probing proton–proton proximities in the solid state

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Progress in Nuclear Magnetic Resonance Spectroscopy 50 (2007) 199–251

Probing proton–proton proximities in the solid state

Steven P. Brown *

Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

Received 5 October 2006Available online 2 February 2007

Keywords: Solid-state NMR; MAS; 1H; Double quantum; Dipolar couplings

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2002. High-resolution 1H solid-state NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

0079-6

doi:10.

* TelE-m

2.1. Magic-angle spinning. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2002.2. Homonuclear 1H decoupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

3. 1H–1H spin-diffusion correlation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
3.1. 1H–1H spin-diffusion CRAMPS experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2043.2. 1H–1H spin-diffusion experiments under fast MAS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2073.3. Quantitative analysis of 1H spin diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
4. 1H Double-quantum spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
4.1. The excitation of 1H double-quantum coherence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2114.2. Rotor-synchronised two-dimensional 1H DQ MAS experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
565/$ -

1016/j.p

.: +44 2ail add

4.2.1. Benzoxazine oligomers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2144.2.2. Alkyl-substituted hexabenzocoronenes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2164.2.3. Polyelectrolyte multilayers and self-assembled monolayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2194.2.4. Host–guest interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2204.2.5. Keto–enol tautomerism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2244.2.6. Proton-conducting materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2264.2.7. Columnar architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2294.2.8. Disordered and heterogeneous materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

4.3. 1H DQ MAS spinning-sideband patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2344.4. 1H DQ CRAMPS experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2414.5. 1H double-quantum heteronuclear correlation experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

5. 1H Triple-quantum MAS experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2446. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

see front matter � 2006 Elsevier B.V. All rights reserved.

nmrs.2006.10.002

4 765 74359; fax: +44 24 766 92016.ress: [email protected]

mailto:[email protected]

single-quantum dimension

doub

le-q

uant

um d

imen

sion

A

A A

A B

B B

B

ωA

ωA

ωA

ωB

+ω

Aω

B+

ωB

ωB

+

single-quantum dimension

sing

le-q

uant

um d

imen

sion

A B

ωA

ωA

ωB

ωB

a

b

Fig. 2. Schematic two-dimensional spectra corresponding to (a) theNOESY-type spin diffusion and (b) the DQ 1H correlation experiments inFig. 1.

200 S.P. Brown / Progress in Nuclear Magnetic Resonance Spectroscopy 50 (2007) 199–251

1. Introduction

The power of NMR as a site-specific probe of structureand dynamics is principally a consequence, on the onehand, of the chemical shift by which different chemicalenvironments are distinguished and, on the other hand,the coupling of nuclear spins so as to reveal through-bondconnectivities or through-space proximities via J or dipolarcouplings, respectively. In particular, two- and higher-di-mensional correlation experiments serve to identify suchcouplings, with COSY (correlation spectroscopy) [1] andNOESY (nuclear Overhauser effect spectroscopy) [2] beingthe archetypal J and dipolar solution-state NMRexperiments.

The focus here is on 1H solid-state NMR dipolar correla-tion experiments. As such the principal emphasis is on thetwo basic 1H solid-state NMR correlation experiments inFig. 1, namely a NOESY-type spin-diffusion experiment inwhich two periods of single-quantum (SQ) coherence(SQC) evolution are separated by a mixing time (Fig. 1a)and a double-quantum (DQ) experiment in which the evolu-tion of DQ coherence (DQC) in t1 is correlated with that ofSQC in t2 (Fig. 1b). Schematic two-dimensional NOESY-type and DQ spectra are presented in Figs. 2a and b, respec-tively. An important distinction is that auto peaks (i.e., AAand BB) are always present on the diagonal in NOESY-typespectra and do not give any information about A–A or B–Bproximities. By contrast, peaks along the F1 = 2F2 diagonalin a DQ spectrum (corresponding to, e.g., AA or BB DQC)can only arise if there is a dipolar coupling between the likenuclei.

This review will show that fast MAS or homonucleardecoupling allows structurally or dynamically informativehigh-resolution 1H–1H correlation experiments to berecorded for an increasing number and wide range of rig-id-solid applications.

Excitation Reconversion

π/2

π/2π/2π/2

t2t1

t1 t2

p =

+2+1 0-1-2

p = 0

−1

+1

τmix

a

b

Fig. 1. The pulse sequence and coherence transfer pathway diagram for(a) a NOESY-type spin diffusion and (b) a DQ 1H correlation experiment.Suitable pulse sequences for the excitation and reconversion of DQcoherence in (b) are discussed in Section 4.1.

2. High-resolution 1H solid-state NMR

In solution, the fast isotropic tumbling of moleculesresults in the averaging to zero of broadening in the NMRspectrum due to anisotropic interactions such as dipolarcouplings and the chemical shift anisotropy (CSA). Thus,the 1H spectrum of a typical small organic molecule consistsof narrow resonances characterised by the isotropic chemicalshift and J couplings. By contrast, for a rigid solid, thecorresponding 1H spectrum is a broad featureless humpbecause of the anisotropic broadening due to the extensivenetwork of dipolar couplings amongst the protons. As a con-sequence, the valuable isotropic chemical shift informationis hidden (see Fig. 3).

2.1. Magic-angle spinning

In solid-state NMR, magic-angle spinning (MAS) [3,4]is a routinely applied line-narrowing technique. For exam-ple, narrow resonances due to the three chemically distinctcarbons are observed in a 13C cross-polarisation (CP) MAS

a

b

c

d

250 200 150 100 050 -50

60 30 0 -30

14 12 10 8 02 -4-26 4

14 12 10 8 02 -4-26 4ppm

Fig. 4. NMR spectra of powdered L-alanine at a 1H Larmor frequency of500 MHz. (a) 13C CP MAS at 5 kHz MAS; 1H MAS at (b) 5 kHz and (c)30 kHz; (d) the high-resolution dimension of a 2D 1H FSLG [30] spectrumat 12.5 kHz MAS. (Parts (b–d): Reprinted with permission from Ref.[268].)

Co

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t(2

001)

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anC

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a

b

Fig. 3. A comparison of (a) a static solid-state and (b) a solution-state 1HNMR spectrum of a typical organic compound. (Reprinted with permis-sion from Ref. [23].)

Copyright(2001)AmericanChem

icalSociety.

S.P. Brown / Progress in Nuclear Magnetic Resonance Spectroscopy 50 (2007) 199–251 201

spectrum of L-alanine at 5 kHz MAS (see Fig. 4a). Bycontrast, the corresponding 1H MAS spectrum at 5 kHzMAS (see Fig. 4b) is still essentially a featureless hump.It is only upon increasing the MAS frequency, mR, that res-onances due to the three distinct hydrogen environmentsare revealed – see the 1H MAS spectrum at 30 kHz MASin Fig. 4c as well as the improvement in resolution uponprogressively increasing the MAS frequency for the 1HMAS spectrum of a representative moderately sized organ-ic molecule (see Fig. 5). This experimental observation hasbeen a driving motivation behind the considerable advanc-es in fast MAS technology [5] in recent years based on theproduction of MAS rotors of ever smaller outer diameter:2.5 mm rotors at 35 kHz MAS [6] have been followed by1.8 mm rotors at 40 kHz MAS [7] and 1.3 mm rotors at60 kHz MAS [8,9].

The difference between 13C and 1H NMR, namely thelinewidth being essentially independent of the MAS fre-quency for the case of 13C, as compared to a progressiveline narrowing upon increasing MAS frequency for 1H isa consequence of the different dominant anisotropic inter-actions, namely CSA for 13C (the heteronuclear 13C–1H

Fig. 5. The effect of increasing the MAS frequency, mR, on the centrebandof a 1H MAS spectrum of a typical moderately sized organic compound.(Reprinted with permission from Ref. [149].)

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t(1

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dipolar couplings are removed by 1H decoupling) andhomonuclear 1H–1H dipolar couplings for 1H. In the lan-guage of Maricq and Waugh [10], the CSA is an inhomoge-neous interaction, where the broadening is refocused over arotor period, while homonuclear dipolar couplings arehomogeneous interactions, such that for three or more cou-pled nuclei (in a non-linear arrangement) the broadening isnot fully refocused over a rotor cycle, since the Hamiltoni-ans do not commute with each other.

Fig. 6 shows the dependence of the 1H full width at halfmaximum (FWHM) linewidth on the MAS frequency for aseries of organic compounds [11]. It is to be noted that the1H linewidths in Fig. 6 do not correspond to thoseobserved in a one-dimensional spectrum, but rather tothe spin-echo linewidth as calculated from fitting the decayin a 1H spin-echo experiment to a simple exponential func-tion. In this way, the additional effects of inhomogeneousbroadening (due to, e.g., anisotropic bulk magnetic suscep-tibility broadening [12,13]) are removed. In addition, thelinewidth data in Fig. 6 is presented as a plot of line-width/drss against drss/mR, where drss refers to the rootsum square of the 1H–1H dipolar coupling (in Hz) to a giv-en 1H nucleus defined by:

drss ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiXk 6¼j

d2jk

s; ð1Þ

where djk is the dipolar coupling constant (in Hz) betweenspins j and k:

djk ¼ � l0c2H�h

4pr3jk

!=2p: ð2Þ

It has been shown that drss is a quantitative measure ofdipolar-coupling strength and that it can be extracted fromfitting the sideband patterns observed in 1H MAS spectra[14,15]. In Fig. 6, the scaling by drss has the advantage of

0

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0 0.5 1 1.5 2

d rss / νr

FW

HM

/d

rss

malonic acid CH2malonic acid COOHhexamethylbenzeneadamantaneadamantane-d16 (96%)d-urea.decanoic acidalanine NH3

alanine CHalanine CH3

+

Fig. 6. Plot of spin-echo linewidth against inverse MAS frequency forvarious organic samples reflecting a wide range of mean dipolar-couplingstrength. The linewidth and MAS frequency are scaled by the root sumsquare dipolar coupling, drss – see Eq. (1). (Reproduced with permissionfrom Ref. [11].)

Co

pyr

igh

t20

06,

Am

eric

anIn

stit

ute

of

Ph

ysic

s.

allowing linewidth data to be compared for samples withvery different mean coupling strengths.

Semi-analytical theories predict that the linewidth isapproximately proportional to the inverse MAS frequency[16]. A consideration of Fig. 6 shows that, for all samples,the linewidth is indeed approximately proportional to theinverse MAS frequency:

FWHM � Gqd2rss=mR; ð3Þ

where q is the proportion of undeuterated (i.e., 1H) hydro-gen nuclei. As described in Ref. [11], G is a constant of pro-portionality that depends on the geometry of the couplingnetwork – for example, G is determined experimentally as0.04 and 0.11 for CH in powdered alanine and the cubicenvironment in powdered adamantane, respectively. It isto be noted that these G parameters are reproduced in peri-odic simulations that model the specific coupling networks[11]. An advantage of the scaling by drss is that the datafrom mobile samples can be used to allow the dependencefor rigid samples to be extrapolated to faster spinning fre-quently than are currently available. In this way, it is ob-served that the spin-echo linewidth tends to zero in thelimit of infinite spinning frequency, i.e., the limit on resolu-tion due to T2 relaxation is too small to detect (in the pres-ence of the linewidth due to the dipolar-coupling network).

For the case of deuterated samples, Eq. (3) shows thatthe 1H linewidth is proportional to the degree of proton-ation. This is consistent with experimental observation,i.e., the 1H linewidth decreases monotonically with thedegree of deuteration [17]. Indeed, the use of deuterationto increase 1H resolution is becoming increasingly impor-tant in solid-state NMR studies of peptides and proteins[17–22].

2.2. Homonuclear 1H decoupling

The improvement in 1H resolution due to brute-forcefast MAS has led to the increasing application of 1H sol-id-state NMR as a probe of structure and dynamics inorganic systems [23–25]. An alternative approach used toobtain high-resolution 1H solid-state NMR spectra is thecombination of a physical rotation of the sample byMAS with carefully synchronised rotations in spin spaceby rf pulses in the CRAMPS (combined rotation and mul-tiple-pulse spectroscopy) approach [26–29]. The traditionalCRAMPS experiment is performed in the quasi-static limit,i.e., at a slow MAS frequency such that the rotor period islong compared to the period of the multiple-pulse cycle.However, in recent years, various methods have been pre-sented that are applicable at faster MAS frequencies, suchas frequency-switched and phase-modulated Lee Goldburg(FSLG [30] and PMLG [31]), multiple-pulse assisted MAS[32], DUMBO [33] (decoupling using mind-boggling opti-misation) and symmetry-based methods [34]. Such multi-ple-pulse sequences [35] can be applied in a windowlessfashion (i.e., continuous rf irradiation, since there is norequirement for windows in which data points are

Fig. 7. 1H–1H (200 MHz) spin-diffusion CRAMPS spectra of siloxanematerials prepared by acid-catalysed polycondensation of mixtures oftetraethoxysilane (TEOS)/C2H5OH/H2O/HCl in a molar ratio of1:4.5:3:0.03 (TE) and TEOS/dimethyldiethoxysilane (DMDEOS)/C2H5OH/H2O/HCl in a molar ratio of 0.75:0.25:4.5:3:0.03 (TE-DM 3–1). TE-D2O refers to a partially deuterated TE sample obtained by simpleexchange with D2O in a closed vessel for 48 h – the resolution is improvedbecause of the loss of the broad signal (centred at 5.2 ppm) due tophysisorbed water, such that three peaks assigned to strongly, weakly andnon-hydrogen-bonded silanols are resolved at 7.0, 5.3 and 1.4 ppm. ForTE-DM 3-1, a peak is observed at 0 ppm due to CH3 groups inDMDEOS. The MAS frequency was 2 kHz and the BR24 [70] multiple-pulse sequence was applied in both t1 and t2. (Reprinted with permission

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acquired) in the indirect dimension of a two-dimensionalexperiment [31], or as a windowed sequence such as w-PMLG [36] or w-DUMBO [37] in the direct acquisitiondimension. These homonuclear decoupling methods canbe robustly applied on a modern console, and Fig. 4dshows that the resolution obtained for such a multiple-pulse sequence (here windowless FSLG) at a moderateMAS frequency of 12.5 kHz is considerably better thanthat achieved under MAS alone at 30 kHz.

3. 1H–1H spin-diffusion correlation experiments

Probing the transfer of z magnetisation between dipo-lar-coupled spins is a commonly employed method forextracting the structural information associated with theinherent distance dependence of the dipolar coupling.For the case of a pair of dipolar-coupled spins, a quan-tum-mechanical analysis of such a transfer of z magneti-sation reveals an oscillatory behaviour. As more andmore spins are considered, the resulting network of cou-plings leads to a cancelling of these oscillations and amagnetisation transfer behaviour that is increasingly morediffusive in character. This reversible coherent evolutionthat occurs via multi-step magnetisation transfer in dipo-lar coupled 1H networks is referred to as 1H spin diffusion[38–41]. 1H spin diffusion has been widely exploited in sol-id-state NMR to probe internuclear proximities over arange of distances from specific H–H constraints on theA scale (0.1 nm) up to distances of 200 nm in polymericmaterials [42]. It is to be noted that 1H spin diffusion inthe solid state differs from the process of relayed 1Hpolarisation transfer based on the multistep NuclearOverhauser Effect (NOE) observed in solution-stateNMR – this latter process occurs via incoherent crossrelaxation induced by the irreversible stochastic modula-tion of local fields by molecular motion.

Spin diffusion can be studied in a one-dimensional Gold-man-Shen type 1H experiment [43], whereby a particularsignal is initially filtered out on the basis of mobility, using,e.g., T1 or T2 relaxation [43,44] or multipulse dipolar filters[44–46]. In such experiments, spin diffusion has predomi-nantly been used to probe magnetisation transfer betweentwo dynamically different components, e.g., to gain insightinto the homogeneity and miscibility of polymer blends[47]. In particular, information is provided about domainsizes in such heterogeneous materials since the magnetisa-tion equilibrates faster for the case of systems with smalldomains as compared to a system consisting of largeparticles.

1H spin diffusion is also commonly indirectly observedby means of heteronuclear magnetisation transfer, i.e.,via cross polarisation, from 1H to, e.g., 13C or 15N, so asto benefit from the higher resolution for the ‘‘dilute’’ nucle-us (see Fig. 4). In this respect, the 1H–13C WISE (widelineseparation) experiment [48], whereby proton spin diffusionduring a mixing time is observed indirectly via a high-reso-lution 13C dimension has been widely applied [47]. More-

from Ref. [63].)


over, the CHHC [49–53] or NHHN [54,55] experiments,where two 13C or 15N evolution periods are correlated bya proton mixing time that is bracketed by two CP stepsare becoming popular for providing distance constraintsin protein samples. Note that a PHHP variant has alsobeen presented and applied to probe an organic–inorganicmaterial [56]. These important classes of experiment will,however, not be discussed further here, since this reviewfocuses, instead, on experiments where proton–protonproximities are probed directly, i.e., two-dimensionalexperiments in which the evolution of 1H coherence in bothdimensions is correlated.

The following sections review applications of the 1H–1Hspin-diffusion NOESY-type two-dimensional experiment

Fig. 8. 1H–1H (200 MHz) spin-diffusion CRAMPS spectra of a-glycine for dmultiple-pulse sequence was applied in both t1 and t2. The observed peaks corgroup (at 8 ppm). The stacked plot in (d) corresponds to the mixing time of 3

of Fig. 1a where CRAMPS (Section 3.1) or fast MAS (Sec-tion 3.2) is required to achieve high resolution. An over-view of methods by which structural parameters can beextracted from a quantitative analysis of 1H spin-diffusionbuild-up behaviour is presented in Section 3.3.

