Nuclear Magnetic Resonance II

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Nuclear Magnetic Resonance II

• Monday Thursday 5-8th week
• Other Lectures

• T. Claridge MT 2002 NMR I
• NMR III follows in MT 2003

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Nuclear Magnetic Resonance II

• Mostly P.J. Hore, Nuclear Magnetic Resonance
• P.J. Hore, J.A. Jones, S. Wimperis, NMR The
  Toolkit
• H. Friebolin One- and Two-dimensional NMR
• H. Günther, NMR Spectroscopy
• A. Carrington and A.D. McLachlan , Introduction
  to Magnetic Resonance
• R. Freeman, A Handbook of nuclear magnetic
  resonance

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SPIN
is a mysterious beast, and yet its practical
effect prevails over over the whole of science.
The existence of spin, and the statistics
associated with it, is the most subtle and
ingenious design of Nature - without it the whole
universe would collapse.
Sin-itiro Tomonaga in The Story of Spin. Nobel
Prize winner in Physics 1965.
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If one knows all the measurements of a house one
can draw a three-dimensional picture of that
house. In the same way, by measuring a vast
number of short distances in a protein, it is
possible to create a three-dimensional picture of
that protein.
Chemists, Biologists.
Kurt Wüthrich
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And Physicists.
The Age of the Quantum Computer
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NMR Quantum Computing
http//www.qubit.org/
Present Computers store memory in
0
False, No
BIT
1
True, Yes
Quantum Computers
based on quantummechanical principles
Quantum Object can be in two states at once!
Coherent superposition of states
QUBIT Quantum Bit, quantum 2-state system
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Quantum Computing and NMR
a
Yca a cb b
b
One qubit can encode at any given t both a and
b
aa, ab, ba, bb
Two Nuclei
2 qubits for 4 stored numbers
Three Nuclei
aaa, aab, aba, abb, baa, bab, bba, bbb
3 qubits for 8 stored numbers
N Nuclei
N qubits for 2N stored numbers!
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Quantum Computing and NMR
Five-Bit NMR Quantum Computing R. Marx, A. F.
Fahmy, J. M. Myers, W. Bermel, S. J. GlaserPhys.
Rev. A 62, 012310-1-8 (2000)
linear coupling along a chain of nuclear spins
the synthesis of a suitably coupled molecule
containing four distinct nuclear species use of a
multi-channel spectrometer
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Quantum Computing
Possible Quantum Computing Systems Ion
traps Quantum Dots Unlikely NMR but good for
initial studies
What will Quantum Computers be good at?

• Cryptography perfectly secure communication.
• Searching, especially algorithmic searching
  (Grover's algorithm).
• Factorising large numbers very rapidly (Shor's
  algorithm).
• Simulating quantum-mechanical systems
  efficiently.

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...and everybody else..
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The Physics of Magnetic Resonance
Quantum mechanical Description
Classical description
Discussion of dynamic or transient effects
Discussion of Resonance Phenomena
14
The Physics of Magnetic Resonance - The Magnetic
Moment
Classically A moving charge has with it
associated a magnetic field.
Electron revolving in a Bohr orbit
Magnetic Momenta
15
Only Particles with non-zero spin quantum number,
I, possess non-zero spin angular momentum, I,
and therefore a magnetic moment, m .
16
The Physics of Magnetic Resonance -The Spin
Quantum Number
Elementary Particles and their Spin
Fermions (I n/2)
Bosons (I n)
Electron I 1/2 Proton I 1/2 Neutron I 1/2
Photon I 1
IN
17
The Physics of Magnetic Resonance -The Spin
Quantum Number
Only nuclei with a non-zero spin quantum number,
I, possess spin.
I
of Protons
of Neutrons
Examples
even odd even odd
even odd odd even
0 1or 2 or 3 or 1/2 or 3/2 or 1/2or 3/2 or
I(12C)0, I(16O)0 I(2H)1, I(10B) 3 I(17O)5/2,
I(13C)1/2 I(15N)1/2, I(35Cl)1/2
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Exercise I
32S
37Cl
I 0 I even I odd
6Li
14N
3H
16O
19F
43Ca
40K
19
Exercise I
I0 I even I odd
20
Gyromagnetic Ratios, NMR frequencies in 9.4 T
field and Natural Abundances
I
1/2
1
1/2
1
1/2
5/2
1/2
1/2
1/2
21
The Physics of Magnetic Resonance - Space
Quantization
Spin Angular Momentum, I, is quantised Magnitu
de Direction
mI -I, -I1, ..(1).., I
ie, (2I 1) orientations
22
The Physics of Magnetic Resonance - Space
Quantization
I 1/2
I 1
a35.26o
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The Physics of Magnetic Resonance- Interaction
with Magnetic Field
mN g I
Nuclear spin
Lets place the nucleus into magnetic field B
z
E - mN . B
B
Assuming the field is along z and very strong
E - mNZ . B
mN
mNZ
E - g h B mI
mI -I, -I1, ..(1).., I
24
The Physics of Magnetic Resonance-The Resonance
Condition
E - g h B mI
25
Mysterious Beast
26
Summary of first lecture
Only Particles with non-zero spin quantum number,
I, possess non-zero spin angular momentum, I,
and therefore a magnetic moment, m .
27
The Physics of Magnetic Resonance-The Vector
Model - a Classical Picture
The Larmor Frequency
28
The Physics of Magnetic Resonance-The
Populations and Bulk Magnetization
z, B0
Boltzmann Statistics
M0
E - g h B mI
a
mI 1/2
b
mI -1/2
29
Examples for Population Ratio
B0 1.41T, n 60 MHz, cf. Earths Magnetic
Field 5 10-5T
B0 21.15T, n 900 MHz,
Nb 0.999855Na
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Result The Energy Difference very small compared
to kT.

