Determination of the crystal distortion caused by stereochemically active lone electron pairs.

偏离理想多面体和多面体排列的结构变形可能有多种原因，并且总是影响固体的晶体化学和晶体物理性质。为了理解结构-性质关系，这对任何应用的发展都是至关重要的，这些扭曲的来源及其精确测量是至关重要的。其中一个因素是立体化学活性孤对（LEP），其强度在理论上可以通过Liebau密度矢量来描述。然而，在实验上，到目前为止，我们只能使用Wang-Liebau偏心率（WLE）参数来访问多面体坐标的原子畸变。这种测量在确定LEP的影响时存在固有缺陷，因为它不允许将这种影响与所有其他可能对失真的影响（例如Jahn-Teller失真，二次伸长或Halasyamani失真）分开。然而，自然界可能提供了探索这个问题的完美工具，因为镧系元素收缩导致第5和第6周期的元素几乎具有相同的尺寸，因此至少在几何上应该导致同构材料。然而，周期5的元素显示出大的LEP，而周期6的元素由于相对论效应吸引而较小。因此，如果选择一对材料，其中一个在相同位置包含周期5元素，另一个在相同位置包含周期6元素，则可以直接评估LEP对WLE的贡献。这将仅给出两个不同的值，但是如果将这对材料视为其中这两种元素可以以任何比例混合的固溶体的极端，则可以获得用于这种评估的精细分辨工具，这对于固态化学和晶体学具有基本价值。（M = Al，Ga，Cr，Mn，Fe）和连接它们的固溶体将为研究和分离孤对效应提供理想的平台，因此我们提出合成这些材料（其中一些已经被我们和其他人描述过），并根据它们的物理性质评估它们的晶体结构。（热膨胀、热相稳定性、带隙行为或磁性）这将给出材料和温度依赖的WLE以及对物理性质的影响。此外，DFT方法将用于计算LDV，提供LEP的电子密度及其方向的信息。积累了这些数据，我们将协同这些发现，并能够产生一个新的概念模型的真实的影响的LEP失真。

Structural distortion away from ideal polyhedra and polyhedral arrangements can have multiple causes and always influences the crystal-chemical and crystal-physical properties of a solid. For the understanding of structure-property relationships, which are crucial for the development of any application, the origin of these distortions and their precise measurement is of pivotal importance.One such factors is a stereochemical active lone pair (LEP), whose strength can be theoretically described by the Liebau density vector. Experimentally however, up to now, we can only access the atomic distortion of a polyhedral coordination using the Wang-Liebau eccentricity (WLE) parameter. This measurement is intrinsically flawed in determining the influence of the LEP, because it does not allow to separate out this influence from all other possible influences on distortion (for example Jahn-Teller-distortion, Quadratic elongation, or Halasyamani distortion). However, nature may offer a perfect tool of exploration of this question because the lanthanide contraction results in the fact that elements of the 5th and 6th period have almost the same size, and hence should – geometrically at least – lead to isostructural materials. However, elements of period 5 display large LEPs, whereas those of period 6 are smaller due to the relativistic effect attraction. Thus, if one chooses a pair of materials, in which one contains a period 5 element and the other a period 6 element at the same position, one can make a direct assessment of the contribution of the LEP to the WLE. This would give only two distinct values, but if one views this pair of materials as the extremes of a solid solution in which these two elements can be mixed in any ratio, one may obtain a finely resolved tool for this assessment, which is of fundamental value for solid state chemistry and crystallography.We believe that mullite-type compound pairs of the composition PbMBO4 / SnMBO4 (M = Al, Ga, Cr, Mn, and Fe) and the solid solutions that connect them will provide the ideal platform to study and separate the influence of the lone pair.We therefore propose to synthesize these materials (some of which have been described by us and others), and to assess their crystal structures in terms of their physical properties (thermal expansion, thermal phase stability, bandgap behavior or magnetic properties) This will give the material and temperature dependent WLE in hand with the influence on the physical properties. In addition, DFT methods will be used to calculate the LDV, providing information on the electron density of the LEP and its direction. Having accumulated these data, we will synergize these findings and be able to generate a new conceptional model of the real influence of the LEP on distortion.