Crystal field stabilization energy: high- and low-spin octahedral complexes.

  We now consider the effects of different numbers of electrons occupying the d orbitals in an octahedral crystal field. For a d¹ system, the ground state corresponds to the configuration t₂g¹ (1.1). With respect to the barycentre, there is a stabilization energy of ^_ 0.4 Δ_oct (Figure 1.1); this is the so-called crystal field stabilization energy, CFSE. For a d² ion, the ground state configuration is t₂g² and the CFSE = - 0:8 Δ_oct (equation 1.1); a d 3 ion (t₂g³) has a CFSE= ^_1.2 Δ_oct.

                 (1.1)

(1.1)                                   (1.2)

   For a d⁴ ion, two arrangements are available: the four electrons may occupy the t2g set with the configuration t₂g⁴ (1.1), or may singly occupy four d orbitals, t₂g³ eg¹ (1.1).

   Configuration 1.1 corresponds to a low-spin arrangement, and 1.2 to a high-spin case. The preferred configuration is that with the lower energy and depends on whether it is energetically preferable to pair the fourth electron or promote it to the eg level. Two terms contribute to the electron-pairing energy, P, which is the energy required to transform two electrons with parallel spin in different degenerate orbitals into spin-paired electrons in the same orbital:

• the loss in the exchange energy  which occurs upon pairing the electrons;
•  the coulombic repulsion between the spin-paired electrons.

    For a given dn configuration, the CFSE is the difference in energy between the d electrons in an octahedral crystal field and the d electrons in a spherical crystal field . To exemplify this, consider a d⁴ configuration. In a spherical crystal field, the d orbitals are degenerate and each of four orbitals is singly occupied. In an octahedral crystal field, equation 20.3 shows how the CFSE is determined for a high-spin d⁴ configuration.

                                  (1.2)

   For a low-spin d⁴ configuration, the CFSE consists of two terms: the four electrons in the t₂g orbitals give rise to a ^_1.6 Δ_oct term, and a pairing energy, P, must be included to account for the spin-pairing of two electrons. Now consider a d6 ion. In a spherical crystal field, one d orbital contains spin-paired electrons, and each of four orbitals is singly occupied. On going to the high-spin d⁶ configuration in the octahedral field (t₂g⁴ eg²), no change occurs to the number of spin-paired electrons and the CFSE is given by equation 1.3.

          (1.3)

   For a low-spin d⁶ configuration (t₂g⁶ eg⁰) the six electrons in the t₂g orbitals give rise to a ^_2.4 Δ_oct term.   

   Added to this is a pairing energy term of 2P which accounts for the spin pairing associated with the two pairs of electrons in excess of the one in the high-spin configuration. Table 1.1 lists values of the CFSE for all dn configurations. Inequality 1.4 holds when the crystal field is weak, whereas expression 1.5 is true for a strong crystal field. Figure 1.1 summarizes the preferences for low- and high-spin d⁵ octahedral complexes configurations in an octahedral crystal field. Inequalities 1.4 and 1.5 show the requirements for high- or low spin.

                                   (1.4)

                                    (1.5)

    We can now relate types of ligand with a preference for high- or low-spin complexes. Strong field ligands such as [CN]^- favour the formation of low-spin complexes, while weak field ligands such as halides tend to favour high-spin complexes. However, we cannot predict whether high- or low-spin complexes will be formed unless we have accurate values of Δ_oct and P. On the other hand, with some experimental knowledge in hand, we can make some comparative predictions: if we know from magnetic data that [Co(H₂O)₆]₃‏ is low-spin, then from the spectrochemical series we can say that [Co(ox)₃]^3- and [Co)CN(₆]^3- will be low-spin. The only common high-spin cobalt(III) complex is [CoF₆]^3-.

Table 1.1 Octahedral crystal field stabilization energies (CFSE) for d n configurations; pairing energy, P, terms are included whereappropriate. High- and low-spin octahedral complexes are shown only where the distinction is appropriate.

Fig. 1.1 The occupation of the 3d orbitals in weak and strong field Fe³⁺‏ (d⁵) complexes.