Advanced NMR Experiments

Most NMR experiments today are more sophisticated that the simple one-pulse
experiments mentioned thus far. These involve sequences of pulses and delays, and
exploit the time dependent behavior of the spin system in question.

There are two classifications of NMR experiments. There are 1-dimensional and
multidimensional NMR experiments.

A one-dimensional experiment gives a spectrum that is a graph of the NMR signal as
a function of frequency. In a one-dimensional experiment the pulse sequence is
designed to give a signal that is dependent in single time variable. Usually, only one
FID is collected.

One-dimensional experiments can be performed for most NMR active nuclei. Often
it is necessary to remove coupling interactions with other nuclei or the signal has to
be enhanced by some multiple pulse technique.

The use of additional pulses to modify the 1-D spectrum is known as spectral editing.
Several techniques are applied to weak rare nuclei, such as carbon, to enhance the
signal intensity and to simplify the corresponding spectra. These will be discusses in
detail later.
An one-dimensional 1H NMR spectrum
ppm
A proton-decoupled carbon spectrum of propanol
A Two-dimensional Spectrum is collected as a series of FID at different
evolution times, these FID differ by a time-dependent phase factor

A multi-dimensional, spectrum the signal is dependent on several time variables,
corresponding to the dimensionality of the experiment.

The most common multidimensional experiment is the two-dimensional experiment,
which is dependent on two time variables. In such an experiment a set of FID’s to be
collected, each representing a time point in the second dimension. In this case the
phase difference between the FID’s is time dependent defining the second time
dimension.

A multidimensional Fourier transform can be applied to convert the multidimensional
time signal to a multidimensional signal dependent on frequency.

A two-dimensional spectrum is a graph with two frequency axes, where the signal
defines a surface. The topographical map can be made to represent this surface,
where contour lines represent equal intensity.
A two-dimensional NMR spectrum

A two-dimensional spectrum is a graph with two frequency axes, where the signal
defines a surface. The topographical map can be made to represent this surface,
where contour lines represent equal intensity.
A contour plot of a two-dimensional NMR spectrum

Multidimensional experiments are used to correlate different nuclei to each other,
by some interaction. These involve very sophisticated pulse sequences and are
used primarily in a qualitative way largely to determine structural details of the
molecule under investigation.

Regardless of the dimensionality of the methods, the experiment is broken up into
three separate events:
1) Preparation time.
2) Mixing and/or evolution time.
3) Observation time.
What you do in the preparation and mixing time largely determined what the
experiment does.
General NMR Pulse Sequence
t1 variable
or
t2 variable
fixed
Preparation
Evolution
Detection
Spectral Editing Experiments

A rare nucleus such as carbon has a relative signal strength to proton of 1/5700 or so.
This means that for a given number of carbon nuclei (5700)2 = 25,000,000, or so,
scans have to be acquired to get the same signal intensity as a the number of hydrogen
nuclei.

To improve the S/N of carbon two major methods have been employed.
i) Decoupling.
Irradiation in the proton channel to remove couplings to carbon and enhances the
carbon signal through the nuclear Overhauser effect.
i) Polarization Transfer
The populations difference between the energy levels defining the carbon
transition are made larger, to enhance the signal.
 Often polarization transfer experiment have the additional advantage in being able to
alter the phase of a carbon signal according to the number of bound proton. Thus the
type of carbon can be readily identified.
Decoupling

Proton decoupling can be performed using both continuous irradiation at low power,
or a series of high power pulses in the proton channel.

