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9 - Two-Dimensional NMR, Part 2: Multiquantum Transitions

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9 - Two-Dimensional NMR, Part 2: Multiquantum Transitions

1. Introduction

2. COSY

3. Multi-quantum filter techniques

4. Inverse correlation: HMQC, HMBC

5. Pulse sequences as building blocks

09-2D NMR: Multiquantum Transitions (Dayrit)

Introduction

- The first 2-D NMR experiment, a COSY sequence, was proposed by Jean Jeener in 1971 in a presentation made at the Ampere International Summer School held in Yugoslavia. In 1975 the first COSY experiment was performed using his ideas.
- As soon as chemists, biochemists and physicists realized the power of 2-D NMR spectroscopy, there came a rapid rise in the development of other, more ingenious pulse sequences.
- In this section, we will discuss some of the 2-dimensional multipulse sequences, including the important class of inverse detection measurements.

09-2D NMR: Multiquantum Transitions (Dayrit)

NMR Selection Rules

One-spin system

- The only transition possible is a single quantum transition (W1): .

W1

Two-spin system

- A single quantum transition (W1) involves a net change in the total spin quantum number, S (=s), m = ±1, e.g., or or
- A zero quantum transition (W0) does not involve a net change in S, e.g., .
- A double quantum transition (W2) involves a net change S = ±2, e.g., .

W1

W1

W2

W0

W1

W1

09-2D NMR: Multiquantum Transitions (Dayrit)

Selection Rules.

1. Only W1 transitions can be directly observed.

2. W0, W2 and other multiple quantum transitions occur with lower probability. These transitions can be effected using suitable pulse sequences, but cannot be directly observed.

- The NMR pulse sequences are designed to select the desired transitions and filter out the rest.

3. For systems with more spins, higher order quantum transitions are available.

W1

W1

W2

W0

W1

W1

09-2D NMR: Multiquantum Transitions (Dayrit)

NMR Selection Rules

- Vector analysis is based on the classical Bloch formulation. While it is a very good model for simple pulse sequences, it is cumbersome for multipulse sequences.
- Vector analysis can be used to analyze single quantum processes only. NMR phenomena, such as coherence transfer, cannot be adequately represented.
- The vector model therefore is only of limited use in many of the more complex 2-D pulse sequences which involve non-single quantum transitions (zero or multiple-quantum).

09-2D NMR: Multiquantum Transitions (Dayrit)

- 2-D Homonuclear Correlation Spectroscopy: COSY
- The original Jeener COSY pulse sequence as given below is still the currently used version:
- 1H: 90x’- t1 - 90x’-AQT(t2)
- COSY can be thought of as the incremented version of SPI or homonuclear decoupling. If one performs a series of homonuclear decoupling experiments by moving the decoupling frequency in uniform steps across the 1H spectral width, the spectra produced can, in principle, reveal the coupling relationships among all the 1H nuclei. COSY achieves the same objective in a single experiment, and with a fraction of the time and effort.

09-2D NMR: Multiquantum Transitions (Dayrit)

Anatomy of the COSY pulse sequence

1H: 90x’- t1 - 90x’-AQT(t2)

(from: Jacobsen, NMR Spectroscopy Explained)

09-2D NMR: Multiquantum Transitions (Dayrit)

COSY

1H: 90x’- t1 - 90x’-AQT(t2)

The behavior of a off-resonance singlet (1 spin, no interactions) can be described as a frequency modulation sequence still using vectors.

- During tD, the vector evolves. At increments of 1/(2 ), the vector is the ±y’ axis, and max / min points are observed. For other values of t1 the second pulse will act only on the y’- component of the vector.
- The FID collected in t2 will therefore be modulated by .

(from: Sanders and Hunter, Modern NMR Spectroscopy)

09-2D NMR: Multiquantum Transitions (Dayrit)

The vector description of COSY

1H: 90x’- t1 - 90x’-AQT(t2)

The previous vector description for COSY worked only because the system was a single spin. However, in the case of 2 or more spins, these spins interact in the x’-y’ plane, and these give rise to multi-quantum transitions.

