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{\it Ab initio} determination of the phase diagram of CO$_2$ at high pressures and temperatures

The experimental study of the CO$_2$ phase diagram is hampered by strong kinetic effects leading to wide regions of metastability and to large uncertainties in the location of phase boundaries. Here we determine the CO$_2$ phase boundaries by means of {\it ab initio} calculations of the Gibbs free energy of several molecular and non-molecular solid phases of CO$_2$. Temperature effects are included in the quasi-harmonic approximation. Contrary to previous results, we find that the boundary between non-molecular phases and phase V has a positive slope and starts at 21.5 GPa at $T$ = 0 K. A triple point between phase IV, V, and the liquid phase is found at 35 GPa and 1600 K, indicating a broader region of stability for the non-molecular phases than previously thought. The experimentally determined boundary line between CO$_{2}$-II and CO$_{2}$-IV phases is reproduced by our calculations, indicating that kinetic effects are not relevant in that transition.