The colour of $KMn{O}_4$ is due to

The oxidation state of Mn in KMnO4 is +7, which means that Mn does not have any d electrons left in its orbital. Actually, Mn7+ complexes should not be colored because electronic transitions are not possible. However, KMnO4 has a deep purple color because of charge transfer from the ligand or we can say O2– to the metal center. This is called a ligand-to-metal charge transfer, which leads to absorption of energy and color