2D NMR Description

7/27/2019 2D NMR Description

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Detailed description of the figures for the 2D NMR experiment (NOESY)

A brief introductory comment:

The principle of 2D NMR spectroscopy is easiest to understand with NOESY. (NOESY standsfor: 2D NOE spectroscopy, where NOE stands for ‘nuclear Overhauser effect’. Albert W.

Overhauser was the physicist who discovered the NOE mechanism for transfer of magnetic polarisation magnetization between spins). The NOESY pulse sequence is the simplestexperiment for understanding 2D NMR spectroscopy. (Richard R. Ernst received the Nobel Prizein Chemistry in 1991 mainly for development of FT NMR and 2D NMR.)

The 2D experiment in a nutshell:

2D NMR experiments (the NOESY experiment is just an example) are performed as a series of FIDs (recorded during t 2) which are identical except for systematic incrementation of the delay t 1 (in NOESY: the delay between the first two 90o pulses) from 0 to, e.g., 50 ms in increments of,e.g., 100 μs. As each FID is digitized, the result presents a 2D data matrix, one axis being t 2, the

other one being t 1. This data matrix presents the ‘time domain’ of the spectrum.The 2D spectrum is obtained by Fourier transform of the time-domain data matrix along the t 1 and t 2 axes (it doesn’t matter which one is transformed first). The resulting 2D data matrix presents the ‘frequency domain’ of the spectrum (in the example of the NOESY spectrum, this isthe spectrum one would plot). By convention, the axes are labelled with ppm values (the ppmscale is proportional to the frequency scale, as ppms are calculated by (

0– ref )/ref , where 0 is

the Larmor frequency and ref the frequency of a reference compound).

Diagonal- and cross-peaks:

If the magnetization precesses with the same frequency during t 2 as during t 1, it gives rise to adiagonal peak. If it precesses with different frequencies, it gives rise to a cross-peak. Cross-peaks

require the transfer of magnetization between A-spins (say, the blue one) and B-spins (say, thered one) during the mixing time m (the delay between the 2nd and 3rd 90o pulse) by NOE. The NOE results in exchange of longitudinal magnetization between A-spins and B-spins, i.e. afraction of A-spin magnetization ends up as B-spin magnetization and vice versa.

(The NOE mechanism is complicated and not part of this lecture. Just note that the magnitude of the NOE depends on the internuclear distance r with r -6, i.e. doubling r reduces the NOE 64-fold.In practice, this means that NOEs can only be measured between spins that are closer than about5 Å.)

The NOESY pulse sequence step by step:1) Equilibrium A-spin magnetization. Also called longitudinal or z-magnetization. It is

parallel to the axis of the magnetic field B0.

2) Transverse magnetization. After a 90ox pulse, it is –y-magnetization.

3) Precession during the delay t 1 results in transverse magnetization somewhere in the x-y plane.

4) The 2nd 90ox pulse converts the magnetization in the x-y plane into magnetization in the x-

z plane.



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5) Let’s retain only the z-component of the magnetization after the 2nd

90o

x pulse and discard

any transverse components. This is done by phase cycling, a procedure which is explained further down. Importantly, part of the A-spin magnetization (blue) is transferred to B-spin

magnetization (red) during the mixing time m by NOE.

6) The 3rd

90o

x pulse turns –z-magnetization into y-magnetization (just as it turned z-

magnetization into –y-magnetization between steps 1 and 2).

Phase cycling (not so important for understanding the 2D experiment):

Phase cycling involves the summation/subtraction of scans recorded with different phases of the pulses. (All other parameters, in particular t 1, are kept the same. ‘Scan’ is the name for a single

recording, while ‘FID’ stands for the sum of one or several scans that is subjected to Fourier transformation. Recording and FID with many scans improves the signal-to-noise ratio. After

each scan, a waiting period is required to re-establish equilibrium magnetization before the nextscan.) In our example, the phase of the 3

rd 90

opulse is changed from x to –x to obtain a second

scan, where the magnetization of interest points along the –y-axis rather than the y-axis. Bysubtracting the result of this second scan from that of the first scan (which was recorded with a

90ox pulse rather than a 90o-x pulse), the signals simply add up.In contrast, this phase cycle subtracts any x-component of the magnetization present at the end of

m (because it is unaffected by the rotation around the x-axis and, hence, doesn’t change its sign).

