Density functional theory (DFT) calculations have been performed for the single and multi-alkaline earth metal atoms doped C₂₄ fullerene. All possible orientations have been optimized with different spin states to achieve the most stable geometry. Be₄@C₂₄ shows the highest interaction energy of −182.87 kcal mol⁻¹ among all complexes. The H-Lgap is increased in single doped complexes but is fairly reduced in all multi-doped cages, and the lowest H-Lgap is observed for Mg₄@C₂₄ (0.83 eV) which indicates the conductor behavior of this newly designed complex. NBO analysis is performed to confirm the charge transfer from metal toward the cage. The largest amount of charge (1.18 |e|) transfer has been observed for endohedral Mg@C₂₄ nanocage. Involvement of new HOMO orbitals (due to excess electrons) is confirmed from total density of states (TDOS) spectra of doped cages. It was observed that doping of alkaline earth metal atoms (Be, Mg and Ca) greatly enhanced the first hyperpolarizability. Among all these AEM_n@C₂₄ (AEM = Be, Mg and Ca, n = 1, 2, 3, 4) cages, Mg₄@C₂₄ shows the highest hyperpolarizability value of 3.62 × 10⁶ au with H-Lgap of 0.83 eV. The results of this study provide a guideline for the synthesis of highly efficient and thermodynamically stable nanocages for the optical and optoelectronic applications.

已经对单碱金属和多碱土金属原子掺杂的C ₂₄富勒烯进行了密度泛函理论（DFT）计算。所有可能的方向都已用不同的自旋状态进行了优化，以实现最稳定的几何形状。Be ₄ @C ₂₄在所有配合物中显示出最高的相互作用能-182.87 kcal mol ^-1。在单掺杂复合物中，H-Lgap增加，但在所有多掺杂笼中，H-Lgap均显着降低，Mg ₄ @C ₂₄的最低H-Lgap（0.83 eV）表示此新设计复合体的导体行为。进行NBO分析以确认电荷从金属向保持架的转移。对于内面Mg @ C ₂₄纳米笼，已观察到最大量的电荷转移（1.18 | e |）。从掺杂笼的总状态密度（TDOS）光谱中可以确认新HOMO轨道的参与（由于电子过多）。观察到，碱土金属原子（Be，Mg和Ca）的掺杂大大增强了第一超极化性。在所有这些AEM _n @C ₂₄（AEM = Be，Mg和Ca，n = 1，2，3，4）笼子中，Mg ₄ @C ₂₄表现出最高的超极化率值3.62×10 ⁶au，H-Lgap为0.83 eV。这项研究的结果为合成用于光学和光电应用的高效且热力学稳定的纳米笼提供了指南。