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

TL;DR

The paper tackles the challenge of designing earth-abundant, metal-free HER catalysts by using graphynes as tunable carbon platforms. A joint DFT and reactive MD framework investigates pristine, B-doped, N-doped, and B-N co-doped γ-graphyne and 6,6,12-graphyne to map near-$E_F$ electronic structure, defect formation energies, and adsorption free energies via the computational hydrogen electrode, followed by finite-temperature hydrogenation tests. Key findings show that BN co-doping stabilizes dopant configurations and reshapes the near-$E_F$ manifold, with ortho BN geometry achieving near-thermo-neutral adsorption on $sp$-proximate carbons in γ-graphyne, while 6,6,12-graphyne is more prone to over-hydrogenation and bond scission; γ-graphyne can sustain controlled hydrogen uptake under BN-ortho, whereas meta/para BN geometries destabilize the lattice. These results establish design principles for graphyne-based HER catalysts that require both favorable $\Delta G_{ads}$ and robust finite-temperature stability, highlighting BN geometry as a key lever for achieving practical catalytic performance.

Abstract

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 $γ$-graphyne and 6,6,12-graphyne (meta/ortho/para). $γ$-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 $π$ 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 $ΔG_{\mathrm{ads}}$ '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 $γ$-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 $ΔG_{\mathrm{ads}}$ and finite-temperature hydrogenation stability.

Figures (6)

• Figure 1: The fully optimized atomic structures of $\gamma$-graphyne (a-f) and 6,6,12-graphyne (g-l) considered in this work. Pristine lattices are shown in (a,g); single substitutional B and N doping at a carbon site in (b,h) and (c,i), respectively; and B-N co-doping in (d,j) meta, (e,k) ortho, and (f,l) para substitutions, defined by the relative placement of the two substitutional dopants.
• Figure 2: Electronic band structures of $\gamma$-graphyne (a-f) and 6,6,12-graphyne (g-l) for pristine, single-doped, and co-doped configurations, including atomic-orbital projections on the dopants. Pristine lattices are shown in (a,g); substitutional B and N doping (C$\rightarrow$B/N) in (b,h) and (c,i), respectively; and B–N co-doping in meta (d,j), ortho (e,k), and para (f,l) substitutions. The colored markers highlight the projected contributions from B (light-coral) and N (blue) states to the corresponding bands, while black lines denote the total band dispersion. Energies are referenced to the Fermi level ($E_F=0$, red dashed line).
• Figure 3: (a) Formation energy values (in $\mathrm{eV/atom}$) for substitutional B, N, and B-N pair doping in $\gamma$-graphyne (red) and 6,6,12-graphyne (blue). (b,c) Hydrogen adsorption free energies $\Delta G_{\mathrm{ads}}$ (in $\mathrm{eV}$) for pristine (G), B-doped (B), N-doped (N), and B-N co-doped (meta/ortho/para) structures. Each marker denotes a distinct adsorption site, annotated by the local carbon hybridization ($sp$ or $sp^{2}$), and the red dashed line marks the thermo-neutral condition $\Delta G_{\mathrm{ads}}=0$. (d,e) Spatial distribution of the hydrogen adsorption free energy ($\Delta G_{\mathrm{ads}}$) for $\gamma$-graphyne and 6,6,12-graphyne, respectively. The color scale ranges from $-1.5$ eV (blue) to $+1.5$ eV (red).
• Figure 4: Final atomic configurations obtained after 500 ps of thermalization for $\gamma$-graphyne (a–f) and 6,6,12-graphyne (g–l). Panels (a–f) correspond to $\gamma$-graphyne in the following configurations: pristine (a), B-doped (b), N-doped (c), and BN co-doped in meta (d), ortho (e), and para (f) substitutions. Panels (g–l) show the corresponding final structures for 6,6,12-graphyne in the same sequence: pristine (g), B-doped (h), N-doped (i), and BN co-doped in meta (j), ortho (k), and para (l) substitutions. All structures correspond to the equilibrated atomic positions after molecular dynamics thermalization.
• Figure 5: Time evolution of the average number of hydrogen bonds obtained from molecular-dynamics simulations for $\gamma$-graphyne (a-f) and 6,6,12-graphyne (g-l). For each system, panels correspond to the same set of structures considered in Fig. 1: pristine, single substitutional B and N doping, and B-N co-doping in meta/ortho/para substitutions (ordered as a-f and g-l, respectively). The stacked areas report the site-resolved contributions to the hydrogen-bond statistics from the different atomic species and local environments (C in $sp$ and $sp^{2}$ coordination, and dopant B/N; color code as indicated). The structural snapshots next to each plot identify the adsorption site(s) and the corresponding carbon hybridization.