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• For [Ti(H₂O)₆]³⁺, this corresponds to a d-d transition (from t2gt_{2g}t2g to ege_geg).
Since there is only one electron in the system, only one transition is possible, which
is represented by a single peak in the UV-visible spectrum.
The absorption band in the spectrum for this complex occurs due to this electron excitation
from a lower-energy t2gt_{2g}t2g orbital to a higher-energy ege_geg orbital, resulting in a
transition that can be detected using spectroscopy techniques.
(b) Selection Rules for d-d Transitions
Selection rules govern the probability of electronic transitions between different energy
levels. For d-d transitions in transition metal complexes, two important selection rules must
be considered:
1. Laporte Selection Rule:
o This rule states that transitions between states of the same parity (symmetry)
are forbidden. In simpler terms, transitions are not allowed between orbitals
that both have the same type of symmetry.
o For d-d transitions, since both the initial and final states are d-orbitals (which
are of the same parity), these transitions are Laporte-forbidden. However, in
real complexes, distortions or mixing of orbitals due to interactions with
ligands can lead to a partial lifting of this restriction, making weak d-d
transitions observable.
2. Spin Selection Rule:
o This rule states that transitions are allowed only if there is no change in the
spin state of the electron during the transition. In other words, transitions
where the total spin quantum number remains the same are spin-allowed.
o For high-spin complexes, d-d transitions are more likely to be spin-allowed.
However, if a transition involves a change in the electron spin state, it
becomes spin-forbidden and is less likely to occur.
Summary of the Spectral Behavior and Rules:
• In complexes like [Ti(H₂O)₆]³⁺, only one spin-allowed d-d transition is observed
because of the d^1 configuration.
• According to the Laporte rule, the transition is forbidden in the strictest sense, but in
practice, octahedral complexes experience distortions (like Jahn-Teller distortions),
which relax the Laporte rule, allowing weak transitions.
• The spin selection rule is satisfied in this case since the transition does not involve a
change in the spin state of the electron.
Therefore, the electronic spectra of [Ti(H₂O)₆]³⁺ feature a single broad absorption band
corresponding to this allowed d-d transition, which is weak due to the Laporte-forbidden
nature but still detectable.