CH437 CLASS 12
NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 6
Synopsis. Decoupling, dipolar relaxation and the Nuclear Overhauser Effect: its origins and uses.
The Nuclear Overhauser Effect
Origins: Decoupling Experiments
So far, when considering the interaction between nuclear spins, the emphasis
has been placed on through-bond interactions: i.e., nuclei interacting via
intervening electron spins. This will be considered a bit further as a first
introduction to the nuclear Overhauser effect (NOE), before examining throughspace dipolar relaxation and the structurally more revealing NOE involving
uncoupled nuclei.
In spin-decoupling (Class 11) (or double resonance) experiments, apart from
spectral simplification due to collapse of spin-spin splitting, signal intensity
enhancement (over and above the mathematical enhancement) is observed for
certain nuclei. As a simple example, for iodomethane (CH3I), consider (a) the
proton-coupled
13C
NMR, (b) the expected broad-band decoupled
13C
NMR and
(c) the actual broad-band decoupled 13C NMR spectrum (below)
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Relative
intensities
3
1
3
1
-23.2  /ppm
(a)
 /ppm
(b)
 /ppm
(c)
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Suppose T1CC is T1 relaxation due to interactions between carbon-13 nuclei. T1HH
is T1 relaxation due to interactions between hydrogen nuclei. T1CH is T1 relaxation
due to interactions between
due to
13C
13C
and hydrogen nuclei. MZ(C) is the magnetization
nuclei. Mo(C) is the equilibrium magnetization of
13C.
MZ(H) is the
magnetization due to hydrogen nuclei. Mo(H) is the equilibrium magnetization of
hydrogen.
The equations governing the change in the z magnetization with time are:
If we saturate the proton spins, MZ(H) = 0.
Letting the system equilibrate, d MZ(C) /dt = 0.
Rearranging the previous equation, we obtain an equation for MZ(C):
2
.
Note that MZ(C) has increased by Mo(H) T1CC / T1CH which is approximately 2
Mo(C), giving a total increase of a factor of 3 relative to the total area of the
undecoupled peaks. This explains the extra factor of three (for a total intensity
increase of 24) for the carbon-13 peak when hydrogen decoupling is used in the
13C
NMR spectrum of CH3I.
Origins of Dipolar Relaxation and the (Through Space) Nuclear Overhauser
Effect
Now consider two uncoupled protons in the same molecule. To give an NMR
signal, excess spin population has to be moved from one energy level to another
(excitation),
followed
by
radiationless
return
to
equilibrium
(spin-lattice
relaxation). The excess energy passes from spins to the lattice (the environment
or surroundings) as heat, but for efficient relaxation, fluctuating magnetic fields of
the right frequency are needed. In most molecules, these fields are produced by
the magnetic moments of other protons in the same molecule, as they tumble
(along with the rest of the molecule) in solution. This dipole-dipole interaction is
the basis of dipolar relaxation.
Dipolar relaxation efficiency (or rate) depends on several factors, as outlined in
the branch diagram below.
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Internuclear distance
Dipolar
relaxation
rate
Effective correlation time
(tc) of the vector that joins
the two nuclei (= the reciprocal
of the rate of tumbling of that
part of the molecule)
Strength and
frequency of
fluctuating
magnetic
fields
Identity of the two nuclei
In particular, NOE and the rates at which they grow and decay are measures of
the strength the dipole interaction between the nuclear spins and hence are
dependent upon internuclear distance and correlation times.
It is these aspects that give NOE its great value as a structural probe
More detailed consideration of two uncoupled nuclei Ha and Hx is considered in
the diagram below.
The use of symbols a and x should be confused with
symbols A and X in coupled spin systems.
Aligned
Opposed
Ha
Hx
Hx Ha
Ha
Bo
Tumbling motion ~ 108 s-1
for large molecules and ~
1011 s-1 for small molecules.