3.1. 1H–1H spin-diffusion CRAMPS experiments

The first application of the two-dimensional 1H–1Hspin-diffusion NOESY-type experiment of Fig. 1a employ-ing CRAMPS (specifically the MREV-8 [57,58] pulsesequence) to obtain high resolution was in 1985 by Carrav-atti et al. [59]. For polymer blends of poly(styrene) (PS)and poly(vinyl methyl ether) (PVME), differences in the

ifferent mixing times. The MAS frequency was 2 kHz and the BR24 [70]respond to the two non-equivalent CH2 protons (low ppm) and the NH3

00 ls. (Reproduced by permission of Elsevier from Ref. [64].)

1H eDUMBO-1

t1

θ1

τsd

t2

acq

π2

π2

π2

DUMBO-1

nθ2 -θ2

1H Chemical Shift (ppm)

1 H C

hem

ical

Shi

ft (p

pm)

135791113

1

3

5

7

9

11

13

CCH CHCH2 CH3NH3N

+H

O COOHCOO−

a

b

Fig. 9. (a) Pulse sequence for the 1H–1H spin-diffusion CRAMPSexperiment due to Emsley and co-workers [66,67]. (b) A two-dimensional1H–1H (500 MHz) spin-diffusion CRAMPS spectrum of the dipeptide b-AspAla obtained with a mixing time of sSD = 220 ls. The MAS frequencywas 22.5 kHz and eDUMBO-1 [66] decoupling and windowed DUMBO-1[33,37] homonuclear decoupling (m1 = 100 kHz) was applied in the t1 andt2 dimensions, respectively. (Reprinted with permission from Ref. [67].)

Co

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t(2

005)

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1H

π

π

2π2

π2

Homo. Dec.

t1

φ2

θ

(xz) +y +yφ1

τm

1H

13C

π2

π2

π2

Homo. Dec.

t1

φ2

θ

(xz) +y +yφ1

+y

τm

a

b

Fig. 10. Pulse sequences for the (a) 1H–1H–1H and (b) 1H–1H–13C three-dimepermission from Ref. [71].)

Table 1Applications of two-dimensional 1H–1H spin-diffusion CRAMPS exper-iments incorporating homonuclear decoupling in t1 and t2

Sample Decouplingmethod

mR/kHz Larmorfreq./MHz

Ref.

PS & PVME blend MREV-8 2.8 300 [59]PEO & resorcinol BR-24 2.5 187 [60]PS & MPV blend MREV-8 1.5 400 [61]PC-PEO blend BR-24 2.5 200 [62]Polysiloxanes BR-24 2.0 200 [63]a-Glycine BR-24 2.0 200 [64]Silica/epoxy films BR-24 2.0 200 [65]b-AspAla

dipeptideDUMBO-1 12.5 & 22.0 500 [66–68]

Histidine.HCl.H2O PMLG-5 10.5 600 [69]Tyrosine.HCl PMLG-5 10.5 600 [69]


intensity of aliphatic–aromatic cross peaks were observeddepending on the solvent from which the blends were cast.

Other applications of the 1H–1H spin-diffusion experi-ment are listed in Table 1. For example, Fig. 7 presents1H–1H spin-diffusion CRAMPS spectra obtained usingthe BR-24 [70] pulse sequence for siloxane materials pre-pared by acid-catalysed polycondensation [63]. The spectracorrespond to a spin-diffusion mixing time of 20 ms suchthat cross peaks are clearly evident between the differentsilanol resonances. Ref. [63] shows that an analysis of thebuildup of cross peak intensity yields the spin-diffusioncoefficients, D (see Section 3.3), and hence estimates ofthe dimensions of the strongly, weakly and non-hydro-gen-bonded hydroxyl clusters in these materials.

While spin-diffusion experiments were initially predom-inantly applied to heterogeneous materials, spin diffusionhas also been demonstrated to be a valuable probe ofmolecular structure on the A scale in crystalline samples.For example, Fig. 8 presents 1H–1H spin-diffusionCRAMPS spectra obtained for crystalline a-glycine [64].At the shortest mixing time of 20 ls, cross peak intensityis observed only between the two non-equivalent CH2 res-onances corresponding to the short H–H distance within

π

t3

t3

φ3

π2

π2 φrec

φrec

Homo. Dec.

t2 θ

(xz) +y+y

CP

φ4

φ3

Homo. Dec. Hetero. Dec.CP

t2 θ

(xz) +y

+y

nsional correlation experiments due to Sakellariou et al. (Reprinted with

Co

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t(2

001)

Am

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OH

CH2CH x 2

NH3+

NH*

CH3

F2 : 1H Chemical Shift / ppm

F1 :

1 H C

hem

ical

Shi

ft /

ppm

13 9 5 1

139

51

COO−

CγOOH

CαH

CO

NH3+

NH

CβH3

CαH CβH2

Fig. 11. The F1 � F2 projection onto a 3D spectrum obtained with the1H–1H–1H (500 MHz) experiment in Fig. 10(a) for powdered L-alanyl-L-aspartic acid. The MAS frequency was 12.5 kHz and FSLG [30]homonuclear decoupling (m1 = 100 kHz) was applied in the t1 and t2

dimensions. (Reprinted with permission from Ref. [71].)

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1H Chemical Shift

13C

Che

mic

al S

hift

1 H Che

mica

l Shi

ft

F 2: 1H Chemical Shift

F1:

1 H C

hem

ical

Shi

ft

14710

10

7

4

1313

1

ppm

ppm

F 3CH (Asp)

CH (Ala)

CγO (Asp)

Fig. 12. F1 � F2 slices extracted at the isotropic carbon resonances along the F

experiment in Fig. 10(b) for powdered L-alanyl-L-aspartic acid. A 1H–13Chomonuclear decoupling (m1 = 100 kHz) was applied in the t1 and t2 dimension[71].)


the CH2 moiety. At longer mixing times, cross peak inten-sity is also observed between the CH2 and NH3 resonances.An analysis of the spin-diffusion coefficients (see Section3.3) determined for the intra-CH2 and CH2–NH3 crosspeaks reveals a factor of three difference; this differencecannot be explained in terms of the different H–H distancesalone, but rather requires the additional consideration ofthe fast NH3 rotation [64].

The applicability of 1H–1H spin-diffusion CRAMPSexperiments to the study of molecular structure is clearlyevident from recent applications using DUMBO[33,37,66] homonuclear decoupling at the much fasterMAS frequency of 22 kHz to the b-AspAla dipeptide (seeFig. 9) [67,68]. As described in Section 3.3, it was shownthat the buildup of intensity for the different resolved peaksin the two-dimensional spin-diffusion spectra can be fittedusing a multi-spin kinetic rate matrix approach so as todetermine the unit cell parameters [67] as well as, in combi-nation with molecular modelling to generate trial struc-tures, the molecular conformation [68].

Three-dimensional spin-diffusion experiments incorpo-rating windowless homonuclear decoupling in t1 and t2

04080160 120

1

4

7

10

13

13 C Chemical Shift / ppm

1 H C

hem

ical

Shi

ft /

ppm

CH3

CH3

CH2CγO

CH2

CH(Asp)

2 CH

NH3

NH

CγOOH

7

CH2

CH3

CH(Ala)

3 dimension from a 3D spectrum obtained with the 1H–1H–13C (500 MHz)slice is also shown. The MAS frequency was 12.5 kHz and FSLG [30]s. The CP contact time was 150 ls. (Reprinted with permission from Ref.

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have also been presented [56,71]. Fig. 10 presents the pulsesequences for a 1H–1H–1H and a 1H–1H–13C experiment,with corresponding spectra of powdered L-alanyl-L-asparticacid (note that this dipeptide has a different chemical struc-ture to the b-AspAla dipeptide in Fig. 9) being presented inFigs. 11 and 12, respectively. Ref. [56] presents spin-diffu-sion spectra of an organic–inorganic zinc phosphonate.

t1 LG t2tmix

{1H-LG}1H MAS 2D e

HO

C6H5

CH2

HO

C6H5

CH2

t1 LG t2tmix

{1H-LG}1H MAS 2D exchange

HO

C6H5

CH2

HO

Cφφ6H5

CH2

t 10mix μs t 500mix μs t 1mix ms

Fig. 13. Two-dimensional 1H–1H (400 MHz) spin-diffusion spectra of anorganic–inorganic zinc phosphonate Zn(O3PC2H4COOH)0.5C6H5NH2.The MAS frequency was 10 kHz and PMLG homonuclear decoupling(m1 = 60 kHz) was applied in t1. (Reproduced by permission of Elsevierfrom Ref. [56].)

{1H-LG} {1H-LG} 1H MAS detected exchange (3D)

2D slice @ 1-7ppm2D slice @ 12.8 ppm

t1 LG t2

tmix

t3 LG

HO

C6H5

CH2

{1H-LG} {1H-LG} 1H MAS detected exchange (3D)

2D slice @ 1-7ppm2D slice @ 12.8 ppm

t1 LG t2

tmix

t3 LG

HO

φ C6H5

CH2

a bFig. 14. A three-dimensional 1H–1H–1H (400 MHz) spin-diffusion spec-trum of an organic–inorganic zinc phosphonate Zn(O3PC2H4-

COOH)0.5C6H5NH2. The MAS frequency was 10 kHz and PMLGhomonuclear decoupling (m1 = 60 kHz) was applied in t1 and t2. F1 � F2

slices extracted at (a) 12.8 and (b) 1–7 ppm corresponding to the sharphydroxyl and broad overlapping CH2 and phenyl resonances are shown.(Reproduced by permission of Elsevier from Ref. [56].)

As well as a spectrum recorded for the two-dimensional1H–1H experiment incorporating homonuclear decouplingin t1 only (see Fig. 13), a three-dimensional 1H–1H–1Hspectrum is presented in Fig. 14.

3.2. 1H–1H spin-diffusion experiments under fast MAS

This section reviews applications of the two-dimensionalNOESY-type spin-diffusion pulse sequence of Fig. 1awhere fast MAS is required to achieve high resolution –this precludes a discussion of the application of this exper-iment to highly mobile systems, e.g., polymers above theglass transition where MAS of a few kHz is sufficient togive narrow resonances, e.g., Ref. [72].

Using perdeuteration to improve the 1H resolution (seeSection 2.1), Zheng et al. have presented 1H–1H spin-diffu-sion spectra for 90% deuterated oxalic acid dihydrate, aspar-tic acid, ammonium hydrogen oxalate hemihydrate andlithium hydrazinium sulphate at 10 kHz MAS [73]. Reverse2H to 1H cross polarisation was employed to overcome theproblem of much longer 1H T1 relaxation times due to thedeuteration. For the specific case of oxalic acid dehydrate(see Fig. 15), a quantitative analysis of the change in the mix-ing-time dependence of the cross peak intensities uponincreasing temperature allowed the determination of the rateand activation energy for 1H/2H exchange between the car-boxyl groups of the oxalate moiety and the water of hydra-tion – this chemical-exchange process was demonstrated tooccur much faster than 1H spin diffusion in these dilute sys-tems (see Fig. 16, where there are no cross peaks at 200 msmixing for perdeuterated aspartic acid).

MAS technology offering rotation frequencies of higherthan 30 kHz has been available only since the late 1990s.Before this time, there are few examples of 1H–1H spin-dif-fusion spectra under MAS alone due to the poor 1H reso-lution achievable for slower rotation frequencies. Schallerand Sebald have presented spin-diffusion spectra of ahydrous silicate glass at 10 kHz MAS [74]. Cross peaksbetween the broad yet resolved OH and H2O resonancesare observed. The absence of these cross peaks whenMREV-8 [57,58] is applied during the mixing time demon-strates that these cross peaks are due to 1H spin diffusion asopposed to chemical exchange or motion. In other exam-ples, Mirau and co-workers have presented spin-diffusionspectra at 13–14 kHz for various polymeric samples [75,76].

Table 2 lists recent applications of the 1H–1H MAS spin-diffusion experiment made possible by fast (>25 kHz)MAS. As an example, Fig. 17 presents 1H–1H spin-diffu-sion spectra obtained at 30 kHz MAS for an organicallymodified silicate gel [77]. At short mixing times (�5 ms),cross peaks are observed between the two types of Si–Hresonances. Only at longer mixing times (>100 ms), docross peaks appear between the Si–H and CH3 resonances.

Fig. 18 presents 1H–1H spin-diffusion spectra obtainedat 30 kHz MAS for an ethylene oxide tethered imidazoleheterocycle, which is a model compound for understandingproton-conducting polymeric materials [79]. At the

Fig. 16. 1H–1H (400 MHz) spin-diffusion spectra obtained at 10 kHzMAS for 90% perdeuterated aspartic acid. (Reprinted with permissionfrom Ref. [73].)

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Table 2Applications of the two-dimensional 1H–1H spin-diffusion experimentunder fast MAS (25+ kHz)

Sample mR/kHz Larmorfreq./MHz

Ref.

Organically modified silicate gel 30 600 [77]PEO/crosslinked-silicone 25 500 [78]Ethylene oxide tethered imidazole

heterocycles30 700 [79]

Imidazole-based composite materials 25 500 [80]Sol-gel hybrid materials 30 600 [81]Polyelectrolyte multilayer films 25 700 [82]Polyelectrolyte multilayers adsorbed

on silica25 500 [83]

Weathered K Al phosphate glass 30 600 [84]Hydrated cement 30 700 [85]PS/PVME blend 29 300 [86]

Fig. 15. 1H–1H (400 MHz) spin-diffusion spectra obtained at 10 kHzMAS for 90% perdeuterated oxalic acid dihydrate. (Reprinted withpermission from Ref. [73].)

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employed mixing time of 50 ms, the observed cross peaksare restricted to 1H–1H proximities within either the rigidordered or mobile disordered parts of the material, demon-strating that there is minimal contact between the two com-ponents of the material. Considering the resonancescorresponding to the disordered parts, cross peaks areobserved between the resonances corresponding to the eth-ylene oxide chain (3–4 ppm), the imidazole CH proton(6 ppm) and a mobile NH (10 ppm) – note that this latterresonance is filtered out in a 1H DQ spectrum (see Section4.2.6). It is evident that the relatively narrow resonancesdue to the mobile parts can be distinguished from thebroader signals of the ordered parts in the low-ppm partof the spectrum. For the ordered part, cross peaks are evi-dent between the aromatic (6 ppm) and the NH resonances(15 ppm). Fig. 19 presents 1H–1H spin-diffusion spectraobtained at 30 kHz MAS for a proton-conducting materialwhere imidazole is covalently linked to a linear polysilox-ane backbone [80]. In this spectrum, all peaks are correlat-ed with each other indicating a disordered mobile material.

3.3. Quantitative analysis of 1H spin diffusion

This section presents an overview of the variousapproaches that have been employed to extract structuralparameters from 1H spin-diffusion experiments (a compre-hensive review of these is beyond the scope of this article).

Commonly, spin diffusion is described phenomenologi-cally on the basis of Fick’s second law, leading to theextraction of the spin-diffusion coefficient, D. For a rigidsolid, D is typically determined to be on the order of

Fig. 17. 1H–1H (600 MHz) spin-diffusion spectra obtained at 30 kHz MAS for an organically modified silicate gel prepared by co-hydrolysingmethyldiethoxysilane (CH3)HSi(OEt)2 (DH) and triethoxysilane HSi(OEt)3 (TH). (Reproduced with kind permission from Springer Science and BusinessMedia from Ref. [77].)

N

NH

OO

N

HN

1

15 10 5 0 ppm20

15

10

5

0

50 ms mixing

rigid

mobile

Fig. 18. A 1H–1H (700 MHz) spin-diffusion spectrum obtained at 30 kHzMAS for an ethylene oxide tethered imidazole heterocycle. (Reprintedwith permission from Ref. [79].)

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4214 12 10 8 6 4 2 0 ppm

-4

-2

14

12

10

8

6

4

2

0

a

Fig. 19. 1H–1H (500 MHz) spin-diffusion spectra obtained at 25 kHz MAS witwhere imidazole is covalently linked to a linear polysiloxane backbone. (Repr


D = 0.6 � 0.8 nm2/ms�1 (note that the numerator anddenominator refer to nanometres and milliseconds, respec-tively), with lower values being observed in mobile solids[41,42]. Various expressions have been presented by whichstructural parameters such as domain size can be extractedfor different heterogeneous systems, e.g., polymeric materi-als of different morphologies and, in particular, taking intoaccount mobile components [42,47,62,87–93]. It is to benoted that this phenomenological approach has also beenapplied, for example, to characterise the interaction ofmobile lipids with a membrane protein [94].

The experimental applications described in the abovetwo sections correspond to the case of so-called spectralspin diffusion where high-resolution techniques allow theprocess of spin diffusion between resolved 1H resonancesto be followed. Spectral spin diffusion is a consequence ofzero-quantum transitions that occur due to overlap of thecorresponding single-quantum transitions. Theoretical

4214 12 10 8 6 4 2 0 ppm

-4

-2

14

12

10

8

6

4

2

0

b

h smix = (a) 20 ls and (b) 2 ms for a proton-conducting composite materialinted with permission from Ref. [80].)

