Journal of Magnetic Resonance 239 (2014) 61–68

Contents lists available at ScienceDirect

Journal of Magnetic Resonance

journal homepage: www.elsevier .com/locate / jmr

Improved decoupling during symmetry-based C9-TOBSY sequences

1090-7807/$ - see front matter � 2013 Elsevier Inc. All rights reserved.http://dx.doi.org/10.1016/j.jmr.2013.11.017

⇑ Corresponding authors. Fax: +41 44 632 16 21 (M. Ernst).E-mail addresses: beme@ethz.ch (B.H. Meier), maer@ethz.ch (M. Ernst).

1 Current address: Bruker BioSpin AG, Industriestr. 26, 8117 Fällanden,Switzerland.

Kong Ooi Tan, Ingo Scholz, Jacco D. van Beek 1, Beat H. Meier ⇑, Matthias Ernst ⇑Physical Chemistry, ETH Zürich, Wolfgang-Pauli-Strasse 10, 8093 Zürich, Switzerland

a r t i c l e i n f o a b s t r a c t

Article history:Received 14 October 2013Revised 26 November 2013Available online 12 December 2013

Keywords:TOBSYSolid-state NMRDecouplingMagic-angle spinning

We show that heteronuclear decoupling during symmetry-based C9 TOBSY sequences can be improvedby using phase-alternating pulse sequences (XiX) instead of cw irradiation. The use of XiX sequencesmakes the optimization of the decoupling rf-field amplitude simpler and lowers the decoupling rf-fieldrequirements to attain a comparable performance. A Floquet analysis of the first-order resonance condi-tions was used to determine the correct timing of the XiX sequence to avoid interference between the Csequence and the decoupling. The decoupling performance is analyzed analytically using Floquet theoryand verified using numerical simulations as well as experimental results.

� 2013 Elsevier Inc. All rights reserved.

1. Introduction sion pulses [7,12,13]. In principle, the symmetry-based pulse se-

In solid-state NMR spectroscopy under magic-angle spinning(MAS), polarization-transfer processes can be mediated by the sca-lar J-coupling or by the anisotropic dipolar coupling. The latter oneis based on couplings which are, in proteins or organic solids, oneor two orders of magnitude stronger than the former ones but areaveraged out by MAS. To employ them, e.g., in the context ofhomonuclear correlation spectroscopy, dipolar recoupling se-quences are required [1–4]. One route to efficiently use the isotro-pic J couplings for polarization transfer in solids is the generationof an effective Hamiltonian that contains only the J-coupling inter-action by averaging dipolar and chemical-shift contributions. Thisis exploited in the through-bond correlation spectroscopy orTOBSY experiment [5–7] (see Fig. 1) which is a viable alternativeto dipolar-coupling based polarization transfer schemes [1–4] inparticular when moderate to fast MAS is applied, referring to spin-ning frequencies above 25 kHz. Since the transfer mechanism isbased on an isotropic interaction, 100% transfer efficiency is theo-retically possible in a given spin pair. In order to generate such aneffective Hamiltonian, the much larger anisotropic interactions(dipolar coupling and chemical-shielding anisotropy) have to besuppressed to a high degree while simultaneously the isotropicchemical shift has to be averaged out in full analogy to the li-quid-state TOCSY experiment [8,9]. These objectives are oftenachieved by using a symmetry-based pulse sequence [10]. Anumber of TOBSY sequences have been published using such C orR-type sequences with either hard pulses [6,11] or adiabatic inver-

quences do not need additional decoupling if the averaging ofthe heteronuclear dipolar couplings by the symmetry-based pulsesequence itself works sufficiently well [14,15]. Such an approachworks best at high spinning and high nutation frequencies. How-ever, in the regime of moderate spinning frequencies, protondecoupling during the mixing time is essential to achieve efficientpolarization transfer.

Proton decoupling during symmetry-based sequences on the Xchannel is usually achieved using cw irradiation on the protons.As a rule of thumb, it was postulated that the rf field on the protonsshould be at least three times the rf field on the X nucleus to achievegood decoupling performance [16,17]. This demand on the protonrf-field amplitude has led to the development of pulse sequenceswith lower rf-field requirements on the X nuclei [18]. An addedcomplication is the fact, that the polarization-transfer efficiencydoes not increase steadily with increasing decoupling rf field butshows strong modulations which make an experimental optimiza-tion of the decoupling field strength more demanding. The strongdependence of the transfer efficiency on the decoupling is a resultof heteronuclear recoupling through matching of the decouplingrf-field amplitude to multiples of the modulation frequency of thesymmetry-based pulse sequence and to the MAS frequency [14].Good decoupling can only be achieved by using either very highrf-field amplitudes or at intermediate rf-field amplitudes wherethe recoupling conditions are avoided. There are pulsed recouplingschemes where more complex decoupling schemes like TPPM [19]have been used during the recoupling sequence [20,21], but such anapproach has, to the best of our knowledge, not yet been reportedduring windowless pulse sequences on the X channel.

