1. Chem 781
Two Dimensional NMR

2. The Basic objective of two dimensional NMR
With INEPT one can transfer proton magnetization to 13C for increased sensitivity
Information about number of coupling partners can be obtained in decoupled 13C spectrum
Can one also obtain the chemical shift of coupling partner
=> The detected signal has to be made dependent on chemical shift taking place prior to detection

3. The prototype Two dimensional NMR experiment
Simplest method is adding delay t1 before acquisition and incrementing this delay in a series of one pulse experiments:

4. A series of free induction decays is obtained that depend on the length of t1.
Fourier transform results in a series of spectra phase modulated by Ω•t1 and decaying eponentially with T2*
A second Fourier transform (this time along t1 ) will give a second frequency axis and a peak at f1 = ΩH / f2 = ΩH.
Is such an experiment useful ?

5. Elements of a useful 2D experiment
The basic experiment above has the same information in both dimensions
For a useful experiment we need an additional step to make the first evolution frequency f1 different from the detection frequency (f2).
some kind of magnetization transfer has to occur between t1 and t2 (mixing). That results in the prototype 2D experiment:
t1 ??? t2
Excitation evolution mixing detection
(can be more
than one pulse)

6. Experiment 3: Coupling information and configuration

7. Use chemical shift for assignment of olefinic carbons

8. Two dimensional INEPT experiments
If an INEPT transfer occurs between t1 and the acquisition time t2 , evolution will take place with f-1 = ΩH during t1 (evolution) and with f-2 = ΩC during t2 (acquisition).
1H magnetization C magnetization
is evolving is detected
f f2

9. 2D INEPT with decoupling
Adding a 180̊ 13C pulse in the center of t1 and refocusing before detection will allow for a fully decoupled 1H/13C correlation spectrum:
decoupling refocusing decoupling
during t during t2
For C-H, D = t = 1/J(CH) For CH2 / CH3 t ≠ D

10. Basic 2-D INEPT without decoupling
2-D INEPT with decoupling in both dimensions
Inverse INEPT or HSQC: Protons are observed in the end. By convention, the observed nucleus is shown on the horizontal axis

11. Sensitivity of NMR Experiments
Signal/Noise ∼ N∙ 𝑛𝑠 ∙ Polarization ∙ μobserved ∙ induction ∙ T2*/T1 ∙QProbe ∙ Efficiency
γB0/kT γ 𝐼(𝐼+1) ∼ ω0 = γB0

12. Dependence of sensitivity on experimental parameters
~ B3/2 stronger magnets help more than linear
~ 1/T but note: T2 will also decrease with lower T, also solvents will
freeze
~ ns1/2 ~N half the concentration will require four times as long for same
S/N. Importance of isotope abundance
~ γ5/2 proton by far most sensitive nucleus
In case of INEPT: protons are initially excited, but carbon is detected:
γexcited ≠ γobserved S/N ~ γexcited • (γobserved)3/2

13. Relative Signal / Noise
The Nature of the observed isotope has a larger influence on S/N than Boltzmann Distribution of the excited magnetization
H/X experiment
Excited nucleus
Detected nucleus
Relative Signal / Noise
X = 13C
X = 15N
1 pulse X X 1
1 pulse X + NOE
X (+ ½H) 3 -4
INEPT / DEPT H 4 10
Inverse INEPT 8 30
X-filtered H, HSQC 32
300
Inverse detection is the way to go

14. Reverse INEPT experiment
It is actually more sensitive to perform the 2D INEPT experiment in the reverse manner:
Excite carbon, evolve 13C in indirect dimension, INEPT transfer from 13C to 1H, and detect proton (with 13C decoupling).
This in the same spectrum as INEPT, just with 1H and 13C axes interchanged and is often referred to as reverse INEPT.

15. Best of both worlds: Heteronuclear Single Quantum Correlation (HSQC)
Even better sensitivity can be achieved by making 1H both the excited and observed nucleus:
One starts by exciting the protons, transfers the magnetization to the 13C via INEPT, evolves the 13C magnetization in the indirect dimension, transfers back to 1H, refocuses and eventually detects 1H.
Note that the HSQC experiment is simpler than a double refocused INEPT experiment:
Evolution of coupling is always for anti phase proton magnetization and is independent of
multiplicity

16. HSQC can be perfomed with no or only partial decoupling
No decoupling Decoupling in f-1 only Decoupling in f-2 only

17. Edited HSQC Experiment
A slight modification of the HSQC experiment results in an edited HSQC experiment:

18. Edited HSQC spectrum
The edited HSQC experiment results in a spectrum where the sign of the coross peak depends on the multiplicity of the carbon as in INEPT
Peaks of opposite sign are typically plotted in different color or linestyle.

