Remarkable nonlinear optical response of M_n@C20 (M = Na & K and n = 1–6); a DFT outcome

Electronic, optical and nonlinear (NLO) optical properties of Na and K (single and multiple) doped C20 fullerene are investigated via density functional theory (DFT) methods. It is observed that the exohedral interaction of single and multi-doped (Na & K) with the C20 surface is highly exothermic, whereas endohedral interaction is highly endothermic (energetically non-favorable). Among all single and multi-doped complexes of C20, K₆@C20 shows the highest thermodynamic stability having interaction energy of −131.76 kcal mol^-1. The HOMO-LUMO energy gaps are effectively reduced, and this reduction is more prominent in multi-doped complexes compared to single atom doped complexes. TDOS plots of all doped complexes confirmed the involvement of metal atoms with C20 in newly generated HOMO orbitals. First hyperpolarizability analysis revealed the NLO response of newly designed single and multi-doped complexes. It is observed that the doping of multiple atoms of metals (Na & K) significantly increased the first hyperpolarizability (β_o), directly related with the NLO response. Among all considered Na and K complexes of C20 fullerene, K₅@C20 has the highest hyperpolarizability value i.e. 1.88×10⁵ a.u.