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.