Pulse Sequence Tools:
Pulse Tool

• Pulse Phase and pulse power
• Phase cycling in 1D and 2D NMR
• Composite Pulse
• BB decoupling
• Selective Pulses
• DANTE Pulse
• Pulse Shaping
• Shifted Laminar Pulse

Pulse Phase and pulse power

When a Pulse is applied the magnetization precess around the pulse axis.
The pulses are usually applied along one of the Cartesian axis (X, Y, -X, -Y).
You can experiment with the phase of a 90 degree pulse and their effect on Z magnetization in the following animation.

The speed of the precession (frequency) depends on the power {gamma*B1} of the applied pulse.
The nutation angle depends on the power of the applied pulse and on the pulse duration (PW = Pulse Width)

When two pulses are applied back-to-back, depending on the phase of the 2 pulses, a 180 Degree or a 0 Degree pulse can result!

This tool is used in the HMQC pulse sequence to apply refocusing (180 deg.) and no refocusing (0 deg.) to heteronuclear coupling on alternate scans. This is demonstrated in the animation: and in the spin echo difference chapter

Phase cycling in 1D and 2D NMR

Phase cycling is describe in more details in it's own section of the pulse sequence tools. Applying pulses along various axis, during a pulse sequence can be used to cancel artefacts. Artefacts can come from different sources:

• Imbalance in the spectrometer hardware
• Coherent noise
• Artefacts generated by a multipulse experiment

These unwanted signals might have a different phase behavior than the real NMR signal. Therefore, by alternating the phase of the pulse and adding or subtracting the NMR signal in the receiver it is possible to cancel these artefacts. One of the first phase cycle that have been proposed is called PAPS (Phase Alternating Pulse Sequence). It consists of pulsing along the X axis during the first transient (generating +My magnetization), and on the next transient, to pulse along the -X axis (generating M-y magnetization). By subtracting the NMR signal obtained during the second experiment from the one obtained on the first transient, one cancels the artefacts that appear along the +Y axis during both transients.
When Quadrature detection is used to acquire the NMR data, CYCLOPS (Cyclically Ordered Phase Sequence) is used to also cancel artefacts generated by imbalances between the X and Y channels. For more details on PAPS or on CYCLOPS consult the animation on Phase cycle in 1D NMR . (See also the Phase cycling chapter)

In Multidimensional NMR, the phase cycling can serve the purpose of labeling the frequency of the indirectly detected domain. To get more information concerning that aspect of phase cycling, you can view the animation on the Phase Cycle in 2D NMR (COSY) . (See also the 2D Phase cycling chapter)

Composite Pulse

The precision of the pulses insures that the various pulse sequences work properly. A square pulse applied with relatively large power will irradiate a wide bandwidth in the frequency domain. The shape of the bandwidth is unfortunately a SINC function. This means that the pulse might be accurate in the center of the bandwidth but not on the edge of a large spectral width. At large offset, the pulse will lack accuracy creating artefacts. Other sources of inaccuracy of the pulses is: r.f. field inhomogeneity and small errors in the timing of the pulse.

Many composite pulse schemes have been proposed to obtain more accurate pulses. a few of them are presented in the table below:

The following animation will give you an idea on how the 90x-180y-90x : 180 Deg. composite pulses do work.

Composite pulse in broadband decoupling

One of the tool that is needed in many pulse sequences, is the ability to decouple many nuclei at the same time (broadband decoupling -BB). In order to irradiate larger window one needs of course higher power. Unfortunately, high power decoupling produce some heat specially in samples containing salt (like biological samples).

An efficient way to achieve BB decoupling depends on the fact that it is possible to refocus heteronuclear coupling (decoupling) by applying an inversion pulse to the nuclei we want to decouple. The inversion pulse must be repeated in a sequence for as long as the decoupling is required. For this technique to work, very accurate 180 degree pulses (respecting the requirement of low power!) are required. Inversion composite pulses used in cyclic sequences are very efficient in decoupling schemes (MLEV-16, WALTZ-4, WALTZ-16 ...). If the letter R represent a composite pulse and R' (R with a bar above in the literature) represents the same inversion sequence in which all the pulses are applied with a 180 degree phase shift, composite inversion cycle containing 4 composite pulses can be written. For example the MLEV-16, composed of 16 composite pulses (4 cycles) with phase permutation, can be represented as:

The more efficient inversion pulse (better offset compensation) used in the WALTZ decoupling can be written as :

WALTZ-4 can be obtain by permuting the phases of the inversion composite pulse as indicated here: RRR'R' in obvious notation, this sequence can be written as: 12'3 | 12'3 | 1'23' | 1'23'. If we combine the contiguous pulses that have the same phase we can write that the WALTZ-4 is constituted of the following pulses: 12'42'3 | 1'24'23'. With more phase permutation one can obtain WALTZ-16 (composed of 16 composite pulses permuted in phase) which is one of the most efficient decoupling sequence.

