The behaviors of aragonite (CaCO$$_3$$ 3 ), strontianite (SrCO$$_3$$ 3 ), cerussite (PbCO$$_3$$ 3 ), and witherite (BaCO$$_3$$ 3 ) at increasing pressure have been studied up to 6 GPa using density functional theory with plane waves. A parallelism of the orthorhombic carbonates with the closed-packed AsNi structure is considered in our analysis, being the CO$$_3^{2-}$$ 3 2 - groups not centered in the interstice of the octahedron. The decomposition of the unit-cell volume into atomic contributions using the Quantum Theory of Atoms in Molecules has allowed the analysis of the bulk modulus in atomic contributions. The bulk, axes, interatomic distances, and atomic compressibilities are calculated. The largest compression is on the c crystallographic axis, and the c linear modulus has a linear function with the mineral bulk modulus ($$K_0$$ K 0 ). Many of the interatomic distances moduli of the alkaline earth (AE) carbonates show linear functions with the bulk modulus; however, the whole series (including cerussite) only gives linear functions when $$K_0$$ K 0 is related either with the CC distances modulus or the modulus of the distances of the C to the faces of the octahedron perpendicular to c. These last distances are the projections of the Metal–Oxygen (MO) distances to the center of the octahedron. $$K_{0AE}$$ K 0 A E carbonates also show linear functions with the atomic moduli of their cations. However, the whole series show a linear relation with the atomic modulus of C atoms. Therefore, the whole series highlight the importance of the C atoms and their interactions in the mechanism of compression of the orthorhombic carbonate series.

The behavior of aragonite (CaCO3), strontianite (SrCO3 ), cerussite (PbCO3) andwitherite (BaCO3 ) at increasing pressure have been studied up to 6 GPa using density func-tional theory with plane waves. A parallelism of the orthorhombic carbonates with theclosed-packed AsNi structure is considered in our analysis, being the CO2− groups not3centered in the interstice of the octahedron. The decomposition of the unit cell volume intoatomic contributions by using the Quantum Theory of Atoms in Molecules has allowed theanalysis of the bulk modulus in atomic contributions. The bulk, axes, interatomic distancesand atomic compressibilities are calculated. The largest compression is on the c crystallo-graphic axis and the c linear modulus has a linear function with the mineral bulk modulus(K0 ). Many of the interatomic distances moduli of the alkaline earth (AE) carbonates show linear functions with the bulk modulus; however, the whole series (including cerussite) onlygives linear functions when K 0 is related either with the CC distances modulus or the mod-ulus of the distances of the C to the faces of the octahedron perpendicular to c. These lastdistances are the projections of the Metal-Oxygen (MO) distances to the center of the octa-hedron. K 0 AE carbonates also show linear functions with the atomic moduli of their cations,however, the whole series show a linear relation with the atomic modulus of C atoms. There-fore, the whole series highlight the importance of the C atoms and their interactions in themechanism of compression of the orthorhombic carbonate series.

Muscovite (Ms) and phlogopite (Phl) series mineral is studied in the 2M1 polytype and modeled by the substitution of three Mg2+ cations in the three octahedral sites of Phl [KMg3(Si3Al)O10(OH)2] by two Al3+ and one vacancy, increasing the substitution up to reach the Ms [KAl2□(Si3Al)O10(OH)2]. The series was computationally examined at DFT using Quantum ESPRESSO, as a function of pressure from − 3 to 9 GPa. Crystal structure is calculated, and cell parameters, and geometry of atomic groups agree with experimental values. OH in the Mg2+ octahedrons are approximately perpendicular to the (001) plane, meanwhile when they are in Al3+, octahedral groups are approximately parallel to this plane. From Quantum Theory of Atoms in Molecules, the atomic basins are calculated as a function of the pressure, K+ and basal O show the largest volumes. The bulk excess volume (Vxs) and the excess atomic volumes are analyzed as a function of the composition and the pressure. K+, basal and apical O Vxs show a behavior similar to the bulk Vxs as a function of the composition, keeping qualitatively this behavior as a function of pressure; substituent atoms do not show a Vxs behavior similar to the bulk and their effect consequently is mostly translated to atoms in the interlayer space. Atomic compressibilities are also calculated. Atomic compressibilities are separated in the different sheets of the crystal cell. Atomic moduli of K and basal O are the lowest and the ones behaving as the bulk modulus of the series. The atomic bulk modulus of the H’s is different depending of their position with respect to the (001) plane.