origin of magnetism … the electron * i am an electron rest mass m e, charge e -, magnetic moment...
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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 !
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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
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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”
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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
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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”
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EPR Spectroscopy
Magnetic Field3340 3390
No coupling
1 x 1H1:1
2 x 1H1:2:1
3 x 1H1:3:3:1
A /G
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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
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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+
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29100 L of a 1 mM solution contains ca. 6 1016 molecules
Instantaneously freeze the solution
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Isotropic molecular shapes: z = x = y
sphere
octahedron tetrahedron
cube icosahedron
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Axial molecular shapes:z ≠ x = y
trigonal bipyramid square-based pyramid
square plane
cylinder and disc
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[VO(acetylacetonate)2]
H3C CH3
O OV
CH3H3C
OOO
[VO(acac)2], 3d1, S = ½
z
x
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Single molecule EPR
N S
(a thought experiment)
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Single molecule EPR
N S
(a thought experiment)
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Single molecule EPR
N S
(a thought experiment)
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Single crystal EPR
N S
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Single crystal EPR
N S
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Single crystal EPR
N S
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Angular variation of resonance
z: θ = 0o; x: θ = 90o
gz > gx means Hzres < Hx
res
z
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“Road map”
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EPR Symmetry
isotropic
axial
rhombic
Arrows denote positions used to measure g-values
z = “parallel”x,y = “perpendicular”
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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
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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!
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