1
1D vs. 2D NMR spectra (general definitions)
A one dimensional NMR spectra has two dimensions: The x axis corresponds to the frequency
axis (the chemical shifts in ppm) and the Y axis corresponds to the intensity (see the following
figure).
Intensity
10
9
8
7
6
5
4
3
2
1 ppm
increasing frequencies
In contrast, a 2D NMR spectrum contains two frequency axes. Intensities present the third axis
and are therefore usually displayed as contour plots (similar to the presentation used in
geographical maps).
F2
F1
Figure:
Two different presentations of a 2D spectrum: Stacked plot (left), contour
(right) [taken from: Derome, A.E., Modern NMR Techniques for Chemistry Research]
plot
Definition: The horizontal axis is defined as F2 (direct dimension) and the vertical axis as F1
(indirect dimension). This definition is valid for Bruker spectrometers, Varian actually uses it the
other way around.
If both dimensions contain chemical shifts, the experiment is called shift-correlated 2D NMR, if
one dimension denotes scalar couplings, the spectra are called J-resolved.
2
Diagonal-, cross peaks
In a [1H, 1H]-COSY-experiment both frequency axes denote proton chemical shifts. Peaks in 2D
spectra will connect nuclei, which are correlated in one way (usually either by scalar or dipolar
couplings). Cross peaks correlate spins with different frequencies:
ν1 ≠ ν2
In homonuclear spectra (those, which contain similar nuclei (e.g. both proton frequencies) in the
two frequency dimensions), peaks are symmetric with respect to the diagonal of the spectrum.
The diagonal peaks correlate identical spins, and are therefore of little analytical use.
ν1 = ν2
The diagonal in some way represents the 1D spectrum.
Each COSY-spectrum contains duplicated sets of cross peaks due to its symmetry. The peaks
(ν1, ν2, cross peak) (ν1, ν1; diagonal peak), (ν2, ν1; cross peak) and (ν2, ν2; diagonal peak)
form the corners of a square. All peaks with ν1 = −ν1 form the anti-diagonal.
ν2
ν1
F1
ν1
(ν1, ν2)
(ν1, ν1)
ν2
(ν2, ν2)
(ν2, ν1)
Diagonal: ν1 = ν1
F2
Anti-Diagonal:
ν 1 = - ν1
3
The principle of 2D NMR spectroscopy
In a standard 1D proton experiment, acquisition of the signal starts (almost) immediately after
the excitation radiofrequency pulse. But how are frequencies encoded in a 2D experiment?
In principle, all 2D experiments are designed according to the same principle: They consist of a
series of 1D experiments, in which a single delay has been altered in length. The building blocks
of 2D experiments are: preparation, evolution, mixing and detection. Both evolution and
detection are time periods, called t1 and t2, during which chemical shift and scalar couplings
evolve. Therefore, signal intensities and phase are variables of
Int = f (t1, t2)
t1
Fig: Working principle of a 2D COSY experiment [taken from: van de Ven, F.J.M., Multidimensional NMR in Liquids]
During the preparation period the system is prepared, the magnetization is usually prepared
along a transverse axis (x or y). During the evolution time t1, magnetization evolves with
chemical shift and/or scalar couplings. During the mixing period coherences are transferred from
one spin (the one that is frequency encoded in F1) to another spin (the one that is detected
during t2). If the two spins are different, such a transfer will give rise to cross peaks, otherwise it
will yield a diagonal peak. The different 2D experiments differ by which mechanism (e.g. scalar
coupling1 or dipolar coupling2) magnetization is transferred. The signal is finally detected during
the detection (acquisition) period.
During recording of a 2D experiment the same NMR experiment is repeated over and over
again, simply setting the evolution time to another value from 1D spectrum to 1D spectrum. The
increment ∆t1, that is added to the evolution time from experiment to experiment, depends on
the spectral width in the indirect dimension.
1
the dipolar coupling, often called dipole-dipole coupling, is mediated via the dipole moment of the spins via
space. Its size depends on the orientation of the molecule with respect to the static field.
2
the scalar coupling, often called spin-spin-couplung, is mediated via electrons through bonds. Its size is
independent of the orientation of the molecule with respect to the static field. Scalar couplings give rise to multiplet
patterns of the signals.
4
How many 1D experiments need to be recorded for the complete 2D spectrum?
For a typical 2D [1H, 1H]-COSY spectrum usually a series of 512 1D spectra is recorded. The
1D spectra contain resonances at identical frequency, but the amplitudes (intensities) of the
signals are modulated (vary) from experiment to experiment.
A Fourier transformation along the direct frequency dimension F2 results in a set of 1D spectra
containing all chemical shifts and couplings, which are active during the acquisition period t2.
