11.3.5: Applications of Tanabe-Sugano Diagrams
- Page ID
- 377930
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The Tanabe-Sugano diagrams can be used to interpret absorption spectra and gain insight into the properties of a coordination complex. For example, you could use the appropriate diagram to predict the number of transitions, assign the identity of a specific transition, or calculate the value of \(\Delta\) for a specific metal complex.
- Determine the \(d\)-electron count of the metal ion of interest.
- Choose the appropriate Tanabe-Sugano diagram: this is the one matching the \(d\)-electron count of the metal ion. There is a full list of Tanabe-Sugano diagrams in the Resources Section.
- Acquire an electronic spectrum of the metal complex and identify \(\lambda_{max}\) for spin-allowed (strong intensity) and spin forbidden (weak intensity) transitions.
- Convert wavelength (\( \lambda_{max} \)) to energy (E) in wavenumbers (\(cm^{-1}\)) and generate energy ratios relative to the lowest-energy allowed transition. (i.e. \(\frac{E_2}{E_1}\) and\(\frac{E_3}{E_1}\)).
- Using a ruler, slide it across the printed Tanabe-Sugano diagram until the E/B ratios between lines is equivalent to the ratios found in step 4.
- Solve for B using the E/B values (y-axis, step 4) and Δoct/B (x-axis, step 5) to yield the ligand field splitting energy, \(Delta\) (Sometimes this is labeled as \(10D_q\), and it is useful to know that \(\Delta=10D_q\)).
A Cr3+ metal complex has strong transitions and \(\lambda_{max}\) at
- 431.03 nm,
- 781.25 nm, and
- 1,250 nm.
Determine the \(Δ_{oct}\) for this complex.
Solution
- Cr has 6 electrons. Cr3+ has three electrons, so it has a d-configuration of d3
- Locate the d3 Tanabe-Sugano diagram
- Convert to wavenumbers:
\[\dfrac{10^7(nm/cm)}{1250\; nm}= 8,000\; cm^{-1}\]
\[\dfrac{10^7(nm/cm)}{781.25\; nm}= 13,600\; cm^{-1}\]
\[\dfrac{10^7(nm/cm)}{431.03\; nm}= 23,200\; cm^{-1}\]
- Allowed transitions are \(\ce{^4T_{1g}} \leftarrow \ce{ ^4_{\,}A_{2g}}\), \(\ce{^4T_{1g} \leftarrow ^4_{\,}A_{2g}}\) and \(\ce{^4T_{2g}\leftarrow ^4_{\,}A_{2g}}\).
| Transition | Energy cm-1 | Ratios to lowest |
|---|---|---|
| \(\ce{^4T_{1g}} \leftarrow \ce{ ^4_{\,}A_{2g}}\) | 23,200 | 2.9 |
| \(\ce{^4T_{1g} \leftarrow ^4_{\,}A_{2g}}\) | 13,600 | 1.7 |
| \(\ce{^4T_{2g}\leftarrow ^4_{\,}A_{2g}}\) | 8,000 | 1 |
- Sliding the ruler perpendicular to the x-axis of the d3 diagram yields the following values:
| Δoct/B | 10 | 20 | 30 | 40 |
|---|---|---|---|---|
| Height E(ν3)/B | 29 | 45 | 64 | 84 |
| Height E(ν2)/B | 17 | 30 | 40 | 51 |
| Height E(ν1)/B | 10 | 20 | 30 | 40 |
| Ratio E(ν3)/E(ν1) | 2.9 | 2.25 | 2.13 | 2.1 |
| Ratio E(ν2)/E(ν1) | 1.7 | 1.5 | 1.33 | 1.275 |
- Based on the two tables above it should be assessed that the Δoct/B value is 10. B is found by dividing E by the height.
| Energy cm-1 | Height | B |
|---|---|---|
| 23,200 | 29 | 800 |
| 13,600 | 17 | 800 |
| 8,000 | 10 | 800 |
- Next multiply Δoct/B by B to yield the Δoct energy. \[10 \times 800 = 8000\; cm^{-1}=Δ_{oct}\]
Each problem is of varying complexity as several steps may be needed to find the correct Δoct/B values that yield the proper energy ratios.