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analysis reveals that this overlap is determined quantita-tively by the zero-quantum lineshape function gZQ(x)[95–97]. Under MAS, Kubo and McDowell have shownthat a uniform spin-diffusion time constant TSD can beevaluated after integration over all crystallite orientationsaccording to [98]:

1=T SD / d2jk½gZQðxRÞ þ gZQð�xRÞ þ gZQð2xRÞ=2

þ gZQð�2xRÞ=2� ð4Þ

While Eq. (4) provides the means to perform an ab initioprediction of experimental spin-diffusion behaviour, thequantitative reproduction of spin-diffusion dynamics re-mains a formidable challenge that is currently not feasiblefor real solid-state structures. This is principally becausethe quantitative determination of gZQ requires the consid-eration of a large multi-spin system – it has recently beenshown that the ZQ lineshape is affected by up to hundredsof neighbouring spins in the lattice [99,100]. Moreover, theanalysis is further complicated by the time dependence ofMAS as well as the need for powder averaging.

To overcome this problem, Emsley and co-workers haverecently proposed the modelling of experimental spin diffu-sion by a phenomenological multi-spin kinetic rate matrixapproach [67,68] that is analogous to treatments widelyused in solution-state NMR to describe multi-site chemicalexchange [101,102] that are based on the full relaxationmatrix protocol introduced by Macura and Ernst [103].In this approach, the peak intensities observed in a two-di-mensional exchange spectrum (see, e.g., Fig. 9) are givenby:

Fig. 20. Spin-diffusion build-up curves for specific resolved peaks extracted frothe dipeptide b-AspAla (see Fig. 9). The experimental values are compared tomatrix approach described by Eqs. (5) and (6) for two trial structures obtained(Reprinted with permission from Ref. [68].)

P ijðsSDÞ ¼ exp½�KsSD�ijM0zj; ð5Þ

where sSD is the spin-diffusion mixing time and M0zj is the

intensity of the jth peak at sSD = 0. K is a N · N matrixof the exchange rates kij between the N different resonancesin the spectrum, which are given by (for i „ j):

kij ¼ AX

k

l0c2H�h

4p

� �21

ðrnijÞk

; ð6Þ

where k indicates the sum over spin-exchange processesoccurring between sites i and j in different molecules inthe crystalline lattice, and A is a phenomenological scalingfactor. The exponent n can either be a fitting parameter orset equal to 6 (see Eq. (2)). In Ref. [67], it is shown that thefitting of experimental 1H–1H spin-diffusion CRAMPSspectra for the b-AspAla dipeptide (see Fig. 9) to Eqs. (5)and (6) is particularly sensitive to the unit cell parameters(assuming a known molecular conformation). Moreover,it has recently been demonstrated that the three-dimension-al solid-state structure of the dipeptide can be determinedto within a rmsd of 0.3 A of the known crystal structureby utilising molecular modelling so as to generate trialstructures for which the calculated spin-diffusion behaviourcan be compared to the experimental data (see Fig. 20)[68].

4. 1H double-quantum spectroscopy

A commonly employed alternative approach for observ-ing proton–proton proximities is 1H double-quantum spec-

m two-dimensional 1H–1H (500 MHz) spin-diffusion CRAMPS spectra ofthe curves (dashed and solid lines) derived from the multi-spin kinetic rate

by molecular modelling that differ from each other by a rmsd of 0.12 A.

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Fig. 21. DQ excitation efficiency for a (90�x � s � 90��x)(90�y � s � 90��y) 90�x DQ-filtered experiment. Solid line: numericaldensity matrix simulation including finite pulse-length effects; dotted line:a direct calculation based on average Hamiltonian theory; diamonds: 1H(500 MHz) experimental data (5 kHz MAS, 3 ls 90� pulse length)obtained for the proton pairs in tribromoacetic acid. (Reproduced bypermission of Elsevier from Ref. [24].)


troscopy [23–25]. A pulse sequence and coherence transferpathway diagram for a generic two-dimensional 1H DQexperiment is shown in Fig. 1(b), while Fig. 2 comparesschematic two-dimensional NOESY-type SQ-SQ andDQ-SQ correlation spectra. An important distinction isthat auto peaks (i.e., AA and BB) are always present onthe diagonal in SQ-SQ spectra and do not give any infor-mation about A–A or B–B proximities. By contrast, peaksalong the F1 = 2F2 diagonal in a DQ-SQ spectrum (corre-sponding to, e.g., AA or BB DQC) can only arise if thereis a dipolar coupling between the like nuclei.

The ready identification of a coupling between two par-ticular nuclei via the characteristic double-quantum fre-quency (equal to the sum of the two individual chemicalshifts) has made two-dimensional DQ spectroscopy a widelyapplied technique in solid-state NMR of spin I = 1/2nuclei. In solution-state NMR, a 13C–13C DQ-SQ two-di-mensional correlation experiment that enables the assign-ment of 13C resonances via the identification of J-coupledcorrelation peaks has been termed the INADEQUATE(Incredible Natural Abundance DoublE QUAntum Trans-fer Experiment) experiment [104,105]. In the solid-state,DQC can be created via either through-bond J orthrough-space dipolar couplings. For example, the refo-cused INADEQUATE experiment [106,107] has identifiedthrough-bond connectivities in, e.g., cellulose polymorphs(13C–13C) [106,108,109], self-assembled hydrogen-bondednucleosides (15N–15N) [110], layered silicates [111] andphosphate glasses (31P–31P) [112]. While such J-correlationexperiments are nowadays being increasingly applied, formany years, it was the dipolar coupling that was almostexclusively used in solid-state NMR correlation experi-ments. In 1992, Nielsen et al. showed that rotational reso-nance [113] can be used to obtain a 13C–13C DQ correlationspectrum of 13C-labelled zinc acetate [114]. Dipolar DQcorrelation experiments have subsequently been appliedto, e.g., proteins (13C–13C) [115–117], silicate frameworks(29Si–29Si) [118] and phosphate glasses (31P–31P) [119–121].

In 1H solid-state NMR, the efficiency of current homo-nuclear decoupling sequences precludes the use of small1H–1H J couplings (typically less than 10 Hz as comparedto 1H linewidths of hundreds of Hz) to create DQC.Hence, all 1H DQ spectra presented to date for rigid sol-ids have employed dipolar couplings to establish DQ:SQcorrelation. This section, after first introducing the pulsesequences used to create 1H DQC, shows how 1H DQMAS spectroscopy probes proton–proton proximities aswell as allowing the quantitative determination of1H–1H dipolar couplings, hence yielding accurate pro-ton–proton distances or insight into dynamic processes.In particular, the focus is on illustrating the wide breadthof application to date of 1H DQ MAS spectroscopy. Thefinal section considers approaches other than brute-forcefast MAS for improving resolution in 1H DQ spectrosco-py, namely 1H DQ-SQ CRAMPS as well as 1H DQ-13Ccorrelation experiments.

4.1. The excitation of 1H double-quantum coherence

In the solid state, the first 1H multiple-quantum (MQ)experiments were performed on static samples by Baumet al. [122,123], with these spin-counting experiments[124] allowing the determination of the size of spin clustersby monitoring the time development of MQ coherence. Ina MQ experiment, it is not enough to simply excite theMQC, attention must be paid to the careful reconversionof the MQC back to the initial state, usually longitudinalmagnetisation, from which directly observable transversemagnetisation can be created by a single 90� rf pulse. Spe-cifically, Baum et al. employed a reconversion sequencewhich is the apparent time reversal of that used for excita-tion, such that the destructive interference of the many MQcoherences (of different orders) is prevented.

For the excitation of DQC under MAS, the interferencewith the sample rotation must be taken into account. Con-sider the 90�–s–90� pulse sequence element employed insolution-state NMR for the excitation of MQ coherence[1]. Under MAS, the excitation (and reconversion) time islimited to sR/2, since the rotor modulation causes theaction of the pulse sequence in the second half of the rotorperiod to be the time reversal of that which occurred in thefirst half of the rotor period – this is illustrated in Fig. 21.Starting with the suggestion of Meier and Earl [125,126],who adapted the static sequences used by Baum et al.[122,123] for MAS by phase switching every half rotor peri-od to prevent the process of self time reversal, many differ-ent approaches have been presented which allow excitation


(and reconversion) times of one or more rotor periods.Such pulse sequences which counteract the effect of MASare referred to as recoupling methods [127,128], examplesof which have been used in homonuclear DQ MASNMR spectroscopy include BABA [129], C7 [130] andPOST-C7 [131], CMR7 [132], DRAMA [133], DRAWS[134], and HORROR [135]. Such sequences can be classi-fied on the basis of symmetry principles introduced byLevitt [136].

The method of choice for 1H DQ MAS experiments atfast MAS frequencies (>30 kHz) has to date been theBABA [129] sequence, which derives its name from thepresence of BAck-to-BAck pulses. The sequence consistsof segments of duration half a rotor period, where anevolution period is bracketed by two 90� pulses, with thephases of the pulses in adjacent segments being shifted by90�. This shifting of the phases achieves a negation of thespin-part of the DQ Hamiltonian, which exactly compen-sates the negation of the spatial part caused by MAS[24,137]. The BABA sequence was used initially in the con-text of a heteronuclear 13C–1H MQ coherence experiment[129], and was adapted for homonuclear 31P DQ MASexperiments [138,139], with modified two- and four-sR ver-sions having been employed, which provide compensationwith respect to offset and pulse imperfections [140]. Thefirst application of the BABA recoupling sequence in 1HDQ MAS spectroscopy coincided with the first 1H DQMAS experiments at 35 kHz MAS using a 2.5 mm MASprobe [6].

An important distinction has to be made between DQrecoupling methods as to whether there is an amplitudeor phase dependence on the rotor phase: sequences suchas BABA or DRAMA have an amplitude-dependence onthe rotor phase, while sequences such as HORROR or

Fig. 22. A two-dimensional 1H (500 MHz) DQ MAS spectrum of polycarbosequence due to Baum et al. [122]: (90y � s1 � 90x � s2 � 90�x � s1 � 90�y) wshifted by 90�. The MAS frequency was 14.8 kHz. The t1 increment was set e

C7 have a phase dependence on the rotor phase. Oneconsequence of this distinction is an improved powder-aver-aged DQ excitation efficiency for the latter phase-dependentsequences. However, in the context of two-dimensional 1HDQ MAS spectroscopy, there is a more important conse-quence which is evident when the t1 increment is not setequal to the rotor period, sR. For an amplitude-modulatedsequence such as BABA or DRAMA, an unusual spinning-sideband pattern is observed in the DQ dimension. As anexample, consider Fig. 22 which presents a two-dimension-al 1H (500 MHz) DQ MAS spectrum of polycarbonate[141], where the amplitude-modulated pulse sequence dueto Baum et al. [122] was employed for the excitation andreconversion of DQC. Unlike in the SQ dimension, wherethe intensity is concentrated in the centrebands (there isonly very weak sideband intensity), in the DQ dimension,there is a relatively weak centreband with the largestintensity at the ±1 sidebands. Similar 1H DQ MAS spin-ning-sideband patterns have been found for adamantane[142] using the DRAMA sequence for DQ excitation andreconversion as well as for barium chlorate monohydrate[143,144] and malonic acid [143] using a 90�–s–90�pulsesequence for DQ excitation and reconversion. The sameunusual concentration of intensity in the odd-orderspinning sidebands is also observed for 13C DQ MASspectra of 13C doubly labelled polyethylene [145] recordedusing the DRAMA sequence for DQ excitation andreconversion.

Such DQ spinning sidebands do not arise by the normalsingle-quantum mechanism, whereby the observed side-band pattern can be considered to map out the anisotropyof the spin interaction which is active during the evolutionperiod. Instead, it has been shown that the origin of suchspinning sidebands lies in the t1-dependent change in the

nate. DQC was excited and reconverted using a single cycle of the pulseith s1 = sR/4 and s2 = sR/2. For reconversion, the phases of all pulses werequal to 3 ls. (Reproduced by permission of Elsevier from Ref. [141].)


Hamiltonian active during the reconversion period relativeto that active during the excitation of DQC [142,143,145].This mechanism has subsequently been termed reconver-sion rotor encoding (RRE) [146]. The analysis of 1H DQMAS spinning sidebands so as to extract the structuraland dynamic information inherent to the 1H–1H dipolarcoupling is discussed in Section 4.3. It is to be noted thatrotor-encoded DQ MAS spinning-sideband patterns arenot observed for sequences with a phase-dependence onthe rotor phase such as HORROR or C7. There is insteada simple frequency shift corresponding to a multiple of thespinning frequency (the particular multiple depends on thespecific sequence) of the correlation peaks [142].

4.2. Rotor-synchronised two-dimensional 1H DQ MAS

experiments

While the first 1H DQ MAS two-dimensional spectrawere recorded with large spectral widths so as to observethe DQ spinning-sideband patterns [141–143], the majorityof subsequently presented 1H DQ MAS experiments havebeen recorded in a rotor-synchronised fashion, i.e.,Dt1 = sR. Rotor synchronisation has the advantage ofreducing the number of t1 increments required, and hencereducing the experimental time for the two-dimensionalexperiment (1H DQ MAS experimental times are usuallynot limited by sensitivity, but rather depend on the require-ment to complete the phase cycle). In addition, the sensitiv-ity is improved by the folding in of signal from thesideband positions into the centreband, as opposed to thesignal intensity being spread over the centreband and side-bands. In a rotor-synchronised experiment, it is a require-ment that the MAS frequency is sufficiently large toensure that the spectral width covers the full range of theDQ peaks. Provided that the States [147] method(SW(F1) = 1/Dt1 = mR) as opposed to the TPPI [148]method (SW(F1) = 1/2Dt1 = mR/2) is employed to obtainsign discrimination in F1, the achievable F1 (DQ) spectralwidth at 30 kHz MAS of 60 ppm (500 MHz) or 43 ppm

Fig. 23. (a) A representative rotor-synchronised 1H DQ MAS spectrum. (b)peaks; the observed AB and CC peaks (filled circles) imply the proton–protoninequivalence of the aromatic protons A, B and C is a consequence of intermole[150].)

(700 MHz) is sufficient given that the 1H SQ chemical shiftrange is usually less than 20 ppm.

The appearance of a representative rotor-synchronised2D 1H DQ MAS spectrum is illustrated in Fig. 23. Sincethe DQ frequency corresponding to a given DQC is simplythe sum of the two SQ frequencies, DQCs between like(AA) and unlike (AB) spins can, in general, be distin-guished in that, in the former case, a single peak at (2mA,mA)is observed, while, in the latter case, two peaks at(mA + mB,mA) and (mA + mB,mB) are observed. (The notation(m1,m2) refers to a DQ peak centred at m1 and m2 in the F1

and F2 dimensions, respectively).To a first approximation, which is fully valid in the limit

of short recoupling times and for an isolated spin pair, itcan be shown that the efficiency of DQC excitation isdirectly proportional to the dipolar-coupling constant, djk

[24,145]. (In this respect, a short recoupling time, srcpl,corresponds to the case where sin(djksrcpl) � djksrcpl). Sincethe reconversion to SQC efficiency has the same depen-dence, the integrated intensity of the DQ peaks due to agiven DQC, in this limiting case, is proportional to d2

jk.The inverse cubed dependence of djk on the internucleardistance, r, between the two nuclei (see Eq. (2)) means thatthe DQ peak intensity is inversely proportional to r6.Therefore, by a simple inspection of which peaks arepresent in a rotor-synchronised 1H DQ MAS spectrum,and, often more importantly, which are absent, muchinsight is obtained into proton–proton proximities. Forexample, in Fig. 23(a), only two of the six possible typesof DQ peaks – see Fig. 23(b) – are observed, which isconsistent with the structural arrangement shown inFig. 23(c). (As discussed below, in this particular case,the inequivalence of the aromatic protons A, B and C isa consequence of intermolecular ring-current effects.) Thereliability of such a semi-quantitative approach has beenclearly demonstrated for cases where an X-ray single-crystal structure is available to corroborate the proton–proton proximity information provided by 1H DQ MASspectra, e.g., Refs. [149–151].

A schematic representation showing the positions of the six possible DQproximities indicated in (c). As discussed below, in this particular case, thecular ring-current effects. (Reproduced by permission of Elsevier from Ref.


The remainder of this subsection reviews the wide vari-ety of applications to date of rotor-synchronised 1H DQMAS spectroscopy to rigid solids. It is to be noted that thisfocus precludes a discussion of the valuable insight intodynamics provided by the determination of 1H–1H dipolarcouplings from 1H double-quantum (DQ) MAS experi-ments for systems such as polymer melts [152] and elasto-mers [153] where narrow (solution-like) 1H spectra areobtained under moderate MAS [154].

4.2.1. Benzoxazine oligomers

The first published application of rotor-synchronised 1HDQ MAS spectroscopy was to the case of alkyl-substitutedbenzoxazine dimers (N,N-bis(3,5-dimethyl-2-hydroxyben-zyl) ‘‘R’’ amine, where ‘‘R’’ = methyl, ethyl, n-propyl,n-butyl) [149]. The motivation for studying these com-

a

b c

d e

Fig. 24. (a) The 1H (500 MHz) MAS (mR = 35 kHz) spectra of the methyl (soregions of rotor-synchronised 1H DQ MAS spectra of (b) the methyl and (c) thereconvert DQ coherence. (d,e) Schematic representations of the proposed arranchain-like structure. (Reprinted with permission from Ref. [149].)

pounds was their role as model compounds for a thenrecently developed class of phenolic materials, the poly-benzoxazines [155], which were found to have a numberof unusual, but commercially favourable, properties, inparticular a near-zero shrinkage or volume expansion uponcuring (polymerisation) as well as low water absorption.

