  H$_2$ evolution reaction (HER) requires an electrocatalyst to reduce the
reaction barriers for the efficient production of H$_2$. Platinum-group metal
(PGM) elements such as Pt, Pd, etc. and their derivatives show excellent
electrocatalytic activity for HER. The high cost and lack of availability of
PGM elements bring constraints over their wide commercial applications, so
discovering noble metal-free electrocatalysts with lower possible reaction
barriers is paramount important. Two-Dimensional Transition Metal
Dichalcogenides (2D TMDs) have emerged as a pinnacle group of materials for
many potential applications, including HER. In this work, we have
computationally designed a pristine 2D monolayer tungsten diselenide (WSe$_2$)
TMD using the first principle-based hybrid Density Functional Theory (DFT) to
investigate its structural, electronic properties and the electrocatalytic
performance for HER. The possible Volmer-Heyrovsky and Volmer-Tafel reaction
mechanisms for HER at the W-edge of the active site of WSe$_2$ were studied by
using a non-periodic finite molecular cluster model W$_{10}$Se$_{21}$. Our
study shows that the pristine 2D monolayer WSe$_2$ follows either the
Volmer-Heyrovsky or the Volmer-Tafel reaction mechanisms with a single-digit
low reaction barrier about 6.11, 8.41 and 6.61 kcal/mol during the solvent
phase calculations of H-migration, Heyrovsky and Tafel transition (TS) states,
respectively. The lower reaction barriers, high turnover frequency (TOF) ~ 4.24
x $10^6$ sec$^{-1}$ and 8.86 x $10^7$ sec$^{-1}$ during the Heyrovsky and Tafel
reaction steps and the low Tafel slope 29.58 mV.dec$^{-1}$ confirm that the
pristine 2D monolayer WSe$_2$ might be a promising alternative to PGM based
electrocatalyst.