In this contribution, we analyze the heteronuclear recouplinginterference between symmetry-based C sequences and cw decou-pling in more detail using operator-based Floquet theory [22,23]

CP

CP

decoupling

nτrτmt1 t2τcp

π/2

m

π/2 π/2

τr

m

ϕ ϕ+π ϕ

90o 360o 270o

2π/9 4π/9 6π/9 8π/9 10π/9 12π/9 14π/9 16π/9ϕ=0

dec.

τzf

decoupling

Fig. 1. Pulse sequence for a two-dimensional homonuclear TOBSY correlationexperiment using a C91

n sequence for the polarization transfer and cw or XiXdecoupling during the mixing time.

62 K.O. Tan et al. / Journal of Magnetic Resonance 239 (2014) 61–68

and then generalize it to amplitude-modulated decoupling se-quences like XiX [24,25]. We show that in the case of TOBSY trans-fer mediated by C91

n sequences with simultaneous XiX decoupling,one can find interference-free windows where the heteronuclearrecoupling is avoided by setting the right XiX modulation frequen-cies. These windows depend only on the modulation frequency andare insensitive to the decoupling rf-field amplitude. This makes theoptimization of the decoupling rf-field amplitudes unnecessaryand, in addition, one can use lower decoupling rf field strengthsto obtain similar polarization-transfer efficiencies. Moreover, theXiX decoupling scheme is less susceptible to rf-field inhomogene-ities since only the modulation frequency of the XiX decouplingdetermines the resonance conditions and not the rf-fieldamplitude.

Amplitude-modulated sequences like XiX have the advantageover phase-modulated sequences like TPPM [19] that they haveonly a single modulation frequency that has to be considered. Insequences like TPPM the effective nutation frequency of the basicbuilding block [26] could also interfere with the modulation fre-quency of the symmetry-based C sequence making it more difficultto find interference free windows.

2. Theory

For our discussion we consider a heteronuclear spin systemwith NI I spins and NS S spins that is, in the usual Zeeman rotatingframe and using spherical-tensor notation [27], characterized by afull time-dependent Hamiltonian of the form

HðtÞ¼XNS

p¼1

X2

n¼�2

xðnÞSpeinxr tTðSpÞ

1;0 þXNI

m¼1

X2

n¼�2

xðnÞImeinxr tTðImÞ

1;0

þXNS

p¼1

XNI

m¼1

X2

n¼�2n–0

xðnÞImSpeinxr t 2ffiffiffi

6p TðSpÞ

1;0 T ðImÞ1;0

þXNS

p¼1

XNI

m¼1

xð0ÞImSp

�1ffiffiffi3p T ðSpÞ

1;0 TðImÞ1;0 þ

Xo<m

X2

n¼�2n–0

xðnÞIoImeinxr tTðIoImÞ

2;0

þXo<m

xð0ÞIoImTðIoImÞ

0;0 þXp<q

X2

n¼�2n–0

xðnÞSpSqeinxr tTðSpSqÞ

2;0 þXp<q

xð0ÞSpSqTðSpSqÞ

0;0

þx1S

XNS

p¼1

ðSpx cosð/ðtÞÞþSpy sinð/ðtÞÞÞþx1IðtÞXNI

m¼1

Imx ð1Þ

Here, the xðnÞSp¼ 2ffiffi

6p d2

n;0ð�hmÞe�incSpP2

m¼�2d2m;nðbSp

Þe�imaSp qðSpÞ2;m rep-

resent the Fourier components of the chemical shift of the S spins

and xðnÞIpfor the I spins, respectively. The Fourier components of

the dipolar couplings are given by xðnÞIoIm¼ d2

n;0ð�hmÞe�incIo Im d20;n

ðbIoImÞqðIoImÞ

2;0 and the isotropic J couplings are defined by xð0ÞIo Im¼

�2ffiffiffi3p

pJIoIm. The irradiation of the S spins by the C-sequence has a

constant rf-field amplitude x1S but a time-dependent phase /ðtÞ[22,23], while the simultaneous decoupling of the I spins has atime-dependent amplitude x1IðtÞ but constant phase due to ourrestriction of the discussion to amplitude-modulated decoupling se-quences. For a Floquet treatment [22,23], we have to perform aninteraction-frame transformation of the time-dependent Hamilto-nian of Eq. (1) into an interaction frame with the rf-field part ofthe Hamiltonian. In the case of no I-spin irradiation, i.e., x1IðtÞ ¼ 0,this leads to a time-dependent interaction-frame Hamiltonian with

only two basic frequencies, xr and xðSÞm ¼ xr=n. The interaction-frame Hamiltonian can be expressed in the form of a Fourier series as

~HðtÞ ¼X2

n¼�2

X1k¼�1

~Hðn;kÞeinxr teikxðSÞm t ð2Þ

with the Fourier components given by [28]

