Question

For every first row 4-coordinate complexes from Sc2+ to Zn2+ what would the expected room temperature magnetic moment be if each were tetrahedral? Square planar? How do these compare for 6-coordinate, octahedral complexes of both?

Answer 1

The configurations corresponding to the T₂ term (from D) or a T₁ term (from an F term) are those where there is a direct contribution to orbital angular momentum expected.

The magnetic moments of complexes with T terms are often found to show considerable temperature dependence. This is as a result of spin-orbit coupling that produces levels whose energy differences are frequently of the order kT, so as a result, temperature will have a direct effect on the population of the levels arising in the magnetic field.

In a Kotani plot μ_eff is plotted against kT/λ and when this corresponds to a value of 1 then μ equals the "spin-only" value. If this is extrapolated to infinity then the value corresponds to μ_S+L.

Measuring the magnetic moment at 80K and 300K often shows up this variation with temperature.

A worked example.

Account for the magnetic moments of the complex, (Et₄N)₂[NiCl₄] recorded at 80, 99 and 300 K.

          80K   99K   300K
          3.25  3.43  3.89 B.M.

Ni²⁺ is a d⁸ metal ion.
The formula suggests a 4 coordinate complex and we can assume that the complex is tetrahedral with a d electron configuration of e⁴ t₂⁴ therefore the spin-only magnetic moment can be calculated as 2.83 BM.

Why did we ignore the possibility of it being square-planar?

The free ion Russell-Saunders ground term is ³F (L=3 and S=1) which will give rise to a lowest energy T term in a tetrahedral field and hence the resultant magnetic moment is expected to be temperature dependent and have a direct orbital contribution.

The observed values may be quite different then to the calculated spin only magnetic moment.

The value of μ_S+L can be calculated as:
μ_S+L= √{4S(S+1)+L(L+1)}

or μ_S+L= √{8+12}

or μ_S+L = √20 = 4.472B.M.

From the observed values it can be seen that the magnetic moment of the d⁸ Ni²⁺ complex is intermediate between the μ_so and μ_S+L values (probably due to partial quenching of the orbital angular momentum contribution) and is dependent on temperature.

Octahedral complexes with between 4 and 7 d electrons can be either high-spin or low-spin depending on the size of Δ When the ligand field splitting has an intermediate value such that the two states have similar energies, then the two states can coexist in measurable amounts at equilibrium. Many "crossover" systems of this type have been studied, particularly for iron complexes.

In the d⁶ case of Fe(phen)₂(NCS)₂, the crossover involves going from S=2 to S=0.

At the higher temperature the ground state is ⁵T_2g while at low temperatures it changes to ¹A_1g. The changeover is found at about 174K.