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7/29/2019 Topic 7 Nuclear Magnetic Resonance
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The Electromagnetic Spectrum
NMR, MRI
EPR/ESR
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What is NMR?
NMR is an experiment in which the resonance
frequencies of nuclear magnetic systems areinvestigated.
NMR always employs some form of magnetic field
(usually a strong externally applied field B0)
NMR is a form of both absorption and emission
spectroscopy, in which resonant radiation is absorbed by
an ensemble of nuclei in a sample, a process causing
detectable emissions via a magnetically induced
electromotive force.
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Things that can be learned from NMR data
Covalent chemical structure (2D structure)
Which atoms/functional groups are present in a molecule How the atoms are connected (covalently bonded)
3D Structure
Conformation
Stereochemistry
Molecular motion
Chemical dynamics and exchange
Diffusion rate 3D Distribution of NMR spins in a medium an image!
(Better known as MRI)
Plus many more things of interest to chemists
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History of NMR
1920-1930: physics begins to grasp the
concepts of electron and nuclear spin
1936: C. J. Gorter (Netherlands) attempts tostudy 1H and 7Li NMR with a resonance
method, but fails because of relaxation
1945-6: E. M. Purcell (Harvard) and F. Bloch
(Stanford) observe 1H NMR in 1 kg of parafin at
30 MHz and in water at 8 MHz, respectively 1952: Nobel Prize in Physics to Purcell and
Bloch
1957: P. C. Lauterbur and Holm
independently record 13C spectra
1991: Nobel Prize in Chemistry to R. R. Ernst
(ETH) for FT and 2D NMR
2002: Nobel Prize in Chemistry to K. Wuthrich
2003: Nobel Prize in Medicine to P. C.
Lauterbur and P. Mansfield for MRI
P. C. Lauterbur F. Bloch
E. M. Purcell R. R. Ernst
Photographs from www.nobelprize.org
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Nuclear Magnetism
A nuclear electromagnet is
created by the nucleons (protonsand neutrons) inside the atomic
nucleus.
This little electromagnet has a
magnetic moment (J T-1)
The magnetic moment is
proportional to the current
flow through the nuclear
loop
The nucleus looks like a dipole to
a distant charge centre
N
SFromhttp://education.jlab.org
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Basic NMR Theory
In a strong applied magneticfield (B
0), certain atomic nuclei
will align or oppose this field.
This alignment is caused bythe magnetic moments of thenuclei, which themselves arecaused by the internalstructure of the nucleus. Two
nuclear properties stand out: Spin (1/2 for1H, 13C, etc)
Gyromagnetic ratio
An excess of alignments isfound in the lower energy state
(determined by a Boltzmanndistribution).
At room temperature, thisexcess is very small, typicallyonly 1 part per trillion!
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Nuclear Spin
In a classical sense the bulk nuclear
magnetization is observed toprecess at the Larmor frequency
(usually several hundred MHz):
The constant is the magnetogyricratio.
2
00
B=00 B =
angular (rad/s) linear (Hz, cycles/s)
B0
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Elements Accessible by NMR
Figure from UCSB MRL website
White = only spin
Pink = spin 1 or greater (quadrupolar)
Yellow = spin or greater
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Pulsed vs. Continuous-Wave NMR
NMR effects are most commonly detected by resonant radio-
frequency experiments
Continuous-wave NMR: frequency is swept over a range (e.g.
