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Spin States

In some transition metal complexes, the electronic configuration of the transition metal can basically possess two different spin states for the same oxidation state (i.e. number of d-electrons): the high-spin and the low-spin configurations. These configurations differ in the kind of occupation of the different orbitals. Ont the one hand, it is possible to occupy all orbitals by unpaired electrons only (high-spin), or by occupying certain orbitals with paired electrons (low-spin). Because energy has to be spend for pairing electrons, it is a question of the energy difference between the t2g and the eg state, whether it is energetically more beneficial to occupy the orbitals with paired or unpaired electrons. For instance, in the case of octahedral coordination, population of one dxy, dxz, dyz orbital results in a stabilzation by 4 Dq (see Ligand Field Theory).


Figure 4: Ligand field scheme of a tetrahedral complex.

Addition of a second electron will gain further 4Dq and for d3 configuration the stabilization energy is −12 Dq. For the d4 configuration two cases occur. On the one hand, by population of a further t2g orbital the stabilization energy would be −16 Dq. But for this energy is required for spin pairing, which reduces the overall energy gain. Therefore, occupation of the eg states may result in larger energy gains, although the ligand field stabilization energy is only −6 Dq (-12 + 6). Thus, if the ligand field splitting energy (∆ = 10 Dq) exceeds the spin pairing energy, the formation of low spin complexes is preferred. For an octahedral ligand field, the high-spin and low-spin configurations are shown for the d5 configuration of the transition metal in figure 5. These two different spin states exist in the octahedral coordination only for d4, d5, d6, d7 electron configurations of the transition metal. In d1 - d3 only the low energy orbitals are occupied and for d8 - d10 the low energy orbitals (t2g orbitals) are always occupied by six electrons. Which of the two spin state is preferred depends on the ligands and the center metal ion. The absolute values for the ligand field splitting energy ∆O depends on the nature of the metal center and the ligands involved. The order of the ligand field splitting energy and with this the preferred spin state can be derived from the spectrochemical series of the ligands and metals/ions. The spectrochemical series for the ligands is:


A lower value in this series means a lower ligand field splitting energy (∆ in figure 5) and thus more likely a high-spin complex.

The spectrochemical series for the metal ions is:



The order of the metal ions follows the same order as for the ligands. A position on the left equals to a smaller ligand field splitting energy. The 3d-metals are found on the left side, while the 4d- and 5d-metals are on the right side. As a result, high spin complexes are rarely known for 4d- and 5d-metal complexes.


Figure 5: Low-spin (left) and high-spin configuration (right) of an octahedral complex.

The ligand field splitting also depends on the coordination environment. For example the ligand field splitting in tetrahedral complexes is lower than in octahedral complexes. Hence, due to the smaller energy difference between the t2 and the e state, low-spin complexes are not known for tetrahedral complexes till now.


  1. RIEDEL, E.: Anorganische Chemie (German Edition), 2004, Walter de Gruyter & Co, ISBN 978–3–11–018168–5.
  2. HOLLEMAN, A. F.; WIBERG, E.; WIBERG, N.: Lehrbuch der Anorganischen Chemie., 1995, Gruyter, ISBN 978–3–11–012641–9.



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