SCO can occur within coordination compounds with mostly first transition row metals as central atom exhibiting a d4-d7 electron configuration and primarily octahedral coordination geometry around the metal centre. Fe2+ represents the vast majority of used metals. The coordinating ligands induce a splitting of the d-orbitals of the central metal ion into the eg* and t2g orbitals, the ligand field splitting ΔO (10Dq). In general, for systems bearing more than three d-electrons, the electron-electron repulsion has to be considered, the total spin pairing energy P. When P >> ΔO, the d-electrons are distributed according to Hund‘s law. This results, for example in a system with 6 d-electrons like Fe2+ in a total spin state of S=2, a strongly paramagnetic HS system (5T2g) with the maximum of unpaired electrons (Figure 1).
If the induced ligand field strength is high enough to surpass the total spin pairing energy (P << ΔO), the spin system will exhibit the maximum number of paired electrons. This corresponds to the diamagnetic LS state with S=0 in a d6 electron system (1A1g). If P is in the same order of magnitude as ΔO, a switching from HS to LS, the SCO, can take place.[18]
Figure 1. Schematic representation of the HS (left) and LS state (right) in an octahedral d6 electron system.
The induced splitting is depending on the chosen ligand as well as on the metal ion. It is related to the position of the ligand in the spectrochemical row and inducing or withdrawing effects of functional groups at the coordinating ligands. Normally no metals in the 4d and 5d transition rows are found to be SCO active. The reason for this lies in an increased ligand field splitting. In complexes of metal ions of the same group and oxidation state and with identical ligand sphere, the ligand field strength increases by around 50 % on going from 3d
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to 4d and from 4d to 5d elements, whereas the spin-pairing energy does not change much in this order.[19] Thus, the LS state is commonly adopted in 4d and 5d elements.
The states of d-orbital configuration for a given electron number under the influence of an octahedral ligand sphere involving the interplay of electron-electron repulsion and orbital momentum, can be calculated as functions of the so-called Racah parameters.[20] The results can be plotted in a Tanabe-Sugano diagram[21] (Figure 2), representing the relative energies of all the Russel-Saunders multiplet terms arising for a given d-electron configuration as a function of the crystal-field splitting parameter ΔO and the electronic energies of the excited states relative to the ground state.
Figure 2. Tanabe-Sugano diagram[21] for octahedral d6 complexes assuming a Racah parameter of B ≈ 1050 cm−1 for iron(II).
According to this, the 5T2g state is the ground state until a certain strength of ligand field (Δcrit). Above this, the 1A1g state (the LS state) becomes the electronic ground state.
Due to the fact that two electrons are occupying the antibonding eg* orbitals in the HS state, whereas in the LS state only non-bonding orbitals are occupied, bond lengths are elongated in relation to the LS state. For a given combination of ligands and metal ion, 10Dq depends on
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the metal-ligand distance as r−n (n=5-6). In iron(II) systems, the difference between the Fe–N or Fe–O bond lengths in the two states ΔrHL = rHS – rLS ≈ 0.2 Å.[18]
Regarding thermally induced SCO, it is important in order to obtain thermally accessible SCO compounds that the energy differences between the two states are in the region of kBT. This is illustrated in Figure 3, where a direct relation is shown between the metal to ligand radius and the energy difference:
ΔE0HL = ΔE0HS – ΔE0LS
In general, the LS state remains the quantum mechanical ground state at all temperatures, but the HS state is the thermodynamically stable state at elevated temperatures.
Figure 3. Potentials for the HS and the LS state along the metal-ligand stretch vibration r(M–L), M = Fe.
The energetic differences between HS and LS state are mainly determined by changes in the entropy ΔS comprising an electronic part due to spin degeneracy in the HS state and resulting higher degree of freedom for the electrons, and a vibrational part due to generally lower vibrational frequencies (weaker metal-ligand bonding) and the resulting higher density of vibrational states in the HS state.
ΔE0HL corresponds to the enthalpy term of the Gibbs-Helmholtz equation, in which the entropical favour of the HS state is also reflected:
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ΔG = ΔH – TΔS
Switching from LS to HS gives a positive reaction enthalpy ΔH (heating up) but also a positive reaction entropy ΔS. At low temperatures, the enthalpy term is dominant and the LS state is favoured whereas the entropy term is outweighing at high temperatures leading to the HS state.[22] At the temperature where both spin states are in equilibrium, what corresponds to T1/2, the free reaction energy is zero, ΔG = 0:
0 = ΔH – T1/2ΔS
Reordering of the Gibbs-Helmholtz equation shows then the temperature dependence of the ST given through entropy and enthalpy:
T1/2 = ΔH/ΔS
According to theoretical and empirical derivations following general assignments can be made in which energy region of ligand field splitting a complex will be present in the HS or LS state, and when it is possible for SCO to occur[18]:
The temperature dependent SCO is usually plotted as a function of high spin fraction (γHS), or as a function of the product of the molar susceptibility with temperature (χMT) versus temperature. This SCO curve can adopt different shapes, e. g. gradual, abrupt, with hysteresis, stepwise or also incomplete. Some examples are presented in Figure 4. The course of the curve is depending to a large extent on the forwarding of the ST information from one molecule to another through the crystal lattice through intermolecular interactions, what is synonymous with cooperative effects. These intermolecular interactions can be van der Waals