  In this work, we investigated the electronic structure and the quantum
capacitance of the functionalized MoS$_2$ monolayer. The functionalizations
have been done by using different ad-atom adsorption on Mo$S_2$ monolayer.
Density functional theory calculations are performed to obtain an accurate
electronic structure of ad-atom doped MoS$_2$ monolayer with a varying degree
of doping concentration. The quantum capacitance of the systems was
subsequently estimated. A marked quantum capacitance above 200 $\mu$F/cm$^2$
has been observed. Our calculations show that the quantum capacitance of
MoS$_2$ monolayer is significantly enhanced with substitutional doping of Mo
with transition metal ad-atoms. The microscopic origin of such enhancement in
quantum capacitance in this system has been analyzed. Our DFT-based calculation
shows that generation of new electronic states at the proximity of the
band-edge and the shift of Fermi level caused by the ad-atom adsorption results
in a very high quantum capacitance in the system.
