# 11.3.5: Applications of Tanabe-Sugano Diagrams

• • Kathryn Haas
• Duke University
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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.

##### How to use the Tanabe-Sugano Diagrams
1. Determine the $$d$$-electron count of the metal ion of interest.
2. 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.
3. Acquire an electronic spectrum of the metal complex and identify $$\lambda_{max}$$ for spin-allowed (strong intensity) and spin forbidden (weak intensity) transitions.
4. 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$$\frac{E_3}{E_1}$$).
5. 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.
6. 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 $$\Delta=10D_q$$).
##### Example $$\PageIndex{1}$$: Chromium Splitting

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

1. Cr has 6 electrons. Cr3+ has three electrons, so it has a d-configuration of d3
2. Locate the d3 Tanabe-Sugano diagram
3. Convert to wavenumbers:

$\dfrac{10^7(nm/cm)}{1250\; nm}= 8,000\; cm^{-1}$

$\dfrac{10^7(nm/cm)}{781.25\; nm}= 13,600\; cm^{-1}$

$\dfrac{10^7(nm/cm)}{431.03\; nm}= 23,200\; cm^{-1}$

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
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
1. 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
1. 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.

This page titled 11.3.5: Applications of Tanabe-Sugano Diagrams is shared under a not declared license and was authored, remixed, and/or curated by Kathryn Haas.