Origin of Magnetism
… the electron *
I am an electron
• rest mass me,
• charge e-,
• magnetic moment µB
quantum
everything, tiny, elementary
* but do not forget nuclear magnetism !
Origin of Magnetism
« Orbital » magnetic moment
« Intrinsic » magnetic moment
µorbital
due to the spin
s = ± 1/2
eµorbital = gl x µB x
µspin
µspin = gs x µB x s ≈ µB
quantum
µtotal = µorbital + µspin
Binomial triangles
“add up 2I + 1
numbers to
obtain the next row”
n
0
1
0
2
0
3
1
1
5
1
6
1
7
8
1
1
4
1
1
8
6
3 4
4 8
1
5
15
35
70
0
4
20
2 2
1
10
35
56
1
6
15
0
3
10
21
28
2
4
# 
0
1
3
5
7
1
1
6
21
56
5 16
6 32
1
7
28
7 64
1
8
Pascal’s triangle, electron spin interacting with n × (I = ½) nuclei,
gives (2 × n × I) + 1 lines of relative intensities shown above
8 128
1
9 256
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
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.
g-value
ge = 2.00231930……..
23
g-values, linewidths and lineshapes
Bp-p
g = 2.0100
Gaussian
g = 2.0023
Lorentzian
g = 1.9900
Bp-p
E = hν = gβeHr
g
714.5 ν(GHz)
Hr (G)
1 mT = 10 Gauss
24
Hyperfine coupling patterns
“a doublet of
1:3:3:1 quartets”
CH3 radical
× 20
23 G
H
a iso
38.3 G
“a 1:3:3:1 quartet”
H
H
C
a iso
13C,
C
H
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”
25
EPR Spectroscopy
3 x 1H
1:3:3:1
2 x 1H
1:2:1
1 x 1H
1:1
A /G
3340
Magnetic Field
No coupling
3390
EPR Spectroscopy
S = +½, I = +1
• e.g. 14N I = ± 1
– To 1 x 14N
S = +½
• 3 lines
• (1:1:1)
S = +½, I = -1
– To 2 x identical 14N
• 5 lines
• 1:2:3:2:1
S = +½, -½
– To 3 x identical 14N
• 7 lines
• 1:3:6:7:6:3:1
S = +½, I = 0
S = -½, I = -1
S = -½
S = -½, I = 0
S = -½, I = +1
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+
28
Instantaneously freeze the solution
100 L of a 1 mM solution contains ca. 6  1016 molecules
29
Isotropic molecular shapes:
z=x=y
octahedron
tetrahedron
sphere
cube
icosahedron
30
Axial molecular shapes:
z≠x=y
trigonal bipyramid square-based pyramid
square plane
cylinder and disc
31
[VO(acetylacetonate)2]
[VO(acac)2], 3d1, S = ½
H3C
CH3
OO O
V
O
O
H3C
CH3
z
x
32
Single molecule EPR
(a thought experiment)
N
S
33
Single molecule EPR
(a thought experiment)
N
S
34
Single molecule EPR
(a thought experiment)
N
S
35
Single crystal EPR
N
S
36
Single crystal EPR
N
S
37
Single crystal EPR
N
S
38
Angular variation of resonance
z
z: θ = 0o; x: θ = 90o
gz > gx means Hzres < Hxres
39
“Road map”
40
EPR Symmetry
z = “parallel”
x,y = “perpendicular”
isotropic
axial
rhombic
Arrows denote positions used to measure g-values
41
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.
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!