Comparison of Broadband Decoupling Schemes

Many NMR measurements such as HSQC or HMQC rely on broadband X nucleus decoupling (X = ¹³C, ¹⁵N, ³¹P .... etc.)..  Broadband decoupling schemes, using conventional rectangular pulses (e.g GARP) require fairly high power levels leading to undesired sample heating.  They are also limited in their effective decoupling bandwidth.  Adiabatic decoupling schemes use shaped adiabatic pulses and have become more and more common over the last couple of decades due, in large part, to the flexibility of modern NMR instruments to generate shaped pulses.  Adiabatic decoupling schemes (e.g. WURST) use much less power than those using conventional rectangular pulses. thereby reducing or eliminating problems associated with sample heating.  Due to the lower power requirements and increased effectiveness over wider frequency ranges, adiabatic decoupling schemes are ideally suited for X nucleus decoupling at higher field strengths. The figure below shows 500 MHz ¹H [³¹P] NMR spectra measured with inverse gated decoupling for the P-CH₃ methyl resonance of dimethyl methylphosphonate  The single scan spectra were collected in a pseudo-2D fashion, as a function of the decoupler offset frequency from -256 ppm to +256 ppm from the ³¹P resonance frequency in 1 ppm steps.  The acquisition time and recycle time for each FID were 2 sec and 4 sec, respectively.   In the left-hand panel, broadband GARP decoupling was employed at a power of 1.22 W  (60 µsec 90° pulses).  In the right-hand panel, WURST decoupling was used at a peak power of 0.755 W (2 ms WURST pulses, bandwidth = 250 ppm).

Clearly, the data collected with WURST decoupling, at lower power, have a much larger decoupling range (250 ppm) compared to the data collected with GARP decoupling (98 ppm).  Furthermore, while the GARP data were collected, the sample temperature increased and had to be compensated for by the variable temperature unit.  No such temperature increase was observed while collecting  the WURST data.  It is also interesting to note that, in the case of GARP decoupling, distorted line shapes are observed just outside of the decoupling range, while for WURST decoupling, the spectra are fully coupled just outside of the decoupling range with a very sharp transition between being fully coupled and fully decoupled.  For broadband decoupling, WURST is best!   

Shaped Pulses

Shaped rf pulses are used frequently in modern NMR experiments for selective excitation and more efficient inversion. The figure below shows some of the pulse shapes in the Bruker shape library measured with an oscilloscope on an AVANCE III console. Each 50.3 MHz rf pulse was 1 msec in duration and was measured at the output of the signal generation unit.

Excitation Profiles for Shaped Pulses

Shaped pulses are very commonly used for selective excitation and nonselective inversion in a large number of NMR pulse sequences. The frequency domain excitation profile of a radio frequency pulse is the Fourier transform of the time dependent pulse shape and determines the width, uniformity and phase of the frequency spectrum excited. Since time and frequency are reciprocals of one another, short rf pulses have very wide excitation profiles and long rf pulses have very narrow selective excitation profiles. In a previous BLOG post the excitation profiles of rectangular pulses of varying duration were determined experimentally. The Fourier transform of a rectangular pulse is a sinc function which is observed to be the experimentally determined excitation profile. Short high power rectangular pulses are very desirable for uniform excitation over wide frequency ranges as the entire NMR spectrum of interest usually occupies only a very small central portion of the central lobe of the sinc shaped excitation profile which, to a first approximation, is flat over the observed spectral width. Rectangular pulses are often not desirable when narrow excitation profiles are required as the excitation is not uniform over the desired region and the ripples of the sinc excitation profile cause nodes of excitation and negative peaks.

The Fourier transform of a sinc function is a box function, so if a long low power sinc shaped rf pulse is used one obtains a narrow flat box shaped excitation profile. This is indeed the case as can be seen in the bottom trace of the figure below. The trace is composed of a series of ¹H NMR spectra of H₂O/D₂O where a truncated, 200 msec, 10 cycle sinc shaped monochromatic rf pulse was applied with varying rf frequency offsets. One can see that the excitation profile is, to a good approximation, a narrow flat box function. The deviation from a flat box function is the result of the truncation of the sinc pulse. It should be noted that the phase of the resonances is not constant across the excitation profile. Sinc pulses are not frequently used for selective excitation because of the phase problem and the fact that very long, minimally truncated pulses must be used. A frequently used alternative to the sinc pulse for selective excitation is the Gaussian shaped pulse. The Fourier transform of a Gaussian is a Gaussian and one therefore will obtain a narrow Gaussian shaped excitation profile when a long low power Gaussian shaped pulse is used. This is shown in the top trace of the figure below. This trace is similar to the bottom trace except a 20 msec Gaussian shaped pulse (with truncation at 1 % of the total height) was used rather than a 200 msec sinc pulse. Although the excitation is not flat, the phase is constant across the excitation profile and the total duration of the pulse is 10 times shorter than the sinc pulse.

Better 180 Degree Pulses

Many pulse sequences use 180 degree pulses. Standard hard pulses are not perfect at inverting all of the lines in a spectrum with a wide spectra width. In such cases a better choice may be a shaped adiabatic pulse. A comparison is shown below for the ¹³C spectrum of ethyl acetate. Each spectrum was acquired with the same number of scans. The trace on the left was acquired with a hard 180 degree pulse and the spectrum on the right was acquired with the CRP60comp.4 pulse from the Bruker pulse shape library. Note the better performance resulting in improved nulls.

Shaped Pulses for Selective Excitation

Short rectangular pulses have broad excitation profiles (see BLOG entry for November 20, 2007) and are used for non-selective uniform excitation. These are often called "hard" pulses. Longer low power shaped pulses are used to excite specific spectral regions for selective excitation. An example of this is shown below.These are often called "soft" pulses.