2D FT-NMR Spectra
w1
w2
The 2D spectrum is the graphical representation of a function,
S(w1,w2), of two independent frequency variables
2D FT-NMR
There are different kind of experiments:
• to resolve overlapping signals
• to increase sensitivity
• to get information not afforded by 1D
methods
2D FT-NMR: experiment stages
A 2D FT-NMR experiment consist of 4 main stages
preparation evolution mixing detection
preparation
During preparation, the spin system is prepared in a non equilibrium
coherent state, which is going to evolve during the following stages.
In the simplest experiments (e.g. COSY) the preparation is a single
pulse
evolution
During evolution (t1), the spin system evolves freely under the relevant
spin Hamiltonian (e.g., chemical shift and scalar). During the evolution
time the frequency labelling for the dimension 1 takes place.
mixing The various kinds of experiments differentiate
according to the mixing process
1.experiments for separarting different intractions (e.g. shift and
coupling constants: J resolved experiments) along two orthogonal
dimensions, thus resolving too crowded 1D spectra. (In this case the
mixing process is bypassed)
mixing
2. experiments for correlating the transitions of coupled spins
(e.g., COSY). During the mixing there is the coherence transfer
(transverse magnetization or multi quantum coherences) from
one transition to another. The mixing is very short, one pulse
(COSY) or a short sequence.
3. experiments for the study of dynamic processes, such as
chemical exchange or NOE (extended mixing time during which
the incoherent magnetization exchange takes place)
detection
During the detection period (t2) the conventional acquisition of the
time signal, originated by the transverse magnetization, is carried out.
In a 2D experiment
many FIDs are
acquired. They
differ only for the
length of the t1
interval
The signal, which is a function of two
time variables, s(t1,t2) is stored in a 2D
matrix , with row corresponding to the
FIDs acquired during t2
NOESY
COSY (90°)y –t1- (90°)y-t2
Frequency labelling during the evolution time (t1)
Let’s consider a sample with only one kind of spins, e.g., il 1H di HOD,
and therefore only one signal.
One starts from equilibrium, with the magnetization aligned along z
M is brough along x’ by a (90°)y pulse
Due to the chemical shift, the magnetization precesses in the
transverse plane with angular frequency WA.
y’ during the interval t1 the magnetization evolves
because of the chemical shift and has components
W0t in the tranverse plane:
x’
Mx’= M0cos(WAt1) and My’= M0sin(WAt1)
A second p/2 pulse along y’ brings the Mx’ component along –z,
whereas leaves unaltered the component along y’ My’= M0sin(WAt1),
which will be acquired during t2.
The first FID, for a very short t1, has very low intensity.
t1 is incremented at the next experiment and the corresponding FID
has starting intensity M0sin(WAt1) and equation
M0sin(WAt1)exp(-iWAt2)
This procedure is repeated for a certain numer of t1.
The trasnverse relaxation cannot be neglected, thus the signal
function of the two time variables is:
s(t1,t2)= M0sin(WAt1)exp(-t1/T2A)exp(-iWAt2)exp(-t2/ T2A)
After obtaining the FIDs, the FT is carried out in
dimension 2, obtaining spectra, the intensity of which is a
function of t1
s(t1,w2)= M0sin(WAt1)exp(-t1/T2A)·T2A/[1+(w2-WA)2T2A2]
w2
Now the FT is carried out along the columns (dimension 1) and the
2D peak is obtained
S(w1,w2)= M0T2A/[1+(w2-WA)2T2A2]· T2A/[1+(w1-WA)2T2A2]
The signal with equal w2 and w1 coordinates is a
diagonal peak
diagonal signals
strychnine 10 %
In the case of COSY experiment
for a system of two nuclei, with
different chemical shifts, WA and
WB, there are the diagonal peaks, COSY
at w1= w2= WA and w1= w2= WB. If
they are scalarly couppled, cross-
peaks, i.e. extradiagonal peaks,
appear symmetrically with
respect to the diagonal, at w1= WA
e w2= WB and at w1= WB e w2= WA,
due to the coherence transfer
caused by the second 90° che
costituisce il processo di mixing.
ethyl crotonate
HETCOR
heteronuclear
correlation 1H
spectroscopy
heteronuclear correlation:
cross-peaks only
direct detection
13C
Inverse Heteronuclear Correlation
enhanced sensitivity because both excitation and detection
are carried on 1H (gH5/2)
strychnine
13C
13C
1H 1H
HSQC HMQC
from INEPT from DEPT
Sensitivity of 2D NMR Spectra
The 2D NMR spectra usuallly take longer than 1D and therefore it is
important to optimize sensitivity
The signal of a 1D spectrun is proportional to the number of samples
points times the average height of the signal “envelope”, “weighted” by a
suited function (e.g. matched filter) in the time domain, 0 < t2< t2Max
S: signal intensity
n: number of scans
S n N sh
N: number of sampled points
<sh> average value of the ‘’envelope” height, h, mulripplied by the
weighting function
The 2D signal is proportinal to the total number of sampled
points (in both dimendiond) and to the average height of the
weighted signal’s ”envelope” in the time domain, i.e. in teh
intervals : 0< t1< t1Max and 0< t2 <t2Max.
S n N1 N 2 sh
For best sensitivity matched filters are used in both dimendions.
It is possible to obtain the same sensitivity (intended as S/N per
unit time) for 1D and 2D spectra provided:
I. the transverse decay an the decay due to the static magnetic
field inhomogeneities are negligible during the evoluion time t1
II. the instrumental stabiity is good so that the t1 noise is negligible
III. same number of peaks, thus the intensit of one line of the 1D
spectrum is not distributed among several 2D peaks
The I criterium requires low resolution in t1. In the case high
resolution in t1 is needed, a little decay of sensitivity in the 2D
spectrum must be reckoned
The III criterium is satisfied in heterocorrelated maps
Optimization of the 2D Spectra
The height of the ”envelope” depends on the interval for relaxation
between two subsequent scans. Ideally it is on the order of 3T1 in order
to avoid the longitudinal interference between the subsequent
experiments, which leads to t1 noise. However, it is more common to
work at the steady state, using 4 or more più dummy scan before the
true accumulations.
It is better to use the least possible resolution in the 1 dimension, to
shorten the experiment time and reduce the efect of the signal decay in
t1. Few datapoints cause the nasty Gibbs oscillation after the FT due to
signal truncation. For these reason apodization function are used. A
sensible choise are the Gaussian functions. The further zero filling
procedure improves the digital resolutioin of the final spectrum.
Quadrature in w1
There are two strategies:
to run a parallel experiment to collect the cosine component
The t1 at which the cosine component is obtained may be either
the same of the sine component
or interspersed with those of the sine component
The two schemes are close to those employed for the conventional
quadrature detection: simultaneous sampling (SHR: States,
Haberkorn, Ruben) or not simultaneous sampling (TPPI: time
proportional phase incrementation).
After the first FT the signal is phased and the imaginary part is
deleted, thus the signals after the second transform can be
phased as pure absorption obtaining the socalled phase-
sensitive spectra
The advantage is that there is further information concerning the
relative phase of the signals and close signals are more easily
distinguished
The disadvatage is that a double amount of computer and disk
memory is used
It is more common to acquire the sine and cosine
component in the same FID during a series of scans acquired
according the EXORCYCLE phase cycle.
The peaks obtained after both FT display a mixture of
absorption and dispersion, so taht cannot be phased as pure
absorption,
and therefore are presented as absolute vale
mixture of absorption and
dispersion
3D: COSY-COSY
after t1 a further evolution time is inserted