several kilohertz), absorption of RF by sample is monitored
Historically first method for NMR
Poor sensitivity
Still used in lock circuits
Pulsed NMR short pulses (at a specific frequency) are
applied to the sample, and the response is monitored. Much more flexible (pulse sequences followed from this)
Short pulses can excited a range of frequencies
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NMR Theory: The Rotating Frame The magnetization precesses at the Larmor frequency, the RF field(s)
oscillate at or near this same frequency
The rotating frame rotates at this frequency, simplifies the picture for
analysis and understanding
Frame rotating at the Larmor frequency
hundreds of MHz Frame is now still
eye
z z
x
y
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Spin Systems
The reason NMR is so applicable to structural problems is
that the governing interactions can be separated andtreated individually
Experimentally, this results in spectral simplification (in that
transitions are not hopelessly entangled) and also allows for
detailed manipulations (pulse sequences) to extract information
This involves separation of electronic Hamiltonian from
the nuclear spin Hamiltonians
NMR is thus simplified in that its data can be linked back
to spin systems. Examples of spin systems:
Several 1H nuclei (i.e. hydrogen) within 2 or 3 covalent bonds of
each other
A 1H nucleus attached to a 13C nucleus
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NMR Theory: RF Pulses
z
x
y
Drawing depicts a 90o pulse
z
x
y
RF pulses are used to drive the bulk magnetization to the desired position
The action of an RF pulse is determined by its frequency, amplitude, length and
phase
For an on-resonant pulse, the right hand rule predicts its action
Drawing depicts a 180o pulse
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NMR Theory: RF Pulses and Spin Echoes
An RF pulse:
Two pulses:
echo
(delays and extra
pulse)
Actually not solid,
contains RF
frequencies
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Selection Rules
Single-quantum transitions (m =
+/- 1) are allowed by angularmomentum rules (which govern
spins in NMR).
Single-quantum states are
directly detected in NMRexperiments
However, it is possible to excite
double-quantum states (or zero-
quantum, triple-quantum, etc),
let them evolve with time, then
convert them back to SQ states
for observation
Energy levels for two coupled spins
showing SQ (single quantum)
transitions ingreenand forbidden
ZQ (zero quantum) and DQ (double
quantum) transitions inred
SQX
X
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NMR Theory: T1 Relaxation
T1relaxation: longitudinal
relaxation (re-establishment
of Boltzmann equilibrium)
by spins interacting with the
lattice
In practice, T1 controls how
quickly FT experiments can
be repeated for signal
averaging
Measurements of T1can
provide useful data on
molecular motions
x
z
y
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NMR Theory: T2 Relaxation
T2relaxation transverse
relaxation (dephasing of
coherence) by spins
interacting with each other
Controls how long
magnetization can be kept
in the x-y plane
Controls the linewidth(FWHH) of the NMR
signals:
x
z
y
*
2
2/1
1
T
=
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NMR Theory: The Chemical Shift
The electrons around a nucleus
shield are circulated by the big
magnetic field, inducing smallerfields.
Anisotropy:
Units ppm:
Shift-structure correlations thebasis of NMR as an analytical
tool.
Shift-structure correlations are
available for1H, 13C, 15N, 29Si, 31P
and many other nuclei
TPPO
PbSO4
x
y
z
( )
ref
refxppm
=610)(
Above: the chemical shift in solids is not a single peak!
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Typical 1H NMR Chemical Shielding
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Typical 13C NMR Chemical Shielding
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Other Nuclei: 17O NMR
Note 17O NMR requires labeling or concentrated solutions, and suffers
from large solution-state linewidths (caused by quadrupolar relaxation)
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NMR Theory: The Chemical Shift
Contributions from electronegativity and ring current
effects:
Correlation of1H Chemical Shift and Group
Electronegativity for CH3X Compounds
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
0.0 1.0 2.0 3.0 4.0 5.0
Relative Chemical Shift ()
GroupElectronegativ
it
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NMR Theory: The Chemical Shift
Contributions from ring current effects
Above center of ring (z-axis): shielding
In plane of ring ( axis): deshielding
Figure from http://www.chemlab.chem.usyd.edu.au/thirdyear/organic/field/nmr/ans02.htm
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NMR J-Coupling
The J-coupling is an effect inwhich nuclear magnetic dipolescouple to each other via the
surrounding electrons. The effect is tiny but detectable!
