  The absorption spectrum of the MnO$_{4}$$^{-}$ ion has been a test-bed for
quantum-chemical methods over the last decades. Its correct description
requires highly-correlated multiconfigurational methods, which are incompatible
with the inclusion of finite-temperature and solvent effects due to their high
computational demands. Therefore, implicit solvent models are usually employed.
Here we show that implicit solvent models are not sufficiently accurate to
model the solvent shift of MnO$_{4}$$^{-}$, and we analyze the origins of their
failure. We obtain the correct solvent shift for MnO$_{4}$$^{-}$ in aqueous
solution by employing the polarizable embedding (PE) model combined with a
range-separated complete active space short-range density functional theory
method (CAS-srDFT). Finite-temperature effects are taken into account by
averaging over structures obtained from ab initio molecular dynamics
simulations. The explicit treatment of finite-temperature and solvent effects
facilitates the interpretation of the bands in the low-energy region of the
MnO$_{4}$$^{-}$ absorption spectrum, whose assignment has been elusive.
