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(F) Magnetic Resonance: A Probe of Chemical Structure
F_I
Chemical Shielding & The Chemical Shift
How does the electronic environment of a nucleus affect its precession frequency? (Spin
Dynamics p.192-193 (1st edn.) p.195-196 (2nd edn.))
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What is the effect of changing the B0 magnetic field on the difference in frequencies of the
NMR signals due to two nuclei in distinct electronic environments? (Spin Dynamics p.56-59
(1st edn.) p.50-53 (2nd edn.))
Isotopomer I
C1H3 C1H216O1H
natural abundance
Isotopomer II
C1H3 C1H216O1H
natural abundance
Isotopomer III
C1H3 C1H216O1H
natural abundance
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How can we obtain a B0-independent measure of the shielding of a nucleus? (Spin Dynamics
p.59-60 (1st edn.) p.53-54 (2nd edn.))
0cs =  Bz =  (B0 + Binduced)
[F1]
0cs =  B0 (1  )
[F2]
ppm = [(0cs  0ref_TMS) / 0ref_TMS]  106
[F3]
Since Binduced  B0,
ppm = [(ref_TMS  cs) / (1  ref_TMS)]  106
 (ref_TMS  cs)  106
PX388 Magnetic Resonance: Section F: MR: A Probe of Chemical Structure
[F4]
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Since

0 = 0  rf
[B2]
ppm = (0cs  0ref_TMS) / (0 in MHz)
[F5]
ppm(site1, site2) = 0cs(site1, site2) / (0 in MHz)
[F6]
0cs(site1, site2) = ppm(site1, site2) * 0 in MHz
[F7]
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F_II
The g Value (EPR)
How can the precession frequency of an electron spin in an organic molecule or inorganic
compound deviate from that of a free electron?
(Weil & Bolton, p.7-11 & 23-27, Rieger p.1-3)

0 = ge B Bz / ℏ

Bz = (g / ge) B0
[F8]

0 = g B B0 / ℏ
[F9]

g = h 0 (in Hz) / B B0
[F10]
PX388 Magnetic Resonance: Section F: MR: A Probe of Chemical Structure
[A14]
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F_III
The Hyperfine Interaction (EPR)
How is the precession of an electron spin altered by coupling to a nuclear spin?
(Weil & Bolton, p.7-11 & 36-38, Rieger p.21-25)
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F_IV
Through-Bond J Coupling (NMR)
How is the precession frequency of a nucleus affected by other chemically-bonded nuclei?
(Spin Dynamics p.212-216 (1st edn.) p.217-222 (2nd edn.))
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What do J-coupled multiplets tell you about molecular connectivities?
(Spin Dynamics p.61-64 (1st edn.) p.56-59 (2nd edn.))
Does a J-splitting change upon increasing B0?
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F_V
Dipole-Dipole Coupling
How is the precession frequency of a nucleus affected by other close-together in space nuclei?
(Spin Dynamics p.203-205 (1st edn.) p.211-212 (2nd edn.))
How does a dipole-dipole coupling depend on orientation?
(Spin Dynamics p.205-207 (1st edn.) p.213-214 (2nd edn.))
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How does the orientation dependence of the dipole-dipole coupling affect solid-state NMR
spectra?
What happens to dipole-dipole couplings in isotropic solution?
(Spin Dynamics p.207-208 (1st edn.) p.215-216 (2nd edn.))
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Why can broadening due to dipole-dipole couplings be problematic in solid-state NMR?
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F_VI
Magic-Angle Spinning
What is magic-angle spinning? (Spin Dynamics p.482 (1st edn.) p.527 (2nd edn.))
What is the effect of magic-angle spinning on NMR spectra of powdered solids?
(Spin Dynamics p.528-529 (2nd edn.))
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F_VII
Chemical Shift Anisotropy
Why is the chemical shift of a nucleus orientation dependent?
(Spin Dynamics p.199-200 (1st edn.) p.197-199 & 204-205 (2nd edn.))
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What does a typical 13C MAS solid-state NMR spectrum look like?
Which NMR orientations survive the isotropic tumbling of molecules in solution?
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F_VIII
Quadrupolar Interaction
Why is NMR of nuclei with I  1 different?
(Spin Dynamics p.170-174 (1st edn.) p.172-175 (2nd edn.))
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How does the quadrupolar interaction affect the NMR spectrum of a spin I = 1 nucleus?
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How does the quadrupolar interaction affect the NMR spectrum of a spin I = 3/2 nucleus?
Summary of isotropic and anisotropic interactions
isotropic
anisotropic
Chemical Shift
J coupling
(through-bond)
dipolar coupling
(through space)
quadrupolar coupling
(I > 1/2)
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(F) Magnetic Resonance: A Probe of Chemical Structure: Key Facts