For both methods cases the proton spins are flipped back and forth very rapidly much
faster than the coupling interaction. As a result the carbon can no longer sense the
orientation of the proton coupled to it, and hence only feels the applied field, and
hence resonates at a single frequency. As a consequence the carbon line will no
longer be split by the coupling interaction.
x
H
C
x
x

Delay

x

 
x
x
x

Acquire

H
C
vc+ J/2
H
H
C
vc- J/2
For both decoupling methods the signal of the carbon line is enhanced by the Nuclear
Overhauser effect. To explain this effect one has to refer to the energy level diagram
of a CH spin pair. The energy level populations differences with the lowest level are
indicated. The intensity of the NMR line depends on this difference in population.
Energy Level Diagram of 13C1H Spin Pair
C
H
0
C
1
Energy

Bo
C
5
C
H
H
4

Notice that transition involving carbons nuclei involve a population difference of
1, and those involving hydrogens have a population difference of 4.

Irradiating the protons causes then to reorient rapidly, effectively saturating them.
As a result the population of the energy levels are equalized. In other words
energy levels that differ by a change in the proton orientation will have the same
population.
C
H
hH
2
C
3
Energy
Saturation
Bo
C
3
C
H
2
H

These energy level populations readjust to this non-equilibrium situation by cross
relaxation between energy levels.

Various cross relaxation paths are activated involving just transitions of carbon
nuclei, or a simultaneous flip of both carbon and proton nuclei.

After some time a steady state situation is achieved, where the population
difference between energy levels corresponding to hydrogen are still equal both
those involving carbons have larger population differences. thus increasing the
signal. The degree of enhancement depends on the efficiency of these relaxation
paths and the irradiation power. (see below)
C
H
1
Cross Relaxation
C
4
Energy
Saturation
Bo
Saturation
C
4

C
H
1
H
The population differences between energy levels involving carbon transition,
are now, 4 to 1, as opposed to 2 : 1 before at equilibrium. Correspondingly the
carbon signal is enhanced. The theoretic maximum for enhancement is given
by the ratio of the gyromagnetic ratio’s, and the ratios of the cross relaxation
rates. In the limit of fast molecular motion, the NOE enhancement factor is:
  1
which is approximately 3 in this case.
H
2 C
Multiplicity Selection
 The one-bond coupling constant between carbon and hydrogen is exploited to
test for the number of hydrogen that are attached to the carbon, This is known
as multiplicity selection.
 The simplest pulse sequence capable of multiplicity selection is known as the
attached proton test, or APT for short.
H
Decoupling
x/2
C
x


Acquire

The phase of a carbon signal in the spectrum depends on the number of protons
attached to it, the delay time, and the size of the coupling constant, which is the
same for all CH3, CH2 and CH groups. Quaternary carbons are not affected by
this pulse sequence.

CH groups have cosine dependence on , ie cosJ while that of a CH2 has a
[1- 2*cos(Jdependence. That of a CH3 is even more complicated.

In order to predict the phase behavior of the carbon signal on has to follow the
carbon magnetization through the pulse sequence.

Recall that for a CH spin pair that there are four magnetizations to consider, two
H magnetization and two C magnetization, which give rise to the double signal
for each nucleus. The carbon magnetization are labeled according to the
corresponding H spin state they are associated with which determines whether
they presses as C + J/2 () or C - J/2 (, in the transverse plane.

The diagram below illustrates the behavior with , in the transverse plane of the
rotating frame on resonance with the carbon signal. Therefore, the relative
motion between the two carbon magnetization are described.
The Evolution of the Carbon Magnetizations of a CH Spin Pair During
the APT sequence, on-resonance.
+ J/2




y'

 = J
y'

- J/2
x'
x'
x

DEC
cos


y'
y'

x'
x'

The evolution under the chemical shift is that of a spin-echo. That is the 90-180--Acq type sequence, hence a second pulse of 180o in the carbon channel.
This sequence returns the magnetization to the y-axis, thus compensating for any
motion due to the chemical shift. The diagram below illustrates the motion of the
carbon nucleus in a rotating frame that is not on resonance with the carbon
chemical shift.
The Spin Echo
+ C

y'
x'
 = 2

y'
x'
x
+ C


y'
x'

y'
x'
The remaining trajectories of the CH2 and CH3 carbon magnetization are handled in a
similar way.

