Equations of state of solid CO$_2$ phases at megabar pressures

The stability of CO$_2$ phases at pressures up to $1600$ GPa is confirmed using evolution methods for predicting crystal structures. Stable CO$_2$ phases are as follows: $I\bar {4}2d$ (to $279$ GPa), $P4_2/nmc$ ($279$–$952$ GPa), $Pbcn$ ($952$–$1018$ GPa), and $Pa\bar {3}$ (above $1018$ GPa). The equations of state for stable CO$_2$ phases up to pressures of about $1600$ GPa are calculated for the first time using ab initio methods and high-temperature calculations within the quasi-harmonic approximation. It is shown that high-pressure $P{{4}_{2}}/nmc$, $Pbcn$, and $Pa\bar {3}$ phases have rather high bulk moduli ($290$–$415$ GPa). Phases with sixfold coordination of carbon atoms ($Pbcn$ and $Pa\bar {3}$) have higher coefficients of thermal expansion in comparison with the $P{{4}_{2}}/nmc$ phase.