19. Example: HSQC of Quinine

20. Quinine - aromatic

21. Quinine - aliphatic

22. HMQC Experiment
Alternative to HSQC: HMQC experiment (Heteronuclear Multiple Quantum Correlation)
HMQC can give the same spectrum as HSQC, but is not as easy to visualize
A modified version of the HMQC will be the experiment of choice for long range correlations.
a) –IyH b) IxHIzC c) –IxHIyC d) –IxHIyC cos(WCt1) e) IxHIzC cos() f) IyH cos(WCt1)
+IxHIxC sin(WCt1)

23. HSQC vs. HMQC
HMQC can give the same spectrum as HSQC, but it is not as easy to understand on the basis of the vector picture
Advantages:
simpler (and hence more robust) pulse sequence (less pulses)
Disatvantages:
12C-H are not as easily suppressed
1H/1H coupling active during t1 and will therefore give broader lines and harder to get phase sensitive spectra
A modified version of the HMQC will be the experiment of choice for long range correlations.

24. Experimental Considerations of 2D NMR: Data size and acquisition time
For a typical 1D spectrum 32,000 data points are taken (aq ≈2 s).
A two dimensional spectrum of this size would consist of 32,000 x 32,000 points, and with 4 bytes/point take ~ 16 GB disk space and memory.
Also with 16 scans each it would take 23 d 16 h to acquire. Clearly we have to rethink our requirements.
=> Reduce td in both t1 and t2 dimensions.
Typically, FID’s of 2048 points each are taken (td[f2]), and experiments are performed (td[f1]). That results in file sizes of around 16 MB.
The reduced digital resolution is made up for by the additional dimension of the experiment. It is also advisable to minimize the spectral window to only the region where signals are expected.
As signal is acquired through many experiments, each experiment can be run with a minimal number of scans for phase cycling

25. Processing to deal with reduced dataset size
The result of these very short acquisition times are truncated FID’s
Therefore almost always a sine function will have to be applied to the data prior to Fourier transform. On Bruker parameter wdw=qsine (squared sine function) and ssb.
ssb = 1 (or 0): sine (starting at 0)
ssb = 2: cosine (starting at 1)
ssb > 2: shifted cosine (resolution enhancement).
For HSQC, ssb(f1,f2) = 2 For COSY: ssb(f1,f2)=0.
For HMBC, ssb(f1)=2, ssb(f2)=0
Also linear prediction can add points to data, in particular in f1 dimension:
me_mod = lpfc ncoef > number of peaks in one 1D slice lpbin = 2 x td
Also doubling si compared to td sometimes improves quality (zero filling). si needs to be a power of 2 for computational reasons.

26. Optimizing sensitivity and resolution
As signal to noise depends both on ns and td[t1] (number of spectra taken), less scans per spectra can be done: with ns = 4 and typical td[t1] settings spectra can be acquired in 30 min - 1h.
increasing ns will only increase S/N
increasing td[1] will increase both S/N and resolution in f1 given that aq[1] < T2*. This is usually the preferable solution
In extreme cases (aq > = T2*) increasing td[1] will not add more signal.

27. Selecting the desired signal
Only protons bound to 13C will contribute to 2D signal at ΩC in f1 (1.1% of all protons).
98.9% of protons are bound to 12C and will not oscillate during t1 and hence give huge signal at ΩC = 0
Perfect HSQC will not excite 12C-H:
In practice the experiment will not be perfect, and the 99.8 % of 12C-H will give some x,y magnetization

28. Reasons of non perfect behavior in HSQC experiment:
Pulses will not be perfect 90 and 180 pulses:
Tuning of probe will vary between samples
Even with perfect tuning, excitation will not be completely uniformly across sample (remember residual signal during 180 pulse measurement)
Excitation not uniform across chemical shift range (off resonance effects)
Relaxation occurs during t and t1 will restore some proton z-magnatization at point d, which will be converted to observable y magnetization by last 90 pulse

