Valentin Ananikov
Ultrabroadband Heteronuclear Decoupling Methods


    Contents


Introduction: Where did the problem come from?

    Broadband decoupling is one of the most used NMR techniques. The problem of effective decoupling is of grate importance today mainly due to continuous increasing of working frequency of the modern spectrometers. Removing spin-spin couplings at high-fields requires more power since a frequency bandwidth of decoupling region is also increasing. Power dissipation in a sample volume causes perceptible overheating and temperature gradients leading, therefore, to significant losses of the spectra quality.
     Next, some difficulties may arise in the case of inverse spectroscopy when 1H{X} decoupling should be applied to the low-g nuclei. Decoupling field strength is defined as gB2, therefore, it is not possible to achieve high field strength without sample heating.
     Another challenging task is an universal experiment for decoupling of high-frequency nuclei with large chemical shift range. For example, 1H{19F} experiment on the 500 MHz spectrometer would require decoupling of the 150 KHz region.
     In this article a short comparative study of modern decoupling methods including some experimental notes will be given. A special attention will paid to shaped pulses based decoupling sequences which allow >0.5 MHz decoupling bandwidth on the routine hardware.



Hard Pulses Decoupling
 Basic Principles

    According to the literarure [1-4] complete decoupling is the condition of reducing of all splittings to zero (or at least make them smaller than the linewidth). The simplest decoupling sequence consists on a series of 180o pulses separated with the delays of the equal length, i.e. for the 13C{1H} experiment:

1H  p   - t - p - t -p - t -p - t- p - t - p - t - ...
13C   p/2   - F - - -F - - -F - - -F - - -F - - -F - ...

where, F is getting one FID point

    Each p pulse changes the direction of the multiplet components precession and in the middle of the delay (t) the components lie along the same axis. The spectrum obtained in this way does not contain any 13C-1H spin-spin couplings.
     On the other hand, if the lifetime tx of the X nucleus in its spin states is shorter compared to 1/JAX, the condition of spin-spin coupling is not met anymore and no coupling is observed. So, if

tx < 1/JAX,

inversion pulses should not be necessarily synchronized with FID sampling.



Hard Pulses Decoupling
 An Overview

     According to the information given in the previous section the main limiting factor for broadband decoupling is the quality of spin inversion. The better the accuracy of the inversion the wider the decoupling region size. It is well known that a single 1800 pulse is very sensitive to the various imperfections, particularly, the degree of spin inversion is strongly dependent on the offset position. Fig.1 represents offset dependence for the single 1800 pulse (see experimental section for calculation details).
180 deg hard pulse. Offset dependence
Fig.1. The time evolution of a nuclear magnetization vector during a series of 1800 pulses with different offset positions.

    Obviously, no decoupling of a reasonable size region may be performed if this type of inversion being used.
     A principal progress in the broadband decoupling was achieved only after introducing composite pulses technique. A composite pulse is a small number of r.f. pulses which has built-in mechanism for errors compensation. On the next step composite pulses are usually grouped into a cycle or supercycle to eliminate residual imperfections. Nowadays all hard-pulses based decoupling methods are realized by the way of multistep continuos pulse trains containing composite pulses as an elementary step. Short description of the most popular methods is given below.

MLEV-16 was the first multipulse decoupling sequence that has accorded wide recognition. It makes use of 90x180y90x composite pulse united into the 16 step cycle:

MLEV-16 = RRRR RRRR RRRR RRRR, MLEV-4 = RRRR
where R=90x180y90x and R=90-x180-y90-x

The inversion properties of the composite pulse are significantly better compared to the simple p pulse as shown on Fig.2. In practice MLEV-16 decoupling may be used if decoupling bandwidth does not exceed 10 KHz, a typical decoupling profile is shown on Fig.3.

MLEV composite pulse. Offset dependence
Fig.2. The time evolution of a nuclear magnetization vector during a series of 90x180y90x composite pulses with different offset positions.


MLEV-16 Decoupling Profile
Fig.3. MLEV-16 Decoupling Profile; bandwidth 7 KHz, step 1 KHz.


