Density functional theory (DFT) and electron propagator theory (EPT) calculations were performed to study ground and excited electronic structures of alkali-metal (M) coordinated 9-crown-3, 24-crown-8, [2.1.1]cryptand, o-Me₂-1.1.1, and 3⁶Adamanzane complexes. Each complex bears an expanded electron in the periphery and occupies diffuse 1p-, 1d-, 1f-type molecular orbitals (or superatomic 1P, 1D, 1F orbitals) in excited electronic states. The calculated superatomic shell model of the M(9-crown-3)₂ is 1S, 1P, 1D, 1F, 2S, 2P, 2D, 1G and it is held by all other complexes up to the studied 1F level. Due to the highly diffuse nature of the electron, the ionization energies of these complexes are significantly lower (1.6–2.0 eV) and hence these complexes belong to the superalkali category. The ab initio EPT ionization energy and the excitation energies of the Li(9-crown-3)₂ were used to evaluate DFT errors associated with a series of exchange correlation functionals that span multiple rungs of Jacob's ladder (i.e., GGA, meta-GGA, global GGA hybrid, meta-GGA hybrid, range-separated hybrid, double-hybrid). Among these, the best performing functional is the range-separated hybrid CAM-B3LYP and the errors are within 6% of high-level ab initio EPT results. The accuracy of CAM-B3LYP is indeed transferable to similar complexes and hence the findings are expected to accelerate the progression of studies of Rydberg-type systems.

中文翻译：

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里德堡型碱金属冠醚、-cryptand 和-adamanzane 配合物的电子结构分析和 DFT 基准测试

进行密度泛函理论（DFT）和电子传播理论（EPT）计算来研究碱金属（M）配位的9-crown-3、24-crown-8、[2.1.1]cryptand的基态和激发电子结构，o -Me ₂ -1.1.1 和 3 ⁶金刚烷配合物。每个配合物的外围都有一个膨胀的电子，并在激发电子态下占据扩散的 1p-、1d-、1f 型分子轨道（或超原子 1P、1D、1F 轨道）。计算得出的 M(9-crown-3) ₂超原子壳层模型为 1S、1P、1D、1F、2S、2P、2D、1G，所有其他配合物均保持在所研究的 1F 水平。由于电子的高度扩散性质，这些配合物的电离能明显较低（1.6-2.0 eV），因此这些配合物属于超碱类别。从头算EPT 电离能和 Li(9-crown-3) ₂的激发能用于评估与跨越雅各氏梯多个梯级（即GGA、meta-GGA）的一系列交换相关函数相关的 DFT 误差。 、全局 GGA 混合、元 GGA 混合、范围分离混合、双混合）。其中，性能最好的函数是范围分离的混合 CAM-B3LYP，其误差在高级从头算EPT 结果的 6% 以内。 CAM-B3LYP 的准确性确实可以转移到类似的复合物，因此这些发现有望加速里德堡型系统的研究进展。