In the COSY analysis of a multi-spin system, such a situation is inevitable because the first 90°x’ pulse places all of the 1H nuclei in the x’-y’ plane. When this happens, multi-quantum transitions take place and vector analysis can no longer provide an adequate description.

09-2D NMR: Multiquantum Transitions (Dayrit)

COSY spectrum

(from: Jacobsen, NMR Spectroscopy Explained)

- F1 signal is determined by JHH

- F2 position is determined by 1H chemical shift

09-2D NMR: Multiquantum Transitions (Dayrit)

- COSY
- 1H: 90x’- t1 - 90x’-AQT(t2)
- This is the COSY90 sequence, where the second pulse is also a 90x’ pulse.
- The 1D spectrum is traced along the diagonal, where the vectors oscillate at during both t1 and t2. The diagonal comprises the self-correlation signals.

diagonal

(from: Sanders and Hunter, Modern NMR Spectroscopy

09-2D NMR: Multiquantum Transitions (Dayrit)

- COSY
- 1H: 90x’- t1 - 90x’-AQT(t2)
- The off-diagonal cross peaks reveal which spins are connected. The signals in the off-diagonal are modulated during t1 by all other spins to which it is connected by J-coupling.
- The top and bottom halves of the off-diagonal spectrum are mirror-images of each other.

Off-diagonal peaks

(from: Sanders and Hunter, Modern NMR Spectroscopy

09-2D NMR: Multiquantum Transitions (Dayrit)

(from: Jacobsen, NMR Explained

09-2D NMR: Multiquantum Transitions (Dayrit)

COSY45

1H: 90x’- t1 - 45x’-AQT(t2)

If the strength of the second pulse is decreased, the crowding along the diagonal is lessened (see expansion in next slide). Unfortunately, the decreased pulse width also decreases sensitivity. In some cases, this can lead to difficulties in identifying the multiplets. COSY60 is used as a compromise.

(from: Friebolin, Basic One-and Two-Dimensional NMR Spectroscopy

09-2D NMR: Multiquantum Transitions (Dayrit)

COSY45

1H: 90x’- t1 - 45x’-AQT(t2)

Expansion of region from 3.4 - 4.2. The signals due to H-5, 8 and 9 are weak and dispersed because they are multiplets. Because they are located around the base of a strong singlet (the methoxy ester), correlations due to these protons are difficult to see. Using COSY45, the diagonal peaks are lessened thereby increasing the chance of observing correlations of signals occurring close to the diagonal.

(from: Friebolin, Basic One-and Two-Dimensional NMR Spectroscopy

09-2D NMR: Multiquantum Transitions (Dayrit)

The Multiple Quantum Filter: MQF

- The information obtained from NMR experiments can be classified into various n-quantum transitions. The strongest signals are the allowed single quantum transitions. However, in many cases where there are strong methyl singlets, the weak methinemultiplets can be obscured.
- Multiple Quantum Filter (MQF) methods were designed to selectively filter out components of a 2-D correlation spectrum, generally the dominant single quantum transitions, in order to allow detection of the weaker non-single quantum transitions, such as, zero and double quantum transitions.
- Because singlets (non-coupled spins) only have single quantum transitions available to them, the intensities of these signals are lessened.

09-2D NMR: Multiquantum Transitions (Dayrit)

- Double Quantum Filtration: DQF-COSY
- Double quantum transitions are available to two-spin H systems such as geminal (-CH2-) and vicinal (-CH-CH-) groups. (DQF is also available in groups with higher spin numbers, eg, -CH-CH2-, along with higher quantum transitions.) DQF-COSY is widely used because it uses only 90° phase shifts which minimize complications:
- 1H: 90x’- t1 - 901 - - 902 -AQTR (t2)
- DQF-COSY uses phase cycling of the second and third pulse and the detector during acquisition.
- The fixed delay, , is inserted only to allow the spectrometer to execute the phase shift.

