1. CHEM 251
INORGANIC CHEMISTRY
Chapter 4

2. Magnetic properties of metal complexes
Diamagnetic complexes, with no unpaired electrons, are repelled by an external magnetic field.
Paramagnetic complexes, which have some unpaired electrons, are attracted into an external magnetic field.
Each electron has a magnetic moment with one component associated with the spin angular momentum of the electron and (except when the quantum number l= 0) a second component associated with the orbital angular momentum.

3. Magnetic properties of metal complexes
For many complexes of first row d-block metal ions, the orbital contribution to magnetic moment is small and therefore can be ignored. The magnetic moment is then called the spin-only magnetic moment. The magnetic moment is determined by the number of unpaired electrons, n. µ(spin-only) = 𝑛(𝑛+2) The total spin quantum number S is equal to n/2, where n is the number of unpaired electrons. Therefore, µ(spin-only) = 4𝑆(𝑆+1)

4. Spin-only calculated magnetic moments compared to observed values
The use of the spin-only formula allows the number of unpaired electrons to be determined and gives information about the metal oxidation state and whether the complex is low- or high- spin.

5. Magnetic Data and Coordination Geometry
The use of magnetic data to assist in the assignments of coordination geometries is exemplified by the difference between tetrahedral and square planar d8 species, e.g., Ni(II), Pd(II), Rh(I) and Ir(I). Whereas the greater crystal field splitting for the second and third row metal ions invariably leads to square planar complexes, nickel(II) is found in both tetrahedral and square planar environments. Square planar Ni(II) complexes are diamagnetic, whereas tetrahedral Ni(II) species are paramagnetic.

7. Magnetic Susceptibility
The effective magnetic moment, µeff, can be measured from the experimentally measured molar magnetic susceptibility, χm, and is expressed in Bohr magnetons (µB). Where,

8. Magnetic Moment The relationship between µeff and χm is the following:
Using SI units for the constants, this expression reduces to the following equation in which χm is in cm3 mol-1:
If Gaussian units are used then the equation used is the following:

9. Experimental determination of magnetic moment
Gouy Balance: The compound for study is placed in a glass tube, suspended from a balance on which the weight of the sample is recorded.
The tube is placed so that one end of the sample
lies at the point of maximum magnetic flux in an electromagnetic field while the other end is at a
point of low flux.

10. Experimental determination of magnetic moment
Initially the magnet is switched off, but upon applying a magnetic field, paramagnetic compounds are drawn into it by an amount that depends on the number of impaired electrons. The change in weight caused by the movement of the sample into the field is recorded, and then it is possible to calculate the magnetic susceptibility of the compound. The Gouy method is therefore making use of the interaction between unpaired electrons and a magnetic field.

11. The effect of Temperature on µeff
So far, the effects of temperature on µeff has been ignored. If a complex obeys the Curie Law: Then, µeff is independent of temperature. However, the Curie Law is rarely obeyed and so it is essential to state the temperature at which a value µeff has been measured.

12. The effect of Temperature on µeff
For a second and third row d-block metal ions in particular, quoting only a room temperature value for µeff is usually meaningless; when spin-orbit coupling is large, µeff is highly dependent on T. For a given electronic configuration, the influence of temperature on µeff can be seen from a Kotani plot of µeff against kT/ λ where k is the Boltzman constant, T is the temperature in K, and λ is the spin-orbit coupling constant. λ is small for first row metal ions, is large for a second row metal ion, and is even larger for a third row ion.

13. The effect of Temperature on µeff
This figure shows a Kotani plot for a t2g4 configuration; four points are indicated on the curve and correspond to typical values of µeff (298K) for complexes of Cr(II) and Mn(III) from the first row, and Ru(IV) and Os(IV) from the second and third rows respectively.

14. The effect of Temperature on µeff
Points to note from these data are: Os(IV) lies on the steepest part of the curve.

15. Spin crossover
accompanies the spin crossover may be gradual or abrupt (as shown in Fig 20.24)

16. Spin crossover

17. Ferromagnetism, antiferromagnetism and ferrimagnetism

18. Ferromagnetic and antiferromagnetic materials

19. Ferromagnetic and antiferromagnetic materials

20. Figure A: Paramagnet vs
Figure A: Paramagnet vs. Ferromagnet Figure B: Antiferromagnetic behavior