Typical J-values
2-4JHH
can range from 15 to +15 Hz
and depends on the number ofbonds, bond angles, and torsion
angles
1JCH
can range from 120 to 280 Hz,
but typically is ~150 Hz in mostorganics
2-4
JCH ranges from 15 to +15 Hzand depends on effects similar tothe 2-4J
HH
The narrow ranges that certain 1H and13C J-coupling values fall into make
spectral editing and heteronuclear
correlation experiments possible!!!
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J-Coupling: Effects on NMR Spectra
Two basic types of coupling
Homonuclear (e.g. 1H-1H)
Heteronuclear (e.g. 1H-19F) Weak coupling
Large difference in frequency
>> J #Lines = 2 nI+ 1
All heteronuclear coupling is
weak
More complex splitting patterns
can be visualized using
Pascals triangle
Strong coupling
Small difference in frequency
~ J Complex patterns
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J-Coupling: Effects on NMR Spectra Example:
monofluorobenzene
Homonuclear couplingbetween 1H:
ortho-coupling
meta-coupling
para-coupling
Heteronuclear coupling
between 1H and 19F:
As above (ortho, meta,
andpara).
Observed from the 19F,
appears as a doublet of
triplets of triplets (ttd)
Fluorine can be decoupled
from the 1H spectrum (not
shown)
para
orthometa
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Structural and Conformational Analysis
J-coupling is widely used (in conjunction with 2D NMR)
to assemble portions of a molecule In this case, the J-coupling is simply detected in a certain
range and its magnitude is not examined closely
J-coupling is also used to study conformation andstereochemistry of organic/organometallic/biochemical
systems in solution
In this case, the J-coupling is measured e.g. to the nearest 0.1
Hz and analyzed more closely
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J-Coupling: Angle Effects
Karplus relationships the
effects of bond and torsion
angles on J-coupling Bond angles, dihedral
(torsion) angles, 4 and 5-
bond anglesIn[1]:= J_ :4.22Cos 2 0.5Cos 4.5
In[3]:= Plot J, , 0,
0.5 1 1.5 2 2.5 3
6
7
8
9
Out[3]= Graphics Dihedral angle (radians)
Couplingconstant(Hz)
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Dipolar Coupling
The magnetic dipolar interaction between
the moments of two spin-1/2 nuclei
One spin senses the others orientation
directly through space
The dipolar coupling is simply related to the
internuclear distance between the spins:
The truncated (secular) dipolar Hamiltonians (relevant to NMR) have the
form:
( ) ( )[ ]++
+= SISISIDH zzrHomonuclea
D 412 cos31
( ) [ ]zzearHeteronuclD SIDH cos31 2=
38 rD SI
20
=
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The Nuclear Overhauser Effect
The idea: detect the cross-relaxation caused byinstantaneous dipolar coupling in an NMR or EPR
experiment.
This was conceived by A. W. Overhauser, while agraduate student at UC Berkeley in 1953
Overhauser predicted that saturation of the conduction
electron spin resonance in a metal, the nuclear spinswould be polarized 1000 times more than normal!!!
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The Nuclear Overhauser Effect
Dipolar coupling is a direct magnetic interaction
between the moments of two spin-1/2 nuclei.
The coherent effects of dipolar coupling areaveraged away in solution-state NMR by rapid
molecular tumbling.
However, the dipolarinteraction can stillplay a role via in
solution-state NMR
via dipolar cross-
relaxation
mechanisms, better
known as the
nuclear Overhauser
effect(NOE).
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NMR Spectrometer Design
The basic idea:
NMR Magnets
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NMR Magnets
Superconducting magnets:
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Resonance
The natural frequency of a inductive-capacitive circuit:
LCr
1=
The NMR system requires a resonant circuit to detect
nuclear spin transitions this circuit is part of the probe
R t Ci it i P b
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Resonant Circuits in Probes
Figure from Bruker Instruments
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NMR Probe Design
The NMR probe
designed to efficientlyproduce an
inductance (~W) and
detect the result (