Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but do not forget nuclear magnetism !

Origin of Magnetism e-e- « Orbital » magnetic moment« Intrinsic » magnetic moment due to the spin quantum µ spin = g s x µ B x s ≈ µ B s = ± 1/2 µ orbital = g l x µ B x µ total = µ orbital + µ spin µ orbital µ spin

Binomial triangles n010#  Pascal’s triangle, electron spin interacting with n × (I = ½) nuclei, (2 × n × I) + 1 lines gives (2 × n × I) + 1 lines of relative intensities shown above “add up 2I + 1 numbers to obtain the next row”

Triangles for quadrupolar nuclei n × (I = 5 / 2 ); add up 2I + 1 = 6 numbers n × (I = 3 / 2 ); add up 2I + 1 = 4 numbers n × (I = 1); add up 2I + 1 = 3 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. average An average (or isotropic) response is detected, provided that the tumbling is fast compared to the frequency of the experiment. g-value g e = ……..

24 g-values, linewidths and lineshapes g = g = g = Gaussian Lorentzian  B p-p  E = hν = gβ e H r 1 mT = 10 Gauss

25 Hyperfine coupling patterns × G CH 3  radical 13 C, 1.11% abundant, I = ½ 2 H = D, % abundant, I = 1 g N ( 1 H) = 5.586; g N ( 2 H) = G “a 1:3:3:1 quartet” “a doublet of 1:3:3:1 quartets” “a 1:2:1 triplet”

EPR Spectroscopy Magnetic Field No coupling 1 x 1 H 1:1 2 x 1 H 1:2:1 3 x 1 H 1:3:3:1 A /G

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

28 Anisotropic = “different in different directions” In a solid sample molecular motion is usually restricted, often only vibrational motion remains. addition EPR spectra are an addition of molecular orientations with respect to the applied magnetic field, and this is simplified by cancellation effects. Axial VO 2+

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

30 Isotropic molecular shapes: z = x = y sphere octahedron tetrahedron 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 ], 3d 1, S = ½ z x

33 Single molecule EPR N S (a thought experiment)

34 Single molecule EPR N S (a thought experiment)

35 Single molecule EPR N S (a thought experiment)

36 Single crystal EPR N S

37 Single crystal EPR N S

38 Single crystal EPR N S

39 Angular variation of resonance z: θ = 0 o ; x: θ = 90 o g z > g x means H z res < H x res z

40 “Road map”

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

Triphenylmethyl radical The radical was discovered by Moses Gomberg in 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. First radical ever in Organic Chemistry

HOW MANY LINES do we expect in the EPR spectrum? It has 3 different groups of protons interacting with the upe: 1)6 Ho 2)6 Hm 3)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!