Here, the \(\hbox {ZrCr}_2\) compound has been investigated as a novel candidate material for supercapacitor electrodes. Moreover, its alloy with Na in replacement of Cr atoms ( \(\hbox {ZrNa}_{0.5}\hbox {Cr}_{1.5}\) ) has been structured in order to prove Na-ion battery applicability and supercapacitance behavior as a hybrid energy material. The density functional theory with the general gradient approximation has been used for the present work calculations. The structural, thermodynamic, and dynamic stability of the compounds have been tested using the cohesive energy, enthalpy of formation energy, and phonon calculation, respectively. The diffusion coefficient for the \(\hbox {ZrNa}_{0.5}\hbox {Cr}_{1.5}\) is 9 \(\times\) 10 \(^{-8}\) \(\hbox {cm}^2\) /s which shows an improvement of 1 \(\times\) 10 \(^{-8}\) \(\hbox {cm}^2\) /s in compare with the pure compound. While its largest value at 300 K for electrical conductivity per relaxation time is 2.64 \(\times\) 10 \(^{20}\) and lower than that for \(\hbox {ZrCr}_2\) . Furthermore, the largest peaks of areal quantum capacitance are 511.06 \(\mu\) F/ \(\hbox {cm}^2\) (at 1.41 V) and 414.03 \(\mu\) F/ \(\hbox {cm}^2\) (at – 0.63 V) for \(\hbox {ZrCr}_2\) and \(\hbox {ZrNa}_{0.5}\hbox {Cr}_{1.5}\) , respectively. These results introduce new candidates for supercapacitance and Na-ion battery industries.
