In this work, the lanthanide (Ln) contraction phenomenon has been analyzed for three-dimensional structures in the solid state. We chose to study an isostructural series of lanthanide organic frameworks (LOFs) of formula [Ln₂(C₄H₄O₄)₃(H₂O)₂]_n·H₂O and 14 crystallographic structures (except promethium complex). The analysis of Ln contraction was made by analyzing the sum of all Ln–O bond lengths and the sum of all O–O distances, for the oxygen atoms of the coordination polyhedra, calculated with different semiempirical quantum mechanical models. The ∑_Ln–O and ∑_O–O for this LOF can be fit to a second-order polynomial. Based on the crystallographic structures, it is concluded that the phenomenon of Ln contraction is observed. Our results also suggest that the semiempirical Sparkle/PM3 and Sparkle/RM1 models reproduce the Ln contraction phenomenon well, and similar fits were obtained for ∑_Ln–O and ∑_O–O bond lengths.

中文翻译：

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镧系有机骨架中的镧系元素收缩：理论和实验研究。

在这项工作中，已对固态的三维结构分析了镧系元素（Ln）的收缩现象。我们选择研究分子式为[Ln ₂（C ₄ H ₄ O ₄）₃（H ₂ O）₂ ] _n ·H ₂ O的镧系元素有机骨架（LOFs）的同构系列，并具有14个晶体结构（structures络合物除外）。对Ln收缩的分析是通过分析配位多面体的氧原子的所有Ln–O键长之和和所有O–O距离之和，用不同的半经验量子力学模型计算得出的。∑ _Ln–O和∑ _O–O该LOF可以适合二阶多项式。根据晶体结构，可以得出观察到Ln收缩的现象。我们的结果还表明，半经验的Sparkle / PM3和Sparkle / RM1模型很好地重现了Ln收缩现象，并且对于_∑Ln–O和∑O _–O键长也获得了相似的拟合。