The complex nature of the f-orbital electronic structures and their interaction with the chemical environment pose significant computational challenges. Advanced computational techniques that variationally include scalar relativities and spin–orbit coupling directly at the molecular orbital level have been developed to address this complexity. Among these, variational relativistic multiconfigurational multireference methods stand out for their high accuracy and systematic improvement in studies of f-block complexes. Additionally, these advanced methods offer the potential for calibrating low-scaling electronic structure methods such as density functional theory. However, studies on the Cl K-edge X-ray absorption spectra of the [Ce(III)Cl₆]^3– and [Ce(IV)Cl₆]^2– complexes show that time-dependent density functional theory with approximate exchange–correlation kernels can lead to inaccuracies, resulting in an overstabilization of 4f orbitals and incorrect assessments of covalency. In contrast, approaches utilizing small active space wave function methods may understate the stability of these orbitals. The results herein demonstrate the need for large active space, multireference, and variational relativistic methods in studying f-block complexes.

中文翻译：

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f 轨道共价理论分析中的过度不稳定与过度稳定

f 轨道电子结构的复杂性质及其与化学环境的相互作用提出了重大的计算挑战。为了解决这种复杂性，已经开发出先进的计算技术，其中包括直接在分子轨道水平上的标量相对论和自旋轨道耦合。其中，变分相对论多配置多参考方法在f块复合体的研究中以其高精度和系统性改进而脱颖而出。此外，这些先进的方法为校准密度泛函理论等低尺度电子结构方法提供了潜力。然而，对 [Ce(III)Cl ₆ ] ^3–和 [Ce(IV)Cl ₆ ] ^2–配合物的 Cl K 边 X 射线吸收光谱的研究表明，具有近似交换的时间依赖性密度泛函理论 –相关核可能会导致不准确，从而导致 4f 轨道过度稳定和共价性评估不正确。相反，利用小型主动空间波函数方法的方法可能会低估这些轨道的稳定性。本文的结果表明在研究 f 块复合体时需要大活动空间、多参考和变分相对论方法。