Prediction of novel high-pressure ${\mathrm{H}}_2\mathrm{O}$-NaCl and carbon oxide compounds with a symmetry-driven structure search algorithm

Crystal structure prediction with theoretical methods is particularly challenging when unit cells with many atoms need to be considered. Here we employ a symmetry-driven structure search (SYDSS) method and combine it with density functional theory (DFT) to predict novel crystal structures at high pressure. We sample randomly from all 1506 Wyckoff positions of the 230 space groups to generate a set of initial structures. During the subsequent structural relaxation with DFT, existing symmetries are preserved, but the symmetries and the space group may change as atoms move to more symmetric positions. By construction, our algorithm generates symmetric structures with high probability without excluding any configurations. This improves the search efficiency, especially for large cells with 20 atoms or more. We apply our SYDSS algorithm to identify stoichiometric (${\mathrm{H}}_2{\mathrm{O})}_n$-(${\mathrm{NaCl})}_m$ and ${\mathrm{C}}_n{\mathrm{O}}_m$ compounds at high pressure. We predict a novel ${\mathrm{H}}_2\mathrm{O}$-NaCl structure with Pnma symmetry to form at 3.4 Mbar, which is within the range of diamond anvil experiments. In addition, we predict a novel ${\mathrm{C}}_2\mathrm{O}$ structure at 19.8 Mbar and ${\mathrm{C}}_4\mathrm{O}$ structure at 44.0 Mbar with Pbca and C2/m symmetry, respectively.

Figure 1

Distribution of initial and final space groups among the 57 347 ${\mathrm{H}}_2\mathrm{O}$-NaCl structures that we generated with our SYDSS algorithm. Both distributions are not identical because the space group may change during the structural relaxation with DFT forces. Some space groups have a low or zero occurrence probability. We set their probabilities to ${10}^{-3}$ to include them in this graph.

Figure 2

In this transition diagram, final vs initial space groups are plotted for the relaxation of 1 to 4 formula unit structures. Transitions to higher space groups are much more frequent because the structural relaxation often increases the symmetry. The large circle indicates one possible pathway to our Pnma structure. The lines separate the seven crystal systems.

Figure 3

The difference in enthalpy, $H_{{\mathrm{H}}_2\mathrm{ONaCl}}-H_{{\mathrm{H}}_2\mathrm{O}}-H_{\mathrm{NaCl}}$, per formula unit as function of pressure. The arrow marks the pressure of 3.4 Mbar where the ${\mathrm{H}}_2\mathrm{O}$-NaCl structure with Pnma symmetry is predicted to form from ${\mathrm{H}}_2\mathrm{O}$ and NaCl. The $P{2}_1$ and $P\overline{1}$ structures were also shown to have lower enthalpies than the endmembers at 5 Mbar but the Pnma structure is energetically favored.

Figure 4

Novel orthorhombic NaCl-${\mathrm{H}}_2\mathrm{O}$ crystal structure with Pnma symmetry. With decreasing size, the spheres denote the positions of Cl, Na, O, and H atoms. The structure has 20 atoms per unit cell but has been doubled in $c$ direction in the right image.

Figure 5

Enthalpy difference per formula unit as a function of composition is plotted. (a) Representative enthalpy calculations for varying compositions at 7 Mbar. (b) Enthalpy calculations at 50 Mbar suggest ${\mathrm{C}}_4\mathrm{O}$ and ${\mathrm{C}}_2\mathrm{O}$ structures would be favorable in systems that contain more carbon than ${\mathrm{CO}}_2$.

Figure 6

Moniclinic ${\mathrm{C}}_4\mathrm{O}$ crystal structure with C2/m symmetry at 45 Mbar. The unit cell with ten atoms as been doubled along every lattice vector to better illustrate the C and O layers in the structure. The C and O atoms are shown in dark and light color, respectively.

Figure 7

Orthorhombic ${\mathrm{C}}_2\mathrm{O}$ crystal structure with Pbca symmetry at 25 Mbar. The unit cell with 24 atoms as been doubled in $b$ direction. The C and O atoms are shown in dark and light color, respectively.

Figure 8

The difference in enthalpy, $H_{{\mathrm{C}}_{\mathrm{n}}{\mathrm{O}}_{\mathrm{m}}}-\left[(n-2m)\times H_{\mathrm{C}}+m\times H_{{\mathrm{C}}_2\mathrm{O}}\right]$, per atom as function of pressure. The first arrow marks the pressure of 19.8 Mbar where the ${\mathrm{C}}_2\mathrm{O}$ structure with Pbca symmetry is predicted to form. The second arrow marks the pressure 44.0 Mbar where the ${\mathrm{C}}_4\mathrm{O}$ structure with C2/m symmetry is predicted to form.