Chemical shielding
The magnetic field, Bz, experienced by a nuclear spin deviates from the applied magnetic
field, B0, because of the effect of B0 on the electrons that surround the atomic nuclei.
Specifically, B0 induces current flow in the electron orbitals, with these circulating electron
currents generating an additional magnetic field at the nucleus.
Since the induced magnetic field due to the electrons is proportional to B0:
0cs =  B0 (1  )
[F2]
where  is the chemical shielding. Importantly, resonances with different chemical shieldings
are chemically different – this makes NMR a very powerful probe of molecular structure.
(NB: the induced magnetic field is usually in the opposite direction to B0.)

Chemical shift
A B0-independent measure of the chemical shielding is obtained by comparing to the
resonance frequency of a reference compound – for 1H, 13C and 29Si NMR, the reference
compound is tetramethylsilane (TMS), Si(CH3)4:
ppm = [(0cs  0ref_TMS) / 0ref_TMS]  106
[F3]
The chemical shift is a dimensionless parameter, but is expressed in ppm since the differences
are small as compared to the Larmor frequency.
The difference between two resonances in Hz and ppm are related by:
ppm(site1, site2) = 0cs(site1, site2) / (0 in MHz)
[F6]
0cs(site1, site2) = ppm(site1, site2) * 0 in MHz
[F7]
NB: The separation of two resonances in Hz is proportional to B0, while the separation of two
resonances in ppm is independent of B0.
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
The g value (EPR)
The magnetic field, Bz, experienced by an electron spin is:

Bz = (g / ge) B0
[F8]
0 = g B B0 / ℏ
[F9]
such that

The deviation of g from that of a free electron, ge = 2.002, is due to the mixing of spin and
orbital angular momentum. g is determined from the experimental resonance frequency:

g = h 0 (in Hz) / B B0

[F10]
The hyperfine interaction (EPR)
The so-called hyperfine interaction of an electron spin with nuclear spins leads to splittings in
EPR spectra, since parallel or anti-parallel configurations of the electron and nuclear spins
have different energies.
Specifically, a resonance of an electron spin coupled to a single nuclear spin splits into 2I + 1
lines, where I is the nuclear spin, e.g., 2 or 3 lines when coupled to a spin I = 1/2 or I =1
nuclear spin, respectively.

Coupling of nuclear spins
Line splittings are observed in NMR spectra due to the coupling together of nuclear spins.
This occurs by two mechanisms:
(i) The through-bond (electron mediated) J coupling
(ii) The through-space (i.e., no requirement for chemical bonding) dipolar coupling.
In both cases, the observed line splittings are independent of B0.
Line splittings due to coupling to a heteronucleus (e.g., 13C to 1H) can be removed by the
method of decoupling, where high-power on-resonance rf irradiation is applied to the
heteronuclei during the acquisition of the FID on the other channel (e.g., 1H decoupling
during the acquisition of a 13C FID in a solution-state NMR experiment removes the J
splittings, compare HO_F3 and HO_F8).
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
The through-bond J coupling:
Due to the different energies associated with parallel or anti-parallel configurations of
electron and nuclear spins.
Multiplet patterns are observed depending on the number of coupled nuclei: 13C1H a doublet;
13C(1H)
2
a triplet with intensities 1:2:1; 13C(1H)3 a quartet with intensities 1:3:3:1.
The J coupling is an isotropic interaction, i.e., the observed splittings are independent of
molecular orientation.

