Origin of Magnetism

5. quantum Origin of Magnetism … the electron * I am an electron • rest mass me, • charge e-, • magnetic moment µB everything, tiny, elementary * but do not forget nuclear magnetism !

6. µorbital = gl x µB x quantum Origin of Magnetism « Orbital » magnetic moment « Intrinsic » magnetic moment µorbital due to the spin s = ± 1/2 µspin e- µspin = gs x µB x s ≈ µB µtotal = µorbital + µspin

18. Binomial triangles “add up 2I + 1 numbers to obtain the next row” Pascal’s triangle, electron spin interacting with n× (I = ½) nuclei, gives (2 × n × I) + 1 lines of relative intensities shown above

19. Triangles for quadrupolar nuclei n× (I = 1); add up 2I + 1 = 3 numbers n× (I = 3/2 ); add up 2I + 1 = 4 numbers n× (I = 5/2 ); add up 2I + 1 = 6 numbers Can observe coupling to quadrupolar nuclei, even if in low symmetry

23. Isotropic = “same in all directions” • In fluid solution a molecule can tumble rapidly, and • presents an “average” to the external magnetic field direction. • An average (or isotropic) response is detected, • provided that the tumbling is fast compared to the frequency of the experiment. ge = 2.00231930…….. g-value

24. Bp-p Bp-p g-values, linewidths and lineshapes Gaussian g = 2.0100 g = 2.0023 Lorentzian g = 1.9900 E = hν = gβeHr 1 mT = 10 Gauss

25. Hyperfine coupling patterns “a doublet of 1:3:3:1 quartets” CH3 radical × 20 23 G 38.3 G “a 1:3:3:1 quartet” 13C, 1.11% abundant, I = ½ 2H = D, 0.0148% abundant, I = 1 gN(1H) = 5.586; gN(2H) = 0.856 “a 1:2:1 triplet”

26. EPR Spectroscopy 3 x 1H 1:3:3:1 2 x 1H 1:2:1 1 x 1H 1:1 A /G No coupling 3340 3390 Magnetic Field

27. S = +½, I = +1 S = +½, I = 0 S = +½ S = +½, I = -1 S = +½, -½ S = -½, I = -1 S = -½, I = 0 S = -½ S = -½, I = +1 EPR Spectroscopy • e.g. 14N I = ± 1 • To 1 x 14N • 3 lines • (1:1:1) • To 2 x identical 14N • 5 lines • 1:2:3:2:1 • To 3 x identical 14N • 7 lines • 1:3:6:7:6:3:1

28. Anisotropic = “different in different directions” • In a solid sample molecular motion is usually restricted, • often only vibrational motion remains. • EPR spectra are an addition of molecular orientations with respect to the applied magnetic field, • and this is simplified by cancellation effects. Axial VO2+

29. Instantaneously freeze the solution 100 L of a 1 mM solution contains ca. 6  1016 molecules

30. Isotropic molecular shapes: z = x = y octahedron tetrahedron sphere cube icosahedron

31. Axial molecular shapes:z ≠ x = y trigonal bipyramid square-based pyramid square plane cylinder and disc

32. [VO(acetylacetonate)2] [VO(acac)2], 3d1, S = ½ z x

33. Single molecule EPR (a thought experiment) N S

34. Single molecule EPR (a thought experiment) N S

35. Single molecule EPR (a thought experiment) N S

36. Single crystal EPR N S

37. Single crystal EPR N S

38. Single crystal EPR N S

39. z Angular variation of resonance z: θ = 0o; x: θ = 90o gz > gx means Hzres < Hxres

40. “Road map”

41. EPR Symmetry z = “parallel” x,y = “perpendicular” isotropic axial rhombic Arrows denote positions used to measure g-values

47. Triphenylmethyl radical First radical ever in Organic Chemistry The radical was discovered by Moses Gomberg in 1900. He tried to prepare hexaphenylethane from triphenylmethylchloride and zinc in benzene in a Wurtz reaction and found that the product, based on its behaviour towards iodine and oxygen, was far more reactive than anticipated.

48. HOW MANY LINES do we expect in the EPR spectrum? • It has 3different groups of protons interacting with the upe: • 6 Ho • 6 Hm • 3 Hp • Therefore, total number of peaks= • (2x 6 x 1/2 +1) * (2x 6 x 1/2 +1) * (2x 3 x 1/2 +1)= 196 peaks!