Q.$\text{KMnO}_4$ and $\text{K}_2\text{Cr}_2\text{O}_7$ are intensely coloured even though $\text{Mn}^{7+}$ and $\text{Cr}^{6+}$ have a $d^0$ configuration with no d-electrons available for a d-d transition. Explain the real source of their colour.

The d-d transition mechanism developed earlier in this chapter explains colour only for ions with a partially filled d subshell -- an electron already present in the metal's d orbitals is excited from a lower-energy to a higher-energy d orbital. $\text{MnO}_4^-$ and $\text{Cr}_2\text{O}_7^{2-}$ are genuine exceptions to any attempt to explain their colour this way, because manganese in $\text{MnO}_4^-$ is in the $+7$ oxidation state (having formally lost all seven of its valence electrons, $3d^54s^2$) and chromium in $\text{Cr}_2\text{O}_7^{2-}$ is in the $+6$ state (having formally lost all six of its valence electrons, $3d^54s^1$). Both metal centres are therefore $d^0$: there are no d electrons present at all, so a d-d transition is structurally impossible, exactly as it is for the genuinely colourless $\text{Sc}^{3+}$ ($d^0$) ion discussed earlier.

Yet $\text{KMnO}_4$ solutions are an intense purple and $\text{K}_2\text{Cr}_2\text{O}_7$ solutions a strong orange -- among the most vividly coloured simple ions in inorganic chemistry. The real mechanism responsible is called charge transfer, and more specifically a ligand-to-metal charge-transfer (LMCT) transition: an electron is excited not between two orbitals both centred on the metal (as in a d-d transition), but from a filled molecular orbital that is largely centred on the surrounding oxygen ligands directly into an empty d orbital on the metal centre. Because the metal ion is highly charged and strongly electron-attracting (a $d^0$, high-oxidation-state metal centre is a particularly good electron acceptor), and because oxygen is a good electron donor, this charge-transfer transition typically requires only a modest amount of energy -- corresponding to a photon in the visible region -- and, being an intrinsically more probable ("allowed") transi …

Confirm both metal centres are d0 (so d-d transition is ruled out), then introduce charge transfer (LMCT) as the correct mechanism and explain why …

Trying to force a d-d-transition explanation onto a d0 ion (a very common error, since these are the most commonly cited coloured transition-metal compounds and students default to the mechanism covered first); n …