~Hð0;kÞ ¼Xo<m

xð0ÞIo ImTðIoImÞ

0;0 þXp<q

xð0ÞSpSqTðSpSqÞ

0;0 þXNI

m¼1

xð0ÞImTðImÞ

1;0

( )dk;0

þXNS

p¼1

xð0ÞSp

X1

s¼�1

aðkÞ1;sTðSpÞ1;s þ

XNS

p¼1

XNI

m¼1

xð0ÞImSp

�1ffiffiffi3p TðImÞ

1;0

X1

s¼�1

aðkÞ1;sTðSpÞ1;s

~Hðn;kÞ ¼Xo<m

xðnÞIoImTðIo ImÞ

2;0 þXNI

m¼1

xðnÞImTðImÞ

1;0

( )dk;0þ

XNS

p¼1

xðnÞSp

X1

s¼�1

aðkÞ1;sTðSpÞ1;s

þXNS

p¼1

XNI

m¼1

xðnÞImSp

2ffiffiffi6p TðImÞ

1;0

X1

s¼�1

aðkÞ1;sTðSpÞ1;s þ

Xp<q

xðnÞSpSq

X2

s¼�2

aðkÞ2;sTðSpSqÞ2;s ð3Þ

Here the aðkÞ‘;s are the Fourier coefficients resulting from theinteraction-frame transformation of the T‘;0 spherical-tensor oper-ators and are defined as

~T‘;0ðtÞ ¼X‘s¼�‘

a‘;sðtÞT‘;s ¼X‘s¼�‘

X1k¼�1

aðkÞ‘;s eikxmtT‘;s ð4Þ

Fig. S1 in the Supplemental information shows a plot of the aðkÞ‘;sFourier coefficients for the C91

6 sequence using POST as a basic C ele-ment [29] as a function of the index k for the three first-rank and thefive second-rank tensor components. They can either be calculatedanalytically [28] or numerically by simulating the interaction-frametrajectory of the T‘;0 spherical-tensor components under the C91

n se-quence. If the condition n0xr þ k0xðSÞm ¼ 0 is fulfilled, this leads to arecoupling with an effective first-order Hamiltonian of the form

�Hð1Þ ¼ ~Hð0;0Þ þ ~Hðn0 ;k0Þ þ ~Hð�n0 ;�k0Þ ð5Þ

Following the treatment by Vinogradov et al. [28], the Fouriercoefficients aðkÞ‘;s for a CNm

n sequence are only non-zero if thecondition

k ¼ zN � sm ð6Þ

is fulfilled where z is an integer. Eq. (6) is equivalent to the symme-try-based selection rules derived from the average Hamiltoniandescription [10]. For a C91

n TOBSY sequence this leads to non-zero

values of aðkÞ‘;s for k equal to 9z for s = 0, 9z ± 1 for s ¼ �1, and9z ± 2 for s ¼ �2 (see Fig. S1). The sparse but regular non-zero val-ues of the Foruier coefficients are the reason for the high recouplingselectivity of the symmetry-based recoupling sequences. The

resonance conditions n0xr þ k0xðSÞm ¼ 0 can be simplified to

k0 ¼ �nn0 by substituting xr ¼ nxðSÞm . Since n0 is restricted to the

(a) (b)

(c) (d)

Fig. 2. Plot of the magnitude of the undesired first-order heteronuclear recoupling for cw irradiation as a function of the ratio x1I=xr for (a) the C916 and (b) the C91

12 TOBSYsequences. The lines connecting the data points are a guide to the eye. Plot of the magnitude of the analytical first-order heteronuclear recoupling under decoupling using XiXirradiation as a function of xðIÞm =xr and x1I=xr for (c) the C91

6 sequence and (d) the C9112 TOBSY sequences. Good decoupling is achieved in areas where the heteronuclear

recoupling terms are small.

K.O. Tan et al. / Journal of Magnetic Resonance 239 (2014) 61–68 63

values of ±1 and ±2 in the first-order Hamiltonian, all C91n sequences

with n ¼ 9p� 3 where p is an integer can be used as TOBSYsequences since they do not recouple any terms in Eq. (3) to first or-der. Therefore, the effective first-order TOBSY Hamiltonian is givenby

�Hð1Þ ¼ ~Hð0;0Þ

¼Xo<m

xð0ÞIoImTðIoImÞ

0;0 þXp<q

xð0ÞSpSqTðSpSqÞ

0;0 þXNS

p¼1

xð0ÞSpað0Þ1;0TðSpÞ

1;0

þXNS

p¼1

XNI

m¼1

xð0ÞImSp

�1ffiffiffi3p TðImÞ

1;0 að0Þ1;0TðSpÞ1;0 þ

XNI

m¼1

xð0ÞImTðImÞ

1;0 ð7Þ

which can be simplified to

�Hð1Þ ¼Xo<m

xð0ÞIoImTðIoImÞ

0;0 þXp<q

xð0ÞSpSqTðSpSqÞ

0;0 þXNI

m¼1

xð0ÞImTðImÞ

1;0 ð8Þ

since the að0Þ1;0 Fourier coefficients are zero if the flip angle of the ba-sic C element is an integer multiple of 2p [28]. In principle, the C91

n

sequences can be used without any additional decoupling on the Ispins since the sequence itself decouples the S spins from the Ispins. In practice, however, due to second-order contributions tothe effective Hamiltonians, additional proton irradiation is almostalways required in order to increase the transfer efficiency.