Because the signals physically give rise to a signal in the detection coil this dimension is called
the direct dimension. Only so-called single-quantum frequencies can be recorded, because only
these will result in a signal in the coil.
FT
Int (t 1 , t 2 ) → Int (t 1 , ν 2 )
Figure: Schematic representation of a set of free induction decays (FIDs) (left) subject to the first fourier
transformation. [taken from: van de Ven, F.J.M., Multidimensional NMR in Liquids]
The modulation of the amplitude of the signals in the different 1D spectra is due to evolution of
chemical shifts and scalar couplings during the evolution time t1. A second Fourier
transformation is performed in the orthogonal dimension (along t1), and data points correspond
to different FIDs.
FT
Int (t 1 , ν 2 ) → Int ( ν1 , ν 2 )
Since the frequencies are derived from the amplitude modulation of the signals indirectly, the F1
frequency dimension is called the indirect dimension. The second FT therefore yields the full
spectrum with two frequency dimensions:
5
Figure:
FT along t1 will yield the full 2D spectrum. Cross peaks may be displayed either as cross peaks with
a contour plot (c) or a stacked plot (a,b) [taken from: van de Ven, F.J.M., Multidimensional NMR in
Liquids]
Depending on whether only scalar couplings or scalar couplings and chemical shifts were active
during t1, a J-resolved or a shift-correlated spectrum will result. In a COSY experiment, chemical
shifts are active during t1 and t2, and coherence transfer takes place via scalar couplings.
How much time and how much disk space are required for recording a 2D experiment?
The NMR signal (the FID) is recorded in stroboscopic fashion; single data points, separated in
time, are measured. Resolution gets better when more data points are recorded. High-resolution
1D proton spectra typically contain 32768 (32K) data points corresponding to 128 kilobyte disk
space. The resolution, assuming a spectral width of 12500 Hz, is then 0.4Hz per data point.
In order to yield the same resolution in both dimensions in the 2D spectrum, 32768*32768 (2
GB) need to be recorded. Even if only a single scan per increment would be used (which is
usually not sufficient), the whole experiment would last almost 2 days. In order to reduce disk
space requirements and, nowadays more important, in order to save measuring time, 2D data
sets are usually recorded with reduced resolution.
For a typical [1H, 1H]-COSY experiment 512 FIDs with 2048 data points each are recorded. The
total disk space requirements are then 2 MB, and the measuring time would last for 18 min.
6
Projections
Along the edges of 2D contour plots the one-dimensional spectra may be plotted. Either internal
projections (generated by projecting all signals onto one axis) or external projection (by plotting
the separately recorded 1D spectrum along the axes) may be chosen. The following figure
displays a 2D [1H, 13C]-HSQC-spectrum. In these experiments proton frequencies are recorded
in F2 and carbon frequencies in F1 in order to correlate protons with their directly attached
carbon nuclei.
ppm
F1
100
110
120
7.0
6.8
6.6 ppm
internal projection
13C−NMR Spektrum as external projection
1H−NMR Spektrum as external projection
F2
internal projection
Internal and external projections are both plotted along the spectrum. Since the internal
projections are generated from the 2D spectrum, which is recorded with reduced resolution,
internal projections have lower resolution. This is obvious from the two signals at 6.6 and 6.8
ppm, for which the small couplings are not resolved in the internal projections. Similarly, the very
close signals at 111 and 112 ppm are not fully resolved in the internal projection.
Two-dimensional spectra have much lower resolution than their 1-dimensional counterparts.
However, since signals are dispersed in two dimensions, signal overlap in the 2D spectrum is
actually much smaller. Therefore, apart from the fact that 2D spectra display correlations
between signals, they also allow to better extract the chemical shifts from the better-dispersed
signals.
7
2D Experiments
The [1H, 1H]-COSY-experiment
The COSY (correlated spectroscopy) experiment correlates nuclei via their scalar couplings.
Chemical shifts are displayed along both frequency dimensions. In contrast to the TOCSY
experiment, correlations will only appear between protons that possess a resolved coupling to
each other.
ppm
6.6
6.7
6.8
6.9
7.0
7.1
7.1
7.0
6.9
6.8
6.7
ppm
Fig: Expansion of the region displaying correlations between aromatic protons in the 2D [1H, 1H]-COSY spectrum of
Melatonin
Active vs. passive couplings
Cross peaks in the COSY spectra display a characteristic fine structure, which reflects the scalar
couplings. Active couplings are those that give rise to the cross peaks; if the cross peak is
observed at the frequencies (νa, νb) then the Ja,b coupling is the active coupling. Active couplings
are in anti-phase; the corresponding peak components display opposite phase. Couplings to all
other nuclei are called passive couplings and display in-phase splittings:
J
J
ppm
anti-phase doublet
ppm
inphase doublet
The cross peak pattern, shown in the figure above, arises only for correlations between nuclei
that possess no further scalar couplings. The separation of the multiplet components is given by
JA,B.
