Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment...
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Transcript of Origin of Magnetism … the electron * I am an electron rest mass m e, charge e -, magnetic moment...
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
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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”
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
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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
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
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“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!