2. Computational method and details
Calcium carbonate hemihydrate (CaCO3·1/2H2O)[8]has a monoclinic structure, belonging to the P121/c1(14) space with lattice parameters a =9.64 Å,b =10.47 Å and c =6.42 Å. The structure of monohydrocalcite (CaCO3·1H2O)[4, 5] is selected as space group: P31(144) with lattice parameters a =10.65 Å, b =10.65 Å andc =7.64 Å. While ikaite (CaCO3·6H2O)[7]belongs to C12/c1 space group (No.15) with lattice parametersa =8.78 Å, b =8.28 Å and c =10.88 Å.
In this work, all calculations were conducted using the Cambridge Serial Total Energy Package (CASTEP) codes based on the density functional theory (DFT)[16], which was the first-principles plane wave pseudopotential method. Ultra-soft pseudopotentials (USPPs)[17] were used for describing the interaction between atomic core and valence electrons in reciprocal space were used, and the valence electron configurations for C, H, Ca and O atoms were 2s 22p 2, 1s 1, 3s 23p 64s 2and 2s 22p 4, respectively. After careful test, 4×4×6, 5×5×8 and 6×8×4 grid of Monkhorst-Pack special k -points in the Brillouin zone (BZ) were used for bulk models CaCO3·1/2H2O, CaCO3·1H2O and CaCO3·6H2O, respectively. In order to ensure the calculations converged for calculation accuracy, the maximum plane-wave basis cutoff energy was 450 eV. The exchange correlation potential within generalized gradient approximation (GGA) was described the Perdew-Burke-Ernzerhof (PBE)[18] and a DFT-D dispersion correction with grimme method was adopted in all calculations to improve the calculation accuracy for weak interaction. During the structural optimization process, Broyden-Fletcher-Goldfarb-Shanno (BFGS)[19] method was used until the total energy changes were converged to 1×10-9 eV/atom, self-consistent field convergence to 2×10-6 eV/atom, maximum force 0.03 eV/Å, respectively. Elastic constants of a solid were calculated by an efficient strain-stress method through a linear least-square fit of the first-principle calculating stress versus strain. The phonon dispersion curves of CaCO3·1/2H2O, CaCO3·1H2O and CaCO3·6H2O were calculated according to the finite displace method.