The table 1 presents the minimized energies of various empty metallacages calculated using Hartree-Fock (HF) and PBE0 theories with the LanL2DZ basis set. The results reveal notable variations in energy differences between the HF and PBE0 methods across different metallacages. For instance, the Endo-N Pd 2 L 4 cage exhibits an energy difference of 20.541 Hartree between HF and PBE0, while the Endo-N Au 2 L 4 cage shows a difference of 20.635 Hartree. These discrepancies highlight that PBE0 generally predicts lower energy values compared to HF. This trend is consistent with the "Jacob's ladder" of exchange-correlation functionals, where PBE0, as a hybrid functional, incorporates both PBE and Hartree-Fock (HF) components, addressing some of the limitations inherent in pure DFT and HF methods. PBE0's lower energy predictions are attributed to its improved treatment of electron correlation and exchange interactions, leading to a more accurate depiction of the metallacages' stability and electronic structure. This enhanced accuracy underscores the advantage of hybrid functionals over pure HF and PBE approaches, reinforcing their importance in obtaining reliable results for metallacage stability assessments. Consequently, the observed energy differences are crucial for evaluating and comparing the theoretical frameworks applied to these structures.