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Abstract Using our recently developed X‐ray diffraction basedforce constantsapproach, we have determined the equilibrium Si isotope fractionation between omphacite/garnet, quartz/kyanite, and quartz/zircon at temperatures relevant to the petrogenesis. We find that Na strongly affects the Si isotope fractionation between omphacite and garnet. Our results have suggested that the omphacite and garnet in eclogite collected in the Dabie Mountain, as well as the kyanite and its host quartz veins, are isotopically in equilibrium, which further suggests that the Dabie Mountain eclogites and its host veins underwent the same high pressure‐temperature condition during their formation. The Si isotope fractionation determined by our methods, together with published mass spectroscopy measurements, DFT‐CIPW calculations and sigmoid fitting on various felsic granites, have suggested that the Si isotope fraction between zircon and whole rock “saturates” at ∼0.45‰ at 1000 K when the SiO₂content in the granite is above ∼70 wt%. 

Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic systems at low electron temperatures is difficult due to their highly delocalized density matrix. Second, modeling metallic warm-dense materials at very high electron temperatures is challenging because it requires the computation of a large number of partially occupied orbitals. This study demonstrates that both challenges can be effectively addressed using the latest advances in linear-scaling stochastic DFT methodologies. Despite the inherent introduction of noise into all computed properties by stochastic DFT, this research evaluates the efficacy of various noise reduction techniques under different thermal conditions. Our observations indicate that the effectiveness of noise reduction strategies varies significantly with the electron temperature. Furthermore, we provide evidence that the computational cost of stochastic DFT methods scales linearly with system size for metal systems, regardless of the electron temperature regime.