Evarestov R A, Gryaznov D, Arrigoni M, Kotomin E A, Chesnokov A, Maier J
Department of Chemistry, St. Petersburg State University, St. Petersburg, Russia.
Department of Theoretical Physics and Computer Modelling, Institute of Solid State Physics, University of Latvia, Riga, Latvia.
Phys Chem Chem Phys. 2017 Mar 22;19(12):8340-8348. doi: 10.1039/c6cp08582b.
In supercell calculations of defective crystals, it is common to place a point defect or vacancy in the atomic position with the highest possible point symmetry. Then, the initial atomic structure is often arbitrary distorted before its optimization, which searches for the total energy minimum. In this paper, we suggest an alternative approach to the application of supercell models and show that it is necessary to preliminarily analyze the site symmetry of the split Wyckoff positions of the perfect crystal supercell atoms (which will be substituted or removed in defective crystals) and then perform supercell calculations with point defects for different possible site symmetries, to find the energetically most favorable defect configuration, which does not necessarily correspond to the highest site symmetry. Using CeO as an example, it is demonstrated that this use of the site symmetry of the removed oxygen atoms in the supercells with vacancies allows us to obtain all the possible atomic and magnetic polaron configurations, and predict which vacancy positions correspond to the lowest formation energies associated with small polarons. We give a simple symmetry based explanation for the existence of controversies in the literature on the nature of the oxygen vacancies in CeO. In particular, the experimentally observed small polaron formation could arise for oxygen vacancies with the lowest C site symmetry, which exist in 3 × 3 × 3 and larger supercells. The results of first principles calculations using a linear combination of atomic orbitals and hybrid exchange-correlation functionals are compared with those from previous studies, obtained using a widely used DFT+U approach.
在缺陷晶体的超胞计算中，通常将点缺陷或空位置于具有尽可能高的点对称性的原子位置。然后，初始原子结构在优化之前常常会被任意扭曲，优化过程会寻找总能量的最小值。在本文中，我们提出了一种应用超胞模型的替代方法，并表明有必要预先分析完美晶体超胞原子（在缺陷晶体中会被替代或去除）的分裂怀科夫位置的点对称性，然后针对不同可能的点对称性进行带有点缺陷的超胞计算，以找到能量上最有利的缺陷构型，而这不一定对应于最高的点对称性。以CeO为例，证明了在有空位的超胞中利用被去除氧原子的点对称性，能够让我们获得所有可能的原子和磁极化子构型，并预测哪些空位位置对应于与小极化子相关的最低形成能。我们基于对称性对文献中关于CeO中氧空位性质的争议给出了一个简单解释。特别是，实验观察到的小极化子形成可能源于具有最低C点对称性的氧空位，这种空位存在于3×3×3及更大的超胞中。将使用原子轨道线性组合和混合交换关联泛函的第一性原理计算结果与之前使用广泛应用的DFT+U方法得到的研究结果进行了比较。
