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B. Jaun, M.-O. Ebert: Structure determination by NMR 3.1

3.1 On the relative sensitivity of NMR experiments

The signal to noise ratio of NMR signals is proportional to:

( excited) ( detected)3/2 B

03/2 (number of transients)1/2

As discussed in the preceding chapter, polarization transfer from1

H (excited) to X (detected) leads toa gain in sensitivity of up to H/X. The gain in sensitivity (see table below) is even larger for methods in

which protons are not only the excited nucleus, but also the detected one.

Relative sensitivity at 100% abundance without NOE

Combination of

nuclei

X excited

X detected

H excited

X detected

X excited

H detected

H excited

H detected

1H/31P 1/10 1/4 2/5 1

1H/13C 1/32 1/8 1/4 1

1H/15N 1/300 1/30 1/10 1

Examples Inv. gated 13C DEPT, INEPT PH-COSY HSQC, HMQC

Relative experiment times for identical S/N

Combination of

nuclei

X excited

X detected

H excited

X detected

X excited

H detected

H excited

H detected

1H/31P 100 16 6.25 1

1H/13C 1024 64 16 1

1H/15N 100000 1000 100 1

The relevant relaxation time for1H-excited methods is T1 of protons, which is usually much shorter

than T1 of X-nuclei. Hence,1H-excitation has the additional advantage that more transients can be

acquired per time because only relaxation of protons has to be awaited in between transients.

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3.2 Introduction to 2D spectroscopy

Example: HSQC proton detected1H-13C-shift correlation via 1JCH

Basic HSQC Pulse sequence: double INEPT transfer from1H to

13C and back.

Because HSQC is based on single quantum coherences of both,1H (I) and the heteronucleus S

(13

C,15

N etc.), it can be described correctly within the vector model of theory. In the following, the

vector model is used to explain how the chemical shift of the S-spin precessing during t 1 is modulating

the final I-spin signal acquired during t2. This is the basis of all n-dimensional NMR methods, but in

most of the 2D-experiments discussed in this course, multiple quantum coherence (for the discussion

of coherence see chapter 4) is involved in the mixing process, which makes its description within the

vector model impossible.

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Generalization:

The generic elements of 2D (and nD) NMR spectroscopy

Whenever the signal actually acquired during t2 is also a function of the evolution time t1, the resulting

series of FIDs (one per t1 increment) can be Fourier transformed for each time variable (t2 and t1)

separately giving an 2-dimensional frequency spectrum. The basic idea of 2D-NMR-spectrocopy is to

generate a particular excited spin state during the preparation period (e.g. with a 90 pulse, or a

polarization transfer step), let the system evolve during time t1 (the evolution period) then use a mixing

element to transfer magnetization (more general: coherence) between spins and finally detect x,y-

magnetization (single quantum coherence) during the detection period t2. The physical basis of the

mixing process is typically either J-coupling or dipolar cross relaxation. For each value of t1, the FID is

stored separately. The resulting array of FIDs is first Fourier transformed under t2 to give an array ofspectra (the interferogram). In the next Fourier transform under t1, the vector constructed from the n

th

data point of each spectrum is then treated as a time-domain signal and is transformed under t1.

Series of FIDs, one tor each t1

Interferogramm

Preparation Evolution Mixing Detection

t2

tm

t1

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2D-spectrum

Quadrature detection in the indirect dimension t1

Echo/anti-echo method (N/P-type selection)

This method uses phase cycles or gradients to select either positve (P-type) or negative (N-type)

coherence order during t1 while eliminating the other one. Depending on whether the signal is

amplitude modulated or phase modulated by t1-evolution, the lineshape of echo-antiecho spectra can

be either pure absorption in both dimensions or mixtures of absorption and disperision. In the latter

case, the resolution is reduced and the spectra have to be plotted in absolute mode.

The hypercomplex method (RSH, States)

In the actual acquisition (t2), the receiver generates two signals by phase detection at 0 and 90, as in

1D-spectroscopy. After digitization the two arrays are stored separately and are used as the real and

imaginary parts in the complex FT. In the indirect dimension t1, the pulse sequence has to generate

two FIDs that are 90 out of phase of each other for each t 1. These are again stored separately in

order to be used as real and imaginary parts for complex FT under t 1. The 90 phase-shifted signal is

obtained by changing the phase of the pulse after the evolution time by 90.

