Reaction thermochemistry of metal sulfides with GGA andGGA+Ucalculations

Sulfurization reaction energies of 24 metal sulfide ($M$-S) systems including $M=$ Li, Na, K, Mg, Ca, Sr, Ba, Zn, Al, Ti, Mn, Fe, Co, Ni, Cu, Mo, Rh, Pd, Ir, Pt, La, Ce, Th, and U are evaluated using generalized gradient approximation (GGA) and $\mathrm{GGA}+U$ calculations. Our results indicate that unlike metal oxides and halides, GGA reaction energy predictions can be improved consistently only if separate energy corrections are used for S in sulfide anion (${\mathrm{S}}^{2\ensuremath{-}}$) and disulfide anion (${\mathrm{S}}_{2}^{2\ensuremath{-}}$) because of the existence of covalent ${}^{\ensuremath{-}}\mathrm{S}--{\mathrm{S}}^{\ensuremath{-}}$ bonds in the latter anion. Enumerating all possible sulfurization reactions between pairs of $d$- and $f$-block metal sulfides within each $M$-S system, we predict effective $U$ values for $\mathrm{GGA}+U$ thermochemistry and confidence intervals for these $U$ values. We find that applying $U$ on the $d$ or $f$ orbitals of these nonsimple metal ions consistently improves GGA reaction energy predictions for most of these systems, except for the reactions where the reaction energy is insensitive to $U$ applied to the metal $M$, and only the S anions perform the redox activity (i.e., change the nominal oxidation state). We show that $\mathrm{GGA}+U$ calculations with the predicted $U$ values and anion-dependent systematic energy corrections provide a significant improvement over standard, uncorrected GGA in predicting cell voltages of a variety of $M$-S based battery systems including $\mathrm{Li}/{\mathrm{FeS}}_{2}$, $\mathrm{Li}/{\mathrm{TiS}}_{2}$, $\mathrm{Li}/{\mathrm{Mo}}_{6}{\mathrm{S}}_{8}$, and $\mathrm{Mg}/{\mathrm{Mo}}_{6}{\mathrm{S}}_{8}$.