29. Removal of 12C-H signal through phase cycling
The problem is the same as constant DC offset
Protons bound to 13C will be effected by pulse on 13C, 12C-H will not.
Switching the phase of the second 13C pulse by 180̊ for the second scan and subtracting the spectrum from the first one will add up 13C-H, but subtract 12C-H:

30. Signal selection/suppression within one scan
Disadvantages of phase cycling:
several scans have to be acquired per spectrum even if sensitivity does not require it
Incomplete subtraction due to instability will generate extra noise in the vertical direction (t1 noise).
Receiver gain has to be set according to full signal rather than the desired signal.
⇒ Signal selection within one scan results in much cleaner
spectra.

31. Use of purge pulses in HSQC
Takes advantage of non uniform B1 field across sample (non uniform exitation)

32. Bilinear Rotation Decoupling(BIRD) Pulses in HMQC
As there is no chemical shift refocusing before transfer, purge pulses will not work for HMQC.
At the same time, 12C-H will be fully exited in HMQC experiment.

33. Pulsed field Gradients
Modern spectrometers are equipped with pulsed field gradients. Like the shim coils they can produce field gradients but
Usually only linear gradients are produced
Gradient coils are built into probe
Gradients are much stronger than the ones produced by shim coils
They can be turned on for only a short time (1-2 ms) and off again for detection
In the presence of a field gradient nuclei in different parts of the sample experience a different field. Any transversal (x,y) magnetization will dephase and cancel the macroscopic
Any magnetization along the z-axis will not be effected
=> Gradients can be used to dephase unwanted magnetization

34. Effect of Gradients only on macroscopic signal
Reversible, refocusing leads to Gradient echo

35. Example of purge gradients in HSQC
After the 90°y pulse at the end of the evolution time (point c in figure) the 12C-H protons are along the y-axis, but the 13C-H protons form H-C z-spin order (IzCIzH)one doublet line inverted A gradient applied at that point will only dephase 12C-H, but not 13C-H

36. Gradient Echos - general
Like field inhomegeneity, the effect of field gradients is reversible. Applying a second gradient of opposite sign, but equal length and intensity will reverse the effect of the previous one
A similar effect is obtained by applying a 180° pulse between two gradients of equal length and strength
In general, the effects of gradients will cancel under the condition
with Gi the gradient strength(length • intensity), (g = gyromagnetic ratio of the nucleus, and pi is the coherence order of the nucleus.
It is p=0 for Iz or Iz HIzC, I = ±1 for Ix or Iy.
180° pulses will change the sign of p.
Antiphase magnetization IxCIz H has pC = 1 and pH = 0.

37. Examples of Gradient echos
Gradient echos are the most efficient way of selecting desired pathways.
In HSQC, the gradients are applied before and after the INEPT back transfer.
For 1H{13C} a ratio of G1:G2 = 4:1 is used,
for 1H{15N} G1:G2 = 10:1.
A similar scheme can be employed for HMQC.

38. HSQC with Gradient echos

39. Quadrature Detection in t1
How to distinguish sign of rotation in indirect dimension
In 1D NMR two detectors are employed, one detecting the y (cos), one the x component (sin)
In 2D NMR, the 90° pulse at the end of t1 will select only x or y component of the magnetization.
For example in the HSQC the second 90°x pulse on 13C will only rotate magnetization along y, but not effect magnetization along x.
For proper detection a second scan will have to be taken with the pulse along y

40. Different quadrature detection schemes
Several schemes exist how to combine the cos and sin components and how to synchronize their acquisition with increment of t1
If sine and cos components are stored in same file one obtains a so called phase modulated signal. While distinguishing the sign of the rotation positive and negative intensities are usually not distinguished and the data are processed in magnitude mode.
If they are stored in separate files they are called magnitude modulated and phase sensitive, and a full phase correction can be performed in both dimensions.
Acquisition of datasets can be simultaneous or sequential with respect to the incremented time t1 (pairs with same t1 or alternating cos and sin for subsequent t1 values)

41. QF: simultaneous, phase modulated magnitude States: simultaneous, magnitude modulated phase sensitive TPPI: sequential magnitude modulated phase sensitive States –TPPI: magnitude modulated phase sensitive Echo-anti echo: phase modulated phase sensitive
Note that in the TPPI method t1 is incremented with half of the dwell time. On Bruker spectrometers, that is realized to set the parameter nd0 to twice the number of occurrences of the incremented delay d0 in the pulse sequence.
If gradient echos are used, quadrature detection by selecting x vs. y magnetization will not work. Either a phase modulated magnitude spectrum is obtained, or a phase sensitive spectrum can be obtained by collecting both the echo and antiecho spectra.

