The band energy differences in the complexes have a significant impact on their electron mobility, as these differences are closely related to the electronic structure and charge transport properties of the materials. Electron mobility refers to the ease with which electrons can move through the complex, which is crucial for efficient catalytic activity, especially in processes like the HER. The consistently negative band energy differences in the Ni (II) complex (-0.755 eV to -1.002 eV) suggest a favorable alignment of energy levels for efficient electron transfer. Lower band energy differences imply that the electrons require less energy to transition from occupied to unoccupied molecular orbitals (e.g., from the HOMO to the LUMO). This facilitates rapid electron hopping and transport across the complex, enhancing electron mobility. High electron mobility ensures that the Ni (II) complex can effectively transfer electrons to protons for reduction, which is critical for HER.