• Most energy levels are nearly equally populated.
  
• The excess in the ground state is of the order of
  Promille (Parts Per Million - ppm).
• The Net Absorption, ie, Signal Intensity depends
  on difference in population!
• Use large magnetic fields and nuclei with large g
  to maximise signal.

31
The Physics of Magnetic Resonance-The Selection
Rules
The Selection Rule for Magnetic Resonance is
Deuterium I 1
Hydrogen I 1/2
E
mI-1/2
forbidden
mI-1
mI0
mI1
mI1/2
cf, gH 6.5 gD
32
Hence, we would expect a different resonance
condition for each magnetic nucleus of different
g.
How BORING!
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The Physics of Magnetic Resonance- The Origin of
Shielding
Atom in magnetic field B0
Bare nucleus in magnetic field B0
B0
B0
Bgen
34
Resonance Condition for shielded nuclei
In absence of shielding
In presence of shielding
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The Physics of Magnetic Resonance- The Origin of
Shieding
sd
Diamagnetic Shielding

• Circulation of electrons in GS of atom/molecule
• opposing magnetic field B0
• easy to calculate for spherical charge
  distribution
• classically orbiting electron
• broadly proportional to electron density around
  atom of interest, 1/r dependence
  (electron-nucleus)
• originates in s orbitals of atoms
• fails for most molecules (non-spherical charge
  distribution)

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The Physics of Magnetic Resonance- The Origin of
Shielding
Shielding is decreased by electronegative atom
nearby
Low electron density H deshielded
High electron density
Fluoromethane
37
Exercise II Which of these protons is strongest
deshielded?
sAgt sE gtsBgt sDgt sc
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The Physics of Magnetic Resonance- The Origin of
Shielding
Classical model fails even for small molecules
(even H2)
Correction through
sp
Paramagnetic Shielding

• Takes into account non-spherical charge
  distribution
• opposite in sign to sd, ie, augments B0
• originates in d and p-electrons of contributing
  atoms
• depends on average excitation energy to excited
  levels

39
The Physics of Magnetic Resonance- The Origin of
Shielding
very large for H, small sp contribution
small, 13C, 19F, 31P possess low-lying excited
states, sp contribution important
40
The Physics of Magnetic Resonance-Further
Contributions to Shielding
Further effects on the shielding caused by
neighbouring groups need to be taken into account
in larger molecules

• neighbouring group anisotropy
• ring current effects
• electronic effects
• intermolecular interactions (H-bonds, solvent IAs)