The through-space dipolar coupling:
is directly proportional to the product of the magnetogyric ratios of the coupled spins, j and
k, and inversely proportional to the cubed separation of the nuclei, rjk:
Dc  j k / rjk3
[F11]
The dipolar coupling is an anisotropic interaction, i.e., the observed splitting, D, depends on
the orientation of the internuclear vector with respect to the B0 magnetic field:
D = Dc (1/2) (3cos2  1)
[F12]
i.e., for a single crystal containing isolated pairs of coupled nuclei, maximum and minimum
splittings, D = +Dc and D = Dc/2 would be observed for  = 0 and 90, respectively,
while when  = 54.7, (3cos2  1) equals zero, and no splitting is observed.
Solid-state NMR is usually carried out on powdered samples, i.e., the observed NMR
spectrum is the superposition of many individual spectra due to many small single crystals
with all possible orientations of the internuclear vector with respect to the B0 magnetic field.
Since all values of  are not equally likely due to the sin term associated with integration
using spherical coordinates, the powder pattern for a sample containing isolated pairs of
coupled nuclei is a Pake doublet lineshape (see HO_F12).
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In isotropic solution, i.e., where the molecules are tumbling fast such that all orientations of
the internuclear vector with respect to the B0 magnetic field are experienced in a short
timescale, the effective dipolar splitting corresponds to the integration:


(1/2) (3cos2  1) sin d = 0
[F13]
0
i.e., no splittings due to dipolar couplings are observed in NMR spectra of isotropic solutions.

Magic-angle spinning (solid-state NMR):
Organic solids do not usually contain well isolated pairs of coupled nuclei, such that typical
solid-state NMR spectra of powdered solids are featureless humps due to there being many
overlapping resonances associated with the dipolar splittings (see HO_F13) among many
coupled nuclei. There is effectively an overload of information with the important resolution
of chemically distinct sites with different chemical shifts being lost.
High resolution can be obtained in solid-state NMR by the technique of magic-angle spinning
(MAS) whereby the sample is physically rotated around an axis inclined at an angle of 54.7
to B0 at rotation frequencies of up to 70,000 rotations a second (70 kHz), using gas bearings.
At slow MAS frequencies (compared to the static powder pattern width), the static pattern
breaks up into narrow lines separated by the MAS frequency, i.e., a spectrum containing a
centreband and spinning sidebands. As the MAS frequency becomes bigger than the width of
the static powder pattern, intensity is increasingly centred in the centreband (see HO_F15).

Chemical Shift Anisotropy (CSA):
The chemical shielding interaction has both an isotropic and an anisotropic contribution:
cs = csiso + csaniso
[F14]
The anisotropic part is referred to as the chemical shift anisotropy and depends on (i) the
anisotropy, , (ii) an asymmetry parameter, CSA, and (iii) the orientation, , of the shielding
tensor (that depends on the electron environment) with respect to the B0 magnetic field
csaniso =  (1/2 (3cos2  1)
(for CSA = 0)
PX388 Magnetic Resonance: Section F: MR: A Probe of Chemical Structure
[F15]
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i.e., for a single crystal, the resonance frequency changes as the orientation changes (this is
illustrated for a 13C resonance in a C=O group in HO_F16).
For a powdered sample, one half of Pake doublet pattern is obtained (see HO_F16).
MAS affects powder patterns due to CSA in the same way as for the dipolar coupling, i.e., at
slow MAS frequencies (compared to the static powder pattern width), the static pattern breaks
up into narrow lines separated by the MAS frequency, i.e., a spectrum containing a
centreband and spinning sidebands. As the MAS frequency becomes bigger than the width of
the static powder pattern, intensity is increasingly centred in the centreband (see HO_F17)
NB: For an isotropic solution, the NMR spectrum depends on:
(i) the isotropic chemical shifts (csiso)
(ii) J splittings (these are orientation-independent).