8
J(A,B)
ppm
F1
J(A,B)
4.00
2.00
ppm
F2
Fig.:
Cross peak of a 2-spin system in the COSY-spectrum
For the following spin system consisting of a linear chain of three protons, in which C is coupled
to A and B coupled to A
C
B
spin-system:
A
the cross peak (νA, νB) would be as illustrated in the following figure:
J(A,B)
J(A,C)
ppm
F1
4.00
J(A,B)
2.00
ppm
F2
Fig.:
Cross peak of the three-spin system in the COSY
The active coupling JA,B leads to the anti-phase splitting. Due to the passive coupling JA,C an
additional in-phase splitting occurs. The distance separation of the in-phase components
therefore allows, in principle, to extract the passive coupling JA,C (however, partial signal
cancellation leads to wrong values for small couplings; these are better extracted from ECOSY
spectra).
9
Artefacts in COSY spectra
• t1-Noise is noise strips running parallel to
ppm
2
the frequency axes. They mostly originate from
instrumental
instabilities,
with
temperature
instabilities are being the most serious source.
4
Since the noise is proportional to the signal
height, they are most prominent for strong
6
signals, e.g. singlet methyl groups or other
sharp
lines.
T1-noise
always
degrades
spectrum quality but becomes particularly
annoying
when
cross
peaks
with
small
3.5
3.0
ppm
Fig.:Example for t1-noise in a COSY-Spectrum
intensities should be interpreted.
• If the chosen relaxation delay is too short, so-called rapid-scanning artefacts are observed.
They occur at the double-quantum frequencies (the sum of the frequencies of the coupled
nuclei) and lead to a second diagonal , twice as steep. They can (and should!) be easily
recognized by the fact that they occur at positions at which no signals are found in the 1D
spectrum.
Fig.: taken from: Cavanagh, J. et al. Protein Spectroscopy
The anti-phase character of COSY cross peaks leads to cancellation of signal intensities for
small couplings. It is important to note that the resolution in the two frequency dimensions is
10
usually very different. Therefore, the two symmetry-related peaks may not both be observed, but
only one of them may occur:
Fig.:
[taken from: Cavanagh, J. et al. Protein Spectroscopy]
11
The [1H, 1H]-TOCSY-experiment
Similar to the COSY, the TOCSY is a homonuclear, shift-correlated 2D NMR experiment, in
which coherence transfer takes place via scalar couplings. Cross-peaks contain both passive
and active couplings in-phase. In contrast to the COSY, correlation between a spin and all other
spins from the same spin system3 may be observed. For example, correlations from the amide
proton will, under favorable conditions, include all side-chain protons from the same amino acid
(e.g. for lysine). Another example would be correlations from the anomeric proton in sugars,
which could display correlations to all other protons from the same sugar unit. The strength of
the experiment lies in the fact that one resolved (non-overlapped) resonance (e.g. the anomeric
proton or the amide proton) may be sufficient to determine, which spins are part of the same
spin system, even if parts of the spin systems heavily overlap with other spin systems. By proper
choice of the length of the mixing time (e.g. 10 ms), coherence transfer can be limited to just
vicinal correlations, thus resulting in a COSY-like spectrum, or to correlations between all
members of the spin system (e.g. for 80 ms). Because the multiplet components are in-phase,
signal cancellation does not occur even if line-widths become larger, and hence a short mixing
time TOCSY is preferable to a COSY for larger molecules.
mixing time 15ms
Fig.:
3
mixing time 100ms
ppm
ppm
6.5
6.5
7.0
7.0
7.2 7.0 6.8 6.6 6.4 ppm
7.2 7.0 6.8 6.6 6.4 ppm
Expansion of the region displaying aromatic correlations of Melatonin, for different settings of the
mixing time.
Definition of a spinsystem: Spins, which belong to the same coupling network are part of the same spin system.
12
The [1H, 1H]-NOESY-experiment
The NOESY is a homonuclear, shift correlated experiment, in which cross peaks result from
dipolar interactions between spins. Dipolar couplings result from through-space interactions and
only depend on the distance of the spins, but not on the number of intervening bonds. They are
observable for nuclei separated by up to 4-5 Å. The efficiency of the NOE transfer additionally
depends on the motional properties of the molecule, and NOEs are generally stronger for larger
molecules.
ppm
ppm
2.6
2.8
4
3.0
3.2
6
3.4
7
Fig.:
6
5
4
3
ppm
3.4
3.2
3.0
2.8
ppm
NOESY-spectrum of Melatonin with expansion. Gray peaks: positive signals, black peaks negative
phase.