Immediate vicinity of nucleus
41
The Shielding of magnetic nuclei - Neighbouring
Group Contributions
arise from the currents induced in nearby groups
of atoms. The effect is either to shield or
deshield the nucleus depending on the relative
geometry of group and nucleus
42
The Physics of Magnetic Resonance- The Origin of
Shielding
is an ANISOTROPIC quantity
Different susceptibilities in the three
dimensions
where
43
Neighbouring Group Anisotropy
sN
Chemical Bonds are in general anisotropic
When magnetic field is applied, magnetic moments
are induced
Additional magnetic field is influencing the
nucleus
Orientation dependent
44
Neighbouring Group Anisotropy - the case of axial
symmetry
sN
r
C
q
McConnell Equation
C
45
Neighbouring Group Anisotropy - the case of axial
symmetry - magnetic moments
sN
B0 parallel to symmetry axis
B0 perpendicular to symmetry axis
For mpargt mper
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Neighbouring Group Anisotropy - the case of axial
symmetry - magnetic moments
sN
Field experienced by nucleus in B0 direction
coord. of neighb. group
Opposite signs for HA and HB
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Neighbouring Group Anisotropy - Examples
sN
mparlt mper
mparlt mper
Paramagnetic current induced when parallel to
bond - deshielding.
Protons shielded
deshielded areas
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Neighbouring Group Anisotropy - Examples
sN
Strongly deshielded proton
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Neighbouring Group Anisotropy - Ring Currents,
sR
sR
Aromats possess large number of delocalised
electrons Magnetic field causes ring current
above and below ring, Bind opposes Bapp
In plane Bind reinforces Bapp
Principally due to diamagnetic moment induced
when B0 is perpendicular to rings plane.
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Neighbouring Group Anisotropy - Ring Currents,
sR
sR
Bapp
Bapp
Ring Current 0
Ring Current at Maximum
Hence, mparlt mper
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Ring Currents - Benzene
sR
deshielded areas
Shielded areas
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Ring Currents - More Examples
sR
53
Exercise II
54
Other sources of chemical shielding-Intermolecula
r Interactions, si
si
H
Heavily deshielded
H
intramolecular
C
O
O
O
H
O
intermolecular
H
O
H
O
H
H
55
Other sources of chemical shielding - Electric
effects
se
Arising from charged or polar groups modify
diamagnetic and/or paramagnetic currents by
polarising local electron distributions and by
perturbation of ground and excited state
wavefunctions
more shielded
56
Summary
s
1H-NMRFor shielding effect we find that
diamagnetic currents are the most important
factor, paramagnetic shielding is less important.
Substituents, Neighbouring Group Anisotropy ,
ring currents and molecular interaction effects
determine the protons shielding. Therefore the
protons in different chemical environments differ
in their resonance frequencies.
13C-NMR These heavier nuclei and their NMR
resonances are mainly determined by spara.
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Chemical Shifts
d
Shielding very complex, s difficult to determine
absolute shift rarely needed
Measure relative to an inner standard, ie
measure difference in resonance frequency between
nucleus studied and reference nucleus, according
to
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d
Chemical Shifts
Chemical shift in ppm independent of magnetic
field strength
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Chemical Shifts
d
Shielding
TMS
60
Chemical shift and Spin-Spin coupling
61
Spin-Spin Couplings - Example Spectrum
J
A Simple Example a 2-spin(1/2) system
CHACl2-CHXCl-CCl3
Strongest deshielding, lowest field highest d
3.4 Hz
3.4 Hz
d6.67 ppm
d4.95 ppm
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Scalar Spin-Spin Coupling- the HA proton NMR
spectrum
J
mI -1/2
HA
mI 1/2
HA
63
Spin-Spin Coupling
J
Resonance Condition for A for DmA1
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Spin-Spin Coupling - The Energy Levels
J
Spin-Spin Coupling
A in field
B in field
X
J/4
For JAXgt0
nB
J/4
nA
nA
nA
X
J/4
nB
J/4
J
J
A
B
n
n
65
About the Labelling of Spin Systems
Spins with very different chemical shifts are
labelled by letters very far apart in alphabet, eg
Correspondingly, nuclei with very similar
chemical shifts are labelled A,B,C etc
66
Multiplet Patterns
J-WC
1) Lets assume weak coupling (WC) 2) Unless
otherwise stated, nuclei have S1/2
67
The Multiplet of the AMX System-(coupling to 2
inequivalent 1/2 spins)
J-WC
1) Lets assume weak coupling (WC) 2) Unless
otherwise stated, nuclei have S1/2
Question What happens to the A-
resonance? Without coupling to M and X, it gives
simply a singlet.
What does coupling to M and X do?
68
250 MHz spectrum of Styrol
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The Multiplet of the AX2 System (coupling to 2
equivalent 1/2 spins)
J-WC

