The stereochemistry of 6s2 (E) lone pair of divalent Pb and trivalent Bi (PbII and BiIII designated by M*) in structurally related PbO, PbFX (X= Cl, Br, I), BiOX (X= F, Cl, Br, I) and Bi2NbO5F is rationalized. The lone pair LP presence determined by its sphere of influence E, equal to those of oxygen or fluorine anions, was settled by its center then giving M*-E directions and distances. Detailed description of structural features of both elements in the title compounds characterized by [PbEO]n and [BiEO]n layers allowed to show the evolution of M*-E distance versus the changes with the square pyramidal SP coordination polyhedra. All are different, in red PbO one finds {PbEO4E4} square antiprism, a {[Bi.E]O4X4Xapical} monocapped square antiprism in PbFX and BiOX and {BiEO4F4}square antiprism in Bi2NbO5F. To analyze the crystal chemistry results, the electronic structures of these compounds were calculated within density functional theory DFT. Real space analyses of electron localization illustrate a full volume development of the lone pair on PbII within {PbEO4E4} in PbOE, {PbEF4X4} in PbFXE and Bi(III) within {BiEO4X4} square antiprisms, contrary to Bi(III) within {[Bi.E]O4F4Fapical} monocapped square antiprism. Larger hardness (larger bulk modules B0) and band gap characterize BiOF versus PbO due to the presence of F which brings antibonding Bi-F interactions oppositely to mainly bonding Bi-O. In PbFX and BiOX series there is a systematic decrease of B0 with the increasing volume following the nature and size of X which is decreasingly electronegative and increasingly large. The electronic densities of states mirror these effects through the relative energy position and relative electronegativities of F/X and O/X leading to decrease the band gap.

中文翻译：

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方形平面配位中 Pb(II) 和 Bi(III) 孤对电子的晶体化学和从头算分析的相干视图

结构相关的 PbO、PbFX (X= Cl、Br、I)、BiOX (X= F、Cl、Br、 I) 和 Bi2NbO5F 是合理的。由其影响范围 E 决定的孤对 LP 的存在，等于氧或氟阴离子的影响范围，由其中心确定，然后给出 M*-E 方向和距离。以 [PbEO]n 和 [BiEO]n 层为特征的标题化合物中两种元素的结构特征的详细描述允许显示 M*-E 距离的演变与方形金字塔 SP 配位多面体的变化。所有都是不同的，在红色 PbO 中发现 {PbEO4E4} 方形反棱镜，PbFX 和 BiOX 中的 {[Bi.E]O4X4Xapical} 单端方形反棱镜和 Bi2NbO5F 中的 {BiEO4F4} 方形反棱镜。为了分析晶体化学结果，这些化合物的电子结构是在密度泛函理论 DFT 内计算的。电子局域化的真实空间分析说明了 PbOE 中 {PbEO4E4} 中 PbII 上孤对的完整体积发展，PbFXE 中的 {PbEF4X4} 和 {BiEO4X4} 方形反棱镜中的 Bi（III），与 {[ 中的 Bi（III）相反Bi.E]O4F4Fapical} 单顶方形反棱镜。较大的硬度（较大的块状模块 B0）和带隙是 BiOF 与 PbO 的特征，因为 F 的存在带来了与主要结合 Bi-O 相反的反键 Bi-F 相互作用。在 PbFX 和 BiOX 系列中，随着 X 的性质和大小的增加，随着体积的增加，B0 系统性地降低，X 的负电性越来越低，越来越大。