Selection Rules for Electronic Spectroscopy

Selection Rules for Electronic Spectra of Transition Metal Complexes.

The Selection Rules governing transitions between electronic energy levels of transition metal complexes are:

ΔS = 0 The Spin Rule
Δl = +/- 1 The Orbital Rule (Laporte)

The first rule says that allowed transitions must involve the promotion of electrons without a change in their spin.

The second rule says that if the molecule has a centre of symmetry, transitions within a given set of p or d orbitals (i.e. those which only involve a redistribution of electrons within a given subshell) are forbidden.

Relaxation of the Rules can occur through:

a) Spin-Orbit coupling - this gives rise to weak spin forbidden bands
b) Vibronic coupling - an octahedral complex may have allowed vibrations where the molecule is asymmetric.
Absorption of light at that moment is then possible.
c) π-acceptor and π-donor ligands can mix with the d-orbitals so transitions are no longer purely d-d.

Types of transition

Charge transfer, either ligand to metal or metal to ligand. These are often extremely intense and are generally found in the UV but they may have a tail into the visible.
d-d, these can occur in both the UV and visible region but since they are forbidden transitions have small intensities.

**Expected intensities of electronic transitions**
Transition type	Example	Typical value of ε m² mol^-1
Spin forbidden, Laporte forbidden	[Mn(H₂O)₆]²⁺	0.1
Spin allowed (octahedral complex), Laporte forbidden	[Ti(H₂O)₆]³⁺	1
Spin allowed (tetrahedral complex), Laporte partially allowed by d-p mixing	[CoCl₄]^2-	50
Spin allowed, Laporte allowed e.g. charge transfer bands	[TiCl₆]^2- or MnO₄^-	1000

Expected Values

The expected values should be compared to the following rough guide.
For M²⁺ complexes, expect Δ = 7500 - 12500 cm^-1 or λ = 800 - 1350 nm.
For M³⁺ complexes, expect Δ= 14000 - 25000 cm^-1 or λ = 400 - 720 nm.

For a typical spin-allowed but Laporte (orbitally) forbidden transition in an octahedral complex, expect ε < 10 m²mol^-1.
Extinction coefficients for tetrahedral complexes are expected to be around 50-100 times larger than for octrahedral complexes.

B for first-row transition metal free ions is around 1000 cm^-1. Depending on the position of the ligand in the nephelauxetic series, this can be reduced to as low as 60% in the complex.

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Created and maintained by Prof. Robert J. Lancashire
The Department of Chemistry, University of the West Indies,
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Created June 2000. Links checked and/or last modified 25th September 2007.
URL http://wwwchem.uwimona.edu.jm/courses/selrules.html