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NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) Magnetic properties of complexes K.Sridharan Dean School of Chemical & Biotechnology SASTRA University Thanjavur – 613 401 Page 1 of 10 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) TableofContents 1 Types of magnetism ..................................................................................................................... 3 1.1 Diamagnetism ........................................................................................................................ 3 1.2 Paramagnetism ...................................................................................................................... 3 1.3 Ferromagnetism .................................................................................................................... 3 1.4 Antiferromagnetism .............................................................................................................. 3 1.5 Variation of magnetic susceptibility with temperature ........................................................ 4 1.6 Curie temperature (TC) .......................................................................................................... 4 1.7 Neel temperature (TN) ........................................................................................................... 4 1.8 Components of paramagnetism ............................................................................................ 4 1.9 Theoretical paramagnetic moment ....................................................................................... 5 2 Quenching of magnetic moments ................................................................................................ 5 3 Magnetic moment & structure ..................................................................................................... 7 3.1 Lanthanides ........................................................................................................................... 8 3.2 Spin‐cross over region and effect of temperature ................................................................ 9 4 References .................................................................................................................................. 10 Page 2 of 10 Joint Initiative of IITs and IISc – Funded by MHRD NPTE EL – Chemistrry and Bioche emistry – Coo ordination Che emistry (Chem mistry of transsition eleme ents) 1 Ty ypes of magnettism 1.1 Diamagn D netism This s arises du ue to paired d electrons. When all the electro ons in a molecule are e pairred, it is ca alled a dia amagnetic compound. c This compound will be slightlyy repe elled by the e external magnetic m fie eld. 1.2 Paramag P gnetism This s is due to o unpaired d electrons in a compound. The compoun nd will be mod derately atttracted by the external magnetic field. The e dipoles w will not be aligned uniform mly but at ra andom in th he absence e of externa al field. 1.3 Ferromag F gnetism In this t compo ound the magnetic m dip poles are a arranged in n a paralle el manner eve en in the absence a off magnetic field. Hen nce, these compound ds will be mag gnetic even n in the abs sence of ex xternal mag gnetic field. These co ompounds are strongly atttracted by external e ma agnetic field d. 1.4 Antiferro A omagnetis sm In this t case, the magne etic dipoles s are arra nged antip parallel. Th hese com mpounds arre weakly atttracted by external fie eld. Paramagn netic netic Ferromagn Antiferromagnetic 10 Page 3 of 1 Joint Initiative of IIT Ts and IISc – Funded by MHRD M NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 1.5 Variation of magnetic susceptibility with temperature The variation of different types of magnetic susceptibility with temperature is shown in Figure 1.5.1. Ferromagnetic Paramagnetic TN TC Antiferromagnetic Diamagnetic Fig 1.5.1 Magnetic susceptibility and temperature 1.6 Curie temperature (TC) At this temperature, ferromagnetism changes to paramagnetism. 1.7 Neel temperature (TN) Antiferromagnetism changes to paramagnetism at this temperature. 1.8 Components of paramagnetism When unpaired electrons are present in a molecule, they have spin and orbital motions. Paramagnetism results due to these spin and orbital angular motion. The spin and orbital motion can couple in three ways, viz., spin-spin, orbitalorbital, and spin-orbital. Page 4 of 10 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 1.9 Theoretical paramagnetic moment This is the magnetic moment incorporating all the three types of coupling, viz., spin-spin, orbital- orbital, and spin-orbital. This is given by Equation 1.1 g J ( J 1), 1.1 where μ is the magnetic moment, J is the total angular momentum quantum number and g is the Landé splitting factor for the electron. Lande splitting factor, g, is defiened by Equation 1.2. g 1 J ( J 1) S ( S 1) L( L 1) 2 J ( J 1) 1.2 where J L S , L S 1,....., L S 1.3 L is the orbital-angular momentum and S is the spin-angular momentum. When the spin-orbit coupling is negligible or absent in a complex but there is significant spin and orbital contribution, the above equation transforms as Equation 1.4.: [4S ( S 1) L( L 1)] 1.4 2 Quenching of magnetic moments The observed magnetic moments in complexes are somewhat less than the expected values Equation 1.4 in the absence of spin-orbit coupling or when it is negligible: The reason for this decrease in the value is that the actual orbital contribution is Page 5 of 10 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) always less than the expected (ideal) value. The orbital angular momentum is high in the free metal ion and it is reduced when ligands are attached to it. When the