origin of magnetism … the electron * i am an electron rest mass m e, charge e -, magnetic moment...

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Page 1: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 2: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 3: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 4: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 5: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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 !

Page 6: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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

Page 7: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 8: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 9: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 10: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 11: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 12: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 13: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 14: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 15: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 16: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 17: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 18: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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”

Page 19: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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

Page 20: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 21: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 22: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 23: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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 averageaverage (or isotropic) response is detected,

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

g-value ge = 2.00231930……..

Page 24: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

24

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

Page 25: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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”

Page 26: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

EPR Spectroscopy

Magnetic Field3340 3390

No coupling

1 x 1H1:1

2 x 1H1:2:1

3 x 1H1:3:3:1

A /G

Page 27: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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

Page 28: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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+

Page 29: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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

Instantaneously freeze the solution

Page 31: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

31

Axial molecular shapes:z ≠ x = y

trigonal bipyramid square-based pyramid

square plane

cylinder and disc

Page 32: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

32

[VO(acetylacetonate)2]

H3C CH3

O OV

CH3H3C

OOO

[VO(acac)2], 3d1, S = ½

z

x

Page 33: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

33

Single molecule EPR

N S

(a thought experiment)

Page 34: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

34

Single molecule EPR

N S

(a thought experiment)

Page 35: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

35

Single molecule EPR

N S

(a thought experiment)

Page 36: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

36

Single crystal EPR

N S

Page 37: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

37

Single crystal EPR

N S

Page 38: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

38

Single crystal EPR

N S

Page 39: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

39

Angular variation of resonance

z: θ = 0o; x: θ = 90o

gz > gx means Hzres < Hx

res

z

Page 40: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

40

“Road map”

Page 41: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

41

EPR Symmetry

isotropic

axial

rhombic

Arrows denote positions used to measure g-values

z = “parallel”x,y = “perpendicular”

Page 42: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 43: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 44: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 45: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 46: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but
Page 47: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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

Page 48: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but

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!

Page 49: Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment µ B everything, tiny, elementary quantum * but