Two-Dimensional NMR Spectroscopy

A general time dependent NMR experiment can be broken up into three events: preparation,
evolution, and detection.

In the two-dimensional experiment a series of spectra are collected where the time of the
evolution period is varied.
General Two-Dimensional NMR Pulse Sequence
Relaxation
Delay
Preparation
Indirect time dimension
Direct time dimension
t1
t2
Evolution
Detection

The resulting data is composed of a series of FID each differing by a phase, which is a function
of the evolution period.

This data set hence has two inherent time dependencies, that of the FID itself, and that of the
phase factor. Thus each FID represents a time point in the indirect dimension. The combined set
of FID can be thought of being a two-dimensional FID which is time dependent along both
dimensions.
A Two-dimensional Spectrum is collected as a series of FID at different
evolution times, these FID differ by a time-dependent phase factor

The two-dimensionally time dependent function can be Fourier-transformed in each dimension,
giving a two-dimensional frequency plot representing the two-dimensional spectrum. These can
be represented as a stack plot of the individual 1-D spectra, or as a contour plot.
A Stack Plot of a Two-Dimensional NMR spectrum.
The Contour Plot Corresponding to the Stack Plot Above.
 A two-dimensional spectrum can be performed where the nucleus is the same or different in
both dimensions. The former is referred to as a homonuclear correlation spectrum whilst the
latter is referred to as a heteronuclear correlation experiment.

In any two-dimensional spectrum correlations between two nuclei are made based on some type
of interaction, depending on the experiment, where this interaction transfers coherence from on
spin onto another.

During the evolution period the magnetization can be attributed to one nucleus and evolves
according to its chemical shift at couplings, it is then transferred to another nucleus through the
coherence transfer mechanism and resonates according to the chemical shift and couplings of
that other nucleus. This magnetization will give rise to a signal at the frequency of the first
nucleus in the indirect dimension and that the second nucleus in the direct dimension, and is
referred to as a cross-peak.

When no transfer occurs the magnetization will precess according the chemical shift and
coupling of the same nucleus in both dimensions and thus will occur at the same frequency in
both the direct and indirect dimension. A signal of this type is referred to as an auto-correlation
peak, or a diagonal peak.
The Two-Dimensional COSY spectrum of an AX spin system
The COSY spectrum of an Azo-sugar.
O
R
N3
HO
OH
Correlation Spectroscopy (COSY)
 The COSY experiment is a 2D NMR experiment where the correlation is based on J coupling
interactions. Thus the cross peak intensity is proportional to the strength of the coupling
interaction.
 This technique unambiguously determines which nuclei are coupled to each other, something
that can not be determined from by 1D experiments with absolute certainty. It thus allows the
experimenter distinguish between groups of coupled spins. Thus sub-spectra individual
components of a multi-component solution can be assigned.
 Another experiment related to COSY is Total Correlation Spectroscopy, TOCSY, which is able
to base correlation on J couplings over long range. (several bonds)
The General COSY Pulse Sequence
Relaxation
90x
90x
Evolution

Acquire
t1
t2
 The system start with the equilibrium z-magnetizations, which after an initial pulse are converted
to transverse magnetizations, which are allowed to evolve under the influence of chemical shift
and coupling terms for the evolution period t1.
 During the evolution period the antiphase magnetization evolves ,just like in INEPT, as a result
of evolution under the J coupling.
 The evolution period ends with a final 900 pulse, where the antiphase magnetization of a given
nucleus is converted by the pulse to the antiphase magnetizations of all the nuclei coupled to it,
resulting in coherence transfer. The antiphase magnetization refocuses and is observed, during
the detection period t2.
 The time dependence in the indirect domain is based on chemical shift and coupling evolution,
and the degree of coherence transfer is determined by the efficiency of the evolution under the J
coupling term. As a result the intensity of the cross peaks will be determined by the coupling
strength and evolution time, and consequently often an additional fixed evolution delay is
inserted after the first pulse to enhance the cross peak intensity from weakly coupled nuclei.
COSY Pulse Sequence Optimized for Long Range Couplings
Relaxation

90x
90x
J
Evolution
Acquire
t1
t2

Sensitivity to the sign of the signal is achieved by adding the data from the basic COSY and
phase modified COSY experiments using an appropriate phase cycle. This is just like quadrature
detection in the direct domain where two signals have to be collected 90o out of phase with each
other. Unlike Quadrature detection the two signals are not save as a complex data set, thus
phasing in the indirect dimension is not possible.

In the processes of achieving sign sensitivity phase information is lost in the indirect domain.
Sine modulated data is being added to Cosine modulated data without correcting the phase,
which would require two separate data sets to be store in memory.

The resulting peak shape upon has both absorptive and dispersive character, in the indirect
dimension. This line shape is known as the phase twist line shape.
The phase twist line shape

Instead of phasing the data at all, which is still possible in the direct dimension, the magnitude of
each data point is calculated and plotted.

This is known as the magnitude spectrum, which is characterized by long tails in both dimensions,
and is thus not amenable to high-resolution studies. Often apodization with a sine bell is used to
remove these tails at the expense of sensitivity.

This type of COSY experiment is referred to as the magnitude COSY. It was most commonly used
in the past due to requiring much less computer memory. It was the only way to obtain fast sign
sensitive data, since the phase cycle involved is minimal.

Today since computer memory is no real issue and upon the development of pulsed field gradient,
removing the necessity of complex phase cycles, the phase sensitive experiment has become most
common.
The phase twist line-shape, compared to the corresponding magnitude spectrum
and that apodized by a sine bell function.

The data from the COSY and Modified COSY pulse sequence can be separately stored in
memory, in what is know as a hyper-complex data set, which is a complex data set in both
dimensions. This data can be Fourier-transformed in both dimensions and corrected in phase
correction in both dimensions, allowing for pure absorption or pure dispersion line shapes line
shapes in both dimension. This approach to phase sensitivity is know as the States-Haberkorn
method.

The resulting phase sensitive COSY spectrum will have cross-peaks the aforementioned antiphase pattern and diagonal peaks that are in-phase. Since this a phase sensitive experiment the
diagonal peaks are seen to be 90o out of phase with respect to the cross-peaks. Either can be
phase to pure absorption.

It is not possible to phase both cross-peaks and diagonal peaks in pure absorption
simultaneously.
Cross peak structure in a phase sensitive COSY experiment with the cross peaks
phase in pure absorption mode.
Diagonal peak structure in a phase sensitive COSY experiment when the cross
peaks phase in pure absorption mode.

One way to obtain the same phase for both cross-peaks and diagonal peaks is to ensure that both
signal arise from the same term from the indirect dimension.

One way to do this is to select the double quantum coherence after the second pulse and converting it
to terms that evolve into detectable signal during the second evolution period. This is known as the
Double-Quantum-Filtered COSY, which has an additional conversion pulse the end.
The Double Quantum Filtered COSY Pulse Sequence.

2
 
2 2 




t1
1
receiver
2
t2
3 4 5
The Phase Cycle for the DQF-COSY Pulse Sequence
Scan



reciever
1
x
x
x
x
2
x
x
y
-y
3
x
x
-x
-x
4
x
x
-y
y
Examples
COSY of CH3CH(NO2)CH3
COSY of (CH3)2CHCH2CH2-O-C(=O)-CH3
COSY Spectrum of Citronellol