The description of the C91n sequences becomes more complex

when there is simultaneous rf irradiation on the protons. In thissituation, the resulting interaction-frame Hamiltonian has threebasic frequencies xr , xðSÞm ¼ xr=n, and the rf-field amplitude x1I

in the case of cw irradiation or the modulation frequency xðIÞm in

the case of an amplitude modulated sequences like the XiX se-quence [24,25]. Again, the Hamiltonian can be expressed in theform of Fourier series as

~HðtÞ ¼X2

n¼�2

X1k¼�1

X1‘¼�1

~Hðn;k;‘Þeinxr teikxðSÞm tei‘xðIÞm t ð9Þ

in which the Fourier components of the Hamiltonian are given by

~Hð0;k;‘Þ ¼Xo<m

xð0ÞIoImTðIoImÞ

0;0 þXp<q

xð0ÞSpSqTðSpSqÞ

0;0

( )dk;0d‘;0

þXNS

p¼1

xð0ÞSp

X1

s¼�1

aðkÞ1;sTðSpÞ1;s

( )d‘;0 þ

XNI

m¼1

xð0ÞIm

X1

s¼�1

að‘Þ1;sTðImÞ1;s

( )dk;0

þXNS

p¼1

XNI

m¼1

xð0ÞImSp

�1ffiffiffi3p

X1

s¼�1

að‘Þ1;sTðImÞ1;s

X1

s¼�1

aðkÞ1;sTðSpÞ1;s

~Hðn;k;‘Þ ¼Xo<m

xðnÞIoIm

X2

s¼�2

að‘Þ2;sTðIoImÞ2;s þ

XNI

m¼1

xðnÞIm

X1

s¼�1

að‘Þ1;sTðImÞ1;s

( )dk;0

þXp<q

xðnÞSpSq

X2

s¼�2

aðkÞ2;sTðSpSqÞ2;s þ

XNS

p¼1

xðnÞSp

X1

s¼�1

aðkÞ1;sTðSpÞ1;s

( )d‘;0

þXNS

p¼1

XNI

m¼1

xðnÞImSp

2ffiffiffi6p

X1

s¼�1

að‘Þ1;sTðImÞ1;s

X1

s¼�1

aðkÞ1;sTðSpÞ1;s ð10Þ

In this representation, the differences between cw irradiation andamplitude-modulated decoupling schemes on the protons are en-coded in the values of the Fourier coefficients að‘Þ1;s and að‘Þ2;s. The val-ues of these coefficients can be determined as described above.

1 2 3 40

50

100

150

200

0

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

1 2 3 40

50

100

150

200

0

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

0

0.2

0.4

0.6

0.8

60120

kHzm(I) kHzm

(I)

0 25 50 75 100 0 40 80 120 160

0 25 50 75 100 0 40 80 120 160

1 2 3 4 1 2 3 4

m r(I)

m r(I)

m r(I)

m r(I)

50 100 150 200 50 100 150 200

1IkH

z

1IkH

zS

2z(t

)S

1z(0

)

S2z

(t)

S1z

(0)

kHzm(I) kHzm

(I)

kHz1I kHz1I

S2z

( t)

S1z

(0)

S2z

(t)

S1z

(0)

(d)(c)

(f)(e)

(h)(g)

1I r 1I r

0 1 2 3 4 50

0.2

0.4

0.6

0.8

1

0 2 4 6 80

0.2

0.4

0.6

0.8

1 0 40 80 120 160 2000 50 100 150 200 (b)(a) 1I kHz1I kHz

S2z

(t)

S1z

(0)

S2z

(t)

S1z

(0)

r = 25 kHz, C961

r = 40 kHz, C9121

Fig. 3. Simulation of the transfer efficiency in a four-spin CH2–C spin system as a function of the rf-field amplitude using cw decoupling on the protons. (a) mr = 25 kHz usingthe C91

6 sequence for a mixing time of time Im = 7.2 ms (b) mr = 40 kHz using the C9112 sequence for a mixing time of sm = 6.24 ms. Simulated polarization-transfer efficiency

under proton XiX decoupling as a function of the rf-field amplitude m1I and the modulation frequency mðIÞm for a fixed mixing time of 7.2 ms. (c) mr = 25 kHz using the C916

sequence (d) mr = 40 kHz using the C9112 sequence. (e) A slice through (c) at the rf-field amplitude m1I ¼ 180 kHz, (f) a slice through (d) at the rf-field amplitude m1I ¼ 180 kHz.

(g) A slice through (c) at the modulation frequency mðIÞm ¼ 75 kHz, (h) a slice through (d) at the modulation frequency mðIÞm ¼ 60 and 120 kHz. Efficient polarization transfer isachieved in areas where the decoupling interference (Fig. 2) is minimal.

64 K.O. Tan et al. / Journal of Magnetic Resonance 239 (2014) 61–68

(a) (b)

(c) (d)

Fig. 4. Experimental polarization-transfer efficiencies in 1,2-13C-glycine ethyl ester as a function of the mixing time and the rf-field amplitude of the cw decoupling onprotons. (a) mr = 25 kHz using the C91

6 sequence (b) mr = 40 kHz using the C9112 sequence. (c) A slice through (a) at the mixing time sm = 6.24 ms, (d) a slice through (b) at the

mixing time sm = 7.2 ms.