orbital contribution to the magnetic moment is zero, we say that the orbital contribution to the magnetic moment is quenched. When the ground state of a complex is either A or E, the orbital contribution will be quenched. In other words, there is no orbital angular momentum for these states. Reason ‘A’ state is non-degenerate because it has only one level. Hence, rotation cannot change one orbital into another equivalent orbital. ‘E’ state is doubly degenerate, which means that there are two energy levels with the same energy. The orbitals giving rise to this are dx2-y2 and dz2. One orbital cannot be changed into another by rotation because their shapes are different. Hence, A and E terms do not have orbital angular momentum. In other words, orbital angular momentum is quenched in these cases. Thus, complexes having A or E ground states will have no orbital angular momentum contribution to the magnetic moment and hence, they will have lower values than expected. T state This is a triply degenerate state caused by the t2g orbitals, dxy, dyz, and dzx. They have similar shape and hence, one orbital can be transformed into another by simple rotation. Thus, if an electron is present in a dxy orbital, it can occupy the dyz or dzx by simple rotation about the proper axis and the electron can Page 6 of 10 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) rotate in an orbit producing magnetic moment. Hence, the orbital angular momentum will not be quenched and the orbital angular momentum contribution will add to the total magnetic moment of the complex Configurations d1 d2 d3 d4 d5 d6 d7 d8 d9 Ground-state term 2 T2g 3 T1g 4 A2g 5 Eg (high-spin) 3 T1g (low-spin) 6 A1g (high-spin) 2 T2g (low-spin) 5 T2g (high-spin) 1 A1g (low-spin) 4 T1g (high-spin) 2 Eg (low-spin) 3 A2g 2 Eg Orbital contribution Yes Yes No No Yes No Yes Yes No Yes No No No 3 Magnetic moment & structure In the case of lanthanide complexes, all types of coupling should be considered, viz., spin-spin, spin-orbital, and orbital-orbital. Incorporating all these, we have equation 1.1, which gives the theoretical magnetic moment for a complex: When the spin-orbit coupling and the orbital angular momentum are zero, the magnetic moment is given by the equation 3.1. 2 S ( S 1) 3.1 The equation 3.1 is known as the spin-only formula to get the magnetic moment. S = n/2, where ‘n’ is the number of unpaired electrons. Substituting this value of S in the equation 3.1 we get Equation 3.2. Page 7 of 10 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 2 (n / 2)(n/ 2 1) 3.2 n(n 2) 3.3 This is known as the spin-only formula. As far as the first row transition metals (3d series) are considered, spin-only formula works well showing that the orbital angular momentum does not contribute significantly to the magnetic moment. Example 1: Iron(III) complex It is a d5 system. The high-spin complex, whose electronic configuration is t2g3eg2, has five unpaired electrons. Using the above equation, we can calculate the magnetic moment using Equation 3.3. 5(5 2) 5.92 B.M . 3.4 However, the experimental value was found to be in the range 5.70-6.00 B.M. In the low-spin complex the electronic configuration g is t2g5eg0. There will be one unpaired electron. That is, n=1. Hence, the calculated value of μ = [n(n+2)]1/2 = 31/2 = 1.73 BM. The experimental value is in the range 2.0-2.5 BM. 3.1 Lanthanides Here, all the three kinds of couplings are significant and hence the spin-only formula will not give the correct value for magnetic moment. The reason is that the d-orbitals are deeply buried and hence are not perturbed by the ligands. Therefore, all the three components of coupling contribute appreciably to the magnetic moment. Page 8 of 10 Joint Initiative of IITs and IISc – Funded by MHRD NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) 3.2 Spin-cross over region and effect of temperature Magnetic measurements will tell us whether the complex is a high-spin or lowspin complex as explained earlier. Many transition metal ions are able to form high-spin and low-spin complexes depending up on the strength of the ligand field. When the ligand is of intermediate field strength, both high-spin and lowspin complexes can coexist in equilibrium. Example: Fe2+ can form both high-spin, Fe(H2O)62+, and low-spin, Fe(CN)62-, complexes. The high-spin complex has electronic configuration, t2g4eg2 and has 4 unpaired electrons. Hence, S=4/2 =2 and is paramagnetic. The electronic configuration of low-spin complex is t2g6eg0. S = 0 and is paramagnetic as there are no unpaired electrons. In octahedral complexes, the d6 system will be having 5 T2g as the ground state in weak-field cases and 1A1g as the ground state in strong-field cases. This is shown below: 5 E Cross-over point 1 ∆ Joint Initiative of IITs and IISc – Funded by MHRD T2g A1g Page 9 of 10 NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition elements) Near the cross-over point, the difference in energy between the two spin states is very small and hence, they exist in equilibrium near this point. The actual population of the states depends on the temperature. For the complexes of iron(II) mentioned above, the high-spin complex is predominant at high temperature and the low-spin complex is predominant at low temperature. 4 References 1. “Inorganic Chemistry: Principles of Structure and Reactivity”, James E.Huheey, Ellen A.Keiter, Richard L.Keiter, Okhil K.Medhi, Pearson Education, Delhi, 2006 2. “Inorganic Chemistry”, Shriver and Atkins, 3/e, Oxford University Press, 2002, 3. “Concise Inorganic Chemistry”, 5/e, Blackwell Science, 2005, 4. “Concepts and Models of Inorganic Chemistry”, 3/e, John Wiley & Sons Page 10 of 10 Joint Initiative of IITs and IISc – Funded by MHRD