mX2
mX1
1 2 1
70
Exercise III - The Multiplet of the AX3 System
(to 3 equivalent 1/2 spins)
J-WC
1 3 3 1
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The Multiplet of the AXn (spin 1/2) System
(coupling to n equivalent spins)
J-WC
AX2
AX3
n1
AX4
Ways of finding a given Amplitude of this line
ways of forming different value for
Ie, the Coefficients in (ab)n
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The Multiplet of the AXn (spin 1/2) System
(coupling to n equivalent spins)
J-WC
PascalsTriangle
A AX1 AX2 AX3 AX4 AX5 AX6
1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10
5 1 1 6 15 20 15 6 1
73
90 MHz spectrum of Ethylacetate
J(A,C)7.1Hz.
B
C
A
74
250 MHz spectrum of Paraldehyde
75
Spectrum of Benzylalcohol
76
Coupling involving spin Igt1/2 nuclei
-1
nX
nA
For JAXgt0
0
nX
nA
nX
1
n
77
Coupling involving spin Igt1/2 nuclei-Examples
10B - 20, I 3
BH4
11B - 80, I 3/2
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Coupling involving spin Igt1/2 nuclei-Examples
I(D) 1
H
C
D
D
H
79
General Multiplicity Rule
Multiplicity 2nI 1
80
The Limits of the Simple Splitting Rules
81
The Limits of the Simple Splitting Rules
Question Is it really likely that spins do not
couple across 2 bonds when the do across 3?
Answer The spin-spin coupling between
magnetically equivalent nuclei does not appear
in the spectrum - but they usually do couple VERY
strongly!!
So why do we not observe them?
82
Magnetic Equivalence
Definition Two nuclei are magnetically
equivalent if
1. They are chemically equivalent. 2. For all
couplings of nucleus i and nucleus j with all
other nuclei of the molecule such as l
ie, all nuclei under consideration possess the
same resonance frequency and only one
characteristic spin-spin interaction with the
nuclei of neighbouring groups.
83
Magnetic Equivalence-Famous Examples
Jad Jac Jbd Jbc
84
Exercise IV Name the equivalent protons
AAXX
AX2
85
A short visit to multiplets in 13C-spectra

• Coupling mainly observed with directly bonded
  protons
• to remove H-proton splitting, decoupling
  techniques employed (high intensity irradiation
  of H-resonance)
• homonuclear couplings not usually observed (cf.
  natural abundance of 13C)

86
Ok, we have now understood that the protons in
methane are magnetically equivalent, but why does
the coupling not produce a splitting in the
spectrum?
87
Scalar Couplings between magnetically equivalent
spins...
do not produce multiplet splittings because of
the changes in transition probablities and NMR
frequencies arising from the mixing of spin
states by spin-spin interaction.
88
The Significance of the Ratio J/(dn)
89
The Origin of the Roof Effect
Strong Coupling Effects
included
ignored
bA bB
bA aB
dn
C
aA bB
aA aB
n
indicates chemical shift of nuclei
C
90
The Origin of the Roof Effect in 2-spin systems
- a little quantum mechanical treat
J/(dn)
q45
q0
0ltqlt45
91
The Roof Effect-Eigenvalues and Eigenstates -
remember DmI 1
92
Now we know that spin couplings affect our
spectra, we wonder What are the mechanisms of
these couplings?
1. The Fermi Contact Interaction
E
destabilised
Contact Interaction
e.g., for C-H coupling over one bond 1J(C-H)500 s
stabilised
For gNgt0
93
Spin Coupling Mechanisms - The Fermi Contact
Interaction
J

• rotating charge of the nucleus produces magnetic
  field
• from far away, point dipole
• field inside sphere differs from dipole field
• interaction between this non-dipolar field and
  electrons magnetic moment is Fermi contact
  interaction

94
Spin Coupling Mechanisms - The Fermi Contact
Interaction
J
Nucleus Y
Electron1
Electron2
Nucleus X
a
a
b
b
Fermi
Fermi
Pauli
antiparallel arrangement of nuclear spins is
favourable Jgt0
95
Spin Coupling Mechanisms - The Fermi Contact
Interaction - CH2
J
Electrons involved in forming the two bonds must
be correlated

• spins of electrons in C-H bond are polarised via
  contact (Fermi) interaction
• Pauli Principle for electrons in bond
• Hunds rule of maximum multiplicity for electron
  spins in different atomic orbitals
• Parallel nuclear spins are stabilised, JHHlt0
• coupling mechanism actually more complex - sign
  not immediately obvious unless low-lying excited
  wave function is known

