The problem of atoms and molecules caged inside fullerenes has attracted renewed interests since a new endohedral species has been experimentally realized (Bloodworth etal 2019 Angew. Chem., Int. Ed. 58 5038). In this sense, detailed theoretical studies on the spectroscopic properties of atoms and ions spatially confined in fullerene-like structures are convenient. Here we perform density functional theory (DFT) and time-dependent DFT (TDDFT) calculations to investigate the electronic, vibrational and optical properties of two-electron atomic systems, X, caged in C₂₀ and C₂₀H₂₀ endohedral complexes; i.e. X@C₂₀ and X@C₂₀H₂₀ (X = He, Li⁺, and Be⁺⁺). Among these endohedral complexes, only the encapsulated Be⁺⁺ ion gives rise to strongly bound complexes, whereas the encapsulated Li⁺ ion depends on the confining environment, and the encapsulated He atom seems to be highly repulsive in both types of cages. Our calculated excitation energies indicate that the lowest-lying singlet states strongly depend on both the nature of the endohedral atom/ion and the type of the carbon cage. Although He@C₂₀H₂₀ and He@C₂₀ are obtained as repulsive complexes, they produce a small effect in the absorption spectra of the complexes. However, the presence of Li⁺ or Be⁺⁺ in the endohedral complexes dramatically changes the electronic absorption profile of these cages. Overall, this study shows that the confinement of a Be⁺⁺ ion in a very restricted space is energetically favorable, being its quantum states controllable by the confining environment.

自从通过实验实现了新的内嵌物种以来，富勒烯中的原子和分子问题重新引起了人们的兴趣（Bloodworth等人2019 Angew. Chem., Int. Ed. 58 5038）。从这个意义上说，对空间限制在富勒烯类结构中的原子和离子的光谱性质进行详细的理论研究是很方便的。在这里，我们执行密度泛函理论 (DFT) 和瞬态 DFT (TDDFT) 计算，以研究笼在 C ₂₀和 C ₂₀ H ₂₀内嵌配合物中的双电子原子系统 X 的电子、振动和光学特性；即 X@C ₂₀和 X@C ₂₀ H ₂₀（X = He、Li ⁺和 Be ⁺⁺）。在这些内嵌配合物中，只有封装的 Be ⁺⁺离子产生强结合的配合物，而封装的 Li ⁺离子取决于限制环境，封装的 He 原子似乎在两种类型的笼中都具有高度排斥性。我们计算出的激发能表明，最低的单线态强烈依赖于内嵌原子/离子的性质和碳笼的类型。虽然He@C ₂₀ H ₂₀和He@C ₂₀作为排斥配合物获得，但它们对配合物的吸收光谱产生很小的影响。然而，Li ⁺或Be的存在内嵌复合物中的⁺⁺显着改变了这些笼的电子吸收曲线。总的来说，这项研究表明，将 Be ⁺⁺离子限制在非常有限的空间中在能量上是有利的，因为其量子态可由限制环境控制。