K.O. Tan et al. / Journal of Magnetic Resonance 239 (2014) 61–68 65

Analytical expressions for the Fourier coefficients of the XiX se-quences as well as graphical plots can be found in the literature[25].

To achieve efficient heteronuclear decoupling, first-order reso-nance conditions that reintroduce parts of the heteronuclear dipo-lar couplings have to be avoided. Such resonance conditions aredefined by n0xr þ k0xðSÞm þ ‘0xðIÞm ¼ 0 and the resulting effectiveHamiltonian is given by

�Hð1Þ ¼ ~Hð0;0;0Þ þX

n0 ;k0 ;‘0

~Hðn0 ;k0 ;‘0Þ ð11Þ

where

~Hðn0 ;k0 ;‘0Þ ¼XNS

p¼1

XNI

m¼1

xðn0ÞImSp

2ffiffiffi6p

X1

sI¼�1

að‘0Þ1;sI

TðImÞ1;sI

X1

sS¼�1

aðk0Þ1;sS

T ðSpÞ1;sS

ð12Þ

and the second term in Eq. (11) sums over all possible sets ofðn0; k0; ‘0Þ that fulfill a given resonance condition. Note that Eq.(12) contains undesirable heteronuclear dipolar components thatlead to a decay of carbon magnetization during TOBSY and, there-fore, lower transfer efficiency. The corresponding magnitude of thiscontribution can be expressed as a function of xðIÞm =xr by summingover all contributions of Eq. (12) and simplifying the expression to

IISxðIÞm

xr

!6

X2

n0¼�2

X1‘0¼�1

X1

sS¼�1

X1

sI¼�1

a�ð‘0xðIÞm =xðSÞm þnn0Þ

1;sS

��� ��� að‘0Þ1;sI

��� ��� ð13Þ

where again in the case of cw decoupling the term xðIÞm =xr has to bereplaced by x1I=xr .

Fig. 2 shows a plot of Eq. (13) which represents the upper limitof the magnitude of the recoupled heteronuclear dipolar coupling

for the case of cw irradiation on the protons for the C916 (Fig. 2a)

and the C9112 (Fig. 2b) TOBSY sequences using POST as a basic C ele-

ment. One can clearly see that there are windows with minimaldecoupling interference around x1I=xr ¼ 3z=2 for the C91

6 se-quence and around x1I=xr ¼ 3z=4 for the C91

12 sequence where zis an integer. Moreover, the plot shows that at higher decouplingfield strength as well as in the case of no decoupling, themagnitude of the interference terms is reduced, which agrees withexperimental observations. The strong modulation of the polariza-tion-transfer efficiency as a function of the decoupling rf-fieldstrength observed experimentally can, indeed, be explained by thiskind of interference profile. Therefore, optimizing the decouplingrf-field amplitude is very important for an efficient polarizationtransfer in the cw case, and using the highest available rf-fieldamplitude does not necessarily give the best result.

For decoupling using the XiX sequence, we have two freeparameters, namely the modulation frequency xðIÞm and the rf-fieldamplitude x1I. Fig. 2c and d shows a plot of the magnitude of thedecoupling interference as a function of xðIÞm =xr and x1I=xðIÞm . Theplot shows that for certain XiX modulation frequencies there areno first-order interference terms for all rf-field amplitudes. Decou-pling at these XiX modulation frequencies has an advantage thatthe rf-field amplitude can be chosen freely without the danger ofaccidentally fulfilling a heteronuclear dipolar recoupling condition.

3. Simulations and experimental characterization

To further characterize the expected decoupling behaviorpredicted by the analytical calculations, numerical simulationswere carried out on a model CH2–C four-spin system using the

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Fig. 5. Experimental polarization-transfer efficiency under proton XiX decoupling in 1,2-13C-glycine ethyl ester as a function of the rf-field amplitude m1I and the modulationfrequency mðIÞm . (a) mr = 25 kHz using the C91

6 sequence around the condition xðIÞm =xr ¼ 3 at a mixing time of 6.24 ms. (b) mr = 40 kHz using the C9112 sequence around the

condition xðIÞm =xr ¼ 1:5 at a mixing time of 6.6 ms. (c) mr = 40 kHz using the C9112 sequence around the condition xðIÞm =xr ¼ 3 at a mixing time of 6.6 ms. (d) A slice through (a)

at the rf-field amplitude m1I ¼ 181 kHz, (e) a slice through (b) at the rf-field amplitude m1I ¼ 164 kHz, and (f) a slice through (c) at the rf-field amplitude m1I ¼ 200 kHz. (g) Aslice through (a) at the modulation frequency mðIÞm ¼ 75:3 kHz, (h) a slice through (b) at the modulation frequency mðIÞm ¼ 60 kHz, and (i) a slice through (c) at the modulationfrequency mðIÞm ¼ 120 kHz.