42. Consequences of different quadrature schemes
Magnitude spectra:
no need for phase correction (easier to process)
experiment may not need all refocusing delays.
Broader lines, cannot distinguish positive and negative signals.
Examples regular COSY, HMBC
Phase sensitive spectra:
Often more demanding processing (automatic phasing with au program)
sharper lines, distinguish positive and negative lines.
Examples: HSQC, NOESY, PE-COSY, DQF-COSY

43. Axial peaks and folding:
The increment t1 (Dt ) is the dwell time in the indirect dimension and determines the spectral width in f1:
Dt = dw(1) = 1/(swh[1]•2)
As there is no frequency filter in the indirect f1-dimension, all exited peaks outside the window will show up but at the wrong frequency.
The location of peaks outside the spectral window will depend on the quadrature scheme used:
In TPPI and States-TPPI they will fold back symmetrically on the same side,
In States they will alias on the opposite end of the spectrum:
The methods also differ in the position of any remaining axial peaks (peaks with no dependence on t1)

44. Echo-Anti echo behaves like States-TPPI with respect to folding and position of axial peaks

45. Structure determination using two dimensional NMR experiments
The most powerful approach to determine the structure of a molecule
Often combination of several experiments is required
Use of connectivity information is more reliable than chemical shift alone

46. 1H{13C} HSQC
allows for measurement of 13C (or X) chemical shift with much higher sensitivity than 1D 13C experiment
allows to connect the protons with their carbon atoms and obtain CH fragments
identify and connect pairs of diastereotopic protons
separate overlapping signals and account for all CHX groups in molecule (do in conjunction with integrations in 1H spectrum)
identify OH and NH as they will NOT give cross peaks

47. Connecting C-H fragments with 1H/1H COSY:
HSQC will not give any connectivity information between the fragments.
An experiment utilizing 3JHH couplings between neighbored CH (or more general any XH-YH) fragments is the H/H-COSY experiment.
The basic COSY experiment is the simplest 2D experiment conceivable as it consists of two 90° pulses seperated by an incremented delay t1:
While this looks much simpler than the 2D INEPT of HSQC experiments the proper theoretical treatment of the COSY experiment is more complex and will be postponed.

48. Reasons why the COSY experiment is not done as a direct analogue to the INEPT experiment
The active coupling is between equal nuclei, it can not be decoupled (or refocused) during shift evolution as every pulse is applied to both coupling partners
=> coupled spectrum with active coupling in anti phase
the relative range of 3JHH is much larger (2-14 Hz) than for 1JCH ( Hz) and thus no one optimal mixing time J exists

49. Appearance of COSY spectrum
The resulting spectrum has a proton axis in each dimension and features two types of peaks:
W(f1) = W (f2) => diagonal peak
W(f1) =| W(f2) => cross peaks

50. Analysis of COSY experiment
Cross peaks occur for each pair of protons coupled by a two or three bond JHH coupling (or more general:by any H-H coupling of significance)
They always occur in pairs for which are arranged symmetric about the diagonal.
Analysis of basic COSY simply searches for cross peaks connecting neighbored protons coupled by 3JHH ... but watch out for the following:
be aware of pairs of diastereotopic protons coupled by 2JHH. Those are normally very strong, but don’t carry connectivity information. You can identify them from HSQC spectrum
In cases of dihedral H-C-C-H angles close to 90° the 3JHH coupling may be very small and the cross peak very weak or not observed
In some cases long range 4JHH and 5JHH may be large enough to result in weak cross peaks
If peaks are very close in chemical shift, the cross peak may overlap with diagonal

51. Example HSQC + COSY: Menthol

52. Step 1: 1D proton and C-13 spectra.
Account for all protons.
Integration gives There
are 8.6 protons between 0.8 –
1 ppm, overlap including some
impurity or incorrect integration.
Count and number all carbons by chemical shift. Correct number of C.
DEPT-135: 3 CH2, 7 CH/CH3. The three C at lowest shift most likely CH3 groups.