Selective Pulses

The pulse tool box would be incomplete without special pulses to suppress unwanted signal or to selectively excite a region in the spectra.

DANTE Pulse (Delays Alternating with Nutation for Tailored Excitation)

This pulse sequence distributes the power over a series of excitation bands by applying a series of short pulses separated with delay. The idea behind DANTE is to apply a small angle pulse and then wait for a small delay during which magnetization evolve according to chemical shift and coupling constant. By applying a second small pulse after the delay, constructive effect will be observed only on the magnetization that is properly lined up (e.g. My magnetization). This pulse train can be applied "On-Resonance" or "Off-Resonance", with fixed pulse phase (e.g. along X axis) or with Quadrature phase cycling. These are describe briefly below and can be viewed in the following animation.

• In the DANTE sequence, the pulse train can be applied "On-Resonance" such that the peak at the carrier offset will be submitted to constructive pulse (as it remain lined up along the Y-axis during the delay). During the delay (tau) that is inserted between the pulses, the magnetization will evolve according to it's frequency respect to the carrier offset. The peaks that precess at the frequency of [F=1/tau] covers a distance represented by the full circle and finds it self lined also along the Y axis and is also submitted to a constructive pulse. The "On-Resonance" will excite peaks located at .... -2F, -F, 0, +F, +2F, ....
• The DANTE sequence can also be applied "Off-Resonance" with a careful adjustment of the delay such that the peak of interest revolve by 360 degree during the delay [Delay = 1/Freq.] and find itself lined up on the Y-axis, ready for the next pulse. This "Off-Resonance" DANTE pulse train will also excite peaks located at .... -2F, -F, 0, +F, +2F, ....
• The DANTE with Quadrature Selective Excitation (QSEX) can also be used to reduce the number of excitation bands. In this technique, a series of n short pulses separated by short delays is applied by varying the phase of the pulses such that the phase cycle follows the the magnetization (for example: +X, -Y, -X, +Y). Only the peak that precess by 90 degree during the delay [F=1/(4*tau)] will experience constructive pulse. This pulse train will excite peaks located at ....-7F, -3F, F, +5F ...

A spectacular use of the DANTE pulse train mixed with pulse shaping and pulse phase variation can be found under the heading "SLP" in the pulse shaping section.

Pulse Shaping

• In rectangular pulses, the power is maintained at its maximum over the full pulse width.
• In shaped pulse, the maximum power is reached temporarily. The "filling factor" is therefore smaller than a rectangular pulse. (For example, the Gaussian pulse have a filling factor of 40%).
• For example, if we compare the rectangular pulse and the gaussian pulse at a fixed power level (63 dB) we can obtain the following characteristics:

	Rectangular	Gaussian
PW90 (us)	10	25 (2.5 times longer)
Power (kHz) (1/PW360)	25 kHz
Bandwidth	140 kHz	110 kHz

• From the above table one can conclude that to excite a bandwidth of 120 Hz, using the gaussian shape one would need to adjust the power such that a 90 degree pulse have a duration of 25 ms.
• The excited bandwidth depends on the shape and on the pulse length.

Selective Pulse (bandwidth of 10-50 Hz => pulse duration of 20-100 ms)

Mainly used in 1D version of the 2D sequences

• 1D-COSY
• 1D-TOCSY
• 1D-NOESY
• 1D-ROESY

Used also to obtain "soft" 2D and "soft" 3D experiments to achieve higher resolution by using smaller window

Semi-selective Pulse (bandwidth of 100-2000 Hz => pulse duration of 500us to 10 ms)

Used mainly in 2D and 3D NMR to narrow the spectral window to a portion of the spectra without "fold-over" from the other region.

A few shaped pulses are presented below.

Gaussian:

• The Gaussian shape is characterized by a Gaussian envelope in the frequency domain (ideal for selective NMR)
• It provides good selectivity on lengthening the pulse.
• Drawback: magnetization do not end up in phase.

Half-Gaussian:

• Properties similar to the Gaussian pulse but produce in-phase magnetization

Tophat

• good 90 degree pulse.
• Flat excitation profile: can be use in selective and in semi-selective experiments

Hyperbolic Secant

• Best 180 degree inversion pulse
• Flat excitation profile: can be used in selective and in semi-selective experiments
• Very easy to use as for a relatively wide range of power levels an exact 180 degree pulse can be achieved.
• Only the pulse duration do control the selectivity

SLP - Shifted Laminar Pulse

• In fact this is a DANTE pulse train without any delay. It can be used with any pulse shape.
• Any of the above pulse shape are generated by applying a series of very short pulses of different amplitude such that a specific shape is generated. The phase of the individual short pulses can also be varied.
• During the pulse duration (each individual units that makes up the shape) it is possible to calculate to precession of the peak we want to selectively excite and vary the phase of the pulse to "follow" that magnetization.
• In fact, it is possible to "follow" as many peaks as we want by calculating the phase of the overall magnetization.
• This technique is able to excite several off-resonance signals