09-2D NMR: Multiquantum Transitions (Dayrit)

Double Quantum Filtration: DQF-COSY

1H: 90x’- t1 - 901 - - 902 -AQTR (t2)

Phase cycling involves a number of repeats of the pulse sequence, usually 4 or 16, where the phase angle of certain pulses and the detector are varied systematically. The set of acquisitions are added and the resulting FID represents one t1 increment.

Four and sixteen step phase cycling schemes are available for DQF-COSY. The 4 step DQF-COSY is as follows:

step: 1 2 3 4

10 0 0 0

20 1 2 3

R0 3 2 1

09-2D NMR: Multiquantum Transitions (Dayrit)

1-D nOe_dif

NOE refers to direct internuclear interaction (through-space) and is an example of dipolar coupling. The 1-D 1H NOE experiment (noe_dif) involves the subtraction of two FIDs wherein the irradiation position is manually set, first on a empty portion of the spectrum (control), and next on a selected nucleus.

1H obs: 90x’ – AQT1 – PD – 90x’ – AQT2 – PD – (repeat)

1H irr: . . . . . . . . . . . . . . . IRR1 . . . . . . . . . . . . . . . . IRR2 . . (repeat)

1H obs: 90x’ – AQT1 – PD – 90x’ – AQT2 – PD

1H irr: . . . . . . . . . . . . . . IRR1 . . . . . . . . . . . . . .IRR2

IRR1 and IRR2 are set alternately on a blank portion of the spectrum, and on the nucleus of interest.

a) 1H NMR spectrum, expansion of 2.3 - 2.6.

b) Irradiation of H-4 leads to an enhancement of the multiplet at ~2.37. This identifies it as H-6 (equatorial).

c) Irradiation of H-19 (axial CH3) leads to an enhancement of the multiplet at 2.47. This identifies it as H-6 (axial).

09-2D NMR: Multiquantum Transitions (Dayrit)

2-D NOE: NOESY

In 2-D NOESY, homonuclear dipolar coupling is selected by the variable interval t1. Since NOEis a time-dependent phenomenon, only those vectors which are properly oriented longitudinally along the ±z-axis during the incremented value of t1 experience dipolar coupling. m is a fixed mixing time during which NOEs are allowed to develop. The third 90°x’ pulse again records only the x’-component of the vector.

90°x’ – t1– 90°x’ – m – 90x’ – AQT(t2) – PD (PD=5 x T1)

09-2D NMR: Multiquantum Transitions (Dayrit)

(from: Neuhaus and Williamson, The Nuclear Overhauser Effect in Conformational and Structural Analysis)

2-D NOE: NOESY

90°x’ - t1- 90°x’ - m - 90x’ - AQT(t2)

Schematic representation of the NOESY experiment for a one-line spectrum. The first 90° pulse is followed by a time t1, which is incremented by regular steps from zero to t1max. This is followed by a second 90° pulse, a mixing time m, and a third 90° pulse, after which the FID is collected (AQT, t2).

09-2D NMR: Multiquantum Transitions (Dayrit)

2-D NOE: NOESY

90°x’ - t1- 90°x’ - m - 90x’ - AQT(t2)

The intensity of each FID is a function of t1. The experiment results in a matrix of points S(t1, t2), in which the intensity varies as cosine function of t1 and t2. The first FT (with respect to t2) turns this into matrix S(t1, F2) (the interferogram), which is an array of 1D spectra in which the line intensity varies as a function of t1. The second FT (with respect to t1) creates the final 2D spectrum S(F1, F2).

09-2D NMR: Multiquantum Transitions (Dayrit)

Inverse (H,C)-Correlation

The sensitivity of the NMR technique depends on the magnetogyric ratio of the nucleus being acquired. For this reason, experiments which acquire 13C are insensitive and time-consuming. We can get around this problem by detecting the 1H signal instead, the more sensitive nucleus.

2-D heteronuclear correlation experiments which acquire 1H are called “inverse detection” experiments.

