Crystal Field Stabilisation Energy (CFSE)

A consequence of Crystal Field Theory is that the distribution of electrons in the d orbitals can lead to stabilisation for some electron configurations.

It is a simple matter to calculate this stabilisation since all that is needed is the electron configuration.

For an octahedral complex, an electron in the more stable t2g subset is treated as contributing -2/5Δ whereas an electron in the higher energy eg subset contributes to a destabilisation of +3/5Δ.

The final answer is then expressed as a multiple of the crystal field splitting parameter Δ (Delta).

Based on this, the Crystal Field Stabilisation Energies for d0 to d10 configurations can then be used to calculate the Octahedral Site Preference Energies, which is defined as: OSPE = CFSE (oct) - CFSE (tet)

Note: the conversion between Δoct and Δtet used for these calculations is:
Δtet = Δoct * 4/9

Crystal Field Stabilisation Energies (CFSE)
and Octahedral Site Preference Energies (OSPE)
Total d-electrons Octahedral   Tetrahedral   OSPE
configuration CFSE configuration CFSE
d0 t2g0 0 Δo e0 0 Δt 0 Δo
d1 t2g1 -2/5 Δo e1 -3/5 Δt -6/45 Δo
d2 t2g2 -4/5 Δo e2 -6/5 Δt -12/45 Δo
d3 t2g3 -6/5 Δo e2t21 -4/5 Δt -38/45 Δo
d4 t2g3eg1 -3/5 Δo e2t22 -2/5 Δt -19/45 Δo
d5 t2g3eg2 0 Δo e2t23 0 Δt 0 Δo
d6 t2g4eg2 -2/5 Δo + P e3t23 -3/5 Δt + P -6/45 Δo
d7 t2g5eg2 -4/5 Δo + 2P e4t23 -6/5 Δt + 2P -12/45 Δo
d8 t2g6eg2 -6/5 Δo + 3P e4t24 -4/5 Δt + 3P -38/45 Δo
d9 t2g6eg3 -3/5 Δo + 4P e4t25 -2/5 Δt + 4P -19/45 Δo
d10 t2g6eg 0 Δo e4t26 0 Δt 0 Δo

Graphically this can be represented by:

This "double-humped" curve is found for various properties of the first-row transition metals, including Hydration and Lattice energies of the M(II) ions, ionic radii as well as the stability of M(II) complexes. This suggests that these properties are somehow related to Crystal Field effects.

In the case of Hydration Energies,

M2+(g) + H2O → [M(OH2)6]2+(aq)

the following Table and graph shows this type of curve. Note that in any series of this type not all the data are available since a number of ions are not very stable in the M(II) state.

Table of hydration energies of M2+ ions
M ΔH°/kJmol-1 M ΔH°/kJmol-1
Ca -2469 Fe -2840
Sc no stable 2+ ion Co -2910
Ti -2729 Ni -2993
>V -2777 Cu -2996
Cr -2792 Zn -2928
Mn -2733

## Site preferences in Spinels

The mineral MgAl2O4 is known as spinel. The structure of which can be described as a cubic close-packed array of oxide ions, between which are tetrahedral and octahedral holes. The placement of M(II) and M(III) ions in these holes fit into two schemes: normal spinels and inverse spinels. Many transition metal ion oxides form spinel type structures of the type AB2O4 or B3O4 where in the latter case the metal exists with the oxidation numbers of +2,+3, +3.

In normal spinels the M(II) ions occupy some of the tetrahedral holes while the M(III) ions occupy some of the octahedral holes.

In inverse spinels, the M(II) ions can be thought of as having swapped with half of the M(III) ions so that the M(II) are in octahedral holes while half the M(III) are now in tetrahedral holes with the other half of the M(III) ions still occupying octahedral holes.

OSPE calculations can be used to correctly predict whether the structure of most spinels containing transition metal ions will be normal or inverse.