The direct determination of silicate melts iron and silicon isotopes signature remains a major challenge of high-temperature isotope geochemistry. For this reason, melts are often approximated by silicate glasses. Calculation of precise equilibrium Si and Fe isotopes fractionation factors between minerals and melt would indeed allow us to distinguish equilibrium fractionation from diffusion-driven kinetic fractionation involved in the iron and silicon isotopes signatures of Earth and other planets. In this study, we use for the first time, first-principles molecular dynamics based on density functional theory to determine iron and silicon isotope compositions of different silicate melts, namely: iron-rich basalt, iron-depleted basalt, basanite, trachyte and phonolite. The 57Fe/54Fe reduced partition function ratios (β-factors) of the different melts span over a 1.1 ‰ range at 1000 Kelvin (K) while 30Si/28Si β-factors are much less influenced by the melt composition with a 0.5 ‰ fractionation range at the same temperature. The main parameter controlling iron isotope fractionation in silicate melts having similar iron oxidation state is, after temperature, the average Fe-O bond length. The chemical environment around iron (e.g. Fe-Fe distances) is suggested to contribute to Fe isotope fractionation as well. Silicon isotopes fractionation seems also affected, but to a lesser extent, by its local chemical composition with decreasing Si-Fe distances leading to slightly higher Si β-factor in the melt. From these melts Fe and Si β-factors, a new set of equilibrium fractionation factors between a variety of minerals and melts has been calculated. These new Δ57Femin-melt and Δ30Simin-melt sets allow us to discuss whether processes such as fractional crystallization, partial melting and diffusion could be responsible for the documented Fe and Si isotopes variations in igneous rocks. Our results suggest that: 1) fractional crystallization may explain at least part of the Fe and Si isotopic evolution during magmatic differentiation, for values up to δ57Fe = 0.65 ‰ and δ30Si = -0.1 ‰, respectively, 2) partial melting of the upper mantle can produce the Mid-Ocean Ridge Basalts (MORB) iron isotopes signature. Finally, we calculated that olivine at equilibrium with a basaltic melt could display an iron isotope composition down to −0.1 ‰ for δ57Fe. Hence, the lower isotopic compositions (δ57Fe < -0.1 ‰) observed in natural olivines are most likely due to diffusion-driven kinetic fractionation.