The underlying effect of the NOESY is the nuclear Overhauser effect. The NOE describes a
phenomenon whereby a non-equilibrium population of α- and β-states relaxes back to its
equilibrium value, such that populations of energy levels of other spins (and hence their signal
intensities) are changed. The sign of the NOE (increase or decrease of signal intensity) depends
on the tumbling properties and is positive for small and negative for large molecules. For
intermediate-size molecules the NOE may actually be small or close to zero:
Fig.:
Dependency of the proton, proton NOE on the molecular reorientation time
Neuhaus, D., Williamson, M., The NOE in Structural and Conformational Analysis]
τc [taken from:
13
Because the sign of the NOE depends on the molecular reorientation time τc of the molecule,
peaks in the NOESY may be positive (large molecules) or negative (small molecules). The
reorientation time is largely influenced by the viscosity of the solvent. Even smaller molecules
therefore tend to behave like large molecules when measured in DMSO. A dramatic influence
on motional properties is also seen by the temperature: As a rule of thumb, changing the
temperature by 20 degrees corresponds to the same change in motional properties, as would be
observed upon doubling the molecular weight. The following table describes the behavior of
molecules of different size in NOESY experiments:
Phase of the
Phase of the cross
diagonal peaks
peaks
positive
negative
positive
Very weak signals
(positive or negative)
positive
positive
Small molecules in
low-viscosity
solvents
Medium-sized
molecules
Large molecules,
viscous solvents
Artifacts in the NOESY
• EXSY-(exchange)-peaks:
They
often
ppm
display large intensities, possess the same
3
phase as the diagonal peaks, and are often
also observed for very short mixing times.
Typical
examples
are
exchange
4
peaks
between amide protons, or sugar hydroxyl
5
protons, and the water signal.
5.0
4.5
4.0
3.5
3.0
ppm
Fig.: NOESY-spectrum containing exchange peaks.
• COSY-peaks (anti-Phase COSY-type peaks; zero-quantum interference peaks): They are
observed between protons that display both dipolar and scalar couplings (e.g. for geminal
protons), and for shorter mixing times. Due to the different relaxation properties of protons in
larger molecules, they disappear in NOESY spectra of proteins. These peaks are manifested by
their COSY-type typical anti-phase peak pattern. When overlapped with genuine NOESY signals
they lead to partial cancellation of NOE cross peak intensity resulting in titled peaks.
• t1-noise und rapid scanning artifacts (see remarks for the COSY-experiment).
14
The [1H, 1H]-ROESY-experiment
The ROESY (rotating frame NOE experiment, sometimes also called CAMELSPIN) experiment
is like the NOESY, a 2D homonuclear shift-correlated experiment, in which coherence transfer is
achieved through dipolar couplings for protons separated by less than 5Å. The NOE transfer
takes place in a rotating frame leading to a different dependence of the sign of the ROE on the
motional properties of the molecule. Effectively, the ROE is always positive (leading to negative
cross peaks for positively phased diagonal peaks). The ROE buildup is twice as fast as the NOE
buildup. During the mixing time T1ρ relaxation takes place, which is similar in size to T2, and
therefore the use of the ROSY is limited to smaller or medium-size molecules.
ppm
2
3
4
5
8
Fig.:
7
6
5
4
3
2
ppm
ROESY-spectrum of a peptide; grey peaks = positive signals, black peaks = negative signals
Artefacts in the ROESY
• TOCSY-Peaks, (in-phase, positive), observed for geminal protons, whose chemical shift
difference is small
• spin-diffusion peaks (ROE-ROE relay peaks) (in-phase, positive)
• TOCSY-ROESY transfer Peaks (in-phase, negative)
•
exchange peaks (positive)
It can be seen that almost all artifacts can be readily recognized from the different sign of the
peaks.
15
The [X, X]-EXSY-experiment
The EXSY experiment is a homonuclear, shift correlated experiment, in which coherence
transfer takes place through chemical or conformational exchange. In fact, the pulse sequence
is the same as the one used for the NOESY. Because exchange is usually faster than the NOE
buildup, shorter mixing times may be used for the EXSY. From recording a series of EXSY
spectra with different mixing times, exchange kinetics may be deduced.
