Electronic Spectra of Transition Metal Complexes

The electronic transitions are high-energy transitions. During this transition, other smaller energy (vibrational and rotational transition) also occurs but the energy difference is small in vibrational and rotational transition. So, it is difficult to resolve.
The electronic transition is governed by selection rules. The transition which obeys the selection rules are called as the allowed transition and the transition disobeys the selection rule, are called forbidden transition.
Allowed transitions are quite common (high intensity) however, Forbidden transitions are not common (low intensity).
The electronic transitions in the transition metal compounds can be categorized into three classes-
Charge Transfer
d–d Transition
f–f Transitions

Charge transfer bands occur when the excited electrons move either from a metal orbital to a ligand orbital (metal → ligand charge transfer – MLCT) or from a ligand orbital to a metal orbital (ligand → metal charge transfer – LMCT).
MLCT transitions are more common than LMCT.

d–d transitions occur when the excited electron moves from one d orbital to another d orbital of the metal.
f-f transition occur when the excited electron moves from f orbital to f orbital of the same metal centre.
The d-d or f-f transitions can further be classified as spin–allowed transition where the spin quantum number in the ground and excited states are the same while in the spin–forbidden transition, the spin state changes during the excitation.

Spectra is due to the transition of an electron from one energy level to another. So, it is of two types. One is Absorption Spectra and the other is Emission spectra.

1. Absorption Spectra

It shows the particular wavelength of light absorbed (i.e. particular amount of energy required to promote an electron from one energy level to higher level).

2. Emission spectra

It shows the energy emitted when the electron falls from the excited level to the lower level. Emission spectra are of three types-
A. continuous spectra
B. band spectra
C. line spectra.

A. Continuous Spectra

Solids like iron or carbon emit continuous spectra when they are heated until they glow. Continuous spectrum is due to the thermal excitation of the molecules of the substance.

B. Band Spectra

The band spectrum consists of a number of bands of different colours separated by dark regions. The bands are sharply defined at one edge called the head of the band and shade off gradually at the other edge. Band spectrum is emitted by substances in the molecular state when the thermal excitement of the substance is not quite sufficient to break the molecules into continuous atoms.

C. Line Spectra

A line spectrum consists of bright lines in different regions of the visible spectrum against a dark background. All the lines do not have the same intensity. The number of lines, their nature and arrangement depends on the nature of the substance excited. Line spectra are emitted by vapours of elements. No two elements do ever produce similar line spectra.

Electronic absorption spectroscopy requires consideration of the following principles-

1. Franck-Condon Principle

Electronic transitions occur in a very short time (about 10^-15sec.) and hence the atoms in a molecule do not have time to change position appreciably during electronic transition. So the molecule will find itself with the same molecular configuration and hence the vibrational kinetic energy in the exited state remains the same as it had in the ground state at the moment of absorption.

2. Electronic transitions between vibrational states

Frequently, transitions occur from the ground vibrational level of the ground electronic state to many different vibrational levels of particular excited electronic states. Such transitions may give rise to vibrational fine structure in the main peak of the electronic transition. Since all the molecules are present in the ground vibrational level, nearly all transitions that give rise to a peak in the absorption spectrum will arise from the ground electronic state. If the different excited vibrational levels are represented as υ1, υ2, etc., and the ground state as υ0, the fine structure in the main peak of the spectrum is assigned to υ₀ → υ₀, υ₀ → υ₁, υ₀ → υ₂ etc., vibrational states. The υ₀ → υ₀ transition is the lowest energy (longest wave length) transition.

3.Transition probability

For absorption spectrum to appear light must be absorbed by the molecule. Light will be absorbed if it can interact with the molecule by its oscillating electric and magnetic fields. For this to take place the dipole moment of the molecule must change during the transition. If the change in dipole moment is quite large, number of photons will be absorbed which further lead to intense bands of large area. Otherwise, small change in the dipole moment will lead to less absorption of photons and hence lesser area and weak absorption bands with low intensity.

Probability of transition ∝ transition moment μ_n
μ_n = ∫Ψ_f μ Ψ_i d𝜏
Ψ_f = final State
Ψ_i = Initial State
μ = electric dipole moment operator
Intensity of absorption ∝ μ_n²
Allowed transition μ_n ≠ 0
Forbidden transition μ_n = 0

Electronic Spectra of [Ti(H₂O)₆]⁺³ Complex Ion

There is only one electron in d-orbital of Ti⁺³ ion (d¹ system). Therefore, the spectroscopic term for the ground state of Ti⁺³ ion is ²D. In the ground state the single electron occupy the lower t_2g orbital. on absorption of radiation the electron gets excited to e_g orbitals. The corresponding description of the t_2g¹ and e_g¹ configurations are T_2g and E_g.

Consequently the absorption spectrum of d¹ system (i.e. Ti⁺³ ion) shows only one band due to ²E_g ← ²T_2g transition.
The absorption band in the spectra of aqueous Ti⁺³ ion is broad and unsymmetrical due to L-S coupling in ground state and J-T distortion in excited state.
In [Ti(H₂O)₆]⁺³ Complex Ion, absorption maximum observed at 20300cm⁻¹ (4900Å) and also the absorption maximum has a shoulder at 17400cm⁻¹ due to J-T distortion. This shoulder is responsible for broad band in the spectrum.