On the use of symmetry in configurational analysis for the simulation of disordered solids
On the use of symmetry in configurational analysis for the simulation of disordered solids
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DOI：
10.1088/0953-8984/25/10/105401
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发表时间：
2013-03-13
影响因子：
2.7
通讯作者：
Dovesi, Roberto
中科院分区：
文献类型：
--
作者：
Mustapha, Sami;D'Arco, Philippe;Dovesi, Roberto
无序系统的量子力学研究的起点通常意味着对配置的有限子集进行计算，这些配置是通过在纯化合物的原始单元的适当超单元内定义感兴趣的成分或从一个端元到另一个端元的一组成分而生成的。本文讨论了对称性用于识别对称性独立构型 (SIC) 的方式。首先，采用Polya的枚举理论来确定在变化和固定成分的情况下，对于编号为2或更多的颜色的SIC的数量。然后，提出了 De Bruijn 的概括，它允许分析颜色对称相关的情况，例如。 g。在磁系统中上下旋转。尽管计算 SIC 的效率很高，但 Polya 和 De Bruijn 的理论都无法帮助解决识别完整 SIC 列表的难题。代表性 SIC 是通过采用基于字典顺序的有序生成方法获得的，该方法具有避免对所有可能配置进行（计算成本昂贵）分析和存储的优点。当颜色数量增加时，该策略可以与满射分辨率原理相结合，这允许从（垂直条 R 垂直条 - 1）颜色情况获得的颜色开始，有效生成垂直条 R 垂直条颜色中的问题的 SIC。整个方案通过三个示例进行记录：具有 C-4v 对称性的正方形的抽象案例以及石榴石和橄榄石矿物家族的真实案例。
The starting point for a quantum mechanical investigation of disordered systems usually implies calculations on a limited subset of configurations, generated by defining either the composition of interest or a set of compositions ranging from one end member to another, within an appropriate supercell of the primitive cell of the pure compound. The way in which symmetry can be used in the identification of symmetry independent configurations (SICs) is discussed here. First, Polya's enumeration theory is adopted to determine the number of SICs, in the case of both varying and fixed composition, for colors numbering two or higher. Then, De Bruijn's generalization is presented, which allows analysis of the case where the colors are symmetry related, e. g. spin up and down in magnetic systems. In spite of their efficiency in counting SICs, neither Polya's nor De Bruijn's theory helps in solving the difficult problem of identifying the complete list of SICs. Representative SICs are obtained by adopting an orderly generation approach, based on lexicographic ordering, which offers the advantage of avoiding the (computationally expensive) analysis and storage of all the possible configurations. When the number of colors increases, this strategy can be combined with the surjective resolution principle, which permits the efficient generation of SICs of a problem in vertical bar R vertical bar colors starting from the ones obtained for the (vertical bar R vertical bar - 1)-colors case. The whole scheme is documented by means of three examples: the abstract case of a square with C-4v symmetry and the real cases of the garnet and olivine mineral families.