Ab initio determination of the phase diagram of $CO_2$ at extreme conditions.
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Carbon dioxide is one of the most stable molecules at ambient conditions, but under extreme conditions of pressure and temperature it has been reported to collapse into extended covalently bonded polymeric polymorphs. Unfortunately the experimental determination of the $CO_2$ phase diagram is hindered by slow kinetics and extensive metastability. At least eleven structures have been reported experimentally (of which seven molecular and four non-molecular). Using a combination of ab initio methods including molecular dynamics and free-energy determination in the quasi-harmonic approximation, we are able to reduce the number of thermodynamically stable phases to five. The only stable non-molecular phase of $CO_2$ is a partially collapsed cristobalite-like structure with tetrahedral carbon coordination similar to silicon in $SiO_2$. At lower pressures we find that the phase diagram contains four molecular phases, two of which are stable only at finite by temperature.