(a) (b)

Fig. 6. Comparison of the experimental polarization-transfer efficiencies in 1,2-13C glycine ethyl ester as a function of the rf-field amplitude of XiX decoupling. (a) mr = 25 kHzusing the C91

6 sequence using cw decoupling (blue squares) and XiX decoupling with a modulation frequency of 75 kHz (red circles) at a mixing time of 6.24 ms. (b)mr = 40 kHz using the C91

12 sequence using cw decoupling (blue squares) and XiX decoupling with a modulation frequency of 60 kHz (red circles) and 120 kHz (black triangles)at a mixing time of 6.6 ms. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

66 K.O. Tan et al. / Journal of Magnetic Resonance 239 (2014) 61–68

(a) (b)

(c) (d)

Fig. 7. Experimental TOBSY spectra recorded with the pulse sequence shown in Fig. 1 on the tripeptide MLF at a MAS frequency of 40 kHz using the C9112 sequence with a

mixing time of 7.8 ms. The spectrum in (a) was recorded using cw decoupling during the mixing time with an rf-field amplitude of m1I ¼ 195 kHz while the spectrum in (b)was recorded using XiX decoupling during the mixing time with a modulation frequency of mðIÞm ¼ 1:5mr ¼ 60 kHz and an rf-field amplitude of m1I ¼ 130 kHz. The slices in (c)and (d) through two selected resonances show that the polarization-transfer efficiency under XiX decoupling (red) is even slightly better than the polarization-transferefficiency under cw decoupling (blue) despite the much lower rf-field amplitude. The spectrum in black is the reference spectrum for a vanishing mixing time. (Forinterpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

K.O. Tan et al. / Journal of Magnetic Resonance 239 (2014) 61–68 67

spin-simulation environment GAMMA [30] with the spin parame-ters of crystalline glycine. Fig. 3 shows a plot of the transfer effi-ciency from the CH2 group to the quaternary carbon atom as afunction of the proton rf-field amplitude for 25 kHz MAS usingthe C91

6 sequence (Fig. 3a) and 40 kHz MAS using the C9112 sequence

(Fig. 3b). Details of the simulation parameters can be found in thefigure caption. The regions of high polarization transfer can be cor-related with the region of low magnitude of recoupled heteronu-clear dipolar coupling in Fig. 2. For the C91

6 sequence (Fig. 3a), wesee a local maximum of the polarization transfer at the ratio ofx1I=xr ¼ 1:5 and 3 which correspond to areas where the first-or-der recoupling Hamiltonian is minimum (see Fig. 2a). The sametype of patterns can be observed for the C91

12 sequence (Fig. 3b)where polarization transfer is increased in areas of low first-orderdipolar recoupling (see Fig. 2b).

Fig. 3c and d shows the same type of transfer-efficiency simula-tions for XiX decoupling as a function of the XiX modulation fre-quency and the rf-field amplitude again for 25 kHz MAS usingthe C91

6 sequence (Fig. 3c) and 40 kHz MAS using the C9112 sequence

(Fig. 3d). There is again high polarization transfer for values ofxðIÞm =xr where we observe no heteronuclear recoupling terms(see Fig. 2). Such areas can be found for xðIÞm =xr ¼ 1;1:5;2 and 3at both 25 and 40 kHz MAS (Fig. 3c and d). Fig. 3e and f showsslices through the 2D plots of Fig. 3c and d for m1I = 180 kHz.Although the conditions for good decoupling are quite narrow inthe xðIÞm =xr dimension, the pulse length of the decoupling sequencecan be adjusted accurately, hence preserving the experimentalrobustness of the decoupling sequence. The dependence on therf-field amplitude x1I is, as expected, more linear which is illus-trated in slices through xðIÞm =xr ¼ 3 (Fig. 3g) for 25 kHz MAS andxðIÞm =xr ¼ 1:5 and 3 (Fig. 3h) for 40 kHz MAS. In contrast to cwdecoupling, the transfer efficiency increases steadily with increas-ing rf-field amplitudes since the first-order resonance conditionsdepend only on xðIÞm but not on x1I. Nevertheless, the increasing

transfer efficiency can only be understood if one considers high-er-order contributions to the effective Hamiltonians, which hasan implicit dependence on x1I.

To verify the results of the theoretical calculations andspin-dynamics simulations, measurements on 1,2-13C glycine ethylester were performed as one-dimensional experiments where aninitial state was prepared with polarization on the CH2 group only.The transfer of polarization to the carbonyl group was then mea-sured as a function of various parameters. All experiments werecarried out on a Varian Infinity+ 500 MHz spectrometer using ahome-built 1.8 mm double-resonance MAS probe [31]. Fig. 4shows the experimental polarization-transfer efficiency as a func-tion of the mixing time and the decoupling rf-field amplitude forspinning frequencies of 25 kHz (Fig. 4a) and 40 kHz (Fig. 4b). Slicesthrough the maximum of the polarization transfer at mixing timesof sm ¼ 6:24 and 7:2 ms, respectively, are shown in Fig. 4c and d.The experimental polarization-transfer profile as a function ofthe cw decoupling rf-field amplitude shows the same features asthe numerical simulations (Fig. 3a and b). The main difference isthat the lines are broadened significantly due to rf-field inhomoge-neities present only in the experimental data and, therefore, thesharp features visible in Fig. 3 are smeared out. The overall lineshapes, however, are very similar and show maxima and minimaat the same positions.