Quadrupolar Interaction:
Nuclei with spin I  1 possess an electric quadrupole moment (i.e., a non-spherical
distribution of electric charge). This interacts with the electric field gradient at the nucleus to
lift the degeneracy of the single-quantum transitions. To first-order (i.e., the quadrupolar
interaction is small compared to the Zeeman interaction – that is responsible for the Larmor
frequency – such that first-order perturbation theory is applicable):
For a spin I = 1 nucleus,
there are two single-quantum transitions (+1  0 and 0  1) at 0  Q.
For a spin I = 3/2 nucleus,
there is a central transition (+1/2  1/2) at 0 (i.e., independent of Q).
and two satellite transitions (+3/2  +1/2 and 1/2  3/2) at 0  Q.
where
Q = CQ (1/2) (3cos2  1)
(for Q = 0)
 is the orientation of the electric field gradient with respect to B0.
PX388 Magnetic Resonance: Section F: MR: A Probe of Chemical Structure
[F16]
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CQ is the quadrupolar coupling constant (in units of Hz) and it depends on the electric field
gradient, eq, and the quadrupole moment, Q:
CQ = e2q Q / h
[F17]
The orientation dependence of the quadrupolar interaction gives rise to broadened lineshapes
for powdered solids:
For a spin I = 1 and Q = 0, the same Pake doublet is observed as for the case of a pair of
dipolar-coupled spin I = 1/2 nuclei (see HO_F21).
For a spin I = 3/2 and Q = 0, the same Pake doublet is observed as for the case of a pair of
dipolar-coupled spin I = 1/2 nuclei together with a narrow central resonance (see HO_F22).
MAS affects powder patterns due to quadrupolar interactions in the same way as for the
dipolar coupling, i.e., at slow MAS frequencies (compared to the static powder pattern width),
the static pattern breaks up into narrow lines separated by the MAS frequency, i.e., a spectrum
containing a centreband and spinning sidebands. As the MAS frequency becomes bigger than
the width of the static powder pattern, intensity is increasingly centred in the centreband.
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(F) Magnetic Resonance: A Probe of Chemical Structure: Questions
1.
A compound has two different 13C sites with chemical shifts equal to 30 and 100 ppm.
(i)
At what magnetic field is the chemical frequency difference equal to 10 kHz?
(ii)
The relative Larmor frequencies of peaks from the two 13C sites are 1 / 2 =
+6.0 kHz and 2 / 2 = 4.0 kHz. What is the ppm value corresponding to
the oscillation frequency of the rf pulse, rf?
(13C) = 6.73 × 107 rad s1T1
2.
An ESR spectrum is recorded for a particular organic radical, using microwave
radiation at 9.418 GHz. The spectrum exhibits three equally spaced resonances of equal
intensity, with the central resonance at a magnetic field of 330.074 mT.
(i)
What is the electronic g-factor of the radical?
(ii)
Give a chemical explanation for the observation of three resonances.
The Bohr magneton
3.
μB = 9.274 × 1024 J T1; Planck's constant h = 6.626  1034 J s
A 2H NMR experiment is performed on a single crystal at a magnetic field strength of
9.4 T. For one particular orientation of the single crystal, a single line is observed in the
NMR spectrum at 30 ppm. For all other orientations, a doublet is observed. At the maximum
splitting, the lines are separated by 245.8 kHz. What will be the frequencies (in ppm) of the
lines corresponding to the maximum splitting when the experiment is performed on a 18.8 T
spectrometer. Assume only a first-order quadrupolar interaction for the 2H nucleus with
 = 0. (To first-order, the quadrupolar splitting is independent of B0.)
(2H) = 4.107 × 107 rad s1T1
PX388 Magnetic Resonance: Section F: MR: A Probe of Chemical Structure