  The objective of our research is to investigate the electrocatalytic
properties of novel metal-free quantum dots (QDs) composed of the recently
discovered 2D material penta-CN2, with the aim of replacing costly and scarce
catalysts such as Pt and Pd. Employing a first-principles density functional
theory (DFT) based approach, the geometries of the three penta-CN2 quantum dots
(QDs) of increasing sizes, 3 x 3, 3 x 4, 4 x 4 are optimized. Through
comprehensive analysis, our research extensively explored the structural
stability of penta-CN2 QDs, delved into their electronic properties, and
assessed their catalytic performance concerning the Hydrogen Evolution Reaction
(HER). Notably, the H-adsorbed penta-CN2 QDs exhibit a significant reduction in
the HOMO-LUMO gap (E_{g}) ranging from 35% to 49% compared to the pristine QD.
Next, we investigated their catalytic performance relevant to HER, using
well-known descriptors: (i) adsorption energy, (ii) over-potential, (iii) Gibbs
free energy and (iv) exchange current density along with the volcano curve. As
far as size dependence of the catalytic performance is concerned, the value of
Delta G^{(av)} is minimum for 3 x 3 penta-CN2 QD, with those of 3 x 4 and 4 x 4
QDs being slightly larger. Our calculations predict a high value of exchange
current density 2.24 x 10^{-3} A-cm^{-2} for one of the sites (N11 for 3 x 3
QD), which we believe will lead to significantly enhanced HER properties. Our
research outcomes hold great promise in advancing the discovery of abundant,
non-toxic, and cost-effective catalysts for HER, playing a vital role in
facilitating large-scale hydrogen production.