96
The Fermi Contact Interaction - Summary
J

• Crucially dependent upon s-electron character of
  ground and first excited state
• not affected by strength or direction of magnetic
  field, ie, independent of spectrometer frequency
• isotropic, not affected by molecular tumbling
• one-bond C-H coupling, 1JCH in range 100-250 Hz
• three-bond H-C-C-H couplings 3JHH

qdihedral angle
97
The Fermi Contact Interaction - Summary
J
98
The Dipolar Coupling-Through Space Coupling
D
Every nucleus with non-zero I, has a magnetic
dipole mgI
Anisotropic quantity
99
The Dipolar Coupling-Through Space Coupling
D
Anisotropic quantity averages out in fast
tumbling molecules in solution
but does not average out in solids!
100
The Dipolar Coupling-Through Space Coupling
D
101
The Dipolar Coupling - a Typical Solid State
Spectrum in strong magnetic field
KAX splitting in spectrum of X caused by dipolar
coupling to A
102
NMR - Experimental Methods
60MHz
1.5 T
600MHz
900 MHz
15 T
22 T
103
NMR - Experimental Methods- CW-NMR
E
B
B
n
104
Now, instead of slowly sweeping RF or magnetic
field...
we can try to excite all resonances or all
nuclei of a given isotope simultaneously by
applying a short, intense burst of RF radiation
to the sample
105
But unlike the piano, the spins recover...

• from the pulse in a few seconds and can then be
  excited again
• brings huge advantages in terms of NMR
  sensitivity
• new experimental tricks possible with pulsed
  methods

106
However, the NMR signal is now obtained as a
function of time.
and is a collection of decaying sin-waves, known
as Free Induction Decay, FID
t
107
The Conversion between Time and Frequency Domain
108
The Influence of the Life-time of the signal
Frequency domain signal broadens as
lifetime decreases
109
and if the amplitudes differ, the same is true
110
Converting spectra from the time to the frequency
domain - Fourier Transformation
111
The Fourier Transformation for simple FIDs
Lets assume the FID is proportional to the
magnetisation in y-direction, then
I(j)0
112
The Advantages of FT-NMR

• hugely increased sensitivity
• time saved can be used to add many spectra, noise
  varies as N1/2 whilst N signal responses just add
• Increase in S/N ratio of N1/2

• possibility of using pulse-sequences

113
The Advantages of FT-NMR
Ehtylbenzene
FID
CW-spectrum, 1000s
FT-spectrum (1000 averages, 1s each)
114
What happens really during a pulse?
Phases of spins are random
115
The Rotating Frame
Difficult to picture!
116
The Rotating Frame

understand linear field as sum of counter
rotating circularly polarised components

117
Circularly Polarised Fields
The time-dependence of a circularly polarised
field
118
The Nature of Linear and Circularly Polarised
Fields



left
right
linear
119
That simplifies things a lot
...only the component that rotates in the same
sense as the Larmor precession of the spins is
retained! The other is hundreds of MHz
off-resonance and will be ignored!
120
The Rotating Frame
Now, view NMR experiment in rotating frame which
rotates about z-axis with angular frequency
wrf, radiofrequency field B1 now appears static
B1 pulse is simply a temporarily applied field
orthogonal to B0
before pulse
during pulse
z
y
x
M aligned along z-axis of rotating frame
M precesses about the B1 field along the x-axis
121
Pulses
122
NMR is a Coherence Phenomenon
coherent electromagnetic radiation induces a
coherence amongst the spins and causes the
orientations of individual magnetic moments in
the x-y plane to be no longer random!
123
A Typical NMR Spectrometer
124
Relaxation
125
Spin Relaxation a Vital Requirement for NMR
126
Spin Relaxation
127
Rotational Motion in Liquids
The tumbling motion of molecules in liquids
tc
4 tc
1/4tc
128
The Origin of Nuclear Spin Relaxation1. Spin
Lattice Relaxation
Magnetic interactions are causing Spin Lattice
Relaxation
Recall Dipolar Interaction (anisotropic)

• instantaneous interaction not negligible
• fluctuation of interaction as molecules
  translate, rotate, vibrate (r and q vary)
• instantaneous local magnetic field might induce
  radiationless transition if at at correct
  frequency

