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Equilibrium Sn isotope fractionation properties between aqueous Sn (2+, 4+) species and Sn-bearing minerals are the key to using tin isotopes to trace the transportation, enrichment, and precipitation of tin in various geological processes. However, the application of Sn isotope geochemistry has been impeded by the absence of equilibrium Sn isotopic fractionation factors between Sn-bearing minerals and fluid and between mineral pairs. In this contribution, we conducted first-principles calculations based on the density functional theory to obtain the equilibrium Sn isotopic fractionation factors between aqueous Sn complexes 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, static first-principles periodic density functional theory methods are performed. The results show that the β factors decrease in the sequence of malayaite (s) S n 4 + > cassiterite (s) S n 4 + > S n 4 + C l 4 H 2 O 2 (a q) > S n 2 + F 3 (a q) − > S n 2 + (O H) 2 (a q) > S n 2 + C O 3 (a q) > stannite (s) S n 4 + > S n 2 + C l 3 (a q) − . The predicted Sn isotope fractionation follows several 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 coordinating with tin, and the equilibrium Sn isotope fractionation factors between mineral pairs are large enough to make them powerful Sn isotope thermometers. (2) For Sn-bearing aqueous species, the β values of tin (4+) complexes are remarkably larger than those of all aqueous Sn2+ species, indicating that higher valence tin is preferentially enriched heavy tin isotopes. For aqueous Sn2+ species, the aqueous species with shorter bonds are more-enriched in heavy Sn isotopes than those with longer bonds. When both the valence state and bond length are different, the valence state is the main factor controlling tin isotope fractionation. (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 precipitation of Sn2+ complexes into stannite. When Sn is transported in hydrothermal solution as Sn2+Cl3–, stannite precipitation leads to the enrichment of light tin isotopes in the residual solution and late minerals. On the contrary, other S n 2 + species S n 2 + F 3 − , S n 2 + (O H) 2 and S n 2 + C O 3 that precipitate as stannite will result in the 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 tend to be enriched in minerals; whereas when aqueous Sn4+ species are precipitated into stannite, heavy Sn isotopes are enriched in the residual fluid and late minerals. The calculated results are essential for further understanding the mechanisms of Sn isotopic fractionation in various Sn-involved geological processes. [ABSTRACT FROM AUTHOR]