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 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 Δ oct /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 Cr 3 + metal complex has strong transitions a nd \(\lambda_{max}\) at 431. 03 nm, 7 81.25 nm, and 1,250 nm. Determi ne the \(Δ_{oct}\) fo r this complex. Solution Cr has 6 electrons. Cr 3 + has three electrons, so it has a d-configuration of d 3 Locate the d 3 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 \(\ce{^4T_{1g}} \leftarrow \ce{ ^4_{\,}A_{2g}}\) 23200 2.9 \(\ce{^4T_{1g} \leftarrow ^4_{\,}A_{2g}}\) 13600 1.7 \(\ce{^4T_{2g}\leftarrow ^4_{\,}A_{2g}}\) 8000 1.0 Sliding the ruler perpendicular to the x-axis of the d 3 diagram yields the following values: Δoct/B 10 20 30 40 Height E(ν3)/B 29.0 45.00 64.00 84.000 Height E(ν2)/B 17.0 30.00 40.00 51.000 Height E(ν1)/B 10.0 20.00 30.00 40.000 Ratio E(ν3)/E(ν1) 2.9 2.25 2.13 2.100 Ratio E(ν2)/E(ν1) 1.7 1.50 1.33 1.275 Based on the two tables above it should be assessed that the Δ oct / B value is 10. B is found by dividing E by the height. Energy cm-1 Height B 23200 29 800 13600 17 800 8000 10 800 Next multiply Δ oct / B by B to yield the Δ oct 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 Δ oct / B values that yield the proper energy ratios.