WALTZ-16 was the next important advance in the history of decoupling. The performance of the MLEV-16 pulse sequence is very sensitive to small errors in the 90o phase shift required for the implementation of the composite pulse. When accurate 90o phase shift in the decoupler channel was a problem on the former generation of NMR instruments it was clear that a pulse train with 180o phase shifts could improve the performance of the whole sequence. Such a composite pulse is known as WALTZ: 90x180-x270x. The inversion characteristics of the WALTZ composite pulse are presented on Fig.4 and corresponding decoupling profile for the 16-step supercylce is shown on Fig.5. Due to relative insensitivity to phase errors produced in the decoupler channel and very small residual couplings WALTZ-16 became a standard for 13C{1H} experiments.

WALTZ composite pulse. Offset dependence
Fig.4. The time evolution of a nuclear magnetization vector during a series of 90x180-x270x composite pulses with different offset positions.


WALTZ-16 Decoupling Profile
Fig.5. WALTZ-16 Decoupling Profile; bandwidth 8 KHz, step 1 KHz.


GARP-1 is one of the first methods that makes use of a composite pulse which has been derived from the numerical optimization procedure. The difference may be understood looking to the text of the decoupling programs (native AVANCE syntax: pcpd - the length of the 90o decoupling pulse, after a star mark - the multiplier, and a colon followed by the decoupler phase value):

;AVANCE DRX500 spectrometer, decoupling programs
;
;MLEV-16              ;WALTZ-16          ;GARP-1
pcpd  :0              pcpd*3:180         pcpd*0.339:0
pcpd*2:90             pcpd*4:0           pcpd*0.613:180
pcpd*2:0              pcpd*2:180         pcpd*2.864:0
pcpd*2:90             pcpd*3:0           pcpd*2.981:180
pcpd  :0              pcpd  :180         pcpd*0.770:0
pcpd  :180            pcpd*2:0           pcpd*0.691:180
pcpd*2:270            pcpd*4:180         pcpd*0.944:0
....                  ....               ....

    In principle, using fractional multipliers one can describe a composite pulse more precisely obtaining improved inversion properties. It is the GARP pulse united to the 4-step RRRR supercycle that made it possible twofold bandwidth gaining and more uniform decoupling profile (Fig.6). The time evolution of a nuclear magnetization vector during the GARP composite pulse is shown here, however, hardly probable the trajectory of the computer optimized composite pulse may give any visual information.

GARP-1 Decoupling Profile
Fig.6. GARP-1 Decoupling Profile; bandwidth 18 KHz, step 1 KHz.


DIPSI decoupling is an another example of the application of straightforward computational approach to the pulse shape designing problem. It has been shown that proton-proton couplings, if they are not first order, could be a limiting factor for obtaining narrow lines in 13C spectra. In some strongly-coupled homonuclear systems WALTZ or MLEV may produce residual splitting even with high decoupler power used. The DIPSI sequences resulted from the optimization procedure taking homonuclear spin-spin interactions into account.

DIPSI-2=RRRR,
where R=320X 410-X 290X 285-X 30X 245-X 275X 265-X 370-X
While the bandwidth is less than in the sequences described above the resolution and sensitivity is better if homonuclear coupling is the major limiting factor.



Hard Pulses Decoupling
 Performance Comparison

    Two most important parameters describing any decoupling method are residual splitting and figure of merit. Residual splitting sets a lower limit for the linewidth in decoupled spectrum and the parameter can be used to estimate relative sensitivity of different decoupling schemes. The figure of merit[3] is given as:
X=2p DB/ gB2
where DB - effective decoupling bandwidth, and gB2/2p - equivalent constant decoupling field strength at the same level of power dissipation in the sample volume.
    The higher the figure of merit the lower the power is needed to decouple all the spins within the given bandwidth. The parameter is of principal importance for broadband applications and various decoupling methods may be discriminated based on the X value. Table 1 contains the information about the decoupling sequences described in the previous section of the article[3,4]. It confirms the conclusions outlined earlier: GARP-1 has the largest bandwidth, however, WALTZ-16 and DIPSI-2 sequences produce the smallest residual splittings.


