3.4 Carbon dioxide

The CO$_2$ molecule has a special significance because it is very abundant in nature and is a model system involving $\pi $ bonding and sp-hybridization of carbon atoms. Similar to methane, carbon dioxide is a vdW crystal with strong (weak) intra-molecular (inter-molecular) interactions at low pressures 100. At room temperature and 1.5 GPa, CO$_2$ crystallizes as dry ice, with a cubic Pa3 structure. At pressures between 12 and 20 GPa, CO$_2$-I transforms to another molecular solid CO$_2$-III 101; 102; 103. The structure of phase III has been determined to be orthorhombic (Cmca) from X-ray diffraction experiments up to 12 GPa. It is known that above 20 GPa a non-molecular phase (called phase V) with tetrahedrally coordinated carbon atoms becomes stable 100.

In the previous prediction 104, unconstrained USPEX calculations succeeded in finding the correct CO$_2$ structures in a wide pressure range. By applying molecular constraint, we have more easily found the Cmca phase, just in 4 generations or $\scriptsize {\sim }$140 structural relaxations (Fig. 3.8). Cmca phase remains the most stable structure made of discrete CO$_2$ molecules at least up to 80 GPa. Both experiment 105 and theory 104; 106 show that CO$_2$ polymerizes above 20 GPa while the molecular form (Cmca phase) exists as a metastable form at low temperatures and higher pressures. This examples shows how imposing constraints gives the most stable molecular form, while unconstrained search finds the global minimum (which for CO$_2$ is non-molecular above 20 GPa). Both cases correspond to situations that are experimentally achievable, and thus important.

Figure 3.8: Crystal structure of CO$_2$ III (space group: Cmca, Z=4).