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According to density functional theory, we investigate the effects of BF3, BF4, BCl3, AlF3, AlCl3, AlBr3, BeF3, GaF3, GaCl3, GaBr3, NO3, BS2, BSO, BO2, F2, PF5, PCl5, and ASF5 molecules on the geometric, electronic, linear, and nonlinear optical properties of an Mg12O12 nanocage. The thermodynamic stability and feasibility of the adsorption process are investigated by analyzing the free energy. It is shown that the adsorptions of almost all molecules on the Mg12O12 surface are exothermic. The calculations of the polarizability of these nanoclusters show that among the studied molecules, BeF3 has the largest influence on the polarizability value (α≈315 a.u., the unit a.u. is short for atomic unit). The static first hyperpolarizability (β0) value is increased in the presence of these superhalogens. This increase is greatest for BeF3 and BF4 of which the highest value of the first hyperpolarizability (β0≈5775 a.u.) is related to a BeF3 c(e@Mg12O12) nanocluster. The adsorption position is a key to estimating the value of increasing the first hyperpolarizability.