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For each t1 value, FID1 and FID2 are stored in separate memory blocks. Together with the two

quadrature signals from channels A and B in t2, one obtains four memory blocks. Complex FT for both,

t1and t2, gives a 2D spectrum that is a matrix of four blocks: rr, ri, ir, and ii. Phase correction in each

direction mixes the two blocks in the corresponding dimension such that in the end, the rr block (the

one that is usually displayed and plotted) contains the 2D spectrum with absorption line shapes in both

dimensions.

TPPI (time-proportional phase incrementation)

Only one FID is acquired per t1 value, but the t1 increment is half of that used with the States method

(doubling the SW in 1). This gives a single block with twice as many FIDs as in the hypercomplex

mode. Each time t1 is incremented, the phase of a pulse is shifted by 90 relative to the receiver

phase. The spectrum obtained after a real FT in t1 can be folded around 1=0 and the reference is

shifted back into the middle of the 1-domain. This procedure is analog to the Redfield method for

quadrature detection in 1D that was used by old Bruker spectrometers (

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The TPPI and States procedures are equivalent with regard to experiment time, S/N and digital

resolution. Certain artifacts, in particular so called axial peaks, appear at the center of the 1 domain

with States but at the edge of the spectrum with TPPI. Folding in

1is also different in the two cases(see folding with real and complex transforms in 1D). A forth scheme is called StatesTPPI. It

combines the advantages of the hypercomplex method with the preferred location of artifacts at the

edge of the spectrum and is therefore used in most cases today.

3.3 HSQC (Heteronuclear Single Quantum Correlation)1H-

13C-correlation over one bond via

1JCH

Revisiting the HSQC experiment we can assign the elements of the pulse sequence as follows: The

preparation part is identical to INEPT (up to time point a). During t1,13

C-magnetization precesses in x,y

while1H-magnetization is in z. Therefore, neither chemical shifts nor homonuclear couplings of

protons evolve during t1. The 180 pulse in the center of t1 refocuses1JCH (therefore, the cross peaks

are not split by1JCH in the 1-dimension of the final spectrum). At the end of the evolution period,

coherence is partially retransferred to1H-SQC, which is detected (reverse polarization transfer).

GARP-broadband13

C-decoupling during t2 collapses the cross peaks which would otherwise be split

by the heteronuclear coupling1JCH of 125-200 Hz in 2 (remember, it is the

13C-satellites in the proton

spectrum, which are actually measured). Since broadband13

C-decoupling of all1H-bearing carbons

(ca. 160 ppm) is demanding on the decoupler and heats the sample, in particular if it has a high

dielectric constant, GARP decoupling during acquisition may be left out at the cost of a more

complicated spectrum. HSQC without decoupling13

C during t2 is also the method of choice for

measuring1JCH.

Because only 1.1% of the protons are bound to13

C, the 100 times stronger signal of the12

C bound

protons has to be suppressed. If the selection is based on phase cycles, very high spectrometer

stability is required whereas with gradient-based selection only the signal of13

C-bound protons

reaches the receiver.

Of the two coils of a heteronuclear probehead, the inner one, which is closer to the sample and

therefore more sensitive, is usually tuned to the detected frequency. For optimal X-detection, the inner

coil is tuned to X and the outer coil is used for1H-decoupling. For

1H-detected heteronuclear

experiments, the opposite arrangement is used:1H on the inner coil and X on the outer coil (so-called

inverse or reverse probes)

The pulse sequence for HSQC shown above is the minimal version. Actual modern pulse sequences

are much more complicated as exemplified by the pulse sequence for multiplicity edited HSQC with

sensitivity enhancement and coherence pathway selection by gradients from todays Bruker library

shown below:

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HSQC gives clean absorption line shapes in both dimensions. However, the HSQC pulse sequence is

more complex and longer than that of HMQC and therefore more dependent on correct pulse

calibrations (modern versions use adiabatic composite pulses for13

C-180). For the same reason,

HMQC often gives better results than HSQC for samples with broad lines (short T2).

Example for proton detected1H-

13C shift correlation: Multiplicity edited HSQC

strychnine

N

O

O

H

H

H

H

N

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Coherence transfer pathway selection by gradients

Strychnine [c=50 mM] in CDCl3. 400/100 MHz. Acquisition: 2k(t2) x 256(t1), 2 scans/t1-increment. Optimized for1JCH=145 Hz. GARP-

13C-CPD-decoupling in t1. Experiment time: 16 min. With adiabatic

13C inversion pulses and

sensitivity enhancement. Processing: 1k x 1k, cos2

window functions in t2 and t1.