Table 1. Performance comparison of different decoupling methods
method residual splitting for J=150 Hz figure of merit
MLEV-16 0.6 Hz 1.5
WALTZ-16 < 0.1 Hz 1.8
GARP-1 0.3 Hz 4.8
DIPSI-2 < 0.1 Hz 1.2



Shaped Pulses Decoupling
 Wideband Spin Inversion

    Changing the properties of a composite inversion pulse is the most common way of developing new decoupling pulse trains, since the rest part remains essentially the same as in the MLEV cycle. A composite pulse may be depicted in two ways: either with delays between the individual components or as a single continuos pulse with different phases. For example both representations of the MLEV composite pulse are shown on Fig.7.

Composite pulse representations

Fig.7. Two different representations of the 90X180Y90X composite pulse.

    However, it is well known that "phase switching delay" should be kept as short as possible: the shorter the delay the better the performance of the composite pulse. In principle composite pulse with "infinite performance" could be created based on the smoothed phase modulation of the r.f. output. The method can be implemented on practice using CHIRP or WURST shaped pulses, that have been optimized for wideband spin inversion (Fig.8).

Smoothed CHIRP pulse

Fig.8. Smoothed CHIRP Shaped Pulse, amplitude(left) and phase(right).

    Probably, this is the most promising approach to broadband decoupling since not only the magnetization vector is carried from the +z axis to the -z axis, but also an adiabatic condition can be reached over a large frequency range. It would be beyond the scope of this article to describe the theory of adiabatic pulses in details, the interested reader is referred to the literature references[3,17-21]. For our purpose it is sufficient to know that the adiabatic condition is satisfied when the magnetization vector is "locked" along the effective field during the entire inversion process, leading to the very efficient use of the available radiofrequency power. Fig.9 and Fig.10 proof almost perfect inversion properties of the adiabatic Smoothed CHIRP pulse.

Smoothed CHIRP pulse. Offset dependence

Fig.9. The time evolution of a nuclear magnetization vector during a series of Smoothed CHIRP pulses with different offset positions.

Smoothed CHIRP pulse. Offset dependence

Fig.10. The time evolution of a nuclear magnetization vector during a series of Smoothed CHIRP pulses with different offset positions (bottom view, i.e. from the -z axis).



Shaped Pulses Decoupling
 Ultrabroadband Decoupling

    Adiabatic spin inversion would allow a decoupling sequence with unusually high figure of merit, indeed, it is. The most popular adiabatic decoupling passage consists on the MLEV-4 element nested within the (0, 150, 60, 150, 0) phase cycle[5]:

CHIRP/WURST=RRRR, R=SP0 SP150 SP60 SP150 SP0,
where SP is corresponding shaped pulse

    A typical decoupling profile at the standard hardware setup for 1H observe heteronuclear decoupling experiment is shown on Fig.11.

CHIRP Decoupling Profile

Fig.11. CHIRP Decoupling Profile; bandwidth 105 KHz, step 5 KHz.

    Under the optimized conditions figure of merit may be significantly enlarged up to X=50-70. Therefore a bandwidth in the range of 0.5-1 MHz is accessible on the modern routine spectrometers. As an example a 570 KHz decoupling profile is presented on Fig.12.

CHIRP Ultrabroadband Decoupling Profile

Fig.12. CHIRP Decoupling Profile; bandwidth 570 KHz, step 30 KHz.

    At this point one can conclude that the performance of the method would be quite sufficient to cover frequency range of all nuclei in any future NMR spectrometers generation even operating at 1 GHz proton frequency.
    However, by no means it indicates a stop-point in the development of new decoupling sequences. Moreover, it is one of the most interesting and promising fields of modern NMR. Decoupling region size of few MHz is expected in the nearest future.