(Assume a nearly spherical
molecule, which tumbles
isotropically)
Hx
Bo
Tumbling
The fluctuating magnetic field at Hx is caused by change
in alignment of Ha with the applied field Bo, upon change
in relative position during tumbling
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The dipolar relaxation of Hx is more efficient in more slowly rotating (tumbling)
systems and when Ha and Hx are close: for NOE observation, r(Ha – Hx) < 0.3 nm
(300 pm).
The origin of NOE may be understood by considering the energy transition
diagram for an uncoupled two-spin system (say, Ha and Hx, as before), below.
+
1
_
W1x
W1a
W2
3
2
W0
E
W1x
_
+
W1a
4
xa
Transitions W 1a correspond to the inversion of spin Ha and W 1x to inversion of
spin Hx. Since Ha and Hx are shielded by their surrounding electrons to different
extents (they are in different magnetic environments), the W 1a and W1x transitions
involve the absorption of different amounts of energy, such that (4)  (2) = (3)
 (1) and (4)  (3) = (2)  (1). Hence, in the absence of spin-spin coupling,
there is one resonance line for each nucleus. The transitions W 0 and W 2 are
forbidden by direct absorption or emission of radiation, because they involve
changing the spins of both nuclei simultaneously, but are very effective
radiationless relaxation transitions.
Under normal thermal equilibrium conditions, the lower energy levels are slightly
more highly populated than the upper levels. If Ha is strongly irradiated by the
decoupling frequency, saturation occurs, such that (1) undergoes a population
increase (+), whereas (3) experiences population decline (-). Similarly, (2) is
increased in population by +, whilst (4) is decreased in population by -. Now,
the intensity of signal of the observed nucleus (Hx) depends on the extent to
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which the sum of the population levels (1) and (3) is less than the sum of levels
(2) and (4). The effect of irradiating Ha does not effect the intensity of the signal
for Hx via the W 1x transitions, since both (4) and (3) have been depleted by  and
both (2) and (1) have been increased by . However, W 0 and W 2 are nonradiative transitions (and are both forbidden for radiative transitions): they
represent dipolar relaxation mechanisms. W 0 is small and so corresponds to
slower tumbling motions of large molecules, hence for these molecules, the
population differences (+ and -) produced by irradiation of Ha will lead to more
(2)  (3) transitions than in the absence of radiation. This results in an increase
of the sum of the populations of levels (1) and (3): it nearly approaches the sum
for levels (2) and (4). As the difference between these sums determines the
intensity of the signal from Hx, the effect of radiating Ha is to decrease this
intensity: this is the negative NOE. On the other hand, W 2 is large and
corresponds to the faster tumbling of smaller molecules, leading to more (1) 
(4) transitions upon irradiation of Ha. This causes the lower energy levels of Hx to
have higher populations than the higher energy levels, so that the effect of
radiating Ha is to increase the intensity of the Hx signal: this is the positive NOE.
General Comments on NOE
Signal enhancement due to NOE is an example of cross-polarization: a throughspace effect in which polarization of spin states of one type of nucleus (say 1H)
caused by irradiation (B1) induces polarization of spin states of another nucleus
(say, 13C or 1H).
In general, the maximum NOE enhancement is given by
NOEmax =
1
2
irr
obs
Here, irr is the magnetogyric ratio of the nucleus being irradiated and obs is that
for the nucleus under observation. The total (maximum) line intensity is given by
1 + NOEmax. Hence, in the case of proton-decoupled
13C
NMR spectra, the
13C
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signal can be enhanced up to 200% by the irradiation of protons. This value is a
theoretical maximum: most actual
13C
lines exhibit less (sometimes much less)
than maximum enhancement.
Uses of NOE
1. In Proton-Decoupled 13 C Spectra
In a proton-decoupled
13C
spectrum, the total NOE for a given
13C
nucleus
increases as the number of nearby protons increases. Hence, the intensities of
signals in a
13C
spectrum (assuming a single carbon of each type) are usually in
the order C < CH < CH2 < CH3. This is often reliable for distinguishing
unprotonated carbon atoms from protonated ones, but otherwise can be
unreliable, as shown in the spectrum below.
