Thermodynamic stability of N₂ clathrate hydrates in the sI and sII structures is investigated using density functional theory with several exchange-correlation functionals, explicitly accounting for composition (cage occupancies) and pressure at T = 0 K. Among the tested functionals, revPBE-D3(0) best reproduces experimental lattice parameters and bulk moduli B₀ . Energetic analyses confirm the strong impact of large cage double occupancy on sI, whereas the convex-hull results show that sI with single occupancy remains thermodynamically stable up to ∼ 0.8 GPa alongside sII with single occupancy. Increasing pressure then stabilizes sII with double occupancy, consistent with its larger large-cage volume and lower framework strain. These results provide a coherent, first-principles thermodynamic framework for N₂ hydrate stability and a baseline for finite-temperature extension.