In Fig. 24(a), the 1D 1H (500.1 MHz) MAS(mR = 35 kHz) spectra of the methyl (solid line) and ethyl(dashed line) dimers are superimposed. Note that thespectra demonstrating the resolution enhancement effectof increasing the mR in Fig. 5 are for this ethyl benzox-azine dimer. Of most importance are the clear differencesbetween the two spectra in the high-ppm region, whichcorresponds to the hydrogen-bonded protons. For theethyl dimer, in addition to the peaks due to the aliphaticand aromatic protons, two resonances at 13.2 and

lid line) and ethyl (dashed line) benzoxazine dimers. (b,c) The high-ppmethyl dimers. One rotor period of BABA recoupling was used to excite andgement of (d) the methyl dimers into pairs, and (e) the ethyl dimers into a

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8.2 ppm can be identified. By comparison, for the methyldimer, a single peak at 11.2 ppm, together with a shoulderat 7.2 ppm (this peak is better resolved in the 1H 2D DQMAS spectrum – see below), is observed.

Fig. 24(b) and (c) show the high-ppm regions ofrotor-synchronised 1H 2D DQ MAS NMR spectrarecorded for the methyl and ethyl dimers, respectively.The labels refer to the SQ resonances of the hydrogen-bonded (A and B), aromatic (C), and aliphatic (D)protons, respectively. For the methyl dimer, an X-raysingle-crystal structure exists, which indicates that thedimers form themselves into pairs [156]. This X-ray studywas, however, not able to locate the positions of the vitalhydrogen-bonded protons. Fig. 24(d) presents a sche-matic representation of a pair of methyl dimers linkedby an extended hydrogen-bonded arrangement, the latterhaving been proposed on the basis of molecular model-ling results.

The validity of the structural model in Fig. 24(d) is prov-en by the 1H DQ MAS spectrum in Fig. 24(b). First, theobservation of two hydrogen-bonded resonances isexplained: A and B correspond to the O–H� � �N and O–H� � �O protons, respectively, while the observation of astrong AB cross peak and the absence of an AA auto peakis consistent with the extended hydrogen-bonded arrange-ment in Fig. 24(d). The presence of a strong CC auto peakis interesting: for an isolated pair of dimers, there are nonearby aromatic protons which are close enough to explainthis observation, rather the crystal structure indicates aclose approach of aromatic protons belonging to differentpairs of dimers.

Although the 1H DQ MAS spectrum of the ethyl dimerin Fig. 24(c) is similar to that of the methyl dimer inFig. 24(b), for example, a clear AB cross peak betweenthe O–H� � �N and O–H� � �O protons can be identified, soproviding evidence for the same type of extended N� � �H–O� � �H–O hydrogen-bonded link in both samples, thereexist some marked differences. The most striking differenc-es between the methyl- and ethyl-dimer spectra are, while

Fig. 25. 1H (700 MHz) MAS (mR = 30 kHz) spectra of a methyl-substituted brecoupling was used to excite and reconvert DQ coherence. The labelling ofaliphatic protons. (Reprinted with permission from Ref. [158].)

for the methyl dimer, there is a strong aromatic auto peak(CC) and only weak intensity corresponding to a DQCbetween a O–H� � �N and an aromatic proton (AC), the sit-uation is reversed for the ethyl dimer.

This difference between the methyl and ethyl dimers canbe explained if one of the aromatic rings is flipped such thatinstead of pairs of hydrogen-bonded dimers there existhydrogen-bonded chains as shown in Fig. 24(e). In addi-tion, this alternative packing arrangement gives rise to aclose proximity of the O–H� � �O proton and the N-ethylchain. The resulting cross peak between the O–H� � �O pro-ton and the ethyl-chain CH2 protons (BD) is, indeed, clear-ly seen in the DQ MAS spectrum of the ethyl dimer(Fig. 24(c)).

A 1H (700 MHz) DQ MAS spectrum of a 15N labelledmethyl benzoxazine dimer has also been presented in Ref.[157], where 15N–1H experiments confirmed the assignmentdiscussed above and allowed the N� � �H distance to bedetermined as 194 ± 5 pm.

Fig. 25 shows 1H (700 MHz) DQ MAS spectraobtained in a follow-up study, for a methyl-substitutedbenzoxazine dimer, trimer and tetramer [158]. It is evidentthat there is an increase in the number of low-field reso-nances corresponding to the number of distinct N� � �Hprotons in the dimer, trimer and tetramer molecular struc-tures. While AB cross peaks between the O–H� � �N andO–H� � �O protons are observed in all three spectra, a cor-relation (AA 0) indicative of close proximity of two distinctO–H� � �N protons is only observed for the trimer. While itwas not possible to obtain crystal structures for the tri-mers and tetramers, the different DQ peak patterns wereexplained on the basis of ab initio chemical shift calcula-tions for geometries determined by molecular modellingand subsequent ab initio optimisation. The increase incomplication in the spectrum on going to the tetramerwas shown to be consistent with the spectrum obtainedfor crosslinked, high molecular weight polybenzoxazinewhere the overlap of different types of hydrogen-bondedresonances leads to a broadened spectrum.

enzoxazine (a) dimer, (b) trimer, (c) tetramer. One rotor period of BABAthe resonances is: A, A 0, A00 N� � �H, B OH, C, D aromatic protons, E, F

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4.2.2. Alkyl-substituted hexabenzocoronenes1H DQ MAS spectroscopy has been extensively applied

in the study of the structure and dynamics of alkyl-substi-tuted hexabenzocoronenes, 1 [159]. In particular, insighthas been provided into the role of aromatic p–p interac-tions in determining the adopted supramolecular structurebecause of the marked sensitivity of the 1H chemical shiftto aromatic ring-current effects [160].

Fig. 26(a) presents a 1H (500 MHz) MAS (35 kHz)

Fig. 26. (a) 1H (500 MHz) MAS (mR = 35 kHz) spectrum and (b) rotor-synchronised 1H DQ MAS NMR spectrum, together with skyline SQ andDQ projections, of HBC-(CD2)C11. One rotor period of BABA recouplingwas used to excite and reconvert DQ coherence. (Reprinted withpermission from Ref. [161].)

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a
spectrum of the solid phase of HBC-(CD2)C11 [161] – thenotation refers to all six R substituents being 12-carbonn-dodecyl alkyl chains, with the sample having beensynthesised with the a-carbons deuterated (87%) in orderto carry out 2H NMR. Considering the individual mole-cules alone (and assuming full conformational flexibilityof the R alkyl groups), the effective sixfold symmetry ofthe aromatic core means that only one distinct aromaticproton resonance is expected, as is indeed found to bethe case in the solution-state 1H spectrum (not shown).However, in Fig. 26(a), three aromatic resonances areclearly identified.
Information about the relative proximities of the threeresolved aromatic protons is provided by the rotor-syn-chronised 1H DQ MAS 2D spectrum of HBC-(CD2)C11

in Fig. 26(b). While the strongest spectral intensity is thelow-ppm diagonal peak due to the many protons in thealkyl chains, the interest is in the peaks in the bottomleft-hand corner of the spectrum due to DQ coherencesinvolving only aromatic protons – this spectral region isactually that shown in Fig. 23(a). As is evident from themolecular structure of HBC-(CD2)C11, the 12 aromaticprotons are grouped in pairs of ‘‘bay protons’’ with a H–H distance of approximately 0.20 nm, while the closest dis-tance to another aromatic proton is 0.41 nm. Therefore,the aromatic region of the DQ MAS spectrum will be dom-inated, for the short DQ recoupling time used, by thedipole–dipole couplings within the three pairs. As notedabove (see discussion of Fig. 23), only two of the six possi-ble types of DQ correlation peaks are observed: CC diago-nal and AB cross peaks that imply the presence of only twotypes of pairs of aromatic protons, HA–HB and HC–HC, ina ratio, as given by the peak intensities, of 2:1.

For unsubstituted HBC, an X-ray single-crystal studyshows that the molecules pack in the so-called herringbone

pattern, which optimises the p–p interactions betweenadjacent discs [162]. In Ref. [161] it was hypothesised thatHBC-(CD2)C11 adopts the same columnar packing of thearomatic cores as in unsubstituted HBC, with the presenceof the long alkyl chains now meaning that the individualcolumns of aromatic cores are much more separated fromeach other. Fig. 27 shows qualitatively how such a stackingof the HBC cores leads to three different aromatic protonenvironments. Three aromatic cores are shown; themolecules above and below the central aromatic core areindicated by dashed and dotted lines, respectively, withthe aromatic protons of the central layer highlighted. Theinterplanar distance in unsubstituted HBC is 0.342 nm,and thus the aromatic protons of one layer will experiencethe ring currents of the extended p-electron systems of adja-cent layers. In HBC-C12, three different aromatic protonenvironments can thus be identified with respect to thedegree to which the proton experiences the ring current ofthe adjacent layers. The unshaded circles represent protonswhich lie neither above nor below the p orbitals of an

Fig. 28. Rotor-synchronised 1H (500 MHz) DQ MAS (mR = 30 kHz)NMR spectrum, together with skyline SQ and DQ projections, of theroom-temperature phase of as-synthesised HBC-C10COOH. Two rotorperiods of BABA recoupling was used to excite and reconvert DQcoherence. (Reproduced by permission of the PCCP Owner Societies fromRef. [212].)

Fig. 27. A representation of the stacking of the aromatic cores in HBC-C12, based on the structure of unsubstituted HBC, which is known, from aX-ray single-crystal study, to crystallise in the so-called herringbonepattern [162]. Three HBC-C12 molecules are shown; the molecules aboveand below the central HBC-C12 molecule are indicated by dashed anddotted lines, respectively. (Reprinted with permission from Ref. [161].)

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adjacent layer, and therefore correspond to the leastshielded resonance (highest ppm). Fully shaded andhatched circles then represent protons which lie over orbelow an inner and outer part, respectively, of an adjacentring system; the fully shaded protons would be expectedto be the most shielded. Assigning the unshaded, hatched,and fully shaded protons in Fig. 27 to the A, B and Cresonances in Fig. 26(b), respectively, the observed presenceof only AB and CC pairs in the ratio 2:1, with the Cresonance having the smallest chemical shift value (mostshielded), is then explained. Thus, the solid-state packingleads to a reduction from sixfold to twofold symmetry foreach individual molecule.

The advances in computing power as well as the devel-opment of methodology means that the use of first-princi-ples calculations (i.e., starting from a quantum-mechanicaldescription) of chemical shifts in the interpretation ofexperimental solid-state NMR results has become increas-ingly popular in the last 5 years, e.g., Refs. [79,151,158,163–211]. For the specific case of model HBC oligomers,the ab initio calculation of 1H chemical shifts [165] allowsthe quantitative assignment of the experimental observa-tion of three aromatic resonances in HBC-C12 (seeFig. 26) to a specific packing arrangement, with the quali-tative hypothesis of the adoption of the structure of unsub-stituted HBC (see Fig. 27) being proved. Moreover, thesecalculations show that the ring-currents effects are quitelong-range, with an aromatic ring still exerting an influence

at a distance of 0.7 nm, i.e., the next nearest HBC neigh-bour must be considered.

Consider the HBC derivative, HBC-C10COOH, whereall six alkyl chains have been capped by a terminal carbox-ylic acid group [212], such that hydrogen bonding as well asaromatic p–p interactions determine the supramolecularassembly. In the solid phase at T = 320 K, the presenceof hydrogen-bonded COOH dimers is demonstrated bythe observation of an auto COOH peak in the 1H DQMAS NMR two-dimensional spectrum – see Fig. 28. Con-sidering the COOH peak in the one-dimensional 1H MASspectra, as shown in Fig. 29(a), both a shift to low ppm ofthe peak position as well as an initial increase followed by asubsequent decrease in the linewidth are observed uponheating – these effects are represented graphically in Figs.30(a) and (b). (It is to be noted that the heating due to fric-tion at 30 kHz MAS is significant, and the correction termrelative to the bearing gas temperature was calibrated usingthe 119Sn resonance of Sm2Sn2O7 as a chemical shift ther-mometer [213].) These observations are interpreted in termsof a chemical-exchange process involving the making andbreaking of hydrogen bonds, with the coalescence pointcorresponding to T = 362 K. The equilibrium constant ata given temperature can be calculated from the observedchemical shift provided that the 1H chemical shifts of thehydrogen-bonded and free states are known. Only theCOOH protons in hydrogen-bonded dimers can give riseto a COOH auto peak in the 1H DQ MAS spectrum(Fig. 28), and thus the chemical shift of the hydrogen-

a

b

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Fig. 30. The effect of temperature on (a) the observed chemical shift and(b) the linewidth (FWHMH) in 1H MAS spectra (Fig. 29(a)), and (c) theintensity in 1H DQ-filtered MAS spectra (Fig. 29(b)) of the COOHresonance for a sample of as-synthesised HBC-C10COOH. In (c), inaddition to the crosses, which represent the experimental DQ-filteredintensities, the intensities which are expected on account of solely thecombined temperature dependence of the equilibrium constant and theNMR bulk magnetisation are shown as circles. Both the experimental andthermodynamically expected intensities are normalised relative to theT = 324 K case. In all plots, best-fit lines are included as a guide for theeye. (Reproduced by permission of the PCCP Owner Societies from Ref.[212].)

a b

Fig. 29. The effect of temperature on (a) 1H (500 MHz) MAS(mR = 30 kHz) and (b) 1H DQ-filtered (using two rotor periods of BABArecoupling) MAS NMR spectra of as-synthesised HBC-C10COOH.(Reproduced by permission of the PCCP Owner Societies from Ref. [212].)


bonded protons can be determined to be 12.1 ppm. Thechemical shift of the free COOH protons cannot be so eas-ily identified; however, the initially observed chemical shiftof 9.0 ppm for the COOH protons on heating into theliquid-crystalline phase is strikingly low, and it is thusassumed that the chemical shift of the free state can beassigned to this value. A thermodynamic analysis yieldsfor the opening of the hydrogen-bonded dimers:DH = 45 ± 4 kJ mol�1 and DS = 113 ± 11 J K�1 mol�1.

In 1H DQ-filtered (DQF) MAS spectra of HBC-C10COOH – see Fig. 29(b) – the intensity of the COOHpeak is observed, upon heating, to reduce faster thanexpected from thermodynamic factors alone, and aboveT = 380 K, no signal is detected – see Fig. 30c, where theexperimentally observed DQ signal intensities for theCOOH protons, relative to the intensity of the T = 324 Kspectrum, are shown as crosses, while circles represent theexpected reduction, again relative to the T = 324 K case,due solely to the combined temperature dependence ofthe equilibrium constant and the bulk magnetisation. AtT = 381 K, where the COOH peak intensity disappearsbelow the noise level in Fig. 29(b), the number of hydro-gen-bonded and free COOH protons are known, on thebasis of the thermodynamic analysis described above, tobe in the ratio �3:2; thus, the loss of signal cannot bedue to the absence of pairs of COOH protons in close prox-imity. To observe a signal in a DQF experiment, the hydro-gen-bonded form must exist for the duration of the DQ

filter part of the NMR experiment, i.e., 133 ls for the spec-tra in Fig. 29(b). It is then apparent that the fall off in theDQ intensity with increasing temperature can be explainedby a decrease in the proportion of hydrogen-bonded dimershaving lifetimes over 133 ls, until at T = 381 K, the con-centration is less than that required to observe an NMR

Table 31H DQ MAS of hexabenzocoronene derivatives, 1

Alkyl substituents Ref.

Rn = (CD2)C11(n-dodecyl) [161,165]Rn = CH(CH3)2 (iso-propyl) [150]Rn = C(CH3)3 (tert-butyl) [150,214]R1,2 = C(CH3)3 (tert-butyl); R3�6 = C12 (n-dodecyl) [24]Rn = CH2CH2CH(CH3)CH2CH2CH2CH(CH3)2 [25]Rn = PhCH2CH2CH(CH3)CH2CH2CH2CH(CH3)2 [25]Rn = CH2CH(C2H5)CH2CH2CH2CH3 [215]Rn = C10COOH [212]R1 = C3COOH;

R2�6 = CH2CH2CH(CH3)CH2CH2CH2CH(CH3)2

[216]

R1 = C10COOH;R2�6 = CH2CH2CH(CH3)CH2CH2CH2CH(CH3)2

[216]

R1,4 = C3COOH;R2,3,5,6 = CH2CH2CH(CH3)CH2CH2CH2CH(CH3)2

[216]


signal. In this way, an analysis of the DQF data yields thetemperature dependence of the dimer lifetimes, and hencethe kinetics of the chemical-exchange process involvingthe making and breaking of hydrogen bonds could bedetermined: the activation energy and Arrhenius parameterequal 89 ± 10 kJ mol�1 and 4.2 · 1016 s�1, respectively.

Fig. 31. 1H (700 MHz) DQ-filtered (top) and rotor-synchronised DQ MAS (mR

derivatives (2a, HBC � 1C3COOH; 2b, HBC � 1C10COOH; 3, HBC � 1,4C3COrecoupling was used to excite and reconvert DQ coherence. The spectra of Hsuppression of the aliphatic peak at 1 ppm. (Reproduced by permission of Wi

Rotor-synchronised two-dimensional 1H DQ MASspectra have been presented for various other HBC deriva-tives – see Table 3 – with different DQ correlation peaksbeing indicative of different three-dimensional solid-statepacking arrangements – for example, consider Fig. 31.