For more reliable criteria regarding numbers of protons bonded to carbon atoms,
see J-scaling (Class 11), DEPT (Class 15) and COSY (Class 16).
2. Determination of Stereochemical Relationship Between Nuclei
Because NOE is a through-space effect, observed nuclei at some distance from
the nucleus under irradiation suffer smaller (positive or negative) intensity
changes. In fact, magnitude of the NOE falls off as a function of the inverse of r 3:
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r
13
C
1
H
NOE = f
1
r3
This can be exploited in the assignment of diastereotopic protons and in the
determination of molecular stereochemistry. An example of the former is given
below and after that there is an example of the latter.
Example 1. Dimethylformamide
..
:O
C
..
N
H
CH3
_ ..
: ..
O
CH3
C
CH3
H
+
N
CH3
The methyl groups are non-equivalent, because of the considerable double bond
character of the C-N bond: their
13C
nuclei resonate at 31.1 and 36.2 ppm: but
which is syn and which is anti (with respect to the H atom)? Irradiation at the 1H
frequency of the aldehyde group leads to a greater Nuclear Overhauser
enhancement of the signal at 36.2 ppm. This must be the one spatially nearer the
aldehyde proton, so the assignment is
..
:O
C
..
N
H
CH3 31.1 ppm
CH3 36.2 ppm
Example 2. Isovanillin
OCH3
HO
Ha
Hc
Hb
CHO
In the 1H NMR spectrum of isovanillin, there are three aromatic ring protons and
although it is possible to assign them according to chemical shift tables,
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observation of NOE can be of additional help. If the sample is irradiated at the
proton frequency of the OCH3 group, the intensity of the signal due to Ha (the
nearest proton to OCH3) is enhanced.
Example 3.
The proximities of the protons indicated by double-headed arrows were
established by observation of NOE from double resonance experiments.
O
H
H
O
O
O
CH3
O
CH3
H O H
or
CH3COO
O
CH3COO
H
CH3
O
H CH3
O
O
Example 4. Configuration of a Synthetic Penicillin Analog
Irradiation of the methyl protons shown causes enhancement of the signals due
to H(10) and H(3), indicating that both of these are spatially close the methyl
group: configuration A is the major one.
H3C
10
H
S
H
N
H 3C
CH 3
S
S
H
N
3 CO2CHPh2
S
O
A
10 H
CH 3
3 CO2CHPh2
O
B
Example 5. Sucrose Octa-acetate
This example illustrates the use of NOE difference spectra
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AcOCH2
O
AcO 4
AcO
5
3
2
OAc
1'
CH2
OAc
O
1
OAc O 2'
AcO
3'
5'
4'
CH2OAc
6'
Irradiation of the H2 (an axial proton) multiplet reveals large NOEs to the two
nearest “cis” protons, H1(equatorial) and H4 (axial), with the “trans” H3 being only
slightly affected, as seen in the NOE difference spectrum below. The large arrow
indicates the frequency of irradiation.
The pulse sequence for the simplest NOE difference experiment is shown below,
along with the corresponding spectra and the difference spectrum. The spectrum
derived from sequence (b) is subtracted from that arising from sequence (a). In
(a), a low-power irradiating pulse of  (180o) duration causes inversion of the zmagnetization of one particular nucleus, say spin 2. This is followed by a delay
() and finally the z-magnetization is made observable by a non-selective /2
(90o) pulse. This gives the irradiated spectrum. The experiment (b) is simply a
pulse-acquisition sequence that results in the normal spectrum.
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Only spins that have received NOE enhancement appear in the difference
spectrum (above, nucleus 1), along with the inverted signal of the irradiated spin
(above, nucleus 2). The above assumes a positive cross-relaxation rate constant,
so the NOE enhancement is positive. In practice, the simple pulse sequence for
(a) shown above sometimes gives rather poor NOE difference spectra and so is
replaced by an inversion sequence that uses pulsed field gradients.
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