The experimental dependence of the polarization-transfer effi-ciency under XiX decoupling has also been measured as a functionof the XiX modulation frequency and the proton rf-field amplitudefor selected areas where good decoupling was expected from thesimulations. Fig. 5 shows experimental polarization-transfer effi-ciencies for MAS frequencies of 25 kHz (Fig. 5a) and 40 kHz(Fig. 5b and c) for modulation frequencies of xðIÞm ¼ 1:5xr

(Fig. 5b) and xðIÞm ¼ 3xr (Fig. 5a and c). As expected, best polariza-tion transfer is obtained when the correct modulation frequency isused as can be seen from Fig. 5d–f which show slices through

68 K.O. Tan et al. / Journal of Magnetic Resonance 239 (2014) 61–68

Fig. 5a–c at a rf-field amplitude of 200 kHz. There is an almost stea-dy increase of the polarization-transfer efficiency with increasingrf-field strength as can be seen from Fig. 5g–i which show a slicethrough the ideal modulation frequencies of Fig. 5a–c.

4. Discussion and conclusion

The simulations and measurement shown in the previous sec-tions clearly show that XiX decoupling is a viable alternative tocw decoupling during TOBSY transfer mediated by C91

n sequences.The advantage of the XiX decoupling during the C91

n sequence isillustrated best in Fig. 6 where the polarization-transfer efficiencyunder cw and XiX decoupling is compared as a function of the rf-field amplitude. At almost all rf-field amplitudes, XiX decouplingleads to an improved polarization transfer. In addition, optimiza-tion of the XiX sequences in terms of the rf-field amplitude isstraightforward. Typically, the hypothesis that the highest rf-fieldamplitude possible will give the best polarization transfer is clearlyinvalid for the cw decoupling during the C91

n TOBSY sequence. Toachieve the same level of polarization transfer, much lower decou-pling fields can be used. This is illustrated in Fig. 7 which showsTOBSY spectra of the tripeptide MLF at a MAS frequency of40 kHz using the C91

12 sequence and cw decoupling (Fig. 7a) witha decoupling rf-field amplitude of m1I ¼ 195 kHz and for compari-son one using XiX decoupling (Fig. 7b) with a modulation fre-quency of mðIÞm ¼ 1:5mr ¼ 60 kHz and a decoupling field strength ofm1I ¼ 130 kHz. Two slices through the resonances of Leu-Ca andMet-Cb (Fig. 7c and d) show that the polarization-transfer effi-ciency of the two spectra is very similar with slightly higher effi-ciencies in the XiX decoupled spectrum while the decouplingpower has been reduced by roughly a factor of two.

We have shown that the oscillating performance of cw decou-pling during the C9 TOBSY sequences could be explained by thefirst-order recoupling in Floquet theory. This undesirable featurecan be mitigated by using XiX decoupling with a carefully selectedbut easily predictable modulation frequency due to the presenceof windows in the decoupling interference plots (Fig. 2). Obviously,not all symmetry-based C/R sequences might have such decoupling-interference free windows, and using XiX decoupling during suchsequences might even worsen the results. We are currently investi-gating under what conditions these windows will appear, and try togeneralize them to arbitrary symmetry-based C or R sequences.

Acknowledgments

We would like to thank Dr. Anders Nielsen and Dr. P.K. Madhufor stimulating discussion. This work was supported by the SwissNational Science Foundation (Grant 200020_134681), the ETHZürich (Grant ETH-04 09-3), and a PEP grant from the Indo-SwissJoint Research Program (ISJRP).

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jmr.2013.11.017.

References

[1] R.G. Griffin, S. Vega, Recoupling of Homo-and Heteronuclear DipolarInteractions in Rotating Solids, NMR Basic Principles and Progress, 1994.

[2] S. Dusold, A. Sebald, Dipolar recoupling under magic-angle spinningconditions, Annu. Rep. NMR Spectrosc. 41 (2000) 185–264.

[3] N.C. Nielsen, L.A. Strassø, A.B. Nielsen, Dipolar Recoupling, Springer, BerlinHeidelberg, Berlin, Heidelberg, 2011.

[4] V. Ladizhansky, Homonuclear dipolar recoupling techniques for structuredetermination in uniformly 13C-labeled proteins, Solid State Nucl. Magn.Reson. 36 (2009) 119–128.

[5] M. Baldus, B.H. Meier, Total correlation spectroscopy in the solid state. The useof scalar couplings to determine the through-bond connectivity, J. Magn.Reson., Ser. A 121 (1996) 65–69.

[6] E.H. Hardy, R. Verel, B.H. Meier, Fast MAS total through-bond correlationspectroscopy, J. Magn. Reson. 148 (2001) 459–464.

[7] E.H. Hardy, A. Detken, B.H. Meier, Fast-MAS total through-bond correlationspectroscopy using adiabatic pulses, J. Magn. Reson. 165 (2003) 208–218.

[8] L. Braunschweiler, R.R. Ernst, Coherence transfer by isotropic mixing –application to proton correlation spectroscopy, J. Magn. Reson. 53 (1983)521–528.

[9] J. Cavanagh, W.J. Fairbrother, A.G. Palmer III, M. Rance, N.J. Skelton, ProteinNMR Spectroscopy: Principles and Practice, Academic Press, Amsterdam,Boston, 2007.