4.2.3. Polyelectrolyte multilayers and self-assembled

monolayers

Fig. 32 presents 1H DQ MAS spectra of the polyelectro-lyte complex (PEC) formed by the strong electrolytespoly(sodium-4-styrene sulphonate) (PSS) and poly(diallyl-diammonium) chloride (PDADMAC) and PSS/PDAD-MAC polyelectrolyte multilayers (PEM) on silica colloids[82,217]. The arrows indicate DQ correlation peaksbetween the PSS aromatic protons and the PDADMACCH3 protons indicating an intimate contact between thetwo polymers in the polyelectrolyte complex and multilay-ers. A 1H DQ MAS spectrum has also been presented forthe polyelectrolyte complex formed by PSS and the weakelectrolyte poly(allylamine) hydrochloride (PAH) [83].The identification of these DQ correlation peaks for thesystems is considerably aided by the filtration in the DQexperiments on the basis of mobility (see the above

= 30 kHz) spectra (bottom) of three alkyl-substituted HBC carboxylic acidOH, see Table 3 for full chemical structures). One rotor period of BABA

BC-1C3COOH and HBC-1C10COOH were recorded with WATERGATEley from Ref. [216].)

10 8 6 4 2 0 ppm20

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0

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15

10

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Fig. 32. 1H (500 MHz) DQ MAS (30 kHz) spectra of (top) the polyelec-trolyte complex (PEC) formed by PSS and PDADMAC and (bottom)PSS/PDADMAC multilayers on silica colloids. Two rotor periods ofBABA recoupling was used to excite and reconvert DQ coherence.(Reproduced by permission of Wiley from Ref. [217].)

Fig. 33. 1H (500 MHz) DQ MAS (30 kHz) spectra of HO2C(CH2)2PO3H2 in (rotor periods of BABA recoupling was used to excite and reconvert DQ cohe


discussion of Fig. 30(c)) of the narrow resonances due towater and hydrogen-bonded silanols [82,217].

Hydrogen-bonding interactions in the self-assembledmonolayers formed by diacids HO2C(CH2)nPO3H2 (n = 2,3, 11, and 15) adsorbed on nano-crystalline TiO2 and ZrO2

have also been studied by 1H DQ MAS [218]. As an example,Fig. 33 compares the 1H DQ MAS spectra obtained forHO2C(CH2)2PO3H in the bulk phases and adsorbed onnanoZrO2 – the different cross peaks are clearly indicativeof different hydrogen-bonding arrangements as shown.

4.2.4. Host–guest interactions1H solid-state NMR is well suited to obtaining structural

and dynamic insight for supramolecular host–guest com-plexes. Consider the specific complex, 2@3. The receptor 2

belongs to a family of molecules termed molecular tweezersdue to their concave–convex topology and propensity toselectively form complexes with electron-deficient aromaticand aliphatic compounds as well as organic cations [219].This and other molecular tweezer host–guest complexes havebeen studied by 1H solution-state NMR, exploiting the largeupfield shifts of the substrate resonances upon complexationcaused by host aromatic ring currents. For the specific com-plex between the naphthalene-spaced tweezer 2 and 1,4-dicy-anobenzene 3, complex formation and dissociation in CDCl3at room temperature is fast with respect to the NMR time-scale, as evidenced by a single guest 1H resonance shiftedby 4.35 ppm relative to that observed for 3 alone. A solid-state investigation has the advantage that the guest remainscomplexed on the timescale of the NMR experiment, andthus the structure and dynamics of the host–guest complexcan be probed directly [151,171,208].

a) the bulk state and (b) adsorbed on nanocrystalline zirconia, ZrO2. Tworence. (Reprinted with permission from Ref. [218].)

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Fig. 34(a) presents a rotor-synchronised 1H (700 MHz)

b

Fig. 34. (a) Rotor-synchronised 1H (700 MHz) DQ MAS NMR spectrum,together with skyline projections, of 2@3. (b) The aromatic region of a1H–13C REPT-HSQC NMR correlation spectrum, together with sumprojections, of 2@3. The recoupling time equalled one rotor period, suchthat predominantly only one-bond correlations are selected. Both spectrawere recorded under MAS at 30 kHz. The notation 2ar and 2al refers tohost aromatic and alkyl protons, respectively, while 3a and 3b refer to thetwo distinct guest aromatic protons. (Reproduced by permission of Wileyfrom Ref. [151].)

DQ MAS NMR spectrum of 2@3 [151]. The assignmentof the resolved 1H DQ peaks is aided by reference toFig. 34(b), where the aromatic region of a 1H–13C hetero-nuclear correlation spectrum of 2@3, recorded with theREPT-HSQC experiment [220,221], is presented. A shortexcitation time was used such that predominantly onlyone-bond C–H correlations are observed. In solution, thearomatic CH resonances of 2 and 3 are found between116.5 and 124.1 and at 131.0 ppm, respectively. The rela-tive insensitivity of 13C chemical shifts to ring-currenteffects then allows the clear assignment of the two separatepeaks at 13C chemical shifts of 129.6 and 128.7 ppm inFig. 34(b) to the guest CHs (labelled 3a and 3b), with thecorresponding 1H chemical shifts being 5.6 and 2.0 ppm,respectively. The pair of cross peaks at a DQ frequencyof 7.6 ppm in Fig. 34(a) can thus be identified as beingdue to two neighbouring guest CH protons.

The observed experimental features can be qualita-tively understood by reference to the structure of 2@3,which is known from an X-ray single-crystal analysis[222]. In Fig. 35(a), the side-by-side arrangement oftwo 2@3 complexes is displayed, while Figs. 35(b), (c)and (d) show views through the different host aromaticmoieties. It is apparent that the two guest aromatic pro-tons experience the ring currents due to the host to dif-ferent degrees.

Ab initio quantum-chemical calculations have beenperformed [151,171], thus enabling a fully quantitativeinterpretation of the experimental results. Good agree-ment is obtained between the monomer calculation for asingle 2@3 complex (monomer) and the experimental sol-id-state guest 1H chemical shifts, indicating that these val-ues are largely determined by intracomplex effects. Incontrast, the marked difference between the solid- andsolution-state 1H chemical shifts of the end pair of hostaromatic protons (H2,3,14,15) can only be explained byconsidering a pair of 2@3 complexes in the arrangementshown in Fig. 35(a) (dimer). By calculating the 1H chem-ical shifts of the guest protons due to the three host aro-matic moieties, namely the central naphthalene unit(Fig. 35(b)), and the inner (Fig. 35(c)) and outer benzenering (Fig. 35(d)), the quantum-chemical calculations werefurther able to elucidate the role of the different chemicalunits. First, it was found that the guest 1H chemical shifts

derived by summing the changes due to the separate aro-matic moieties are in good agreement with the values cal-culated for the whole system. It can thus be concludedthat the only influence of the linking units is to determinethe positioning of the host aromatic moieties. Second, thedifference between the guest 1H chemical shifts is mainlydue to the arrangement of the guest with respect to theinner benzene ring (Fig. 35(c)).

Fig. 36 presents slices at a DQ frequency of 7.6 ppm tak-en from 1H DQ MAS spectra of 2@3 (see Fig. 34) recordedat different temperatures. The peaks due to the guestprotons, Ha (5.6 ppm) and Hb (2.0 ppm), disappear upon

a b

Fig. 36. The effect of temperature, T, on slices at a DQ frequency of7.6 ppm taken from 1H (700 MHz) DQ MAS NMR spectra of 2@3. Atthe bottom, the dynamic processes consistent with the observed NMRresults are shown. The two processes, (a) and (b), cannot be distinguishedby current NMR experiments. (Reproduced by permission of Wiley fromRef. [151].)

a

b

c

d

Fig. 35. The solid-state packing arrangement of 2@3, as determined by anX-ray single-crystal investigation [222]. Large white, large black, and smallwhite circles represent nitrogen, carbon, and hydrogen atoms, respectively.In (b), (c) and (d), views through the naphthalene, inner benzene and outerbenzene rings, respectively, are shown. The distance from Hb to the centreof the inner benzene ring is 260 pm (view (c)) as opposed to 404 pm to themiddle of the naphthalene unit (view (b)) and 314 pm to the centre of theouter benzene ring (view (d)). Specific carbon and hydrogen atoms arelabelled according to the above chemical structure. (The notation xa refersto the quaternary carbon between carbons x and x+1.) (Reproduced bypermission of Wiley from Ref. [151].)


heating, indicating dynamic processes, (see Fig. 36) wherethe two types of guest protons are exchanged by either(A) a 180� flip about the long axis of the guest, or (B) arotation between two equivalent sites in the complex.

Inclusion compounds formed by polymers such aspoly(dimethylsiloxane) (PDMS) with small molecules suchas c-cyclodextrin represent an interesting class of material.As illustrated in Fig. 37, cyclodextrins are able to arrangethemselves so as to form channel-like cavities such that in

an inclusion compound the polymer chains exhibit unidi-rectional ordering. The 1H DQ-filtered spectra inFig. 37(a) demonstrate that the narrow resonances corre-sponding to mobile protons, e.g., free water, are removedas compared to the one-pulse spectrum. In this way, theintimate contact of the polymer CH3 protons with thecyclodextrin hydroxyl protons can be identified by the pairof cross peaks indicated by the bold horizontal line in the1H DQ MAS spectrum in Fig. 37(b) [223]. (Clear analogiescan be noted to the 1H DQ MAS 1D filtered and 2D spec-tra presented for the polyelectrolyte complex and multilay-ers in Section 4.2.3.)

As a further example, consider tris(o-phenylenedi-oxy)spirotriphosphazene (TPP) which forms asupramolecular structure with channels of diameter�4.5 A. Fig. 38 presents a 1H DQ MAS spectrum of TPPwith the linear-chain alkane C9H20 [224]. The intimate

a b

Fig. 37. (a) 1H (500 MHz) one-pulse and DQ-filtered MAS (30 kHz) spectra and (b) a two-dimensional DQ MAS spectrum of an inclusion compoundformed by poly(dimethylsiloxane) (PDMS) with c-cyclodextrin (CD). ‘‘ch’’ indicates the signal due to a cyclohexane impurity. In the structure picture, theCH3 groups in light grey are pointing away from the viewer. (Reproduced by permission of Wiley from Ref. [223].)


contact of the host and guest is indicated by the cross peakat a DQ frequency of �0.8 + 7.5 = 6.7 ppm between thealkane protons (shifted to a low-ppm value due to ring-cur-rent effects) and the aromatic TPP protons. Ref. [224] fur-ther shows that the relative intensity of the alkane crosspeak as opposed to the alkane diagonal peak decreases

slightly upon increasing temperature (in the range 320–390 K), with the relative cross peak intensity also changingfor inclusion compounds with different linear alkanes.

The final example in this section concerns the trappingof solvent molecules in supramolecular organic nanotubesformed by calix[4]hydroquinone (CHQ) crystallised from

Fig. 38. 1H (500 MHz) DQ MAS (30 kHz) spectrum of the inclusioncompound of tris(o-phenylenedioxy)spirotriphosphazene (TPP) with thelinear-chain alkane C9H20. Four rotor periods of BABA recoupling wasused to excite and reconvert DQ coherence. (Reprinted with permissionfrom Ref. [224].)

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Fig. 39. 1H (700 MHz) DQ MAS (30 kHz) spectrum of supramolecularorganic nanotubes formed by calix[4]hydroquinone (CHQ) crystallisedfrom a water/acetone mixture. One rotor period of BABA recoupling wasused to excite and reconvert DQ coherence. (Reproduced by permission ofElsevier from Ref. [179].)


a water/acetone mixture [179]. Fig. 39 presents a 1H DQMAS spectrum; the double-headed arrow shows a DQ sig-nal linking the acetone methyl protons with the CHQ aro-matic protons. This demonstrates that the acetonemolecules do not form a separate phase, but are rathertrapped inside the CHQ bowls and are thus in close contactwith the aromatic rings in the CHQ nanotube.

4.2.5. Keto–enol tautomerism

As is apparent from Figs. 24, 25 and 33 above, the sen-sitivity of the 1H chemical shift to hydrogen bondingmakes 1H solid-state NMR ideally suited to followingchanges in hydrogen-bonding arrangements [28]. In par-ticular, the identification of specific proton–proton prox-imities in 1H DQ MAS spectra makes the techniqueideally suited to probing temperature-dependent changesin the equilibrium between the tautomeric structures ofthe ureido-pyrimidinone moieties shown in Fig. 40[24,225]. In the keto form, there are three distinct hydro-gen bonding arrangements: intramolecular NH� � �O, andintermolecular NH� � �N and NH� � �O; these correspondto the Ha, Hb, and Hc resonances in the 1H DQ MASspectrum at the top of Fig. 41(b), with DQ peaks corre-sponding to the Hb–Hb and Hb–Hc close proximities

Fig. 40. Tautomeric structures of the ureido-pyrimidinone moiety. Theletters a and b denote the keto and enol tautomers, respectively. In thesupramolecular polymers, 3, the monomers are short linear aliphaticchains with hydrogen-bonding entities at both ends. (Reproduced bypermission of Elsevier from Ref. [24].)

a

c

b

Fig. 41. (a) Tautomeric rearrangement of the ureido-pyrimidinone moi-eties observed for the supramolecular polymer (see 3a and 3b in Fig. 40)upon heating. (b) Regions of 1H (700 MHz) DQ MAS (30 kHz) spectracorresponding to the hydrogen-bonded resonances. One rotor period ofBABA recoupling was used for the excitation and reconversion of DQcoherence. (c) The temperature-dependent change in the tautomerconcentrations as determined by the 1H DQ signal intensities. (Repro-duced by permission of Elsevier from Ref. [24]).

a b

Fig. 42. 1H (700 MHz) DQ MAS (30 kHz) spectra of the keto dimer (2a in Fig.reconversion of DQ coherence. While (a) corresponds to a conventional 1H DQmagnetisation that had passed a preceeding 1H–15N REPT-HSQC filter thatElsevier from Ref. [226]).


being observed. By contrast, for the enol form, the threedistinct hydrogen bonding arrangements are intermolecu-lar OH� � �O and NH� � �N and intramolecular NH� � �N;these correspond to the Ha, Hb, and Hc resonances inthe 1H DQ MAS spectrum at the bottom of Fig. 41(b),with DQ peaks corresponding to the Ha–Hb and Hb–Hb

close proximities being observed. The observation of dis-tinct DQ peaks for the two tautomeric forms allows theconcentration of the two forms to be determined fromthe 1H DQ signal intensities – see Fig. 41(c), which showsthe change in the equilibrium upon increasing thetemperature.

Fig. 42(a) presents a 1H DQ MAS spectrum for the ketodimer (2a in Fig. 40). It is evident that the cross peaksbetween the hydrogen-bonding resonances Ha and Hc

and the aliphatic protons (at 1 ppm) are missing at thealiphatic SQ frequency. This phenomenon is commonlyobserved for cross peaks to alkyl chain protons. Ref.[226] presents a filtering experiment which yields cleancross peaks to such alkyl protons. For the spectrum inFig. 42(b), the 1H DQ MAS pulse sequence was appliedto 1H magnetisation that had passed a preceding 1H–15NREPT-HSQC [220,221] filter that selects the N–H reso-nances (Ha and Hb) – note that the dimer was synthesisedfrom 15N1-guanidine, C(15NH)(NH2)2 such that one inthree nitrogens at the Ha and Hb sites are 15N labelled.The consequence is that only DQ coherences correspond-ing to close proximities involving the 15NH protons (Ha

and Hb) give rise to cross peaks in Fig. 42(b), and notablya clean pair of cross peaks involving the aliphatic protons isnow observed.

Armstrong et al. have also presented a 1H DQ MASspectrum of the same keto dimer, 2a in Fig. 40, but withR1 = CH3 [227]. As seen in Fig. 43, the same Hb–Hb andHb–Hc cross peaks are observed as in Fig. 42(a), though

40). One rotor period of BABA recoupling was used for the excitation andMAS experiment, in (b) the 1H DQ MAS pulse sequence was applied to 1Hselects the N–H resonances Ha and Hb. (Reproduced by permission of

N

NH

OO

N

HN

n

ppm

16 14 12 10 8 6 4 2 0 ppm

30

25

20

15

10

5

0

ppm

0

a

b

1H SQ / ppm15 10 5 0

3020

100

1 H D

Q /

ppm

Hb-Hb and Hb-Hc

Ha-Haliphatic

Hd-Haliphatic

Hd-Hd packing

Fig. 43. 1H (400 MHz) DQ MAS (35 kHz) spectra of the keto dimer (2a inFig. 40, with R1 = CH3). Two rotor periods of BABA recoupling wereused for the excitation and reconversion of DQ coherence. (Reproducedby permission of Wiley from Ref. [227]).

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iley

&S

on

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imit

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note the absence here of cross peaks between Hc and thealiphatic resonances.

16 14 12 10 8 6 4 2 0 ppm

ppm

30

25

20

15

10

5

ppm

16 14 12 10 8 6 4 2 0

30

25

20

15

10

5

0

c

Fig. 44. 1H (700 MHz) DQ MAS (30 kHz) spectra of ethylene oxidetethered imidazole heterocycles, n = (a) 1, (b) 2, or (c) 5. (Reprinted withpermission from Ref. [79].)