In the case of the CH2 there are 3 carbon magnetization, with frequencies, as C + J
(), C ( and  C - J (which corresponding to the 4 possible
combinations of the spin orientations of the two neighboring protons.

In the case of the methyl carbon CH2 there are 4 carbon magnetization, with
frequencies, as C + 3J/2 (), C + J/2 ( and  C – J/2
(and and C + 3J/2 (), which corresponding to the 8 possible
combinations of the spin orientations of the three neighboring protons
The APT Spectrum of Geraniol
Polarization Transfer Experiments

Another way to enhance the signal intensity of a rare nucleus is to increase the
population differences in the energy level involving the transition of the rare nucleus
by transferring polarization from the abundant nucleus.

This can be achieved with the multipulse experiment known as INEPT, which stand
for Insensitive Nuclei Enhancement by Polarization Transfer.
The INEPT pulse Sequence
x
2
H
y
x
2


x
x
C

2

Acquire

In the INEPT pulse sequence, the two proton magnetization build up antiphase xmagnetization. The simultaneous 900 pulses in the carbon and proton channels
convert this proton antiphase magnetization to carbon antiphase magnetization, with
population differences corresponding to proton transition. The resulting carbon
spectrum for a C-H spin pair is an antiphase doublet, with an intensity 5 to –3
compared to the natural abundance spectrum.

The 5 to –3 antiphase doublet is actually composed to twp arts, that is the natural
abundance signal, which is a 1 to 1 in-phase doublet with a –4 to 4 antiphase doublet
superimposed.

The signal from a CH2 is a 5 to 0 to –3, triplet, and that of a CH3 is a 5 to 5 to –3 to –3
quartet.
Trajectory of the transverse proton magnetizations during the INEPT
pulse sequence giving rise to antiphase x-magnetization
+ J/2
J


 = J/4J = /4


y'

- J/2
y'

x'
x'
x(H), x(C)

- J/2

J


y'


x'

y'
x'
+ J/2
The net effect of the INEPT pulse sequence is that is behaves as if it were an
inversion pulse selective to just one proton transition, causing only two energy levels
to be interchanged.
The effect of the INEPT pulse sequence on the energy level populations
of a CH spin pair
4
4
C1
C1
1
1
H
H
H
H
4
0
5
C1
0
5
C2
J
C
C2
C1
C2
J
C2
C

These antiphase signals complicate the spectra, and the INEPT sequence as shown
above does not allow for proton decoupling to be employed.

Decoupling will cause the antiphase component to self-cancel leaving behind only
the natural abundance signal of the normal carbon spectrum.
INEPT Spectra of a mixture of CHCl3, CH2Cl2 and CH3OH (Top:
INEPT without decoupling; bottom: coupled 13C spectrum)

In order to be able to decouple the antiphase carbon signal has to be refocused into an
in-phase doublet. This is achieved in the Refocused INEPT pulse sequence, shown
below.
The refocused INEPT pulse sequence
x
2
H
y
x
y
x
C




x
2
Decouple

Acquire
x
2




The refocusing part of the sequence, refocuses the antiphase component, however the
in-phase, natural abundance component, in made antiphase. As a consequence the
natural abundance portion of the signal self cancels, leaving only the component
arising from polarization transfer from the proton behind. The resulting single is 4
times as intense, ie the enhancement is given by the ratio of the gyromagnetic ratios.
Refocused INEPT spectra of the aforementioned mixture. (Top:
decoupled; Bottom: coupled)

Similar to the APT sequence the INEPT sequence I sensitive to multiplicity and can
be used to identify the type of carbon by modulating it phase. Again the phase
modulation dependent on the strength of the coupling constant and the delay time.
The echo time dependency of the CH and CH2 groups
explained in terms of a vector treatment.
The variations of CH, CH2 and CH3 carbon signals with the echo
time in terms of evolution angle under the scalar coupling term