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Magnetic Properties of TMs So far we have seen that some important properties of TM complexes such as the magnitude of Δ are a function of the electronic configuration of the d orbitals Î number of unpaired electrons. One method of determining the number of unpaired electrons is by looking at the magnetic susceptibility of a complex Î measure of the force exerted by magnetic field on a unit mass of complex is related to the population of unpaired electrons/per unit weight Î per mole. The Gouy method is a simple technique to determine the magnetic dipole moment μ. This involves weighing a sample of the TM complex in the presence and absence of a strong magnetic field. By careful calibration using a known standard, such as HgCo(SCN)4 the number of unpaired electrons can be determined. Magnetic Properties of TMs To predict the magnetic moment, we can use the simple spin-only formula derived from Curie’s law: μ = √[4S(S+l)] Bohr Magneton (BM) where S is the spin quantum number (½ for each unpaired electron). An alternative representation is: μ = √[n(n+2)] Bohr Magneton (BM) where n is the number of unpaired electrons. These simple formulae give good results for most first row transition metal compounds, although it can be refined to include orbital contributions. For many of these complexes the spin contribution is so predominant that measured values of μ = no. of unpaired electrons. Hence we can simplify to say that: paramagnetism of the complexes of the first transition series corresponds to a ‘spin-only’ value. Note: for d electrons = 1-3 or 8-9 in an octahedral complex, the value of μ is not affected by weak field-strong field considerations. Magnetic Properties To calculate the spin-only magnetic moment of compound Î • the number of d-electrons in the central metal ion, • the stereochemistry • weak field-strong field. E.g. Î K3[Fe(oxalate)3] 3H2O metal ion Fe3+ number of d 5 electrons stereochemistry octahedral High Spin/Low Spin High Spin # of unpaired 5 electrons magnetic moment √(35) any coordination K2CuCl4 Cu2+ 9 tetrahedral Not relevant 1 √(3) B.M High-spin / Low-spin crossovers 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. Also departures from spin-only values are generally recorded for lowspin d5 and high-spin d6 and d7 complexes. Q. Account for the temperature dependence of the effective magnetic dipole moment for the iron (II) complex Fe(phen)2(NCS)2, shown below. Answer: This is a case that involves a spin crossover for the d6 Fe(II) ion. The crossover involves going from high spin S = 2 (t2g4eg2) to low spin S = 0 (t2g6eg0). μ = √[4(4+2)] = 4.9 B.M. μ = √[0(0+2)] = 0 B.M. Î orbital contributions To account for orbital contribution the spin only magnetic moment is modified as Î μS+L= √{4S(S+1)+L(L+1); where L = sum of orbital QN (e.g. for n = 3 Î L = 0+1+2 =3) For the d6 high spin case S = 2 and L = 3. μeff= √{4S(S+1)+L(L+1) = √ 24 + 12 = 6.0 B. M. For the d6 low spin case S = 0 and L = 3 μeff= √{4S(S+1)+L(L+1) = √ 0 + 12 = 3.5 B. M. For the high spin complex, the spin only contribution predominates, even at high temperatures, while for the low spin complex the value of μS+L = 1.5 B. M. observed at the cross over point is probably due to partial quenching of the contribution due to orbital angular momentum at low temperatures.