The detail of the incorporation of carbon dioxide in silicate melts at upper mantle conditions is still badly known. To give some theoretical guidance, we have performed first-principle molecular dynamics simulations (FPMD) to quantify the speciation and the incorporation of carbon dioxide in two CO2-rich silicate melts (~ 20 wt% CO2 at 2073 K and 12 GPa), a basaltic and a kimberlitic composition chosen in the CaO-MgO-Al2O3-SiO2 system. In the basaltic composition, carbon dioxide is incorporated under the form of a minority population of CO2 molecules and a prevailing population of carbonate ions (CO32 −). In contrast, the amount of CO2 molecules is found to be very small in the kimberlitic melt. Moreover, a new (transient) species has been identified, the pyrocarbonate ion C2O52 − issued from the reaction between CO2 and CO32 −. With regard to the structure of the CO2-bearing melts, it is shown that the carbonate ions modify the silicate network by transforming some of the oxygen atoms into bridging carbonates, non-bridging carbonates, and free carbonates, with a distribution depending on the melt composition. In the basaltic melt a majority of carbonate ions are non-bridging or free, whereas in the kimberlitic melt, most of the carbonate ions are under the form of free carbonates linked to alkaline earth cations. Surprisingly, the addition of CO2 only has a weak influence on the diffusion coefficients of the elements of the melt. The consequence is that the strong enhancement of the electrical conductivity reported recently for carbonated basalts (Sifré et al., 2014, Nature 509, 81), can be reproduced by simulation only if one assumes that the ionic charges assigned to the elements of the melt depend, in a non-trivial way, on the CO2 content. Finally, a comparison of the FPMD calculations with classical molecular dynamics simulations using an empirical force field of the literature (Guillot and Sator, 2011, GCA 75, 1829) shows that the latter one needs some improvement.