First Principles Calculations.

We conducted the calculations using the GPAW code (55) with both generalized gradient approximations (GGAs) and local density approximation for the exchange correlation potentials. For GGA, we used Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional (56). For the projected augmented wave (57) method adopted here, a plane-wave cutoff of 1,100 eV was sufficient to converge the unit-cell electronic energy to the millielectronvolt level and reduce the residual atomic forces to 0.02 eV/Å. We obtained the crystal structure model of Ct by adopting the unit-cell volume value from Stv at 1 bar and the unit-cell parameter ratios from those at 140 GPa (20). We constructed two groups of models: Ct8 (2×2×2 supercell, a total of 48 to 54 atoms) and Ct12 (2×2×3 supercell, a total of 72 to 78 atoms). A total of six different models were calculated: dCt8 and dCt12 (no H atoms), hCt8-4H and hCt12-4H (one Si defect or 4H in the supercells; 3.84 and 2.54 wt % H2O, respectively), and hCt8-8H and hCt12-8H (two Si defects or 8H in the supercells; 7.89 and 5.17 wt% H2O, respectively). We used Monkhorst–Pack sampling (58): a total of 16 points (2×2×4) for the Ct8 cells and 8 points (2×2×2) for the Ct12 cells. For the starting crystal structure, we adopted the H coordination presented in Spektor et al. (8). For the H-bearing structures, H atom positions were also varied together with all other atoms during simulations. We conducted simultaneous optimization for the atomic positions and lattice constants using the Broyden–Fletcher–Goldfarb–Shanno algorithm in the Atomic Simulation Environment (59) at 1 bar and in the static lattice approximation (e.g., 0 K without zero-point motion). In the models with two defects, we arranged them at the maximum possible distances from each other.