The inverse-detecting NMR experiment, which is the counterpart of HETCOR (for directly bonded C-H), is called Heteronuclear Multiquantum Correlation (HMQC).

09-2D NMR: Multiquantum Transitions (Dayrit)

Inverse (H,C)-Correlation

The basic HMQC pulse sequence (with phase cycling) is:

1H: 90x’ - 180°2 - AQT(t2)

13C: - 2 - 90 - t1 - 90° - 2 - BB

An elaborated HMQC pulse sequence is:

1H: 90x’ - - 180x’ - - 90y’ - t1/2 - 180y’ - t1/2 - 90x’ - - 180°x’ - - AQT(t2)

13C: - 180x’ - - 90x’ - t1 - 90x’ - - 180°x’ - - BB

where: = 1/(4 1JCH) = 1.7 ms

09-2D NMR: Multiquantum Transitions (Dayrit)

- HMQC
- 1H: 90x’ - - 180x’ - - 90y’ - t1/2 - 180y’ - t1/2 - 90x’ - - 180°x’ - - AQT(t2)
- 13C: - 180x’ - - 90x’ - t1 - 90x’ - - 180°x’ - - BB
- preparation / refocusing | evolution | mixing / refocusing |detection
- The HMQC experiment can be described as follows:
- INEPT sub-sequence: The preparatory period starts with a 1H 90°x’ and refocusing sequence. The simultaneous 90° pulses allows the transfer of information from 1H to 13C of vectors in the x’, y’ transverse plane (via the 1H component M cos .
- Recall the INEPT sequence:
- 1H: 90x’ - - 180y’ - - 90y’ . . . . . . .
- 13C: . . . . . . . . . 180 - - 90x’ - AQT
- Polarization transfer takes place in INEPT and the preparation phase in HMQC.

Polarization transfer

09-2D NMR: Multiquantum Transitions (Dayrit)

- HMQC
- 1H: 90x’ - - 180x’ - - 90y’ - t1/2 - 180y’ - t1/2 - 90x’ - - 180°x’ - - AQT(t2)
- 13C: - 180x’ - - 90x’ - t1 - 90x’ - - 180°x’ - - BB
- preparation / refocusing | evolution | mixing / refocusing |detection
- During the evolution time, the magnetization is allowed develop among the 13C spins.
- Reverse INEPT sub-sequence: During the mixing / refocusing time, the polarization information is returned to 1H for detection. {BB 13C} removes heteronuclear coupling so that the 1H signals are singlets.
- Recall the Reverse INEPT pulse sequence:
- 1H: . . . . . . . . . 180x’ - - 90y’ - - 180x’ - - AQT
- 13C: 90x’ - - 180x’ - - 90y’ - - 180x’ - - BB
- [ reverse INEPT ] - [ spin echo ]

Polarization transfer

09-2D NMR: Multiquantum Transitions (Dayrit)

- HMQC
- 1H: 90x’ - - 180x’ - - 90y’ - t1/2 - 180y’ - t1/2 - 90x’ - - 180°x’ - - AQT(t2)
- 13C: - 180x’ - - 90x’ - t1 - 90x’ - - 180°x’ - - BB
- preparation / refocusing | evolution | mixing / refocusing |detection
- Therefore, one can HMQC as a combination pulse sequence using the following building blocks:
- INEPT - evolution (t1) - reverse INEPT - acquisition (t2)
- HMQC filters out the signals from single quantum1H transitions (which is actually the 1H spectrum!), and detects only the multiple quantum transitions (simultaneous 1H-13C transition).
- HMQC gives information on directly bonded C-H groups.

Polarization transfer

Polarization transfer

09-2D NMR: Multiquantum Transitions (Dayrit)

HMQC

Sample: neuraminic acid derivative, 9.6 mg in D2O, 5 mm sample tube.

