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Origin of Magnetism

quantum. Origin of Magnetism. … the electron *. I am an electron. • rest mass m e , • charge e - , • magnetic moment µ B. everything, tiny, elementary. * but do not forget nuclear magnetism !. µ orbital = g l x µ B x. quantum. Origin of Magnetism. « Orbital » magnetic moment.

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Origin of Magnetism

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  1. 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 !

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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

  7. 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”

  8. 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

  9. 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

  10. 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+

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

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

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

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

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

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

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

  18. Single crystal EPR N S

  19. Single crystal EPR N S

  20. Single crystal EPR N S

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

  22. “Road map”

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

  24. 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.

  25. 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!

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