First-principles density functional theory (DFT) is used to study the solid-state modifications of carbon dioxide up to pressures of 60 GPa. All known molecular CO2 structures are investigated in this pressure range, as well as three non-molecular modifications. To account for long-range van der Waals interactions, the dispersion corrected DFT method developed by Grimme and co-workers (DFT-D3) is applied. We find that the DFT-D3 method substantially improves the results compared to the uncorrected DFT methods for the molecular carbon dioxide crystals. Enthalpies at 0 K and cohesive energies support only one possibility of the available experimental solutions for the structure of phase IV: the R3c modification, proposed by Datchi and co-workers [Phys. Rev. Lett. 103, 185701 (2009)]. Furthermore, comparing bulk moduli with experimental values, we cannot reproduce the quite large--rather typical for covalent crystal structures--experimental values for the molecular phases II and III.