No. of scans: 4

Column points: 512 (in 38 s increments)

Data points: 4k

Total time: 1 h

(from: Friebolin, Basic One-and Two-Dimensional NMR Spectroscopy

09-2D NMR: Multiquantum Transitions (Dayrit)

- HMBC
- The “inverse-detection” equivalent of long-range heteronuclear correlation (COLOC) is known as Heteronuclear Multibond Correlation (HMBC).
- 1H: 90x’ - 1 - 2 - t1/2 - 180°y’ - t1/2 - AQT (t2)
- 13C: 1 - 180 - 2 - 90 - t1 - 90x’
- where: 1 = 1/(2 1JCH) and 2 = 1/(2 nJCH), where n = 2 - 4.
- The HMBC experiment can establish correlations between 1H and 13C nuclei via long range couplings (from nJCH where n= 2-4).

09-2D NMR: Multiquantum Transitions (Dayrit)

HMBC

1H: 90x’ - 1 - 2 - t1/2 - 180°y’ - t1/2 - AQT (t2)

13C: 1 - 180 - 2 - 90 - t1 - 90x’

preparation | evolution | detection

where: 1 = 1/(2 1JCH) and 2 = 1/(2 nJCH)

- However to detect the long-range nJCH couplings, the stronger signals from 1JCH couplings have to be eliminated. This is accomplished by the first stage of the sequence which uses a fixed waiting time, 1 = 1/(2 1JCH), as a filter. The second part, where 2 = 1/(2 nJCH), selects the antiparallel 13C vectors to transfer polarization to 1H. This polarization is allowed to evolve during t1.
- HMBC is a filter for multiquantum1H-13C transitions.

09-2D NMR: Multiquantum Transitions (Dayrit)

- HMBC
- 1H: 90x’ - 1 - 2 - t1/2 - 180°y’ - t1/2 - AQT (t2)
- 13C: 1 - 180 - 2 - 90 - t1 - 90x’
- where: 1 = 1/(2 1JCH) and 2 = 1/(2 nJCH)
- It should be noted that because the HMBC sequence takes a relatively long duration relative to the 1H T1, it loses 1H magnetization along the way. For example, to take some typical values:
- for 1JCH = 145 Hz, 1 = 3.4 ms nJCH = 4 Hz, 2 = 125 ms
- Thus, the total duration of a single HMBC sequence can reach approx.: (3.4 ms + 125 ms + 20 ms) ~ 150 ms before acquisition. Because of the duration of 2, the insertion of an additional 13C refocusing sequence (2-180°- 2) at the end of which BB{13C} cannot be implemented, as in the case of HMQC (a mixing time), because of signal die-off.

09-2D NMR: Multiquantum Transitions (Dayrit)

- Pulse sequences as building blocks
- As already mentioned earlier, pulse sequences can be put together like building blocks to create new NMR experiments which can reveal various internuclear interactions. Some examples:
- Spin-echo as refocusing sequence
- J-modulation to select correlation signal
- Antiparallel vector arrangement for polarization transfer
- HMQC: built from INEPT and reverse INEPT
- The difficulties usually faced are weak signals and hardware limitations.

09-2D NMR: Multiquantum Transitions (Dayrit)

Pulse sequences as building blocks

Other combinations have been created, such as COSY + NOESY (CONOESY):

90x’- t1 - 90x’-AQT1(t2) - tm - 90x’-AQT2

| cosy | noesy |

fixed nOe mixing time, tm = 0.1 - 0.5 s

AQT1 gives COSY FIDs, and AQT2 gives NOESY FIDs; the two sets are stored separately.

09-2D NMR: Multiquantum Transitions (Dayrit)

- NMR pulse sequences in retrospect
- Over the last 40 years, NMR has moved from a specialist area in physics to a technique of wide utility spanning chemistry, biology, medicine, and engineering. Much of this is due to the development of multipulse sequences for routine 1- and 2-dimensional NMR experiments. This has elevated NMR to the status of the most powerful spectroscopic methods.
- There are several special interest applications of NMR:
- Organic spectroscopy, natural products chemistry
- Quantitative NMR
- Structural and functional biology; proteomics
- Solid-state NMR, materials science
- NMR of other elements; inorganic applications
- Imaging: MRI, fMRI

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