The geometric, electronic and nonlinear properties of exohedral and endohedral single and multiple alkali metal (Li, Na and K) atom doped C₂₄ fullerene are studied. First, the most stable orientations at the most stable spin state are evaluated. Complexes with odd metal atoms are stable at doublet spin state and complexes with even number of metal atoms are stable at singlet spin state. Thermodynamic analysis shows that Li₄C₂₄ among all complexes with highest thermodynamic stability has interaction energy of −190.78 kcal mol⁻¹. The energy gaps (G_H-L) are fairly reduced in single and multi-doped cages, and the lowest energy gap is observed for K₄C₂₄ complex. NBO analysis is performed to validate the charge transfer from alkali metal toward C₂₄. The largest amount of charge (0.95 |e|) transfer is monitored in exohedral K₂C₂₄ complex where the highest charge transfer is for potassium (K) metal. Total density of states (TDOS) spectra of doped complexes justify the involvement of alkali metals and nanocage in new HOMO formation for the excess electrons. First hyperpolarizability is descriptor of NLO properties of single and multi-doped complexes are calculated. It is observed that doping of alkali metal atoms (Li, Na and K) greatly enhances the first hyperpolarizability. Among all the complexes of C₂₄, Na₃C₂₄ shows the highest hyperpolarizability value of 2.74 × 10⁵ au. The results of this study are a guideline for the computational designing of highly efficient and thermodynamically stable complexes for the optical and optoelectronic technologies.

研究了外表面和内表面单和多碱金属（Li，Na和K）原子掺杂的C ₂₄富勒烯的几何，电子和非线性性质。首先，评估在最稳定的自旋状态下最稳定的取向。具有奇数金属原子的配合物在双峰自旋态下稳定，而具有偶数金属原子的配合物在单重态自旋态下稳定。热力学分析表明，在所有具有最高热力学稳定性的配合物中，Li ₄ C _24的相互作用能为-190.78 kcal mol ^-1。在单掺杂和多掺杂笼中，能隙（G _H-L）均被减小，并且对于K ₄ C ₂₄观察到最低的能隙复杂的。进行NBO分析以验证从碱金属向C ₂₄的电荷转移。在外面K ₂ C _24配合物中监测到最大量的电荷转移（0.95 | e |），其中最高的电荷转移是金属钾（K）。掺杂复合物的总状态密度（TDOS）光谱证明了碱金属和纳米笼子参与了多余电子的新HOMO形成。第一超极化性是描述单和多掺杂复合物的NLO性质的描述符。观察到，碱金属原子（Li，Na和K）的掺杂极大地增强了第一超极化性。在C _24的所有络合物中，Na ₃ C ₂₄显示出最高的超极化率值2.74×10 ⁵ au。这项研究的结果为光学和光电技术的高效和热力学稳定配合物的计算设计提供了指导。