Janus MXenes have exhibited many novel properties because of broken inversion symmetry. We systematically investigate the mechanical, electronic, and optical properties and the quantum capacitance ($C_{\mathrm{Q}}$) of Janus $\mathrm{Zr}M\mathrm{C}{T}_2$ ($M=\mathrm{Ti}$, Cr, Mn, Hf; $T=\mathrm{O}$, F, OH) by first-principles calculations. All systems except $\mathrm{ZrCrC}{\left(\mathrm{OH}\right)}_2$ are mechanically stable; ${\mathrm{ZrHfCO}}_2$ is the most resistant to deformation in all directions. ${\mathrm{ZrTiCO}}_2$ and ${\mathrm{ZrHfCO}}_2$ are nonmagnetic semiconductors; the substitution of O with the F group makes ${\mathrm{ZrHfCF}}_2$ and ${\mathrm{ZrTiCF}}_2$ become nonmagnetic conductors, and the substitution of O with the OH group makes $\mathrm{ZrHfC}{\left(\mathrm{OH}\right)}_2$ and $\mathrm{ZrTiC}{\left(\mathrm{OH}\right)}_2$ become magnetic metals. Obvious anisotropy of static dielectric constants $\left[{\varepsilon }_1\left(0\right)\right]$ along the $x$ and $y$ axes is observed for ${\mathrm{ZrTiCF}}_2, {\mathrm{ZrMnCF}}_2, \mathrm{ZrMnC}{\left(\mathrm{OH}\right)}_2$, and ${\mathrm{ZrHfCF}}_2$. $\mathrm{ZrTiC}{\left(\mathrm{OH}\right)}_2$ has the strong absorption of 24.93% along the $x$ axis. For ${\mathrm{ZrTiCT}}_2$, compared with O termination, F and OH terminations greatly improve the maximum $C_{\mathrm{Q}}$ of the system under positive bias in narrow voltage. Compared with O termination, F and OH terminations improve the top $C_{\mathrm{Q}}$ of ${\mathrm{ZrHfCT}}_2$ and ${\mathrm{ZrCrCT}}_2$ under negative bias. The $C_{\mathrm{Q}}$ and surface storage charge ($Q$) of $\mathrm{Zr}M\mathrm{C}{T}_2$ ($M=\mathrm{Ti}$, Mn, Hf) with mixed termination are also explored.

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• Electronic structure
• 2-dimensional systems
• Janus materials
• Density functional theory
• First-principles calculations