Controlling HER activity and stability of $\gamma$- and 6,6,12-Graphyne through engineered B-N doping: DFT and Reactive MD simulations

Graphynes offer a chemically heterogeneous $sp/sp^{2}$ carbon framework with distinct electronic regimes and site-selective reactivity. Here, Density Functional Theory and Reactive Molecular Dynamics Simulations are combined to evaluate pristine, B-doped, N-doped, and B-N co-doped $\gamma$-graphyne and 6,6,12-graphyne (meta/ortho/para). $\gamma$-graphyne is a semiconductor, while 6,6,12-graphyne exhibits an anisotropic Dirac-like semi-metallic dispersion. B/N substitution reconstructs near-$E_F$ states via dopant $\pi$ hybridization, and B-N pairing stabilizes defects through donor-acceptor compensation, with the ortho substitutions being the most favorable. Hydrogen adsorption remains weak on pristine lattices but becomes locally optimized upon doping, with near thermo-neutral $\Delta G_{\mathrm{ads}}$ 'hot spots' predominantly on $sp$-proximate carbon sites adjacent to the dopants. Reactive MD at 300 K further reveals an activity stability trade-off: B-N ortho in $\gamma$-graphyne sustains controlled hydrogen uptake without catastrophic bond scission, whereas B-N meta/para degrade, and 6,6,12-graphyne is generally more susceptible to over-hydrogenation. These results identify the B-N geometry as a key design variable for graphyne-based HER catalysts, which require both a favorable $\Delta G_{\mathrm{ads}}$ and finite-temperature hydrogenation stability.