Calculation of the energetics for the oxidation of Sb(III) sulfides by elemental S and polysulfides in aqueous solution

Recent experimental studies have reported the existence of two new Sb sulfide species, Sb₂S₅²⁻ and Sb₂S₆²⁻, in alkaline sulfidic solutions in equilibrium with stibnite, Sb₂S₃, and orthorhombic S. These species contain Sb(V), which has also recently been identified in similar solutions using EXAFS by other researchers. This represents a significant change from the consensus a decade ago that sulfidic solutions of Sb contained only Sb(III) species. I have calculated from first principles of quantum mechanics the energetics for the oxidation of the Sb(III) sulfide dimer Sb₂S₄²⁻ to the mixed Sb(III,V) dimer Sb₂S₅²⁻ and then to the all Sb(V) dimer, Sb₂S₆²⁻. Gas-phase reaction energies have been evaluated using polarized valence double zeta effective core potential basis sets and Moller-Plesset second order treatments of electron correlation. All translational, rotational and vibrational contributions to the gas-phase reaction free energy have been calculated. Hydration energies have been obtained using the COSMO version of the self-consistent reaction field polarizable continuum method. Negative free energy changes are calculated for the oxidation of the dianion of the III,III dimer to the III,V dimer by both small polysulfides, like S₄H⁻, and elemental S, modeled as S₈. For the further oxidation of the III,V dimer to the V,V dimer the reaction free energies are calculated to be close to zero. The partially protonated Sb III,III dimer monoanion HSb₂S₄⁻ can also be oxidized, but the reaction is not so favorable as for the dianion. Comparison of the calculated aqueous deprotonation energies of H₂Sb₂S₄, H₂Sb₂S₅ and H₂Sb₂S₆ and their dianions with values calculated for various oxyacids indicates that the III,V and V,V dimers will have pK_a2 values <5, so that their dianions will be the dominant species in alkaline solutions. These results are thus consistent with the recent identification of Sb₂S₅²⁻ and Sb₂S₆²⁻ species. I have also calculated the Raman spectra of Sb₂S₅²⁻ and Sb₂S₆²⁻ to assist in their identification. The calculated vibrational frequencies of the III,V and V,V dimers are characteristically higher than those of the III,III dimer I previously studied. The III,V dimer may contribute shoulders to the Raman spectrum.