Equilibrium Sn isotope fractionation properties between aqueous Sn (2+, 4+) species and Sn-bearingminerals are the key to using tin isotopes to trace the transportation, enrichment, and precipitation of tinin various geological processes. However, the application of Sn isotope geochemistry has been impededby the absence of equilibrium Sn isotopic fractionation factors between Sn-bearing minerals and fluidand between mineral pairs. In this contribution, we conducted first-principles calculations based on thedensity functional theory to obtain the equilibrium Sn isotopic fractionation factors between aqueous Sncomplexes and minerals. For Sn-bearing complexes in solution, the reduced partition function ratios (β)are determined by taking snapshots from the molecular dynamics trajectories and computing the average β of the snapshots based on the lowest energy atomic coordinates. For Sn-bearing minerals, staticfirst-principles periodic density functional theory methods are performed. The results show that the βfactors decrease in the sequence of malayaite(s) (Sn4+) > cassiterite(s) (Sn4+) > Sn4+Cl4(H2O)2(aq) > Sn2+F3−(aq) >Sn2+(OH)2(aq) > Sn2+CO3(aq) > stannite(s) (Sn4+) > Sn2+Cl3−(aq). The predicted Sn isotope fractionation followsseveral distinct patterns. (1) For minerals, the Sn isotope fractionations (1000lnαminerals-stannite) of cassiteritestannite and malayaite-stannite mineral pairs are controlled by the properties of elements coordinatingwith tin, and the equilibrium Sn isotope fractionation factors between mineral pairs are large enoughto make them powerful Sn isotope thermometers. (2) For Sn-bearing aqueous species, the β values oftin (4+) complexes are remarkably larger than those of all aqueous Sn2+ species, indicating that highervalence tin is preferentially enriched heavy tin isotopes. For aqueous Sn2+ species, the aqueous specieswith shorter bonds are more-enriched in heavy Sn isotopes than those with longer bonds. When both thevalence state and bond length are different, the valence state is the main factor controlling tin isotopefractionation. (3) During the precipitation of various Sn2+ aqueous complexes into cassiterite or malayaite,heavy Sn isotopes tend to be enriched in minerals, while there are two situations for the precipitationof Sn2+ complexes into stannite. When Sn is transported in hydrothermal solution as Sn2+Cl3–, stanniteprecipitation leads to the enrichment of light tin isotopes in the residual solution and late minerals. Onthe contrary, other Sn2+ species [Sn2+F3−, Sn2+(OH)2 and Sn2+CO3] that precipitate as stannite will result inthe enrichment of heavy tin isotopes in the residual solutions . In addition, the direct precipitation of Sn4+complexes into cassiterite, malayaite, or stannite also produces considerable tin isotope fractionation.During precipitation, Sn4+ aqueous complexes form cassiterite or malayaite, and heavy Sn isotopes tendto be enriched in minerals; whereas when aqueous Sn4+ species are precipitated into stannite, heavy Snisotopes are enriched in the residual fluid and late minerals. The calculated results are essential for furtherunderstanding the mechanisms of Sn isotopic fractionation in various Sn-involved geological processes.