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4.2.6. Proton-conducting materials1H solid-state NMR provides valuable information

about the hydrogen-bonding protons of proton-conductingmaterials. In Fig. 18 of Section 3.2, 1H–1H spin-diffusionspectra were presented for an ethylene oxide tethered imid-azole heterocycle [79]. Fig. 44 presents 1H DQ MAS spec-tra obtained for the same materials [79] – (Fig. 44(a)corresponds to the same chain length heterocycle as inFig. 18). As is discussed above in Sections 4.2.2 and4.2.3, resonances due to mobile protons are filtered out in1H DQ spectra. This is evident upon comparing Figs. 18and 44 in that no DQ peaks are observed, for example,for the resonance at 10 ppm due to mobile NH protons.(An alternative approach illustrated in Fig. 11 of [25] isto perform a DQ-filtered spin-diffusion experiment, suchthat only peaks due to the rigid components are observedin the exchange spectrum. Note that Massiot and co-work-ers have employed this approach to study water-bearing sil-icate and aluminosilicate glasses [228].)

The DQ cross peaks at 6 + 15 = 22 ppm in the spectra inFig. 44(a) correspond to the intramolecular proximity ofthe aromatic and the NH protons of the imidazole ring –note the resolution of two distinct NH resonances. Animportant feature of all three 1H DQ MAS spectra inFig. 44 is the absence of cross peaks corresponding to theclose proximity of an imidazole NH proton to either anoth-er NH proton or to the ethylene oxide linking chain. Thisindicates that for the considered family of materials, theimidazole rings form a hydrogen-bonded structure that is

Fig. 45. 1H (600 MHz) DQ MAS (60 kHz) spectrum of 1,10-(1-H-imidazol-5-yl)decanephosphonic acid. The bottom spectra indicate the DQ peaksinvolving the four hydrogen-bonding resonances, (A–D). (Reprinted with permission from Ref. [9].)

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a

b

c e

d

b d

a

c e

Fig. 46. 1H (700 MHz) DQ MAS (30 kHz) spectra of imidazolium-methylsulphonate recorded using five different pulse sequences: (a) Standard 1H DQMAS pulse sequence using one rotor period of BABA recoupling for the excitation and reconversion of DQ coherence. (b–e) The WATERGATE andDANTE sequences are employed to selectively suppress and selectively excite the CH3 resonance (Ha), respectively. In (b) and (c), the selective suppressionor detection is in t2, while in (d) and (e) there is a selective suppression or selective excitation of DQC. The shaded regions in the DQ spectra indicate wherepeaks have been removed as a consequence of the employed selective suppression or excitation method. (Reproduced by permission of Elsevier from Ref.[231]).



based on single and spatially separated N–H� � �N bridges.As such the imidazole NH protons do not interact withthe ethylene oxide linker units, but rather the imidazolerings form a hydrogen-bonded structure amongstthemselves.

Fig. 45 illustrates the resolution that is achievable in a1H DQ MAS spectrum at the very fast MAS frequencyof 60 kHz for 1,10-(1-H-imidazol-5-yl)decanephosphonicacid, a potential proton-conducting membrane [9]. Fourdifferent hydrogen-bonding resonances (A–D) are resolved,with DQ peaks among the hydrogen-bonding resonancesand to the aromatic (E–G) and aliphatic (H) beingobserved and assigned in Fig. 45.

A 1H DQ MAS spectrum has also been presented for aproton-conducting material where imidazole is covalentlylinked to a linear polysiloxane backbone [80], while one-di-mensional DQ-filtered spectra have been presented fordicyanoimidazole polymers [229] and the classic proton-conducting polymers Nafion and a sulphonated poly(etherether ketone) (S-PEEK) [230].

Fig. 46 presents 1H DQ MAS spectra of imidazolium-methylsulphonate [231]. The four resolved resonancescorrespond to the two imidazole NH protons (Hd), the

Fig. 47. An investigation of defects in the self-assembled supramolecular structof a precipitated sample and after thermal annealing. Two rotor periods ofcoherence. For the precipitated sample, DQ cross peaks corresponding to aobserved; this is indicative of unwanted backfolding of the dendrons. Upon ththese defects, as is evidenced by the disappearance of the corresponding DQ c

imidazole CH protons (Hc and Hb, in a ratio 1:2) andCH3 protons (Ha). DQ diagonal and cross peaks corre-sponding to both intramolecular and intermolecularproton–proton proximities are observed. Fig. 46 illustratespulse sequences employing the WATERGATE [232] andDANTE [233] pulse sequences used to either selectivelysuppress or selectively excite a particular resonance [231].The spectra in Fig. 46 obtained using these pulse sequenceswere recorded using a specially built 2.5 mm MAS probeincorporating pulse-field gradient (PFG) coils [231]. Thedifferent possibilities for editing the 2D spectra by the useof selective suppression or excitation applied in t2 or soas to selectively suppress or selectively excite DQC is illus-trated in Fig. 46, where the WATERGATE or DANTEsequences were applied to the CH3 resonance. The shadedregions in the DQ spectra indicate where peaks have beenremoved as a consequence of the selective suppression orexcitation method employed.

4.2.7. Columnar architectures

Percec and co-workers have prepared a library based ona semi-fluorinated tapered dendron that is functionalised atits apex with a diversity of aromatic groups that can act as

ure of the dendron-TNF system. 1H (700 MHz) DQ MAS (30 kHz) spectraBABA recoupling was used for the excitation and reconversion of DQproton–proton contact between the TNF and dendron phenyl rings areermal annealing, the system undergoes a ‘‘self-repair’’ process which healsross peaks. (Reproduced by permission of Elsevier from Ref. [25]).

a

b

Fig. 48. 1H (700 MHz) DQ MAS (30 kHz) spectra of a large discotictrisamide that forms at room temperature a liquid-crystalline phase basedon hexagonally ordered columns. In the standard 1H DQ MAS spectrum(a), the long alkyl chains give rise to strong t1 noise due to motionallyinduced relaxation processes occurring during the pulse sequence. Thealkyl signal and its associated t1 noise is removed by the use ofWATERGATE (see Fig. 46(b)) to selectively suppress signals due to thealkyl chain protons. Specific DQ peaks linking the two amide protons at12.9 and 13.7 ppm to different aromatic CH protons are indicated byhorizontal lines. (Reproduced by permission of Elsevier from Ref. [231]).

Table 41H DQ MAS of disordered and heterogeneous materials

Material Ref.

All-silica ZSM-12 zeolite [237]Poly(ethylene oxide) (PEO)/crosslinked-silicone network [78]Organically modified polysiloxane network [63]Templated mesoporous silicate thin films [238]Precipitated amorphous silica and modifier [239]Phenyl-functionalised templated organosilica [240]Poly(methacrylic acid) (PMMA) hydrogels [241]N-isopropylacrylamide (NiPAAm) and methacrylic acid (MAA)

hydrogels[242]

Polymer functionalised carbon nanotubes [243]Organometallic zirconia species on silica surfaces [244]Weathered potassium aluminium phosphate glass [84]Hydrated cement [85]

Fig. 49. 1H (500 MHz) DQ MAS (25 kHz) spectra of a semi-interpene-trating polymer network formed by PEO (10%) and a crosslinked silicone(90%). The structure of the crosslinked silicone is shown at the top.(Reproduced by permission of Wiley from Ref. [78]).


donors or acceptors in charge transfer applications [234].The resulting functional dendrons are programmed to selfassemble into cylinders containing the optoelectronic ele-

ment in their core, with the supramolecular cylinders selforganising into homeotropically aligned hexagonal or rect-angular liquid crystals.

Rotor-synchronised 1H DQ MAS spectra provide evi-dence for the separation from each other of the 4,5,7-trini-trofluorenone-2-carboxylic acid (TNF) acceptor molecules

Fig. 50. 1H (200 MHz) DQ MAS (10 kHz) spectrum of a siloxane materialprepared by the acid-catalysed polycondensation of a mixture of TEOS/DMDEOS/C2H5OH/H2O/HCl in a molar ratio of 0.75:0.25:4.5:3:0.03 (TE-DM 3-1). The C7 sequence was used for the excitation and reconversion ofDQ coherence. DQ peaks linking the strongly hydrogen-bonded (sHB)silanols (7 ppm) and the DMDEOS CH3 groups (0 ppm) are indicated by adashed horizontal line. Vertical traces at the SQ frequencies of 7 and 0 ppmare shown below the spectrum. (Reprinted with permission from Ref. [63].)

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Fig. 51. 1H (600 MHz) DQ MAS (30 kHz) spectra of a surfactant-templated mesoporous silicate film. Two rotor periods of BABA recou-pling were used for the excitation and reconversion of DQ coherence.(Reproduced by permission of Wiley from Ref. [238]).

a

b

Fig. 52. 1H (500 MHz) DQ MAS (30 kHz) spectra of surface-modifiedprecipitated amorphous silica (Ultrasil VN3, Degussa). Surface modifica-tion was achieved by heating for 24 h with (a) 30% w/w bis(triethoxysi-lylpropyl) tetrasulfane or (b) ethanol, followed by subsequent drying invacuo. Four rotor periods of BABA recoupling were used for theexcitation and reconversion of DQ coherence. The grey shaded areasindicate the regions over which the sum projections were taken, while thickhorizontal lines indicate dipolar contacts between OH protons associatedwith the silica surface (5–7 ppm) and the surface attached molecules.(Reprinted with permission from Ref. [239].)

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(in the centre of the columns), the dendron phenyl rings (inthe inner shell of the columns) and the alkyl chains (in theouter shell). As illustrated in Fig. 47, this separation is notcompletely achieved when the material is precipitated fromsolution, but rather requires the system to be enabled to selforganise over the course of a cooling process after thermalannealing from the melt into the glassy hexagonal phasesvia a liquid-crystalline phase [25]. Rotor-synchronised

-41216 8 4 0 ppm30

20

10

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-412 8 4 0 ppm30

20

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324 K 353 K

-412 8 4 0 ppm30

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10

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-412 8 4 0 ppm30

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10

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381 K 410 K

A A

A A

B B

B B * B*

AA AA

Av AA

AB

BB BB

AB

AB

BB

-10 -10

-10-10

DQ

SQ

DQ

SQ

DQ

SQ16

1616

SQ

DQ

a

c

b

d

Fig. 53. 1H (500 MHz) DQ MAS (30 kHz) spectra of a driedpoly(methacrylic acid) PMMA sample collapsed (by the addition of0.1 M HCl solution following swelling in distilled water) at pH 1.2.Two rotor periods of BABA recoupling were used for the excitationand reconversion of DQ coherence (Reproduced by permission of Wileyfrom Ref. [241]).

20

30

20

10

15 10 5 0ppm

-10

-10

0

pH 10

pH 5.5

pH 4.5

pH 1.2

B2

B2 B1

BB2BB1AB2AB1

Dou

ble

Qua

ntum

, DQ

BB2BB1AB2AB1

BB2BB1AB2AB1

BB2BB1AB2AB1

B1

30

20

10

-10

0

30

20

10

-10

0

30

20

10

-10

0

Fig. 54. 1H (500 MHz) DQ MAS (30 kHz) spectra of dried poly(meth-acrylic acid) PMMA samples treated at different pH. Two rotor periods ofBABA recoupling were used for the excitation and reconversion of DQcoherence (Reproduced by permission of Wiley from Ref. [241]).


1H DQ MAS spectra of these semi-fluorinated dendronswith various electron-donor groups in the solid- andliquid-crystalline phase have recently been published[235].

As a second example, consider the large discotic trisa-mide in Fig. 48 that consists of C3-symmetrical moleculeswith intramolecular hydrogen bonds that form at roomtemperature a discotic liquid-crystalline phase based onhexagonally ordered columns [236]. There are nine n-C12H25 sidechains that give rise to strong t1 noise in thestandard 1H DQ MAS spectrum [231] (Fig. 48a) which isdue to motionally induced relaxation processes occurringduring the pulse sequence. The alkyl signal and its associ-ated t1 noise is removed by the use of WATERGATE(see Fig. 46b) to selectively suppress signals due to the alkylchain protons. DQ peaks linking the two amide protons at12.9 and 13.7 ppm to different aromatic CH protons areindicated by filled horizontal lines in the 1H DQ MAS spec-trum in Fig. 48b. While the 13.7 ppm NH proton has aclose proximity to three different aromatic CH protons,the 12.9 ppm NH proton is only close to the CH aromaticproton at 5.8 ppm. On the basis of this observation, the12.9 ppm resonance is assigned to the inner NH� � �Nhydrogen bonds in the structure, since here only the CHprotons of the central phenyl ring are close enough in spaceto give rise to a NH–CH DQ coherence, while there aremore aromatic CH protons in close proximity at the outerNH location.

4.2.8. Disordered and heterogeneous materials

This final section considers the application of 1H DQMAS to other disordered and heterogeneous systems suchas polymeric, glassy and mesoporous materials as well assurface species – see Table 4.

Fig. 49 presents a 1H DQ MAS spectrum of a semi-in-terpenetrating polymer network formed by PEO (10%)and a crosslinked silicone (90%) [78]. As well as DQpeaks for the separate components: Me–Me, Me–Ph,Ph–Ph (silicone) and PEO–PEO, clear cross peaks areobserved between the PEO resonances and the methyland phenyl resonances of the silicone. This is indicativeof an intimate mixing of the PEO and silicone compo-nents. Interestingly, two narrow resonances (at 3.0 and3.4 ppm) are observed in a one-pulse 1H MAS spectrum.It is only the 3.0 ppm peak that exhibits DQ peaks, sug-gesting the that the 3.4 ppm peak corresponds to an inde-pendent phase-separated more mobile PEO domain. It is

Proton Single-Quantum Frequency (ppm)

Pro

ton

Dou

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Qua

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Fre

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ppm

)

12 10 8 6 4 2

25

20

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Proton Chemical Shift (ppm)12 10 8 6 4 2 0

Si-HSi-R

12 10.1Si-OH


Pro

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)

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12 10 8 6 4 2 0

Si-HSi-OH

Si-R

4.13.6

OSi

O SiO

OO

ZrH

HO

O

H

OSi

O SiO

OO

ZrH

H HO

O

OSi

O SiO

OO

ZrO

HO

O

O HH

OSi

O SiO

OO

ZrO

H HO

O

Ha b

Fig. 55. 1H (500 MHz) MAS and DQ MAS (30 kHz) spectra of (a) [Zr–H] and (b) [Zr–OH] organometallic species formed on a silica surface. The samplein (a) was obtained by the reaction of [(”SiO)Zr(CH2tBu)3] with H2 at 150 �C, with the precursor having been prepared by reacting at 25 �C [Zr(CH2tBu)4]on a silica partially dehydroxylated at 500 �C. The sample in (b) corresponds to reacting the sample in (a) with N2O (300 equiv.). One rotor period ofBABA recoupling was used for the excitation and reconversion of DQ coherence (Reprinted with permission from Ref. [244].)

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to be noted that the resonance at 3.0 ppm is shifted to alower-ppm value as compared to that for PEO, suggest-ing an influence of ring currents due to the silicone aro-matic groups.

Consider the 1H DQ MAS spectrum in Fig. 50 of asiloxane material prepared by acid-catalysed polyconden-sation [63]. A corresponding 1H–1H spin-diffusionCRAMPS spectrum was presented in Fig. 7c. An impor-tant distinction is that resonances due to the mobile weaklyand non-hydrogen-bonded hydroxyl protons are notobserved in the 1H DQ MAS spectrum in Fig. 50. Theobservation of DQ cross peaks involving the stronglyhydrogen-bonded silanol (7.0 ppm) and the DMDEOS

CH3 (0 ppm) resonances demonstrates the involvement ofmethyl groups in the formation of strongly hydrogen-bonded clusters.

A further example of the use of 1H DQ MAS to probespecific proton–proton proximities is provided by thespectrum in Fig. 51 for a templated mesoporous silicatethin film prepared by adding 4% polyoxyethylene(10)cetyl ether to an acidic TEOS silica sol [238]. Of specificinterest are the DQ cross peaks linking the resonancesdue to the silanols and the oxymethylene protons of thesurfactant (see schematic structure in Fig. 51). It is tobe noted that such peaks indicative of hydrogen bondingbetween the surfactant and the silanol are not observed


for a 1H DQ MAS spectrum of an untemplated silicatefilm.

In a related study, Saalwachter et al. have applied 1HDQ MAS to the study of molecular contacts betweenmodifier molecules and the surface of precipitated amor-phous silica [239]. Fig. 52 presents 1H (500 MHz) DQMAS (30 kHz) spectra where surface modification wasachieved by heating for 24 h with (a) 30% w/w bis(trieth-oxysilylpropyl) tetrasulfane or (b) ethanol, followed bysubsequent drying in vacuo. Thick horizontal lines indi-cate dipolar contacts between OH protons associated withthe silica surface (5–7 ppm) and the surface attachedmolecules.

1H DQ MAS has also been used to study changes inhydrogen bonding in hydrogels formed by poly(methacryl-ic acid) (PMMA) [241] and N-isopropylacrylamide (NiP-AAm) and methacrylic acid (MAA) [242]. Consider the1H DQ MAS spectra in Fig. 53 for a dried PMMA samplecollapsed at pH 1.2 [241]. The resonances A and B corre-spond to the aliphatic and COOH protons, respectively.A marked BB diagonal peak corresponding to the forma-tion of hydrogen-bonded COOH dimers forms is observedfor the spectrum at 324 K. Upon heating, the intensity ofthis BB diagonal peak decreases. At 381 K, two distinctCOOH resonances (B and B*) can be identified, with thediagonal peak for the B resonance being more intense,indicative of stronger hydrogen bonding (as is also indicat-ed by the higher 1H chemical shift). It is also informative toconsider the changes in 1H DQ MAS spectra for PMMAsamples treated at different pH values (see Fig. 54) [241].At pH 10, there are as expected no COOH resonances.While at a pH of 1.2, COOH diagonal peaks are observedfor the two B resonances, at a pH of 5.5, a COOH diagonalpeak is only observed for the higher ppm B resonance,again indicative of stronger hydrogen bonding.

