A Magnetic Personality? - Paramagnetism and Diamagnetism

if we examine the set of d electrons for d4 to d7 there is choice available as regards the arrangement of electrons in the octahedral d subshells. These configurations display options for electron arrangement, namely high spin and low spin. The differentiation depends on the size of the energy gap (Δ_o) compared with the amount of spin pairing energy (P), with a large Δ_o favouring low spin arrangements. As discussed in the last section the size of Δ_o is ligand-dependent, especially depending on the type of donor atom, and also is influenced appreciably by the charge on the metal ion; P varies dominantly only with the metal centre and its oxidation state. In general, where P > Δ_o the complex will be high spin, whereas where P<Δ_o the complex will be low spin (Table 7.7). Note how, as the ligand changes from F to NH₃ for do Co(III), and from OH₂ to CN for do Fe(II) the spin state switches; if this model is correct, this should be experimentally observable. It is the magnetic properties that most clearly illustrate this behaviour.

In terms of magnetism there are two classes of compounds, distinguished by their behaviour in a magnetic field: diamagnetic - repelled from the strong part of a magnetic field; and paramagnetic - attracted into the strong part of a magnetic field. Ferromagnetism can be considered a special case of paramagnetism.

All chemical substances are diamagnetic, since this effect is caused by the interaction of an external field with the magnetic field produced by electron movement in filled orbitals. However, diamagnetism is a much smaller effect than paramagnetism, in terms of its contribution to measurable magnetic properties. Paramagnetism arises whenever an atom ion or molecule possesses one or more unpaired electrons. It is not restricted to transition metal ions and even non-metallic compounds can be paramagnetic; dioxygen is a simple

example. However this definition is significant in terms of the variable number of unpaired electrons that can be present in a transition metal complex. Since we are dealing with five d orbitals, the maximum number of unpaired electrons that can be associated with one metal ion is five- simply, there can be only from zero to five unpaired electrons or six possibilities. Experimentally dia- and para-magnetism can be detected by a weight change in the presence of a strong inhomogeneous magnetic field. With the sample suspended in a sample tube so that the lower part lies in the centre of a strong magnetic field and the upper part outside the field, the experimental outcome is that diamagnetic materials are heavier whereas paramagnetic ones are lighter than in the absence of a magnetic field. Even the number of unpaired electrons can be determined by experiment based on theories that we shall not develop fully here. However, we will explore the factors that contribute to the magnetic properties, usually expressed in terms of an experimentally measurable parameter called the magnetic moment (μ).

We are dealing in our model with electrons in orbitals, which are defined to have both orbital motion and spin motion; both contribute to the (para)magnetic moment. Quantum theory associates quantum numbers with both these motions. The spin and orbital motion of an electron in an orbital involve quantum numbers for both spin momentum (S) which is actually related to the number of unpaired electrons (n) as S = n/2 and the orbital angular momentum (L). The magnetic moment (u) (which is expressed in units of Bohr magnetons μB) is a measure of the magnetism, and is defined by an expression (7.1) involving both quantum numbers.

μ = [4S (S+ 1) + L (L+ 1)]^1/2                                    (7.1)

The introduction of an equation involving quantum numbers may be daunting, but we are fortunately able to simplify this readily. Firstly, for first-row transition metal ions, the effect of L on μ is small, so a fairly valid approximation can be reached by neglecting the L component, and then our expression reduces to the so-called 'spin-only'

approximation (7.2).

μ =[4S(S+1)]^1/2                                                  (7.2)

where the only quantum number remaining is S. Now, we may readily replace this quantum number by using the S = n/2 relationship, the substitution then leading to the 'spin-only' formula for the magnetic moment (7.3).

μ = [n(n+2)]^1/2                                      (7.3)

Thus, we have reduced our expression to one involving simply the number of unpaired electrons. Using this 'spin-only' Equation (7.3), the value of μ can be readily calculated and predictions compared with actual experimental values (Table 7.8).

It is clear that the experimental values can be used effectively to define the number of unpaired electrons, and thus the spin state of a complex. For example Co(II) is a d2 system, which will have three unpaired electrons if high spin and one unpaired electron if low spin, with calculated magnetic moments of 3.88 and 1.73 μg respectively. If a particular complex has as experimental magnetic moment of 3.83 μg, then it must, by comparison with the two options, be high spin. The technique can very effectively distinguish between high and low spin states. For Co (III) (d⁶) for example, [Co(NH₃)₆]³⁺ (low spin n = 0) has an experimental magnetic moment close to zero whereas [CoF₆]^3- (high spin n = 4) has an experimental magnetic moment of nearly 5 μg readily differentiated. The simple ligand field model that we have developed has triumphed again, and it is its applicability for dealin   simply with an array of experimental data such as magnetic behaviour that has led to its longevity.

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