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The absorption spectrum of the MnO$_{4}$$^{-}$ ion has been a test-bed forquantum-chemical methods over the last decades. Its correct descriptionrequires highly-correlated multiconfigurational methods, which are incompatiblewith the inclusion of finite-temperature and solvent effects due to their highcomputational demands. Therefore, implicit solvent models are usually employed.Here we show that implicit solvent models are not sufficiently accurate tomodel the solvent shift of MnO$_{4}$$^{-}$, and we analyze the origins of theirfailure. We obtain the correct solvent shift for MnO$_{4}$$^{-}$ in aqueoussolution by employing the polarizable embedding (PE) model combined with arange-separated complete active space short-range density functional theorymethod (CAS-srDFT). Finite-temperature effects are taken into account byaveraging over structures obtained from ab initio molecular dynamicssimulations. The explicit treatment of finite-temperature and solvent effectsfacilitates the interpretation of the bands in the low-energy region of theMnO$_{4}$$^{-}$ absorption spectrum, whose assignment has been elusive.

Modeling the absorption spectrum of the permanganate ion in vacuum and in aqueous solution