表时间：
2013-05-28
影响因子：
3.7
通讯作者：
Csanyi, Gabor
中科院分区：
文献类型：
--
作者：
Bartok, Albert P.;Kondor, Risi;Csanyi, Gabor
我们回顾了最近发表的一些表示原子邻域环境的方法，并从忠实性和对势能面的适宜性两个方面分析了它们的相对优点。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和对物理学基本对称性的不变性：相同物种的原子的旋转、反射、平移和排列。我们证明了某些最初看起来完全不同的广泛使用的描述符是一般方法的特殊情况，在这种方法中，有限组的基函数随着角波数的增加被用来展开原子邻域密度函数。利用小星系团的例子系统，我们定量地表明，这种展开需要随着近邻数目的增加而被进行到越来越高的波数，以便获得忠实的表示，并且描述符的变体以非常不同的速率收敛。我们还提出了一种完全不同的方法，称为原子位置平滑重叠，它通过直接定义任意两个邻域环境之间的相似性来避开这些困难，并证明了它仍然与不变描述子密切相关。我们通过将模型拟合到小硅团簇和大块晶体的势能面来测试各种表示的性能。
We review some recently published methods to represent atomic neighborhood environments, and analyze 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 neighborhood 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 neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood 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.