<p>In this study, the energetically most favorable configurations of Na and Na⁺ complexes with (Fe₃O₄)_{<i>n</i>=1−3} and (Fe₂O₃)_{<i>n</i>=1−3} nanoclusters, denoted as Na/Na⁺(Fe₃O₄)_{<i>n</i>=1−3} and Na/Na⁺(Fe₂O₃)_{<i>n</i>=1−3}, were systemically identified. The influence of Na and Na⁺ adsorption on the spin density distribution, charge distribution, and electronic band gap of the nanoclusters were systemically examined. The thermal ionization energy of Na adsorbed on the nanoclusters was determined within the framework of the neutral dissociation-ionization (NDI) mechanism. The influence of nanocluster size on the thermal ionization energy of Na was systematically examined. An oscillatory trend was observed for the (Fe₃O₄)_{<i>n</i>=1−5} clusters, wherein the calculated thermal ionization energies of clusters with even <i>n</i> were lower than those of their odd-<i>n</i> counterparts. For (Fe₂O₃)_{<i>n</i>=1−10} clusters, the thermal ionization energy of Na exhibited a decreasing trend with increasing cluster size, asymptotically a limiting value of 4.33&#xa0;eV. Moreover, the thermal ionization energy of Na adsorbed on the Fe₃O₄ (111) (4.36&#xa0;eV) and Fe₂O₃ (111) (4.41&#xa0;eV) nanosurfaces were calculated, both of which were in close agreement with that of bulk Fe₃O₄ (4.92&#xa0;eV). The calculated thermal ionization energies of Na were employed to estimate the thermal ionization efficiency of Na (<i>α</i>, defined as the population ratio of Na⁺ to neutral Na in the gas phase) for the selected clusters utilizing the Saha-Langmuir (SL) equation. An increase in <i>α</i> was observed with cluster size for the selected (Fe₂O₃)_<i>n</i> clusters. In contrast, for the (Fe₃O₄)_<i>n</i> clusters, <i>α</i> values for clusters with even <i>n</i> consistently exceeded those of clusters with odd <i>n</i>.</p> Graphical Abstract <p></p>