Origin of Magnetism … the electron *

I am an electron

• rest mass me, • charge e-, • magnetic moment µB

everything, tiny, elementaryquantum

* but do not forget nuclear magnetism !

Origin of Magnetism

e-

« Orbital » magnetic moment « Intrinsic » magnetic moment

due to the spin

quantum

µspin = gs x µB x s ≈ µB

s = ± 1/2

µorbital = gl x µB x

µtotal = µorbital + µspin

µorbital

µspin

Binomial triangles

n 0 1 0 #

1 0 1 1 0 2 2

2 0 1 2 1 0 3 4

3 1 3 3 1 4 8

4 1 4 6 4 1 5 16

5 1 5 10 10 5 1 6 32

6 1 6 15 20 15 6 1 7 64

7 1 7 21 35 35 21 7 1 8 128

8 1 8 28 56 70 56 28 8 1 9 256

Pascal’s triangle, electron spin interacting with n × (I = ½) nuclei,gives (2 (2 × × n n × I) + 1 lines× I) + 1 lines of relative intensities shown above

“add up 2I + 1numbers toobtain 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

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Isotropic = “same in all directions”

• In fluid solution a molecule can tumble rapidly, and

• presents an “average” to the external magnetic field direction.

• An averageaverage (or isotropic) response is detected,

• provided that the tumbling is fast compared to the frequency of the experiment.

g-value ge = 2.00231930……..

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g-values, linewidths and lineshapes

g = 2.0100

g = 2.0023

g = 1.9900

Gaussian

Lorentzian

Bp-p

Bp-p

E = hν = gβeHr

(G)Hν(GHz)714.5

gr

1 mT = 10 Gauss

25

Hyperfine coupling patterns

× 2023 G

H

isoa

CH3 radical

13C, 1.11% abundant, I = ½2H = D, 0.0148% abundant, I = 1gN(1H) = 5.586; gN(2H) = 0.856

C

isoa

38.3 G

C HH

H

“a 1:3:3:1 quartet”

“a doublet of 1:3:3:1 quartets”

“a 1:2:1 triplet”

EPR Spectroscopy

Magnetic Field3340 3390

No coupling

1 x 1H1:1

2 x 1H1:2:1

3 x 1H1:3:3:1

A /G

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

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.• EPR spectra are an additionaddition of molecular

orientations with respect to the applied magnetic field,

• and this is simplified by cancellation effects.

Axial VO2+

29100 L of a 1 mM solution contains ca. 6 1016 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]

H3C CH3

O OV

CH3H3C

OOO

[VO(acac)2], 3d1, 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 = 0o; x: θ = 90o

gz > gx means Hzres < Hx

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 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.

First radical ever in Organic Chemistry

HOW MANY LINES do we expect in the EPR spectrum?

C

Ho

Hm

Hp

Hm

Ho

It has 3 different groups of protons interacting with the upe:1)6 Ho2)6 Hm3)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!