Understanding the behavior of simple molecular systems under the combined effect of high pressure (P) and temperature (T) has important implications in the modeling of planetary interiors, in the chemistry of detonation, and in the synthesis of new materials. Extreme conditions of P and T can be partially accessed in the laboratory either in heated diamond-anvil cells or in shock wave experiments, where dramatic changes in the chemical and physical properties of simple molecules have been reported. Depending on the detailed situation, compression may result in the formation of intermolecular bonds, or in disproportionation, or even in full dissociation into the constituent elements. In such a context, the theoretical prediction of stable or metastable structures and of their properties is highly desirable. However, this requires an accurate quantum description, capable of discriminating the often subtle changes in the nature of chemical bonds. First-principles molecular dynamics methods with variable-cell, constant-pressure dynamics—a natural derivation of the two revolutionary methods introduced more than 20 years ago by Michele Parrinello together with Roberto Car and Anees Rahman—offer a unique tool for this kind of exploration. Molecular CO2 was independently observed [5] and predicted to transform into extended quartz-like covalent solids at moderately high pressures (about 50 GPa). The actual structure of this high-pressure phase, as well as its P–T range of thermodynamic stability, are still widely debated. High temperatures (thousands of Kelvin) were crucially required in the synthesis of an extended covalent network, both in experiments and in theoretical simulations, which indicated that large reaction barriers are overcome in the synthesis. One possible explanation is that these barriers are associated with the rehybridization of carbon atomic orbitals, from linear (sp) in the molecule, to tetrahedral (sp) in all candidates for the extended solid proposed so far. Carbon is well-known to change its hybridization state with pressure. For example, carbon’s hybridi-