The previously proposed theoretical and experimental structures,bond characterization,and compressibility of Mg(BH4)2 in a pressure range from 0 to 10 GPa are studied by ab initio density-functional calculations.It is found that the ambient pressure phases of meta-stable I41/amd and unstable P-3ml proposed recently are extra stable and cannot decompose under high pressure.Enthalpy calculation indicates that the ground state of F222 structure proposed by Zhou et al.[2009 Phys.Rev.B 79 212102]will transfer to I41/amd at 0.7 GPa,and then to a P-3m1 structure at 6.3 GPa.The experimental P6122 structure (α-phase) transfers to I41/amd at 1.2 GPa.Furthermore,both I41/amd and P-3m1 can exist as high volumetric hydrogen density phases at low pressure.Their theoretical volumetric hydrogen densities reach 146.351 g H2/L and 134.028 g H2/L at ambient pressure,respectively.The calculated phonon dispersion curve shows that the I41/amd phase is dynamically stable in a pressure range from 0 to 4 GPa and the P-3ml phase is stable at pressures higher than 1 GPa.So the I41/amd phase may be synthesized under high pressure and retained to ambient pressure.Energy band structures show that they are both always ionic crystalline and insulating with a band-gap of about 5 eV in this pressure range.In addition,they each have an anisotropic compressibility.The c axis of these structures is easy to compress.Especially,the c axis and volume of P-3m1 phase are extraordinarily compressible,showing that compression along the c axis can increase the volumetric hydrogen content for both I41/amd and P-3m1 structures.