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

Step 1: Understanding the question.
The visible absorption band of \( [\text{Ti(H}_2\text{O})_6]^{3+} \) shows asymmetry due to distortions in the electronic structure.
Step 2: Analyzing the options.
- (1) Laporte allowed transition: This is a transition that is symmetry-allowed under the Laporte selection rule but does not explain the asymmetry of the band. - (2) Laporte forbidden transition: This refers to transitions that are symmetry-forbidden but does not explain the distortion responsible for the asymmetry. - (3) Dynamic John-Teller distortion: This is the correct answer. The asymmetry is caused by the dynamic distortion of the complex due to the degenerate electronic states in \( [\text{Ti(H}_2\text{O})_6]^{3+} \). - (4) Intensity stealing transition: This does not explain the asymmetric nature of the absorption band.
Step 3: Conclusion.
The correct answer is (3) Dynamic John-Teller distortion, as the asymmetry arises due to this effect.

Answer 2

\( [\text{Ti(H}_2\text{O})_6]^{3+} \) is a \( d^{1} \) octahedral complex, and its single visible absorption band (the \( {}^2E_g \leftarrow {}^2T_{2g} \) transition) is noticeably asymmetric or split rather than a single clean peak. Let's evaluate what could cause this asymmetry.

1. Laporte allowed transition: A Laporte-allowed transition (such as a charge-transfer transition) would normally give a strong, symmetric band, not an asymmetric d-d band. This does not describe the observed asymmetry, and in any case, d-d transitions in an octahedral field are Laporte forbidden, not allowed.
2. Laporte forbidden transition: It is true that the d-d transition here is Laporte forbidden, which is why the band is weak, but being forbidden only explains the low intensity of the band, not why the band appears asymmetric or split into two components.
3. Dynamic John-Teller distortion: The excited \( {}^2E_g \) state of this \( d^{1} \) ion is itself orbitally degenerate and Jahn-Teller active, so it constantly distorts between different geometries. This dynamic distortion splits the single expected transition into two closely spaced components, producing the asymmetric or shouldered shape of the observed band. This is the accepted explanation for this specific complex.
4. Intensity stealing transition: Intensity stealing (vibronic coupling that borrows intensity from an allowed transition) can explain why a forbidden transition is visible at all, but it does not by itself account for the specific asymmetric splitting seen for this particular ion; that splitting is attributed to the excited-state distortion.

The asymmetry is a direct signature of the excited state itself being distorted, not of selection rules or borrowed intensity.

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