For complexes with D ground terms only one electronic transition is expected and the transition energy corresponds directly to Δ. Hence, the following high spin configurations are dealt with: d

D Orgel diagram

On the left hand side d

For simplicity, the g subscripts required for the octahedral complexes are not shown.

For complexes with F ground terms, three electronic transitions are expected and Δ may not correspond directly to a transition energy. The following configurations are dealt with: d

F Orgel diagram

On the left hand side, d

Again for simplicity, the g subscripts required for the octahedral complexes are not shown.

On the left hand side, the first transition corresponds to Δ, the equation to calculate the second contains expressions with both Δ and C.I. (the configuration interaction from repulsion of like terms) and the third has expressions which contain Δ, C.I. and the Racah parameter B.

^{4}T_{2g}←^{4}A_{2g}transition energy = Δ^{4}T_{1g}(F) ←^{4}A_{2g}transition energy = 9/5 * Δ - C.I.^{4}T_{1g}(P) ←^{4}A_{2g}transition energy = 6/5 * Δ + 15B' + C.I.

On the right hand side,

The first transition can be unambiguously assigned as:

But, depending on the size of the ligand field (Δ) the second transition may be due to:

for a weak field or

for a strong field.

Note however that most textbooks only give Tanabe-Sugano diagrams for octahedral complexes and a separate diagram is required for each configuration.

In this method the energy of the electronic states are given on the vertical axis and the ligand field strength increases on the horizontal axis from left to right.

Linear lines are found when there are no other terms of the same type and curved lines are found when 2 or more terms are repeated. This is as a result of the "non-crossing rule".

The baseline in the Tanabe-Sugano diagram represents the lowest energy or ground term state.

The electronic spectrum of the V

These have been assigned to the following
spin-allowed transitions.

^{3}T_{2g} |
<--- | ^{3}T_{1g} |

^{3}T_{1g}(P) |
<--- | ^{3}T_{1g} |

^{3}A_{2g} |
<--- | ^{3}T_{1g} |

The ratio between the first two transitions is calculated as ν2 / ν1 which is equal to 25400 / 17400 = 1.448.

In order to calculate the Racah parameter,

Tanabe-Sugano diagram for d2 octahedral complexes

On moving up the line from the ground term to where lines from the other terms cross it, we are able to identify both the spin-forbidden and spin-allowed transition and hence the total number of transitions that are possible in the electronic spectrum.

Next, find the values on the vertical axis that correspond to the spin-allowed transitions so as to determine the values of ν1/B, ν2/B and ν3/B. From the diagram above these are 28.78, 41.67 and 59.68 respectively.

Knowing the values of ν1, ν2 and ν3, we can now calculate the value of B.

Since ν1/B=28.78 and ν1 is equal to 17,400 cm

or B=604.5cm

Then it is possible to calculate the value of Δ.

Since Δ/B=30.9, then: Δ=B*30.9 and hence: Δ = 604.5 * 30.9 = 18680 cm

Calculate the value of B and Δ for the Cr

SOLUTION.

These values have been assigned to the following
spin-allowed transitions.

From the information given, the ratio ν2
/ ν1 = 24000 / 17000 = 1.412^{4}T_{2g} |
<--- | ^{4}A_{2g} |

^{4}T_{1g} |
<--- | ^{4}A_{2g} |

^{4}T_{1g}(P) |
<--- | ^{4}A_{2g} |

Using a Tanabe-Sugano diagram for a d3 system this ratio is found at Δ/B=24.00

Tanabe-Sugano diagram for d3 octahedral complexes

Interpolation of the graph to find the Y-axis values for the
spin-allowed transitions gives:ν1/B=24.00Recall that ν1=17000 cm

ν2/B=33.90

ν3/B=53.11

17000 /B =24.00 from which B can be obtained, B=17000 / 24.00 or B=708.3 cm

This information is then used to calculate Δ.

Since Δ / B=24.00 then Δ = B*24.00 = 708.3 * 24.00 = 17000 cm

It is observed that the value of Racah parameter B in the complex is 708.3 cm

The Nephelauxetic Series is as follows:

F^{-}>H_{2}O>urea>NH_{3}>en~C_{2}O_{4}^{2-}>NCS^{-}>Cl^{-}~CN^{-}>Br^{-}>S^{2-}~I^{-}.

Ionic ligands such as F

A set of qualitative diagrams have been drawn for each configuration (which include the missing T terms) and along with the newest release of "Ligand Field Theory and its applications" by Figgis and Hitchman [12(b)] represent the only examples of Tanabe-Sugano diagrams that provide a comprehensive set of terms for spectral interpretation.

2. Physical Inorganic Chemistry, S.F.A.Kettle, Oxford University Press, New York, 1998.

3. Complexes and First-Row Transition Elements, D.Nicholls, Macmillan Press Ltd, London 1971.

4. The Chemistry of the Elements, N.N.Greenwood and A.Earnshaw, Pergamon Press, Oxford, 1984.

5. Concepts and Models of Inorganic Chemistry, B.E.Douglas, D.H.McDaniel and J.J.Alexander 2nd edition, John Wiley & Sons, New York, 1983.

6. Inorganic Chemistry, J.A.Huheey, 3rd edition, Harper & Row, New York, 1983.

7. Inorganic Chemistry, G.L.Meissler and D.A.Tarr, 2nd edition, Prentice Hall, New Jersey, 1998.

8. Inorganic Chemistry, D.F.Shriver and P.W.Atkins, 3rd edition, W.H.Freeman, New York, 1999.

9. Basic Principles of Ligand Field Theory, H.L.Schlafer and G.Gliemann, Wiley-Interscience, New York, 1969.

10. Y.Tanabe and S.Sugano, J. Phys. Soc. Japan, 9, 1954, 753 and 766.

11(a). Inorganic Electronic Spectroscopy, A.B.P.Lever, 2nd Edition, Elsevier Publishing Co., Amsterdam, 1984.

11(b). A.B.P.Lever in Werner Centennial, Adv. in Chem Series, 62, 1967, Chapter 29, 430.

12(a). Introduction to Ligand Fields, B.N.Figgis, Wiley, New York, 1966.

12(b). Ligand Field Theory and its applications, B.N. Figgis and M.A. Hitchman, Wiley-VCH, New York, 2000.

13. E.Konig, Structure and Bonding, 9, 1971, 175.

14. Y. Dou, J. Chem. Educ, 67, 1990, 134.

15. Inorganic Chemistry, K.F. Purcell and J.C. Kotz, W.B. Saunders Company, Philadelphia, USA, 1977.

Return to Chemistry, UWI-Mona, Home Page

Copyright © 2019 by Robert John Lancashire, all rights reserved.

Created and maintained by Prof. Robert J. Lancashire,The Department of Chemistry, University of the West Indies,

Mona Campus, Kingston 7, Jamaica.

Created February 2000. Links checked and/or last modified 2nd April 2019.