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The contribution of computational/theoretical studies is nowadays essential to understand complex materials,thanks to predictive power of state-of-the-art modelling techniques.In this thesis we investigate two inresting and challenging problems in geophysics based on Ab-initio quantum mechanical calculations,Stability of Sepentine Polymorphs and thermal conductivity of Magesium Silicate(pv).Massively parallel super-computers have been used since the systems studied are computationally demanding in terms of CPU time and memory usage. The first part of the thesis is devoted to the Relative Stability Field and Elasticity Contrast of Serpentine polymorphs at pressure and temperature conditions relevant to the oceanic lithosphere and subduction zone.We conduct first principles calculations to determine the relative stability field and elasticity contrast of serpentine polymorphs at pressure and temperature conditions relevant to the oceanic lithosphere and subduction zone.At high pressures(＞4GPa),the corrugated form of serpentine polymorph(antigorite,Atg)plus brucite(Brc)assemblage is thermodynamically more favorable compared to its planar counterpart(lizardite,Liz).The phase boundary between Liz and Atg+Brc exhibits a negative slope in the whole P-T range,indicating this transition can be driven by increasing either pressure or temperature.Near0GPa,the slope is about-33K/GPa.As pressure exceeds1GPa,the transition temperature starts to decrease more rapidly.Because of the corrugated nature of its constituent layers,Atg is more susceptible to intra-layer deformations(7to36％smaller C11,C22,C12and C66at ambient conditions)while more resistant to interlayer shear deformation(25％larger C44,36％larger C55)than Liz.In contrast,their responses to the interlayer compressive deformation(C33)are similar.For isotropic polycrystalline aggregates at pressures between0to4GPa,Atg exhibits a smaller bulk modulus(12to15％)and a larger shear modulus(6to11％)than Liz,while their density contrast is within1％.Accordingly,a Liz/Atg transition is accompanied by a decrease in Vp(2to3％),an increase in Vs(3to5％),and a more pronounced drop in Vp/Vs(6to8％).These results may help to identify and characterize serpentine polymorphs produced under various geological settings. The second part is focused on the Lattice Thermal Conductivity of MgSiO3perovskite(pv)by ab initio lattice dynamics calculations combined with exact solution of linearized phonon Boltzmann equation.At room temperature,of pristine MgSiO3pv is found to be10.7W/(m·K)at0GPa.It increases linearly with pressure and reaches59.2W/(m·K)at100GPa.These values are close to multi-anvil press measurements whereas about twice as large as those from diamond anvil cell experiments.The increase ofκwith pressure is attributed to the squeeze of weighted phase-spaces phonons get emitted or absorbed.Moreover,we findκexhibits noticeable anisotropy,withκzz being the largest component and(κmax-κmin)/(κ)being about25％.Such extent of anisotropy is comparable to those of upper mantle minerals such as olivine and enstatite.By analyzing phonon mean free paths and lifetimes,we further show that the weak temperature dependence ofκobserved in experiments should not be caused by phonons reaching‘minimummean free paths.These results clarify the microscopic mechanism of thermal transport in MgSiO3pv,and provide reference data for understanding heat conduction in the Earths deep interior.