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Section 8.3.5: Applications of Tanabe-Sugano Diagrams

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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 Section 8.3.5: Applications of Tanabe-Sugano Diagrams is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Kathryn Haas.