Hornfeck Wolfgang
Institute of Physics of the Academy of Sciences of the Czech Republic, Na Slovance 2, 182 21 Praha 8, Czech Republic.
Acta Crystallogr A Found Adv. 2020 Jul 1;76(Pt 4):534-548. doi: 10.1107/S2053273320006634. Epub 2020 Jun 30.
An extension is proposed of the Shannon entropy-based structural complexity measure introduced by Krivovichev, taking into account the geometric coordinational degrees of freedom a crystal structure has. This allows a discrimination to be made between crystal structures which share the same number of atoms in their reduced cells, yet differ in the number of their free parameters with respect to their fractional atomic coordinates. The strong additivity property of the Shannon entropy is used to shed light on the complexity measure of Krivovichev and how it gains complexity contributions due to single Wyckoff positions. Using the same property allows for combining the proposed coordinational complexity measure with Krivovichev's combinatorial one to give a unique quantitative descriptor of a crystal structure's configurational complexity. An additional contribution of chemical degrees of freedom is discussed, yielding an even more refined scheme of complexity measures which can be obtained from a crystal structure's description: the six C's of complexity.
有人提出对克里沃维切夫引入的基于香农熵的结构复杂性度量进行扩展，同时考虑晶体结构所具有的几何坐标自由度。这使得在约化晶胞中具有相同原子数，但在分数原子坐标方面自由参数数量不同的晶体结构之间能够进行区分。香农熵的强可加性属性被用于阐明克里沃维切夫的复杂性度量，以及它如何因单个魏科夫位置而获得复杂性贡献。利用相同属性可以将所提出的坐标复杂性度量与克里沃维切夫的组合复杂性度量相结合，从而给出晶体结构构型复杂性的唯一定量描述符。还讨论了化学自由度的额外贡献，得出了一种更精细的复杂性度量方案，该方案可从晶体结构描述中获得：复杂性的六个“C”。