Any y-component of the magnetization present at the end of m is turned into longitudinal

magnetization by the 90ox pulse. Longitudinal magnetization does not precess and therefore does

not induce a current in the coil (i.e. it is not detected).

Two-dimensional Fourier transform:

a) FT t 2 -> 2

Each FID recorded with different t 1 delay is Fourier transformed into a spectrum. This can be

viewed as converting the t 2 axis into an 2 axis. (Note: = 2, where is frequency in Hz.) Theresult is illustrated for four different FIDs recorded with different t 1-times:

i) t 1= 0. The spectrum contains a peak for the A-spins and a smaller one for the B-spins (which

originates from the NOE during m).

ii) t 1 so that At 1 = /2, i.e. the A-spin magnetization precessed by precisely 90o

during t 1. No

magnetization is observable, because x-magnetization present at the end of t 1 remains x-

magnetization after the 2nd

90ox pulse and, hence, is destroyed by phase cycling.

iii) t 1 so that At 1 = , i.e. the A-spin magnetization precessed by precisely 180o during t 1. The A-

spin magnetization simply changes sign by the end of t 1. Therefore, all signals resulting from this

magnetization are inverted.

iv) t 1 so that At 1 = 3/2, i.e. the A-spin magnetization precessed by precisely 270o

during t 1. Thisturns it into magnetization aligned with the x-axis at the end of t 1 which is destroyed by phase

cycling.

Clearly, the t 1-2 data matrix contains signals at the 2 frequencies of the A-spin and the B-spin

which oscillate in sign and magnitude as a function of t 1. Looking along the t 1 axis, the signal

intensities observed at 2 = A are modulated like a damped cosine function. The cosine function

arises from the fact that of the magnetization precessing during t 1, only the projection onto the y-



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axis is selected. The dampening arises from T 2 relaxation during t 1. The signal of the B-spin

oscillates with the same frequency as the signal of the A-spin (namely A). Check out for

yourself why this is so!

b) FT t 1 -> 1

Fourier transform of the t 1-2 data matrix in the t 1 dimension converts the t 1 axis into the 1 axis.This transforms the modulation of the signal amplitudes into signals at 1 = A. There is one

diagonal peak (at 1 = 2 = A) and one cross-peak (at 1 = A / 2 = B).

Starting from B-spin magnetization:

At the start of each scan, not only A-spin magnetization is present, but also B-spin magnetization.Of course, the pulse sequence works in the same way for the B-spins as for A-spins: B-spin

magnetization precesses during t 1, part of it gets transferred to A-spin magnetization during m by

NOE, etc. The same pictures can be drawn, exchanging blue and red, and A and B. The complete

NOESY spectrum thus contains two diagonal peaks (at 1 = 2 = A and at 1 = 2 = B) and

two cross-peaks. (Where is the second cross-peak?). The NOESY spectrum is symmetric aboutthe diagonal, because the likelyhood of magnetization transfer from A-spins to B-spins is the

same as for that from B-spins to A-spins.

Final remarks about sensitivity:

For a single scan, a good signal-to-noise (S/N) ratio is obtained by recording the signal until it

starts to disappear in the noise.

The signal-to-noise (S/N) ratio in an FID increases with the square-root of the number of scans, because the signals add up coherently, whereas uncorrelated noise increases with the square-root

of the number of scans. Doubling sensitivity requires 4 times more scans.

In a two-dimensional NMR experiment, every point of the 2D data matrix contributes to the S/Nratio of the final two-dimensional peak. As a 2D NOESY spectrum is typically recorded with,

e.g., 512(t 1)x2048(t 2) data points, the S/N ratio of the 2D peaks can be remarkably good.



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2D NMR Description