Thermodynamical study of N$_2$ clathrate hydrate from DFT calculations

TL;DR

This paper addresses the thermodynamic stability of nitrogen clathrate hydrates in the sI and sII forms under pressure using first-principles DFT. It benchmarks several exchange-correlation functionals and identifies revPBE-D3(0) as the most accurate for lattice constants and bulk moduli, enabling a zero-temperature phase diagram via convex-hull analysis. By computing guest–host and host–host energies across cage occupancies and pressures, the study reveals that single occupancy remains stable up to about $0.8$ GPa, while double occupancy in the larger cages stabilizes the sII phase at higher pressures, with the DO configurations approaching parity with phase separation at the highest pressures studied. The work provides a coherent thermodynamic framework at $T=0$ K and a baseline for finite-temperature extensions and for exploring alternative host frameworks under compression.

Abstract

Thermodynamic stability of N$_2$ 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 B$_0$ . 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 $\sim$ 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 N$_2$ hydrate stability and a baseline for finite-temperature extension.

Figures (7)

• Figure 1: Lattice parameter as a function of large cage occupancy for sI (left) and sII (right) structures, obtained with various DFT functionals: PBE (black circles), vdW-DF (red squares), vdW-DF2 (blue diamonds), and revPBE-D3(0) (green triangles). Crosses indicate experimental values measured at $80$ K and at $0$ K (the latter extrapolated from the $80$ K data according to Ref. Petuya2018a), both at atmospheric pressure (color-coded as indicated in the figure).
• Figure 2: Bulk modulus $B_0$ as a function of the large cage occupancy for sI (left) and sII (right) structures obtained with various DFT functionals: PBE (black circles), vdW-DF (red squares), vdW-DF2 (blue diamonds), and revPBE-D3(0) (green triangles). Crosses indicate experimental values measured at $273$ K for several compositions (purple crosses) and for a fixed composition (orange crosses) Chazallon2002, see the text for details. Error bars are also indicated for DFT and experimental values.
• Figure 3: Lattice parameter as a function of pressure in GPa for sI (left) and sII (right) structures, obtained with revPBE-D3(0) functional for different large cage occupancies $\theta_{LC}$. Symbols indicate experimental values extrapolated to 0K according to Ref. Petuya2018a. Large cage occupancies are indicated in the caption and directly on the figure for the sII various composition case (purple stars).
• Figure 4: Guest-host energy $E^{GH}$ (left) and host-host energy $E^{HH}$ (right) as a function of the large cage occupancy $\theta_{LC}$, obtained with various DFT functionals: PBE (black circles), vdW-DF (red squares), vdW-DF2 (blue diamonds), and revPBE-D3(0) (green triangles) for sI (solid lines) and sII (dashed lines) structures.
• Figure 5: Guest-host energy $E^{GH}$ (left) and host-host energy $E^{HH}$ (right) as a function of pressure in GPa, obtained with revPBE-D3(0) functional for different large cage occupancies $\theta_{LC}$. Solid and dashed lines correspond to sI and sII structures, respectively.