Table 3 Summary of the reactivity descriptors based on koopman’s approximation calculated at DFT/ωB97XD/6-311 + + g(d, p)/LANL2DZ computational method.

Complex	E_HOMO	E_LUMO	Eg	IP	EA	Μ	Η	S	ω	E_FL
Ni-Cu-C₆₀	− 7.308	− 2.953	4.356	7.308	2.953	5.131	2.178	0.230	6.043	− 5.130
Ni-Fe-C₆₀	− 6.985	− 2.379	4.606	6.985	2.379	4.682	2.303	0.217	4.759	− 4.682
Ni-Zn-C₆₀	− 5.609	− 3.999	1.610	5.609	3.999	4.804	0.805	0.621	14.334	− 4.804
Ni-Cu-C₆₀@C₆H₆	− 6.768	− 2.883	3.884	6.768	2.883	4.825	1.942	0.257	5.994	− 4.825
Ni-Fe-C₆₀@C₆H₆	− 7.015	− 2.034	4.982	7.015	2.034	4.525	2.491	0.201	4.110	− 4.525
Ni-Zn-C₆₀@C₆H₆	− 5.244	− 4.214	1.030	5.244	4.214	4.729	0.515	0.971	21.713	− 4.729
Ni-Cu-C₆₀@CH₂O	− 6.927	− 2.437	4.490	6.927	2.437	4.682	2.245	0.223	4.881	− 4.682
Ni-Fe-C₆₀@CH₂O	− 7.132	− 2.338	4.793	7.132	2.338	4.735	2.397	0.209	4.677	− 4.735
Ni-Zn-C₆₀@CH₂O	− 5.316	− 3.720	1.597	5.316	3.720	4.518	0.798	0.626	12.783	− 4.518

All units are in electron Volt (eV), except for chemical softness (S) with its unit in eV^− 1.

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