The complexation reactions between lanthanide 3⁺ cations and 2,9-bis(1,2,4-triazin-3-yl)-1,10-phenanthroline and its derivatives were studied with density functional theory Perdew-Burke-Ernzerhof functionals. The complexes consisted of one lanthanide cation and two ligand molecules. Complexation reactions were found to be exothermic and spontaneous in the gas phase. Absolute values of complextion energy and enthalpy increase in the lanthanide series and follow linear trends of lanthanide atomic number. All the bond lengths decrease in the lanthanide series with increasing charge density.

中文翻译：

---

2,9-双（1,2,4-三嗪-3-基）-1,10-菲咯啉（BTPhen）及其衍生物与镧系元素的DFT研究

用密度泛函理论Perdew-Burke-Ernzerhof泛函研究了镧系元素3 ⁺阳离子与2,9-双（1,2,4-三嗪-3-基）-1,10-菲咯啉及其衍生物之间的络合反应。该络合物由一个镧系阳离子和两个配体分子组成。发现络合反应在气相中是放热的和自发的。镧系元素中络合能和焓的绝对值增加，并遵循镧系元素原子数的线性趋势。镧系随电荷密度的增加，所有键长均减小。