Abstract The stereochemistry of 6s 2 (E) lone pair LP characterizing Tl I , Pb II , Bi III , and Po IV (M ∗ ) in fluorides and oxides as well as in mixed valence compounds is examined within a coherent crystal chemistry and ab initio visualizations and analyses. Besides square planar environments, large coverage of tetrahedral, triangular bipyramidal, square pyramidal, octahedral and hexahedral geometries is presented and addressed. In our formal image ns 2 lone pair is considered as a free electron doublet concentrated in a centroid, called Ec, which generates around it an electronic cloud, detected in the crystal network as an empty volume, attached to M ∗ , opposite to bonding coordination and where physical condensation (pressure) can eventually distort but not compress. Finally the lone pair E is defined by a sphere of influence found to occupy a volume close to oxygen or fluorine anions. Only crystal network by its architecture more or less dense can really modify M ∗ –E eventually to m*–E = 0 coalescence of the center of volume of influence E with the cation center transforming M ∗ in a large cation [M ∗ E] n + comparable to K + , Cs + or Ba 2+ . The crystal chemistry analyses combined with electron localization function ELF from density functional theory DFT based calculations allow defining E volume and plasticity, M ∗ –E directions and distances of the different extended case studies. Original features highlighted with ELF and electronic densities of states and chemical bonding plots characterize the mixed valence compounds containing both LP-bearing (ex. Tl I , Pb II , Bi III ) and non LP bearing (Tl III , Pb IV , Bi V ) ions.

中文翻译：

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Tl(I) 到 Po(IV) 6s2 孤对四面体、三角双锥体、方锥体、八面体和六面体几何结构：晶体化学和从头算可视化和分析

摘要 表征氟化物和氧化物以及混合价化合物中的 Tl I 、Pb II 、Bi III 和 Po IV (M ∗ ) 的 6s 2 (E) 孤对 LP 的立体化学在相干晶体化学和 ab initio可视化和分析。除了方形平面环境外，还介绍并解决了四面体、三角双锥体、四方锥体、八面体和六面体几何的大范围覆盖。在我们的正式图像中，ns 2 孤对被认为是集中在一个质心中的自由电子双峰，称为 Ec，它在它周围生成一个电子云，在晶体网络中检测为一个空体积，连接到 M*，与键合配位相反并且物理冷凝（压力）最终会变形但不会压缩。最后，孤对电子 E 由发现占据接近氧或氟阴离子的体积的影响范围定义。只有通过其结构或多或少密集的晶体网络才能真正将 M * -E 最终修改为 m * -E = 0 影响 E 的体积中心与阳离子中心在大阳离子中转化 M * 的聚结 [M * E] n + 与 K + 、Cs + 或 Ba 2+ 相当。晶体化学分析与来自密度泛函理论 DFT 计算的电子定位函数 ELF 相结合，允许定义不同扩展案例研究的 E 体积和塑性、M * -E 方向和距离。用 ELF 和电子态密度以及化学键图突出显示的原始特征表征了含有 LP（例如 Tl I、Pb II、Bi III ）和非 LP（Tl III 、