The purple colour of $\mathrm{KMnO}_{4}$ is due to the transition

The permanganate ion has an intense purple colour. Mn (+ VII) has a d $^{0}$ configuration. So the colour arises from charge transfer and not from d-d spectra. In $\mathrm{MnO}_{4}{ }^{-}$an electron is momentarily changing $\mathrm{O}^{-}$- to $\mathrm{O}^{-}$and reducing the oxidation state of the metal from $\mathrm{Mn}(\mathrm{VII})$ to Mn (VI). Charge transfer requires that the energy levels on the two different atoms are fairly close. $\mathrm{O}=(8)=2,6$ $\quad\quad\quad\quad$ K L $\mathrm{Mn}(25)=2,8,15$ $\quad\quad\quad\quad$ K L M hence the charge transfer occurs from $\mathrm{L} \rightarrow \mathrm{M}$