As a final example to illustrate the wide applicability of1H DQ MAS rotor-synchronised spectra, consider theapplication to organometallic species formed on a silica sur-face in Fig. 55 [244]. The sample in (a) was obtained by thereaction of [(”SiO)Zr(CH2tBu)3] with H2 at 150 �C, with theprecursor having been prepared by reacting at 25 �C[Zr(CH2tBu)4] on a silica partially dehydroxylated at500 �C. Notably, two high-ppm resonances correspondingto two distinct zirconium hydride surface species areobserved in the one-pulse 1H MAS spectrum at 10.1 and12 ppm. Only the signal at 12 ppm gives rise to a diagonalpeak allowing its assignment to the ZrH2 species. The10.1 ppm resonance is assigned to the well-isolated ZrHproton, which shows only a weak correlation at a DQ fre-quency of 14.5 ppm with the SiH resonance (at 4.4 ppm).The sample in (b) corresponds to reacting the sample in(a) with N2O (300 equiv.) so as to create metal hydroxides– note the absence of the high-ppm resonances due to thezirconium hydride species. The 1H DQ MAS spectrumagain allows the assignment of the resonances at 3.6 and4.1 ppm to the Zr(OH)2 and Zr(OH) species, respectively,because of the presence and absence of a diagonal peak.

4.3. 1H DQ MAS spinning-sideband patterns

The previous section has demonstrated that semi-quanti-tative information about proton–proton proximities can beobtained from rotor-synchronised 1H DQ MAS spectra fora wide variety of applications. This section shows how1H–1H dipolar couplings can be extracted from 1H DQMAS spinning-sideband patterns obtained when Dt1 „ sR,soastoallowthedeterminationofspecificproton–protondis-tances or the quantitative investigation of dynamic processes.

As described in Section 4.1, characteristic 1H DQ MASspinning-sideband patterns are observed for DQ recouplingmethods which have an amplitude dependence on the rotorphase such as BABA or DRAMA. This is a consequence ofthe t1-dependent change in the Hamiltonian active duringthe reconversion period relative to that active during theexcitation of DQC [142,143,145], with the mechanism hav-ing been termed reconversion rotor encoding (RRE) [146].

For an isolated spin pair and using NsR of the BABArecoupling method for both the excitation and reconver-sion of DQCs, the DQ time-domain signal is given by[145]:

sðt1; t2 ¼ 0Þ ¼ hsin½3p2djk sinð2bÞ cosðcþ 2pmRt1ÞNsR�� sin½3p2djk sinð2bÞ cosðcÞNsR�i; ð7Þ

where b and c are Euler angles relating the principal axessystem of the dipolar-coupling tensor to the rotor-fixedreference frame, and the Ææ brackets denote a powderaverage. Simulated DQ MAS spinning-sideband patternsgenerated in the time domain using Eq. (7), with thepowder average being performed numerically, for differentvalues of the product of djk and srcpl are shown in Fig. 56.A particularly striking feature is that only odd-order spin-ning sidebands are observed; there is no intensity at thecentreband and even-order sideband positions. The con-centration of intensity at the odd-order spinning side-bands was noted for the 1H DQ MAS spectrum ofpolycarbonate [141] presented in Fig. 22. The presenceof weak intensity at the centreband and also even-ordersidebands in the experimental spectrum (Fig. 22) is a con-sequence of evolution during t1 of a DQC, due to a par-ticular two spins, under dipolar couplings to other spins;in Ref. [146], this mechanism, by means of which spinningsidebands are, in fact, most commonly generated, wastermed evolution rotor modulation.

The spinning-sideband patterns in Fig. 56 are observedto be very sensitive to the product of djk and srcpl, withan increase in this product leading to the appearance ofhigher-order spinning sidebands. Importantly, since srcpl

is known, the absolute value of djk can be extracted to ahigh degree of accuracy by an analysis of DQ MAS spin-ning-sideband patterns – this is the basis by which pro-ton–proton distances as well as dynamic processes can bequantitatively determined. For example, in Ref. [143], itis shown that 1H–1H dipolar couplings and henceproton–proton distances can be determined for barium

Fig. 56. Simulated homonuclear DQ MAS spinning-sideband patternsgenerated in the time domain using Eq. (7), with the powder average beingperformed numerically, for different values of the product of the dipolarcoupling djk and the recoupling time srcpl. (Reprinted with permission fromRef. [23].)

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Table 5The extraction of proton–proton distances from 1H DQ MAS spinning-sideband patterns

Sample Ref.

Ba(ClO3)2.H2O [143]Malonic acid [143]HBC-(CD2)C11 [161]Trichloroacetic acida [245]All-silica ZSM-12 zeolite [237]Bilirubin [246]Keto and enol tautomers [225]Dendron-TNF supramolecular structure [25,234]

a Determined from 1H rotor-encoded longitudinal magnetisation(RELM) experiments.

Table 6The quantitative probing of dynamic processes using 1H DQ MASspinning-sideband patterns

Material Ref.

HBC-(CD2)C11 liquid-crystalline phase [161]Triphenylene liquid-crystalline phase [150]c-Cyclodextrin inclusion compound with PDMS [223,247,248]Dendritic polymers [249]Hydrated sodium hexaniobate [250,251]Precipitated amorphous silica and modifier [239]Pyrene/naphthalene dendron liquid-crystalline phases [235]


chlorate monohydrate Ba(ClO3)2ÆH2O and malonic acid byfitting the experimental patterns to sideband patterns sim-ulated for an isolated spin pair. Good agreement with theproton–proton distances known from neutron diffractioncrystal structures was obtained. Tables 5 and 6 summarise

the use of 1H DQ MAS spinning-sideband patterns toextract proton–proton distances and to quantitativelyprobe dynamic processes, respectively.

Fig. 57 presents 1H DQ MAS spectra for bilirubin bywhich the distance between the hydrogen-bonded NH pro-tons was accurately determined [246]. Bilirubin is anunsymmetrically substituted tetrapyrrole dicarboxylic acid,which is found in the body as a product of the metabolismof haemoglobin from red blood cells. Bilirubin itself isintrinsically unexcretable, and its removal from the bodyrequires it first to be conjugated enzymatically with glucu-ronic acid in the liver. An insufficient elimination of biliru-bin which is a yellow–orange pigment results in jaundice;this condition is usually associated with a pathologic liverdisease, e.g., hepatitis, or an insufficiency of the bilirubinglucuronyl transferase enzyme, the latter being commonlythe case in newly born infants.

The insolubility of bilirubin is a consequence of strongintramolecular hydrogen bonding, with the crystal struc-ture [252,253] indicating that the carboxylic acid group ofone dipyrrinone unit adopts an ideal geometry for intramo-lecular hydrogen bonding with the lactam and pyrrole moi-eties of the other dipyrrinone unit. The exact localisation ofprotons by X-ray scattering is very difficult. Indeed, in thefirst X-ray single-crystal study [252], the positions of thevital hydrogen-bonded protons were very poorly defined.Furthermore, although Le Bas et al. went to considerabletrouble to obtain a single crystal of suitable quality toallow the location of the hydrogen-bonded protons, theywere still forced to artificially calculate the position ofone of the three hydrogen-bonded protons in each half ofthe bilirubin molecule [253]. There is, therefore, still uncer-tainty in the proton–proton distances derived from the X-ray structure.

Fig. 57a presents the part of a 2D rotor-synchronised 1HDQ MAS spectrum corresponding to the hydrogen-bondedresonances. Only the proton corresponding to the middlehydrogen-bonded peak at 10.8 ppm can then be seen tobe in close proximity to both the other two hydrogen-bonded protons, and is thus assigned to the lactam NHproton. The solid-state 1H chemical shifts are very similarto the solution-state values obtained using chloroform asa solvent, where there is strong evidence that the intramo-lecular hydrogen-bonding arrangement shown in Fig. 57persists. On this basis and considering the intensities of

a

b

d

c

e

Fig. 57. (a) 1H (700 MHz) DQ MAS (mR = 30 kHz) spectrum of bilirubin. The region corresponding to the hydrogen-bonded resonances is shown. Onerotor period of BABA recoupling was used for the excitation and reconversion of DQ coherence. (b,d) 1H (700 MHz) DQ MAS (30 kHz) NMR spinning-sideband patterns obtained for the NH1 hydrogen-bonded resonance of bilirubin. BABA recoupling sequences of duration (b) two or (d) three sR wereused for the excitation and reconversion of DQCs. The corresponding best-fit simulated three-spin 1H DQ MAS spinning-sideband patterns are presentedin (c) and (e). (Reprinted with permission from Ref. [246].)

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the respective DQ peaks, the SQ resonances at 9.1 and13.9 ppm can be assigned to the pyrrole NH and carboxylicacid OH protons, respectively.

In Figs. 57b and d, 1H DQ MAS spinning-sideband pat-terns obtained for the lactam (at 10.8 ppm) NH resonanceof bilirubin, with srcpl equal to (b) two and (d) three rotor

Fig. 58. (a) The sandwich-type packing of TNF molecules in the dendron-TNF system. (b) 1H (700 MHz) DQ MAS (30 kHz) spinning-sideband patternfor the aromatic protons in TNF, recorded using eight rotor periods of BABA recoupling for the excitation and reconversion of DQ coherence. Theproton–proton distance between the aromatic protons is hence determined to be 0.35 nm. This implies a sandwich-type packing of pairs of TNF molecules,as shown in (a). Combining the NMR information with that provided by X-ray diffraction, it can be concluded that the dendron-TNF molecules selfassemble into a cylindrical superstructure with TNF stacks in the centre, surrounded by helically arranged dendritic sidegroups, as shown in (c).(Reproduced by permission of Elsevier from Ref. [25]).


periods at a mR = 30 kHz are shown. In the rotor-synchro-nised 1H DQ MAS spectrum in Fig. 57a, in addition to theintense NH–NH DQ peaks, weaker DQ peaks due toDQCs involving the OH and aliphatic protons areobserved. An inspection of the spectra in Figs. 57b and(d) reveals the existence of spinning sidebands due to allthese different DQCs – note that the DQ peak for theNH–NH pair is at the second-to-left position.

In Ref. [246], a protocol is presented whereby the dom-inant dipolar coupling djk, and hence the shortest proton–proton distance, can be determined by finding the best-fitsimulated three-spin spectra on the basis of a comparisonof the extracted integrated experimental sideband intensi-ties with those in the simulated spectra. In this way, the dis-tance between the lactam and pyrrole NH protons inbilirubin is determined to be 0.186 ± 0.002 nm (corre-sponding to a dominant djk of 18.5 ± 0.5 kHz), provingan exceptionally close approach of two protons beingnon-covalently bonded to the same atom. The accuracy isbetter than what can be reliably expected from a standardX-ray structural analysis. The corresponding best-fit simu-lated three-spin spinning-sideband patterns are shown inFigs. 57c and e. The analysis also yields a distance betweenthe lactam NH and carboxylic acid OH protons of0.230 ± 0.008 nm (corresponding to a perturbing djk of

9.9 ± 1.0 kHz), and an H–H–H angle of 122� ± 4� – notethat the precision of these values is less than for the case ofthe shortest proton–proton distance.

Consider the dendron-TNF supramolecular structurefor which rotor-synchronised 1H DQ MAS spectra areshown in Fig. 47. Fig. 58b presents a 1H DQ MAS spin-ning-sideband pattern for the aromatic protons in TNF,for which the best-fit yields a proton–proton distancebetween the aromatic protons of 0.35 nm [25,234]. Thisimplies a sandwich-type packing of pairs of TNF mole-cules, as shown in Fig. 58a. Combining the NMR informa-tion with that provided by X-ray diffraction, it can beconcluded that the dendron-TNF molecules self assembleinto a cylindrical superstructure with TNF stacks in thecentre, surrounded by helically arranged dendritic side-groups, as shown in Fig. 58c.

The HBC derivatives discussed in Section 4.2.2 repre-sent a relatively new family of discotic aromatic mesogen,which have a number of favourable properties as comparedto the more established triphenylenes; for example the mes-ophases are stable over a very wide temperature range [254]and exhibit an exceptionally high one-dimensional chargecarrier mobility [255]. In the following, it will be shownthat the recording of 1H DQ MAS spinning-sideband pat-terns allows the order parameter of the molecules in the


liquid-crystalline (LC) phases to be quantitativelydetermined.

Fig. 59 presents experimental 1H DQ MAS spinning-sideband patterns for the aromatic protons in (a) the crys-talline and (b) the LC phases of HBC-(CD2)C11 (see Table3 of Section 4.2.2) [161]. The MAS frequency was 35 and10 kHz in (a) and (b), respectively, with two rotor periodsbeing used for excitation/reconversion in both cases, suchthat srcpl equals 57 and 200 ls in the two cases. The dottedlines represent best-fit spectra simulated using the analyti-cal time-domain expression for an isolated spin pair inEq. (7). As noted in Section 4.2.2, the aromatic protonsexist as well-isolated pairs of bay protons, and, thus, ananalysis based on the spin-pair approximation is appropri-ate here. As is evident from the insets on the right ofFig. 59, the DQ MAS spinning-sideband patterns are verysensitive to the product of the djk and srcpl. The best-fitspectra for the solid and LC phases then correspond todjk equal to 15.0 ± 0.9 and 6.0 ± 0.5 kHz, respectively.

Comparing the evaluated djk values for the crystallineand LC phases, a reduction by a factor of 0.40 ± 0.04 isobserved, corresponding to an order parameter of0.80 ± 0.08. In the LC phase, fast axial rotation of the mol-ecule about an axis perpendicular to the ring (passingthrough the centre of symmetry) is expected. For a mole-cule undergoing such a motion, the dipolar coupling con-stant is reduced by a factor of 1/2(1 � 3cos2h), where h isthe angle between the principal axes system (here the inter-nuclear vector) and the molecular rotation axis. (Note that

a

b

Fig. 59. Extracted columns from 1H (500 MHz) DQ MAS two-dimensional spethe aromatic protons at 8.3 ppm in the solid phase (T = 333 K), and (b) the aromspectra, generated according to the spin-pair expression in Eq. (7), are shown (frequency, mR, equal to 35 and 10 kHz was used for the solid and LC phasessequence being used for the excitation and reconversion of DQCs in both caseresidual undeuterated a-carbon protons are marked by *. The insets to the righpatterns to the product djk srcpl. (Reprinted with permission from Ref. [161].)

this dynamic averaging term is not included in the earlierdefinition of djk in Eq. (2).) Thus, for the case where theinternuclear vector is perpendicular to the rotation axis(h = 90�), a reduction by a factor of 0.5 is expected. Thevalue of 0.40 can be explained by postulating the presenceof out-of-plane motion in addition to the axial rotation.The ability to probe such motion is of much importance,since it is likely to impair efficient charge carrier mobility.

It is to be noted that dynamic processes can also beprobed by recording 1H–13C heteronuclear MQ spinning-sideband patterns that, in direct analogy to 1H DQ MAS,allow the determination of the 1H–13C dipolar coupling.The order parameter for the molecules in the LC phaseof HBC-C12 has been determined from 1H–13C heteronu-clear MQ spinning-sideband patterns to be 0.78 ± 0.09[256], in agreement with the above analysis of 1H DQMAS spinning-sideband patterns. 1H–13C methods benefitfrom the better inherent resolution for 13C and have beenwidely applied [25,257].