53. Step 2: HSQC: connect protons to carbons
Identify the pairs of CH2 protons, these will also show a cross peak in the COSY (2JHH)
Number protons according to carbon spectrum
1-3 are indeed methyl groups as only then the integrations make sense
there are a total of 8 menthol protons between ppm
OH does not give a cross peak

55. Step 3: connect neighboring C-H (or O-H) groups
Find starting point:
assign most downfield signal 10 to C-1.
Connect 1-OH, , 9-5.
Note that 7/6 shows up only on one side of diagonal.
The 8A/7A cross peak might be due to HC4-C-C6H long range coupling

56. assign methyl groups:

58. Assignment experiments:

59. Connecting across tertiary carbons: HMBC
In addition to 3 bond H-H couplings long range two and three bond C-H couplings can be utilized to establish connectivity along H-C-C and H-C-C-C.
The experiment is derived from the HMQC experiment employing a delay time J
optimized for two- and three bond C-H couplings (2,3JCH = 4-12 Hz, t = ms).
The second refocusing delay is normally omitted and the experiment recorded without 13C decoupling during acquisition and magnitude display.
Often an additional 90° 13C pulse is employed (grey in the figure) to suppress one bond correlations.

60. Experimental details of HMBC spectrum
the proton chemical shift during mixing time J is NOT refocused.
Also proton-proton coupling will be active during both t and t1.
=> Spectrum is not phasable and usually displayed in magnitude mode.
As there is no refocusing after t1, proton signal will be in anti phase
No decoupling possible during acquisition
In-phase magnetization will build up during acquisition according to sin(pJCHt2) no signal for t2 = 0
=> sine shifted windows function needed (ssb=0)
=> acquisition time needs to be sufficient for signal to develop

61. Appearance of HMBC spectra
Schematic HSQC and HMBC spectra. Note that HSQC peaks will show up as weak doublets in the HMBC spectrum as no C-H decoupling is employed during t2.

62. Analysis of HMBC spectrum
The 2D spectrum shows crosspeaks between a proton and carbon shifts separated by two and three bonds.
always check with HSQC experiment to identify residual one bond correlations. These will show up as weak doublets.
The experiment can be used to assign tertiary carbons (C=O, >C< from neighboring C-H groups)
Allows to make connections across non protonated atoms (C=O, >C<, -O-, >N- etc.).
This can be done by direct correlation (H-C-X-CH) or connecting two CH groups to a common C atom (H-C-CO-O-C-H)
also NH and OH peaks can give cross peaks (H-N-C or H-O-C)
Intensity of cross peak will depend on value of JCH, so some three bond interactions may be weak or missing if dihedral angle (H-C-X-C) is close to 90°
While very powerful the fact that both two- and three bond interactions show up causes many peaks in the spectrum and makes the assignment sometimes ambigious

63. Most connectivity problems will be solved by a combination of HSQC, COSY and HMBC,
analysis normally takes place in that order
Sensitivity is usually 1H > COSY > 1H{13C} HSQC > 1H{13C} HMBC > 1D 13C

64. EXAMPLE Camphour: HSQC/COSY/HMBC
STEP 1: 1D spectra
13C: number of carbons, 1 C=O
1H: number of protons
combine with mass to get molecular formula
STEP 2: HSQC
identify diastereotopic pairs of protons
relate protons to carbon atoms
STEP 3: COSY
connect neighbored CH fragments
STEP 4: HMBC
Connect across tertiary atoms

71. Nuclei other than 1H{13C} HSQC / HMBC most common for C-13 NMR
But the same principle can be extended to any combination of spin ½ nuclei as long as one of them is high in natural abundance: 1H{31P}, 1H{29Si}, 1H{15N}
1H{15N} most important after 1H{13C} in typical organic molecules

72. Considerations 1H{15N} correlations
1JNH Hz
natural abundance of 15N only 0.4 % (nine times the experiment time needed compared to C-13 at natural abundance) => but labeling possible
N-H protons often exchanging, making one bond correlations often challenging to observe
It is usually not practical to obtain 1D 15N spectrum
Protein NMR uses isotope labeling and often H2O instead of D2O as solvent