Experimental Details

    All decoupling profiles were obtained on AVANCE DRX500 spectrometer. WALTZ-16 and MLEV-16 experiments were acquired at 13C{1H} condition, GARP and CHIRP with inverse 1H{13C} setup. Using 13C enriched CH3I sample in acetone-d6 in all cases (J(1H-13C)=150 Hz).
    The decoupling profiles shown on Fig.3 and Fig.5, as well as on Fig.6 and Fig.11 were recorded at the same decoupler power level. In the ultrabroadband experiment (Fig.12) decoupler power was increased by the factor of two.
    For WALTZ-16 decoupling a 90o proton pulse of 80-100us length is required, for GARP-1 sequence 60-70us 90o X nuclei pulse, and adiabatic CHIRP passage needs 180o pulse in the range of 500us-3ms.
    The simulation of the time evolution of a nuclear magnetization vector (Fig.1, Fig.2, Fig.4, Fig.9, Fig.10) in 3D space was made using Bloch equation inside NMR-SIM software package[22]. Offset dependencies were obtained via the series of calculations moving offset from the resonance position with constant step.



References

            General information and related articles
1. E.Derome, Modern NMR Techniques for Chemistry Research, Pergamon Press, Oxford, 1987, 280pp.
2. R.R.Ernst, G.Bodenhausen, and A.Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford, 1987, 610pp.
3. R.Freeman, Spin Choreography, Spectrum Academic Publishers, Oxford, 1996, 391pp.
4. A.J. Shaka, "Decoupling Methods", in Encyclopedia of Nuclear Magnetic Resonance, vol. 3, p.1558, (Eds.-in-Chief D.M.Grant and R.K.Harris), John Wiley & Sons, Chichester-NewYork-Brisbane-Singapore, 1996.
5. R.Tycko, A.Pines, and R.Gluckenheimer, J.Chem.Phys., 1985, 83, 2775.
            The theory of decoupling
6. J.S.Waugh, J.Magn.Reson., 1982, 50, 30.
7. D.Suter, K.V.Schenker, and A.Pines, J.Magn.Reson., 1987, 73, 90.
see also ref.[15] and ref.[3].
            Composite Pulses
8. M.H.Levitt, "Composite Pulses", in Encyclopedia of Nuclear Magnetic Resonance, vol. 2, p.1396, (Eds.-in-Chief D.M.Grant and R.K.Harris), John Wiley & Sons, Chichester-NewYork-Brisbane-Singapore, 1996.
            MLEV
9. M.H. Levitt, R.Freeman, J.Magn.Reson., 1981, 43, 502.
10. M.H. Levitt, R.Freeman, and T.Frenkiel, J.Magn.Reson., 1982, 47, 328.
11. M.H. Levitt, R.Freeman, and T.Frenkiel, J.Magn.Reson., 1982, 50, 157.
12. M.H. Levitt, R.Freeman, and T.Frenkiel, Adv.Magn.Reson., 1983, 11, 47.
            WALTZ
13. A.J. Shaka, J.Keeler, T.Frenkiel, and R.Freeman, J.Magn.Reson., 1983, 52, 335.
14. A.J. Shaka, J.Keeler, and R.Freeman, J.Magn.Reson., 1983, 53, 313.
            GARP
15. A.J.Shaka, P.B.Barker, and R.Freeman, J.Magn.Reson., 1985, 64, 574.
            DIPSI
16. A.J.Shaka, C.J.Lee, and A.Pines, J.Magn.Reson., 1988, 77, 274.
            CHIRP/WURST
17. R.Fu, G.Bodenhausen, Chem.Phys.Lett., 1995, 245, 415.
18. R.Fu, G.Bodenhausen, J.Magn.Reson. Ser.A, 1995, 117, 324.
19. E.Kupce, R.Freeman, J.Magn.Reson. Ser.A, 1995, 115, 273.
20. E.Kupce, R.Freeman, J.Magn.Reson. Ser.A, 1995, 117, 246.
21. E.Kupce, R.Freeman, J.Magn.Reson. Ser.A, 1996, 118, 299.
            Software
22. NMR-SIM version 2.6, Copyright (C) 1997 by Bruker Analytik GmbH.



The appropriate reference to this article:
Ananikov V.P., "Ultrabroadband Heteronuclear Decoupling Methods", 1998; http://nmr.ioc.ac.ru/val/shapes/c-w/c-w.htm


August 22, 1998 Copyright (C) Ananikov VP

Valentin Ananikov
NMR Group
N.D. Zelinsky Institute of Organic Chemistry
http://nmr.ioc.ac.ru/Staff/AnanikovVP/