[10] M.H. Levitt, Symmetry-Based Pulse Sequences in Magic-Angle Spinning Solid-State NMR, eMagRes, 2007.

[11] J.C.C. Chan, G. Brunklaus, R sequences for the scalar-coupling mediatedhomonuclear correlation spectroscopy under fast magic-angle spinning, Chem.Phys. Lett. 349 (2001) 104–112.

[12] J. Leppert, O. Ohlenschläger, M. Görlach, R. Ramachandran, Adiabatic TOBSY inrotating solids, J. Biomol. NMR 29 (2004) 167–173.

[13] O.C. Andronesi, D. Mintzopoulos, J. Struppe, P. Black, A. Tzika, Solid-state NMRadiabatic TOBSY sequences provide enhanced sensitivity for multidimensionalhigh-resolution magic-angle-spinning 1H MR spectroscopy, J. Magn. Reson.193 (2008) 251–258.

[14] I. Marin-Montesinos, D.H. Brouwer, G.C. Antonioli, W.C. Lai, A. Brinkmann,M.H. Levitt, Heteronuclear decoupling interference during symmetry-basedhomonuclear recoupling in solid-state NMR, J. Magn. Reson. 177 (2005) 307–317.

[15] C.E. Hughes, S. Luca, M. Baldus, Radio-frequency driven polarization transferwithout heteronuclear decoupling in rotating solids, Chem. Phys. Lett. 385(2004) 435–440.

[16] Y. Ishii, J. Ashida, T. Terao, C-13–H-1 dipolar recoupling dynamics in C-13multiple-pulse solid-state Nmr, Chem. Phys. Lett. 246 (1995) 439–445.

[17] B.Q. Sun, C.M. Rienstra, P.R. Costa, J.R. Williamson, R.G. Griffin, 3D 15N–13C–13C chemical shift correlation spectroscopy in rotating solids, J. Am. Chem.Soc. 119 (1997) 8540–8546.

[18] M. Hohwy, C.M. Rienstra, C.P. Jaroniec, R.G. Griffin, Fivefold symmetrichomonuclear dipolar recoupling in rotating solids: application to doublequantum spectroscopy, J. Chem. Phys. 110 (1999) 7983–7992.

[19] A.E. Bennett, C.M. Rienstra, M. Auger, K. Lakshmi, R.G. Griffin, Heteronucleardecoupling in rotating solids, J. Chem. Phys. 103 (1995) 6951–6958.

[20] C.P. Jaroniec, B.A. Tounge, J. Herzfeld, R.G. Griffin, Frequency selectiveheteronuclear dipolar recoupling in rotating solids: accurate 13C–15Ndistance measurements in uniformly 13C, 15N-labeled peptides, J. Am.Chem. Soc. 123 (2001) 3507–3519.

[21] M.J. Bayro, R. Ramachandran, M.A. Caporini, M.T. Eddy, R.G. Griffin, Radiofrequency-driven recoupling at high magic-angle spinning frequencies:homonuclear recoupling sans heteronuclear decoupling, J. Chem. Phys. 128(2008) 052321.

[22] M. Leskes, P.K. Madhu, S. Vega, Floquet theory in solid-state nuclear magneticresonance, Prog. NMR Spectrosc. 57 (2010) 345–380.

[23] I. Scholz, J.D. van Beek, M. Ernst, Operator-based Floquet theory in solid-stateNMR, Solid State Nucl. Magn. Reson. 37 (2010) 39–59.

[24] A. Detken, E.H. Hardy, M. Ernst, B.H. Meier, Simple and efficient decoupling inmagic-angle spinning solid-state NMR: the XiX scheme, Chem. Phys. Lett. 356(2002) 298–304.

[25] M. Ernst, H. Geen, B.H. Meier, Amplitude-modulated decoupling in rotatingsolids: a bimodal Floquet approach, Solid State Nucl. Magn. Reson. 29 (2006)2–21.

[26] I. Scholz, P. Hodgkinson, B.H. Meier, M. Ernst, Understanding two-pulse phase-modulated decoupling in solid-state NMR, J. Chem. Phys. 130 (2009) 114510.

[27] M. Mehring, Principles of High-resolution NMR in Solids, Springer-Verlag,Berlin, New York, 1983.

[28] E. Vinogradov, P.K. Madhu, S. Vega, Strategies for high-resolution protonspectroscopy in solid-state NMR, Top. Curr. Chem. 246 (2004) 33–90.

[29] M. Hohwy, H.J. Jakobsen, M. Edén, M.H. Levitt, N.C. Nielsen, Broadband dipolarrecoupling in the nuclear magnetic resonance of rotating solids: acompensated C7 pulse sequence, J. Chem. Phys. 108 (1998) 2686–2694.

[30] S.A. Smith, T.O. Levante, B.H. Meier, R.R. Ernst, Computer-simulations inmagnetic-resonance – an object-oriented programming approach, J. Magn.Reson., Ser. A 106 (1994) 75–105.

[31] A. Samoson, T. Tuherm, J. Past, Ramped-speed cross polarization MAS NMR, J.Magn. Reson. 149 (2001) 264–267.