75. C-C correlation with INADEQUATE (Incredible Natural Abundance DoublE QUAntum Transfer Experiment)
Disadvantages of HMBC:
ambiguity ( HC-C and HC-X-C connectivities can not be distinguished),
the potential dependence of the cross peak intensity on dihedral angles
frequent overlap in the proton dimension
One alternative is the INADEQUATE Experiment:
utilizes one bond 13C-13C couplings.
This experiments selects only molecules which have two 13C atoms (i.e. 0.01% of all molecules) and is thus 100 × less sensitive than a regular 13C experiment.
The acquisition dimension is a regular 13C spectrum, and the indirect axis displays the sum of the 13C shifts of the 13C-13C pairs (i.e. *CA+*CB):

76. Appearance of INADEQUATE

77. Example: Menthol

78. Limitations of INADEQUATE
Potentially the most powerful method in elucidating C-C connectivities
BUT: it lacks sensitivity: Only 1 in 10,000 molecules have two C-13 atoms.
C-13 is both excited and observed nucleus
Should only attempted with samples where a 13C spectrum with S/N > 10 can be obtained with one scan (which is almost never the case).
In the example shown for menthol about 0.5 g of sample were used.

79. Relayed H-H correlation with TOCSY
H-H correlation can be done by employing a spin lock pulse instead of the second 90° pulse in COSY.
In its simplest form it is just one long pulse
(tP =10-80 ms, gB1/2p ≈10 kHz)
As SL it is applied || to the magnetization My it will not rotate the spins, but it will prevent chemical shift precession from occurring and keep the magnetization along the y axis (hence the name spin lock).
However coupling will occur and magnetization will be transferred between coupled spins.

80. In practice, TOCSY experiments are performed with a series of spin lock pulses instead of one long pulse similar to the decoupling schemes.
For tSL ≈ 10 ms a spectrum similar to COSY will be obtained. However, since the spin lock pulse also acts as a purge pulse, TOCSY spectra can be acquired with one scan per increment even without gradients
For longer tSL (50-80 ms) relayed transfer occurs between neighbored CH groups
In a chain CHA-CHB-CHC HA will not only give a crosspeak with its neighbor HB, but also with HC.
Ideally each proton shows crosspeaks with all members in the spin system. Therefore the name TOCSY for TOtal Correlation SpectroscopY.

81. In practice, TOCSY experiments are performed with a series of spin lock pulses instead of one long pulse similar to the decoupling schemes

82. Application of TOCSY Experiments
The main advantage is that in case of heavy overlap in one part of the spectrum shifts can be identified using only few separated protons (example HN protons in polypeptides).
COSY spectrum of metallothionein: NH region (left) aliphatic region (right)

83. TOCSY spectrum allows assignment of amino acids from NH-region alone.
Ideally, each N-H signal correlates with all protons in the amino acid.
No crosspeaks between protons in different amino acids.
Cys-4
Cys-5

84. Combining sequences
Many experiments can be considered as combination of the above experiments
These basic mixing schemes as can be used as building blocks:
INEPT, COSY, TOCSY, HMQC, INADEQUATE.
We will later learn NOE-transfer

85. HSCQ-TOCSY: TOCY + HSQC: get a TOCSY spectrum which has the shifts of the attached carbons in the indirect dimension. Advantage of C-13 resolution in indirect dimension, but only 1% the sensitivity.
HSQC-COSY in a similar manner one can combine HSQC and COSY

86. HSQC-TOCSY of Gramicidin

87. ADEQUATE: HSQC + INADEQUATE: inverse detected version of the INADEQUATE experiment. More feasible than the INADEQUATE for real compounds, but much less (up to a factor 100) less sensitive than a HMBC. Looses resolution in direct (f2) dimension. Looks like HMBC with 2 bond correlation only (1,1-ADEQUATE).
Combining HMBC with INADEQUATE gives
n,1-ADEQUATE.

88. Example ADEQUATE:

90. 3-D NMR
Adding a second or more incremented delays allows to add a third or more dimension to the experiment: INEPT-t1-INEPT-t2-TOCSY-acqusition (t3) gives a 3D HSQC-TOCSY

91. 3D HNCO