  The present study investigates the catalytic performance of a $hg-C_{3}N_{4}$
quantum dot aimed at enhancing electrochemical water splitting, using the
first-principles density functional theory. The size of the considered quantum
dot lies within the range reported experimentally (2nm - 4nm) [Zhou et al. ACS
Nano 9, 12480 (2015)]. The nitrogen vacancies are created in the considered
$hg-C_{3}N_{4}$ structure to simulate the realistic scenario, as the presence
of nitrogen and carbon defects are reported in the synthesized $hg-C_{3}N_{4}$
quantum dots. First, the structural and vibrational properties are computed to
ensure the stability of the nitrogen deficient $hg-C_{3}N_{4}$ quantum dots,
and subsequently, their electronic and hydrogen evolution reaction (HER)
properties are investigated. The calculate HER parameters, i.e., adsorption
energies, Gibbs free energies, and overpotentials demonstrate that the
considered $hg-C_{3}N_{4}$ quantum dot with nitrogen vacancies can be used as a
moderately effective electrocatalyst for HER performance. We also considered
the quantum dot to be dissolved in water and ethanol, and find that the
overpotential gets drastically reduced to 16 mV for the alcohol dissolved
quantum dot, while some significant reduction is seen for the aqueous solution
also. As a result, this study suggests that the nitrogen-deficient
$hg-C_{3}N_{4}$ quantum dots dissolved in ethanol are excellent candidates for
catalysis aimed at sustainable hydrogen production via electrochemical water
splitting.
