Selection Rules for Electronic Spectra of Transition Metal Complexes
- Page ID
- 1772
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The Selection Rules governing transitions between electronic energy levels of transition metal complexes are:
- ΔS = 0 The Spin Rule
- Δl = +/- 1 The Orbital Rule (or 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 center 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 these rules can occur through:
- Spin-Orbit coupling: this gives rise to weak spin forbidden bands
- Vibronic coupling: an octahedral complex may have allowed vibrations where the molecule is asymmetric.
Absorption of light at that moment is then possible. - Mixing: π-acceptor and π-donor ligands can mix with the d-orbitals so transitions are no longer purely d-d.
Transition Types
- 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.
| Transition type | Example | Typical values of ε /m2mol-1 |
|---|---|---|
| Spin forbidden, Laporte forbidden |
[Mn(H2O)6]2+ | 0.1 |
| Spin allowed (octahedral complex), Laporte forbidden |
[Ti(H2O)6]3+ | 1 - 10 |
| Spin allowed (tetrahedral complex), Laporte partially allowed by d-p mixing |
[CoCl4]2- | 50 - 150 |
| Spin allowed, Laporte allowed e.g. charge transfer bands |
[TiCl6]2- or MnO4- | 1,000 - 106 |
Expected Values
The expected values should be compared to the following rough guide.
- For M2+ complexes, expect Δ = 7,500 - 12,500 cm-1 or λ = 800 - 1,350 nm.
- For M3+ complexes, expect Δ= 14,000 - 25,000 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 1,000 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.