129
Rotational Motion in Liquids
The tumbling motion of molecules in liquids
tc
4 tc
1/4tc
130
tc-The rotational Correlation Time
tc...time taken for the root-mean square
deflection of the molecules to be about 1 radian
(? 60o)
tc-1 is a frequency, namely the root-mean square
rotational frequency
131
The Spectral Density Function
Spectral Density J(w) is proportional to the
probability of finding a component of the random
motion at a particular frequency
For small molecules, less viscous solutions, high
temperature correlation time short since fast
tumbling, J(w) extends to higher frequencies w
132
Spin-Lattice Relaxation and Molecular Tumbling
Apparently, Spin Lattice Relaxation is caused by
fluctuating local fields causing the magnetic
nuclei to flip between their spin states.
Apt, the characteristic time for this process is
called the spin lattice relaxation time, T1
T1 depends on the probability that local magnetic
fields are oscillating at (resonant!) NMR
frequency, w0
T1 is therefore proportional to the spectral
density, J(w)
133
Molecules in Water - A Rule of ThumbExercise V
If Mr100, tc100 ps if Mr10 000, tc10 ns
On PJ Hores spectrometer 400 MHz, ie, w0
/2p4x10s-1
Maximum relaxation occurs for 400 ps
Is T1 slow or fast for a molecule of Mr300?
Is T1 slow or fast for a molecule of Mr100 000?
134
Spin-Lattice Relaxation

• Random fields mechanism predicts

135
2. Spin-Spin Relaxation
Clearly, as the spin-lattice relaxation
characterised by T1 reduces the lifetime of spin
states, it will cause line broadening according
to
136
Spin-Spin Relaxation
We face a similar problem to the pawn broker in
NMR with the time keeping of precessing nuclear
spins as weak magnetic interactions perturb the
exact nuclear precession frequencies.
137
Spin-Spin Relaxation
Dependence of T1 and T2 on rotational correlation
time
Become the same when tumbling becomes fast wrt
resonance frequency, ie, in extreme narrowing
limit
138
Quadrupolar Relaxation
Fact Every Nucleus with Igt1/2 possesses an
electric quadrupolar moment additionally to its
magnetic moment
Distribution of nuclear charge is not spherical
but of the form of an ellipsoid
Lower energy
Hence, there is an electrostatic energy that
varies with orientation
139
Quadrupolar Interactions

• Electric quadrupoles DO NOT interact with uniform
  electric field but only with field gradients
• in sufficiently high symmetry environments
  (shperical, cobitc, tetrahedra etc) the electric
  field gradients cancel, hence there is no net
  quadrupolar interaction
• is an anisotropic interaction
• produces lines splittings in NMR spectra of
  single crystals
• induces spin relaxation and hence, line
  broadening
• multiplet splittings lost

Large QC
14N, 17O, 35Cl
Examples
140
Spin Relaxation and the Vector Model
What happened during a p/2 radio-frequency pulse
along x?
What will relaxation do?
T1
T2
141
What happens to the magnetisation following a p/2
pulse?
T2
T1
142
Chemical Exchange
The NMR Spectrum of Ethanol
What happens?
143
Chemical Exchange-Dynamic Equilibria
Consideration of processes capable of modifying
or even removing some of a molecules structure
180o rotation
Example
144
Chemical Exchange-Dynamic Equilibria
partial double bond character rotation hindered
different chemical environments
nB
nA
nB
nA
?
145
The Effect of the Rate of Exchange between Sites
I and II - Symmetrical Exchange
Slow exchange between I and II
Fast exchange between I and II
146
Slow and Fast Exchange
Slow or Fast?
Exchange broadened but still at their individual
frequencies
Single resonance line
147
1.The Slow Exchange Regime
Increase in Linewidth
Exchange broadened but still at their individual
frequencies
Becomes wider with increasing exchange rate
148
1.The Slow Exchange Regime
Life-time broadening (uncertainty broadening)
149
2.The Fast Exchange Regime
Two resonances have merged into one
Increase in Linewidth
Becomes narrower with increasing exchange rate
150
2.The Fast Exchange Regime
151
3. Intermediate Exchange
The condition for the two resonances to merge
into a single broad line
valley between two lines has now JUST disappeared
152
Exercise VI
O
Me
Me
N N
N N
Me
Me
What is the average lifetime of the two
conformations when the two resonance line will
collapse into one?
153
Exercise VI
154
Unsymmetrical Two-Site Exchange
What if the two sites have different
concentration/population?
O
Me
Me
kI
N N
N N
kII
I
II
kI kII
pI pII
At equilibrium
pI kI pII kII
155
Unsymmetrical Two-Site Exchange - line broadening
1. The Slow Exchange Limit
Two resonances with
Life Time Line Broadening
2. The Fast Exchange Limit
A single resonance at weighted average frequency
With Life Time Line Broadening
156
Unsymmetrical Two-Site Exchange - line broadening
II
I
slow
fast
157

