We show that force matching can be used to determine accurate empirical repulsive energies for the density functional tight binding method (DFTB) for chemical reactivity in condensed phases. Our approach yields improved results over previous parametrizations for molten liquid carbon and a phenolic polymer under combustion conditions. The method we present here allows for predictions of chemical properties over longer time periods than accessible via Kohn–Sham density functional theory while retaining its accuracy.Although alkali-alkali earth carbonates have not been reported from mantle-derived xenoliths, these carbonates may have a substantial role in mantle metasomatic processes through lowering melting temperatures. On the Na2Mg(CO3)2–K2Mg(CO3)2 join only the Na-end-member eitelite (R3̄ space group), was reported in nature. The K-end-member (R3̄m) readily hydrates even at low temperatures, therefore, only baylissite, K2Mg(CO3)2·4H2O, has been observed. Because of the role of (K,Na)Mg-double carbonates in mantle metasomatism, we performed high P-T experiments on K2Mg(CO3)2, (K1.1Na0.9)2Mg(CO3)2, and Na2Mg(CO3)2. Structure refinements were done upon compression of single crystals from 0 to 9 GPa at ambient temperature employing synchrotron radiation. Fitting the compression data to the second-order Birch-Murnaghan EoS resulted in V0 = 396.2(4), 381.2(5), and 347.1(3) Å3 and K0 = 57.0(10), 54.9(13), and 68.6(13) GPa for K2Mg(CO3)2, (K1.1Na0.9)2Mg(CO3)2, and Na2Mg(CO3)2, respectively. These compressibilities are lower than those of magnesite and dolomite. The KMg-double carbonate transforms into a monoclinic polymorph at 8.05 GPa; the high-P phase is 1% denser than the low-P polymorph. The NaMg-double carbonate has a phase transition at ~14 GPa, but poor recrystallization has prevented structure refinement. The parameters for a V-T EoS were collected at 25–600 °C and ambient pressure and are α0 = 14.31(5) × 10−5 K−1 and 16.73(11) × 10−5 K−1 for K2Mg(CO3)2 and Na2Mg(CO3)2, respectively. Moreover, fitting revealed an anisotropy of thermal expansion along the a- and c-axis: α0(a) = 2.84(6) × 10−5 and 4.78(5) × 10−5 K−1 and α0(c) = 10.47(11) × 10−5 and 8.72(5) × 10−5 K−1 for K2Mg(CO3)2 and Na2Mg(CO3)2, respectively.