There are large discrepancies existing in equilibrium Mg isotope fractionation calculations and experimental investigations for cases related to mineral vs. solution. To clarify this confusing issue, a newly designed clustermodel- based quantum chemistry method, i.e., volume variable cluster model (VVCM), is used to provide equilibrium Mg isotope fractionation factors between Mg-bearing carbonates (calcite, aragonite, dolomite and magnesite), amorphous calcium carbonates (ACCs), brucite and aqueous species (i.e., Mg-(aq)(2+), MgHCO3(aq)+ and MgOH(aq)+). We find that local configuration sampling of aqueous species is essential to provide precise fractionations between mineral and solution. The phonon-based periodic boundary method is also used for several minerals and it obtains very similar fractionations with VVCM results. 

Our results are very close to those of Pinilla et al. (2015) although via completely different approaches. Both of them have included the effect of local configuration disorder. However, both of them are significantly different from some of experimental results for cases of carbonates vs. solutions. The existence of various Mg-bearing species in fluids of experiments, the direct incorporation of hydrated Mg2+ into the solids, the Mg2+ concentration effect, and the existence of intermediate precursors (e.g., ACCs) are several possible causes for the mismatches. Relative to coexisting aqueous Mg2+, we find that ACCs will enrich heavy Mg isotopes, i.e., similar to 1.45 parts per thousand at 25 degrees C, agreeing with previous experimental estimation. Equilibrium Mg isotope fractionation factors between brucite and solutions are also predicted. Besides, we applied VVCM to predict the Mg isotope fractionations between high-temperature phases, i.e., forsterite, diopside, enstatite, tremolite and spinel. The predicted beta factors are in the order of spinel > tremolite > diopside > enstatite > forsterite. This study provides a base for understanding the accumulating Mg isotope data.