Examples of Spectra Influenced by Chemical
Exchange
1,2 Diphenyldiazetidinon
2-Methyloxepine
158
Examples of Spectra Influenced by Chemical
Exchange cont.
Cis-Decaline-Ring Conversion
159
Examples of Spectra Influenced by Chemical
Exchange cont.
Valence Tautomerism-Bullvalene
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Examples of Spectra Influenced by Chemical
Exchange
Ethanol-Proton-Exchange - intermolecular hydrogen
transfer
HB
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Examples of Chemical Exchange
Ethanol-Proton-Exchange
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The Time and Line Width Dependence of the NMR
Signal
Spin Lattice Relaxation
Spin Spin Relaxation
Chemical Exchange
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Measurement of Relaxation Times -Spin-Lattice
Relaxation
The Inversion-Recovery Experiment
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The NMR Signal as a Function of t
p/2
t1
t2
t3
t4
z
z
z
z
y
y
y
y
x
x
x
x
NMR Signal I(t)
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Inversion Recovery-Measurement of T1
Obtain T1 of any signal by plotting
against
Fully relaxed signal intensity
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Inversion Recovery for the 1H-NMR spectrum of
Toluene
168
Measurement of Relaxation Times -Spin-Spin
Relaxation
The Spin-Echo Experiment
echo

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Measurement of Relaxation Times -Spin-Spin
Relaxation
What is the effect of relaxation on the echo
amplitude?
random magnetic fields destroy phase
coherence (fluctuating magnetic fields due to
random molecular motion) not refocused by p pulse
NMR Echo of each signal
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The Spin-Echo Experiment
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Last Exercise
Predict the appearance of the following spin
systems in an NMR spectrum AM2X2 AM2X2 AX(I3/2)
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Principles of 2-Dimensional NMR
Father of 2D NMR Jeener, Belgium Main
Developers RR Ernst (Switzerland), R Freeman
(UK, Oxford)
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Principles of 2-Dimensional NMR
2D NMR is a domain of FT and pulsed spectroscopy
174
Principles of 2-Dimensional NMR
The time-intervals of 2D NMR
175
A 2D NMR Experiment
Series of one-dimensional NMR spectra must be
recorded
176
A 2D NMR Experiment
Amplitude Modulation
Phase Modulation
t1
t1
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Obtaining a 2D NMR Spectrum
Fourier transformation of FID signal, S(t1, t2)
must be performed to obtain 2D spectrum as
function of two frequency variables S(F1, F2)
Spin-spin coupling was active during t1, hence F1
contains coupling constant
Larmor precession active during t2, hence F1
contains chemical shift
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What happens during the pulse sequences?
Pulse Sequence
?
179
What happens during the second p/2x Pulse?
180
What happens during the pulse sequences?
t2
Pulse Sequence
?

181
A Simple 2D NMR Spectrum results
F2
F1
W
W
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Correlated Spectroscopy (COSY)
Pulse Sequence
p/2x
p/2x
Aim To discover spin-spin couplings in a
molecule. Answer Which resonance belongs to
which nucleus?
t2
t1
Schematic COSY spectrum of an AX system
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COSY-More Examples
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Exchange Spectroscopy (EXSY) and NOESY (Nuclear
Overhauser Spectroscopy)
Pulse Sequence
p/2x
p/2x
p/2
tM
t1
t2
1st pulse produces transverse magnetisation
during t1developing of transverse magnetisation
according to Larmor frequency 2nd pulse produces
longitudinal z-magnetisation mixing time tM
magnetisation transfer 3rd pulse production of
detectable transverse magnetisation that depends
on t1 and on efficiency of magnetisation transfer
(function of exchange rate constants)
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Example of an EXSY Spectrum
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Nuclear Overhauser Spectroscopy
Change of magnetisation now based on Nuclear
Overhauser Effect (NOE) (see Hore and Gunther),
peaks on off-diagonal yield again information
about spin correlations. For more detail, see
Hore Nuclear Magnetic Resonance.
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COSY of an AMX - system