Question

The asymmetric nature of the visible absorption band of \( [\text{Ti(H}_2\text{O})_6]^{3+ \) is due to}

• A. Laporte allowed transition
• B. Laporte forbidden transition
• C. Dynamic John-Teller distortion
• D. Intensity stealing transition

Hint:

The John-Teller effect occurs when degenerate electronic states cause distortion in the geometry of the complex, leading to asymmetric absorption bands.

Answer 1

The Correct Option is C

\( [\text{Ti(H}_2\text{O})_6]^{3+} \) is a \( d^{1} \) complex, so it has only one absorption band, coming from the electron being excited from the \( t_{2g} \) level to the \( e_g \) level.
The excited state, \( {}^2E_g \), is an orbitally degenerate state, and such degenerate states are unstable and distort geometrically, exactly as described by the Jahn-Teller theorem.
Because this distortion happens dynamically (the geometry keeps fluctuating), the single \( {}^2E_g \) level effectively splits into two closely spaced energy levels, which appear as two overlapping, slightly separated bands rather than one symmetric peak.
This is why the observed visible band looks asymmetric or shouldered rather than a clean, single peak.
\[ \boxed{\text{Dynamic John-Teller distortion}} \]

Answer 2

A useful way to separate these four options is to ask precisely what each phenomenon is capable of explaining: is it the existence of the band, its intensity, or its shape?

1. Laporte allowed transition: This term describes transitions where the parity of the orbitals changes, giving strong bands. Since d-d transitions here do not change parity, this term does not even apply, so it cannot be the explanation.
2. Laporte forbidden transition: This explains why the d-d band is weak in intensity (since it is formally forbidden by symmetry), but a forbidden transition would still appear as a single symmetric peak if nothing else were happening; it says nothing about the peak's shape.
3. Dynamic John-Teller distortion: This addresses the shape of the band directly. Since the excited \( {}^2E_g \) state is degenerate and Jahn-Teller active, the complex distorts and the degeneracy is lifted, splitting one transition into two unequal, overlapping components. This produces exactly the observed asymmetric band shape.
4. Intensity stealing transition: This addresses why a forbidden transition is observed at all (it borrows intensity via vibronic coupling with an allowed transition), but again, it explains the intensity of the band, not its asymmetric shape.

Since the question specifically asks about the asymmetric shape of the band, and only the Jahn-Teller distortion of the excited state accounts for that shape, this is the correct choice.

Therefore, the correct answer is Dynamic John-Teller distortion.