The energy of the sampled structures was minimized by adjusting atomic coordinates to satisfy a tolerance of 1 × 10 -8 kcal/mol using MD potentials. Subsequently, structural optimization was further investigated using DFT calculations with the Vienna Ab initio Simulation Package (VASP). The projector-augmented wave (PAW) method was used to describe the electron-core interactions. The modified Perdew-Burke-Ernzerhof GGA for solids (PBEsol), which accurately reproduces the experimental enthalpy of vaterites, was adopted for the DFT calculations. The atomic positions and cell lengths were optimized to achieve a convergence of 10 -3 eV/ Å for the force components acting on each atom.