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3.4 HMQC (Heteronuclear correlation through MultipleQuantum Coherence)

Pulse sequence of HMQC:

The first 901H-pulse generates

1H-SQC; the first 90

13C-pulse transforms this partly into

heteronuclear double and zero quantum coherence. The 1H-180 pulse in the middle of t1 refocuses

the1J

CHcoupling and swaps ZQC (evolution with

C-

H) and DQC (evolution with

C+

H). At the

end of t1, the effects of1H chemical shifts during the two halves of t1 cancel, and only C labeling

remains. Homonuclear1H-

1H-couplings evolve during t1 as well as t2. This homonuclear coupling leads

to a tilt in the cross peaks and reduces the possible resolution in the t1-domain. For small to medium

sized molecules, HSQC therefore gives better S/N for a given experiment time and better resolution in

1 than HMQC.

3.5 HMBC (Heteronuclear correlation through multiple

bonds)1H-13C-correlation over several bonds via 2 ,3 , (>3 )JCH

Pulse sequence:Long range variant of HMQC with low pass filter to suppress one-bond correlations.

Most1H-

13C-scalar coupling constants over two and three bonds are in the 0 to 10 Hz range,

comparable to1H-

1H couplings (see collection in compendium). Coupling constants

4JCH over more

than three bonds are usually very weak and are rarely detected by HMBC with typical delays for

evolution of the long-range coupling of 70 ms (optimal for2,3

JHC = 8 Hz). Because the 2-bond and 3-

bond coupling constants cover the same range 2-bond and 3-bond correlations cannot bedistinguished in HMBC spectra. Although less sensitive than HSQC and HMQC, HMBC is more

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sensitive than INADEQUATE by several orders of magnitude and delivers the same type of

information: connectivity of the carbon skeleton including quaternary carbons. In contrast to

INADEQUATE, HMBC also correlates fragments across heteroatoms.

The following modifications are made to the HMQC sequence in order to measure long-range

correlations:

A so-called low pass filter eliminates signals of directly bound protons. It works because of the

difference of more than one order of magnitude between 1JCH and2,3JCH. When the magnetization of

directly bound protons is in antiphase (after 1/(21JCH) s), the small long-range couplings are still mostly

in phase. A 90 pulse at this time converts the magnetization due to directly bound protons into DQC

and ZQC but does not affect the signals of remote protons. A second, much longer delay brings the

long range coupling into antiphase. From thereon the sequence is identical to HMQC. Because

considerable signal is already lost due to relaxation during the long delay 1/(22,3

JCH), no attempt at

refocusing is made (that would require a second delay of equal length), and no13

C-broadband

decoupling is applied during t2. The line shapes are mixed absorptive/dispersive because the

homonuclear 1H-1H-coupling constants are comparable to those of heteronuclear long range

couplings. Therefore, the spectra have to be processed in magnitude or power mode and the cross

peaks appear tilted.

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Example for HMBC

Coherence transfer pathway selection by gradients

Strychnine [c=50 mM] in CDCl3 400/100 MHz. Acquisition: 4k(t2) x 512(t1), 2 scans/t1-increment. Optimized for

2,3JCH=8 Hz. Experiment time: 45 min.

Processing: 2k x 1k, sine window functions in t2 and t1, absolute value plot.

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3.5 Proton detected H,X-COSY for abundant X nuclei

This1H-detected method is convenient for the correlation of protons with abundant X-nuclei such as

31P. The pulse sequence is the direct heteronuclear analog of COSY with two simultaneous 90 pulses

on1H and X acting as the mixing pulse. At the beginning of the sequence, all natural

1H-magnetization

is destroyed by a train of 180 pulses on1H. Therefore, only the chemical shift and coupling of X

evolve during the evolution time t1. The resulting 2D spectrum shows cross peaks in antiphase

absorption in both dimensions.

Example:1H,

31P-COSY allows to correlate sequential sugar units in oligonucleotides through three-

bond couplings between the sugar protons and the31

P of the phosphodiester linkage CHOPO2O-

CH-. In the example of a non-natural oligonucleotide with arabinopyranose sugars below, each

phosphorus shows cross peaks to the 2'-H of the preceding and the 4'-H2 of the following sugar in the

sequence (plus a weak4JHP W-type cross peak to the 3-H of the following sugar).

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