In the present work, based on the density functional theory and crystal structure prediction algorithms, we found novel structures of alkali metal orthocarbonates Li4CO4-C2/c, Na4CO4-C2/c, and K4CO4-P21/c. The pressure of thermodynamic stabilization of the obtained orthocarbonates with respect to decomposition into the corresponding carbonate and oxide ranges from 21 GPa (for K4CO4) to 25 GPa (for Li4CO4). All obtained structures contain isolated groups of [CO4]tetrahedra. The structures of lithium and sodium orthocarbonates were found to be isotypic. As well as alkaline earth orthocarbonates, orthocarbonates of alkali metals are structurally similar to orthosilicates of the same metal. Na4CO4-C2/c was found to be dynamically stable at ambient pressure, while all other structures are destabilized on decompression. In addition, the P-T phase diagrams of lithium, sodium, and potassium oxides have been calculated for the first time. All oxides have a high-pressure phase transition from the Fm3¯ m (anti-fluorite) structure to the Pnma (anti-cotunnite) structure at 34 GPa for Li2O, at 10 GPa for Na2O, and at 5 GPa for K2O at low temperatures. In the Na2O and K2O systems, high-temperature phase transition to the P6¯ 2m (barringerite) structure was revealed at temperatures above 1300 and 650 K, respectively.
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