O
H
H
N
N
O
ppm
2
ppm
7.0
4
6
7
Fig.:
6
5
4
3
2 ppm
7.5
7.5
7.0
ppm
[1H, 1H]-EXSY-spectrum displaying exchange between the two rotamers in the figure on top.
Artefacts in EXSY spectra:
• NOESY-Peaks
16
The [13C, 13C]-INADEQUATE-experiment
Like the COSY experiment the INADEQUATE provides spectra of the homonuclear, shiftcorrelated type. INEADEQUATE experiments are mainly used for
natural abundance
13
C signals of
13
13
13
13
C, C correlation spectra of
C molecules. The INADEQUATE contains a very efficient filter to suppress
12
C, C isotopomers. This filter selects for
which can only be formed by a pair of coupled
13
13
13
C, C double quantum coherences,
C nuclei. In F1 the double quantum frequencies
are recorded, and hence the cross peaks have the following coordinates: F2: ν(a), F1:
ν(a)+ ν(b). Because
13
13
C, C isotopomers are
very rare (0.01*0.01=0.0001) in
13
C natural
abundance molecules, extremely concentrated samples are required. The experiment is very
powerful, and very useful for highly substituted compounds, in which proton density is low.
The following figure displays an expansion of an INADEQUATE experiment recorded on
melatonin:
C12
N
H3CO 12
10
C9
C7/C8
C6
O
Melatonin
5
C11 C10
C
ppm
CH3
H
8
9
6
7
C5
140
11 N
H
150
160
170
150
Fig.:
140
130
120
110
ppm
Expansion of a 2D INADEQUATE spectrum recorded on melatonin
Cross peaks are spilt into doublets by the one-bond C-C coupling. The two coupled resonances
can be recognized as two separate peaks at a common frequency in F1 (on a horizontal line).
Sometimes one of the two peaks is missing due to low signal-to-noise. The coupled partner can
be easily calculated, because its frequency plus the frequency of the coupling partner must add
up to the F1 frequency.
17
The [1H, 13C]-HSQC-experiment
The HSQC experiment is the most popular heteronuclear shift correlation experiment. Nuclei,
13
1
usually separated by one bond are correlated via their scalar couplings. In [ C, H[-HSQC
spectra, no correlations to quarternary carbons are observed. Since the one-bond proton-carbon
or proton-nitrogen couplings are large and rather uniform, these spectra are quite sensitive.
ppm
100
110
120
7.2
Fig.:
7.1
7.0
13
6.9
6.8
6.7
6.6 ppm
1
Expansion of a [ C, H[-HSQC recorded on Melatonin
Artefacts in the HSQC
•
Folding in F1
If the spectral width of the indirect dimension is chosen too small (this is sometimes done on
purpose) folding (or aliasing) of signals occurs. Whereas folded signals in the direct dimension
are usually strongly attenuated by audio filters (and do not occur at all in the oversampling
mode), folding in F1 gives signals with full intensity at erroneous positions in the spectrum.
Depending on the quadrature detection mode in F1 (real or complex acquisition) signals may be
folded about the near or the distant edge:
Fig.: Folding in data sets with real (left) or complex (right) acquisition.
18
The [1H, 13C]-HMBC-experiment
The HMBC experiment like the HSQC gives heteronuclear shift-correlation spectra. In contrast
to the HSQC, coherences are transferred through the much smaller long-range couplings. The
1
13
3
long-range couplings span rather a wide-range. The H, C J coupling, for example, displays a
Karplus-type dependence on the dihedral angle. Therefore, some couplings may be close to
zero, and such correlations will then of course be absent from the spectrum. Depending on the
2
3
system under study, the J or the J coupling may be larger, so that these spectra contain much
ambiguity. Nevertheless, the HMBC is a very useful experiment, because it contains correlations
to quarternary carbons.
ppm
155
160
165
170
7.0 6.5 6.0 5.5 5.0 4.5 4.0 3.5 3.0 2.5 2.0
Fig.:
13
ppm
1
Expansion of the [ C, H]- HMBC-spectrum of Melatonin
Artefacts
• HMBC spectra often contain correlations due to 1JC,H-couplings. Since HMBC spectra are
not usually decoupled during acquisition, these couplings will show up as rather larger (e.g. 200
Hz) doublets. The HMBC contains a filter for such correlations, which however fails to work
when the one-bond couplings differ significantly from standard values (e.g. from 140Hz,
aromatic carbons).
ppm
25
30
1J(C,H) coupling
35
40
3.5
3.0
2.5
2.0
ppm
Fig.: HMBC-spectrum displaying correlations due to the 1JC,Hcouplings
• axial peaks (artifacts which can be found on a horizontal line along the center frequency)
• folded signal similar to the situation encountered for HSQC spectra