1H DQ MAS experiments have also been applied tocharacterise the water and hydroxyl environments in poly-oxoniobate materials, so as to gain insight into the waterdynamics. Fig. 60a presents a 1H DQ MAS spectrum ofNa7[HNb6O19]Æ15H2O [250], with the spectrum being dom-inated by the strong auto correlation for the water protonsat 6.3 ppm. Fig. 60b presents F1 slices taken at the waterchemical shift (6.3 ppm) from 1H DQ MAS spectra [251]recorded at 33 kHz MAS with two (B) and four (D) rotorperiods of BABA recoupling. The spectra are not well fitted

ctra of HBC-(CD2)C11, showing the DQ spinning-sideband patterns for (a)atic protons at 6.2 ppm in the LC phase (T = 386 K). In each case, best-fit

shifted to the left to allow a better comparison) as dotted lines. A spinning, respectively, with the two rotor-period compensated BABA recouplings. In (a), additional peaks corresponding to DQCs between aromatic andt of the experimental spectra show the sensitivity of the spinning-sideband

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Fig. 60. (a) 1H (600 MHz) DQ MAS (30 kHz) spectrum of Na7[HNb6O19]Æ15 H2O. Two rotor periods of BABA recoupling were used for the excitationand reconversion of DQ coherence. (b) F1 slices taken at the water chemical shift (6.3 ppm) from 1H DQ MAS spectra recorded at 33 kHz MAS with two(B) and four (D) rotor periods of BABA recoupling. The spectra in A and C are simulations assuming a Gaussian distribution of dipolar couplings with amean djk = 23 kHz and a standard deviation of (A) 3.0 and (C) 3.4 kHz. (b) A plot of the Gaussian distribution of dipolar couplings used to perform thesimulation in (C). (Reprinted with permission from Ref. [250]. Copyright (2004) American Chemical Society. Reproduced by permission of Elsevier fromRef. [251]).


a c

b d

Fig. 61. (a) 1H (500 MHz) DQ MAS (13 kHz) spectra of alanine, recorded using (a) MAS alone or MAS and WHH-4 [258] homonuclear decoupling in (b)t2, (c) t1 and (d) t1 and t2. DQ coherence was excited and reconverted using the 90� � sR/2 � 90� pulse sequence element. For t1 decoupling, bracketingmagic-angle pulses (54.7�) are applied with phase 315� and �315� before and after WHH-4 decoupling. The chemical shift axes have not been corrected,such that the scaling factor of 0.60 is apparent. (Reproduced by permission Elsevier from Ref. [6]).

b c

fe

a

d

Fig. 62. (a–c) One-dimensional 1H (600 MHz) CRAMPS and (d–f) two-dimensional 1H DQ CRAMPS spectra of (a,d) monoethyl fumaric acid, (b,e)glycine, and (c, f) histidineÆHClÆH2O. PMLG5 and wPMLG5 homonuclear decoupling were applied in t1 and t2, respectively. DQ excitation andreconversion was achieved using the C94

1 pulse sequence at a MAS frequency of 9.1 kHz. Artefact peaks in the 2D spectra are circled. (Reproduced bypermission Elsevier from Ref. [261]).



on the basis of a single dipolar coupling, suggesting a dis-tribution of dipolar couplings. (It is to be noted that the fit-ting of experimental 1H DQ MAS spinning-sidebands forthe O–CH2 resonance in a triphenylene derivative in Ref.[150] also required the postulation of a distribution of dipo-lar couplings.) The spectra in A and C in Fig. 60b are best-fit simulations assuming a Gaussian distribution of dipolarcouplings with a mean djk = 23 kHz and a standard devia-tion of (A) 3.0 and (C) 3.4 kHz. The mean dipolar couplingis reduced by a factor of 0.69 as compared to the dipolarcoupling of 33.4 kHz for rigid water, hence providing valu-able quantitative insight into water dynamics in thehexaniobate.

4.4. 1H DQ CRAMPS experiments

The above sections have demonstrated the wealth ofstructural and dynamic information that is provided by1H DQ spectroscopy using fast MAS (P30 kHz) to obtainhigh resolution. The emphasis, however, has been on reso-nances due to hydrogen-bonded and aromatic protons thatare shifted away from the aliphatic resonances, and arehence better resolved. In Section 2.2, it was shown that1H resolution can be considerably improved as comparedto fast MAS by the application of homonuclear decouplingpulse sequences in the CRAMPS approach (see Fig. 4). Inthis section, it will be shown that the combination of DQspectroscopy with CRAMPS line-narrowing techniquesachieves a considerably improved resolution as comparedto MAS alone, allowing, in particular, the resolution of dis-tinct aliphatic resonances.

Fig. 61 presents 1H DQ MAS (13 kHz) spectra of ala-nine using (a) MAS alone or MAS and WHH-4 [258]homonuclear decoupling in (b) t2, (c) t1 and (d) t1 and t2

[6]. It is evident that the use of multiple-pulse assistedMAS [32,137,259,260] considerably improves the resolu-tion as opposed to MAS at 13 kHz. However, in the samepaper [6], it was shown that the achievable resolution wascomparable to that under the newly available 35 kHzMAS, with fast MAS methods avoiding the complicationsinvolved in setting up CRAMPS experiments and dealingwith artefact peaks.

Recently, Madhu et al. [261] and Brown et al. [262]have shown that the resolution can be considerablyenhanced in two-dimensional 1H DQ experiments byemploying more advanced homonuclear decouplingsequences than WHH-4. Fig. 62 presents (a–c) one-di-mensional 1H (600 MHz) CRAMPS and (d–f) two-di-mensional 1H DQ CRAMPS spectra of (a, d) monoethylfumaric acid, (b, e) glycine, and (c, f) histidine.HClÆH2O.In the two-dimensional 1H DQ CRAMPS experiments,PMLG5 [31] and wPMLG5 [36] homonuclear decouplingsequences were applied in t1 and t2, while DQ excitationand reconversion was achieved using the C94

1 [136] pulsesequence at a MAS frequency of 9.1 kHz. All DQ corre-lation peaks corresponding to close proton–proton prox-imities are observed; notably, baseline resolution is

achieved for the aliphatic resonances in monoethylfumaric acid (Fig. 62d), while the resonances due to thetwo distinct CH2 protons in glycine are resolved inFig. 62e.

Fig. 63 presents the pulse sequence and coherencetransfer pathway diagram for the 1H DQ CRAMPSexperiment presented in Ref. [262]. eDUMBO-122 [66]and windowed DUMBO-1 [33,37] homonuclear decou-pling sequences are applied in t1 and t2, while DQ excita-tion and reconversion is achieved using the POST-C7[131] recoupling sequence. A 1H DQ CRAMPS spectrumof the dipeptide b-AspAla obtained at mR = 12.5 kHzusing the pulse sequence of Fig. 63 is shown inFig. 64a. For comparison, a rotor-synchronised 1H DQMAS spectrum obtained using the BABA recouplingsequence at 30 kHz MAS is shown in Fig. 64b. The DQCRAMPS experiment delivers a resolution enhancementof at least a factor of five in both the single- and dou-ble-quantum dimensions. This drastic improvement in res-olution is especially visible in the aliphatic region of thespectra. Thus the CH3, the two diastereotopic CH2 andthe two CH resonances are clearly resolved in the hori-zontal projection of Fig. 64a, whereas there are onlytwo resolved peaks in the alkyl region of the F2 projec-tion of Fig. 64b. Note that proton linewidths of less than0.5 ppm were measured for the aliphatic correlations inthe DQ dimension, and that these linewidths are some-times much less than twice the SQ widths (which arethemselves all under 0.3 ppm).

Table 7 lists the resolved DQ correlations in the 1H DQCRAMPS spectrum in Fig. 64a. Notably, the high-resolu-tion DQ spectrum provides a clear assignment of the reso-nances due to the two diastereotopic CH2 protons and thetwo CH resonances. This is illustrated by Figs. 65 and 66which display traces parallel to F1 extracted from the 2D1H DQ CRAMPS spectrum at 2.2, 2.7, 4.1, and 5.0 ppm,corresponding to the CH2 and CH resonances. For thetraces in Fig. 65 corresponding to the two CH2 protons,the strongest DQ peak is that involving the two CH2 pro-tons themselves (at 4.9 ppm). The other DQ peak in thebottom trace at 2.7 + 8.0 = 10.7 ppm indicates that the2.7 ppm CHb

2 proton is pointing towards the NH of theamide linkage, while the DQ peaks in the top trace at2.2 + 4.1 = 6.3 ppm and 2.2 + 7.5 = 9.7 ppm indicate thatthe 2.2 ppm CHa

2 proton is pointing towards the Asp CHand NH3 protons. In the traces in Fig. 66 correspondingto the two CH resonances, the most intense DQ peaksare with the (a) CH3 (at 5.9 ppm) and the (b) NH3 (at11.6 ppm) resonances, such that they correspond to the(a) Ala and (b) Asp CH protons.

Fig. 67 presents rows (corresponding to the 15 DQ fre-quencies in Table 7) extracted from 1H DQ CRAMPSspectra of the dipeptide b-AspAla recorded using POST-C7 recoupling times of 22.8, 45.7, 68.5, 114, 160, and228 ls. The rate of buildup for the distinct DQ peaks canbe seen to depend as expected on the corresponding pro-ton–proton dipolar coupling. For example, the fastest

1H POST-C7eDUMBO-122 DUMBO-1

acq

θ1 −θ1θ2 −θ2

π2

t1

POST-C7

t2 n

p = 0+1

−1−2

+2

Fig. 63. Pulse sequence and coherence transfer pathway diagram for the1H DQ CRAMPS experiment presented in Ref. [262]. eDUMBO-122 [66]and windowed DUMBO-1 [33,37] homonuclear decoupling are applied int1 and t2, while DQ excitation and reconversion is achieved using thePOST-C7 [131] pulse sequence.

20 18 16 14 12 10 8 6 4 2 0 ppm

2.2 ppm

2.7 ppm

CHa

HNH3 CH3 (inter)CH

NH

Proton Double-Quantum Frequency

b

a

CH

Hb

Fig. 65. Traces parallel to F1 extracted from the 2D 1H DQ CRAMPSspectrum in Fig. 64(a) at F2 = 2.2 and 2.7 ppm, corresponding to theresonances of the two distinct non-equivalent protons in the CH2 moiety.Note that the peak at 3.1 ppm in the F2 = 2.2 ppm trace corresponds to anintermolecular CH2–CH3 proximity.

30

25

20

15

10

5

-5

0

15 10 5 0

30

25

20

15

10

5

-5

0

a

b

3.6

ppm

0.4

ppm

1.5 ppm

0.3 ppm


Proton Double-Q

uantum Frequency (ppm

)Proton D

ouble-Quantum

Frequency (ppm)

CCH CHCH2 CH3NH3N+ H

O COOHCOO−

Fig. 64. (a) Two-dimensional 1H (500 MHz) DQ CRAMPS spectrum ofthe dipeptide b-AspAla recorded using the pulse sequence of Fig. 63 withmR = 12.5 kHz. The excitation and reconversion periods were of duration68.6 ls (corresponding to three basic POST-C7 elements). The proton RFfield was set to m1 = 87 kHz during the POST-C7 blocks, and to 100 kHzfor decoupling during t1 and t2. (b) Two-dimensional 1H (500 MHz) DQMAS (30 kHz) spectrum of the dipeptide b-AspAla using the BABA pulsescheme (one rotor period) to excite and reconvert the DQ coherences.(Reprinted with permission from Ref. [262].)

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Table 7Observed DQ peaks in the 1H DQ CRAMPS spectrum of b-AspAla inFig. 62(a)

Sum of SQ frequencies

(ppm)

DQ frequency

(ppm)

1 CH3–CH3 0.9 + 0.9 1.82 CH3–CHa

2 0.9 + 2.2 3.1

3 CHa2–CHb

2 2.2 + 2.7 4.94 CH3–CH(Ala) 0.9 + 5.0 5.95 CHa

2–CH(Asp)

2.2 + 4.1 6.3

6 CH3–NH 0.9 + 8.0 8.97 CHa

2–NH3 2.2 + 7.5 9.78 CHb

2–NH 2.7 + 8.0 10.79 CH(Asp)–

NH3

4.1 + 7.5 11.6

10 CH(Ala)–NH 5.0 + 8.0 13.011 CH3–OH 0.9 + 12.9 13.8

12 NH3–NH3 7.5 + 7.5 15.013 CH(Asp)–OH 4.1 + 12.9 17.0

14 CH(Ala)–OH 5.0 + 12.9 17.915 NH3–OH 7.5 + 12.9 20.4

a,bThe assignment of the two resonances due to the two diastereotopicCH2 protons is illustrated in Fig. 65.Intermolecular proximities are in italics.


CCH CHCH2 CH3NH3N

+H

O COOHCOO−

CHCH3

20 18 16 14 12 10 8 6 4 2 0 ppm


CHNH

CCH CHCH2 CH3NH3N

+H

O COOHCOO−

20 18 16 14 12 10 8 6 4 2 0 ppm


CHCH2

CHH3N

+

CH

COOH

a

b

Fig. 66. Traces parallel to F1 extracted from the 2D 1H DQ CRAMPSspectrum in Fig. 64(a) at F2 = 5.0 (a) and 4.1 ppm (b), corresponding tothe CHala and CHasp resonances, respectively. Note that the peak at17.0 ppm in (b) corresponds to an intermolecular CHasp–OH proximity.

x 0.125

x 0.5

x 0.5

0

1

2

3

4

5

nrcpl

1 2 3 5 7 10

ig. 67. Rows extracted from 1H DQ CRAMPS 2D spectra of theipeptide b-AspAla recorded using nrcpl POST-C7 elements correspondingo recoupling times of 22.8, 45.7, 68.5, 114, 160, and 228 ls. The DQrequencies of the displayed rows, labelled 1–15, (1.8, 3.1, 4.9, 5.9, 6.3, 8.9,.7, 10.7, 11.6, 13.0, 13.8, 15.0, 17.0, 17.9, and 20.4 ppm) correspond to the5 proton–proton proximities listed in Table 7.


buildup is observed for row three corresponding to theintra CH2 DQ peaks, where maximum intensity is observedfor a recoupling time of 45.7 ls, while for most DQ peaks,the maximum signal corresponds to three C7 elements(68.5 ls). For the DQ peaks involving the OH proton(see, e.g., rows 13–15), the proton–proton distances arelonger (at least 2.5 A, usually intermolecular) and the max-imum signal is shifted to a longer recoupling time (similarintensity is observed at 68.5 and 114 ls).

As a further example, Fig. 68 presents a 1H DQCRAMPS spectrum of the K salt of penicillin G, obtainedusing the pulse sequence in Fig. 63 at 12.5 kHz MAS [207].Using a through-bond 1H–13C HSQC spectrum alsorecorded at natural abundance as well as first-principleschemical-shift calculations, it was possible to assign theresolved 1H resonances, as shown at the top of Fig. 68.Specifically resonances due to the three distinct CH(3,5,6) and two distinct CH2 (16a, 16b) protons areresolved.

1

2

3

4

5

6

7

8

9

1

1

1

1

1

1

Fdtf91

4.5. 1H double-quantum heteronuclear correlationexperiments

An alternative approach by which the resolution ofpeaks corresponding to 1H DQ coherence can be improvedis the recording of a two-dimensional correlation experi-ment with a high-resolution heteronuclear (e.g., 13C or15N) dimension. Reif et al. have presented in Ref. [263] a1H(DQ)–15N correlation experiment (see Fig. 69a) wherethe evolution in the indirect dimension of 1H DQC createdusing the CMR7 [132] sequence is correlated via CP withdetected 15N SQC in the direct dimension. Fig. 69b showsa two-dimensional 1H(DQ)–15N spectrum obtained withthis experiment at 8.9 kHz MAS of [2H, 15N]-N-Ac-Val-Leu-OH. The use of deuteration achieves high resolutionin the 1H dimension for the residual protons, such that dis-tinct 1H DQ peaks due to NH(Leu) + NH(Val) andOH + NH(Val) are resolved in Fig. 69b.

Lesage et al. describe in Ref. [264] a heteronuclear exper-iment in which a high-resolution 1H DQ dimension

9 8 7 6 5 4 3 2 1 0

16

14

12

10

8

6

4

2

0

Proton single-quantum frequency (ppm)

Pro

ton

doub

le-q

uant

um fr

eque

ncy

(ppm

)

109

14

5 616a 16b

32‘-6’

N

N

O H

S

O O-

OK+

1

2

3

794

5

8

6

11

10

12

15

14

13

16

1‘

2‘3‘

4‘

5‘ 6‘

H Hab

Fig. 68. 1H (500 MHz) DQ CRAMPS spectrum of penicillin G, obtainedusing the pulse sequence in Fig. 63 at 12.5 kHz MAS. DQ correlation peaksare indicated by solid lines (intramolecular correlations <2.75 A), shortdashed lines (intermolecular correlations <2.75 A), and long dashed lines(intra- and intermolecular correlations >2.75 A) The one-dimensional 1HCRAMPS spectrum is shown above with the assignment of the peaks.(Reproduced by permission of the PCCP Owner Societies from Ref. [207]).

a b

Fig. 69. (a) A 1H(DQ)–15N correlation experiment where the evolution of 1HSQC in the direct dimension (t3). (b) A two-dimensional 1H(DQ)–15N spectrumwith 0.45 ms of CMR7 [132] recoupling to create and reconvert DQC. The use oprotons. (Reproduced by permission of Elsevier from Ref. [263]).


(employing DUMBO-1 [33] homonuclear decoupling) iscorrelated by CP with a 13C dimension. Fig. 70b presentsa two-dimensional 1H (DQ)–13C spectrum obtained in thisway for the microcrystalline deuterated 85-residue proteinCrh [264]. Fig. 70 also presents a 2D DQ-filtered 1H–13CHETCOR spectrum (Fig. 70a) as well as a 2D 13C–13C rfassisted diffusion spectrum (Fig. 70c). The figure drawsparticular attention to the 1H DQ resonances associatedwith the Thr12 and Thr57 residues at 12.3 and 13.1 ppm,respectively, due to a DQ coherence between the OH(labelled Hc 1) and HN protons (note that the CH protonsare not observed, since it is the OH and NH sites where1H–2H exchange occurs). It is notable that no 1H resonanc-es due to the water protons are observed, with this being aconsequence of the residence times of these water moleculesbeing shorter than the time required to create and recon-vert DQC.

5. 1H triple-quantum MAS experiments

In analogy to DQ MAS, 1H triple-quantum (TQ) MASexperiments [265] can also be performed so as to observethe dipolar coupling of three protons. As an example,Fig. 71 compares 1H (500 MHz) DQ and TQ MAS spectrarecorded for L-alanine [6,24] at 35 kHz MAS, using oneand two cycles, respectively, of the BABA recouplingsequence for MQ excitation and reconversion. (For TQexcitation, bracketing pulses were included to prepare aninitial state of SQ coherence.) Three resonances corre-sponding to the CH3, CH and NH3 protons are resolvedin the one-dimensional SQ spectrum (see the horizontalprojection corresponding to the DQ-filtered spectrum inFig. 71a). In the 1H DQ MAS spectrum in Fig. 71a, strongAA and CC peaks are observed on the F1 = 2F2 diagonalcorresponding to 1H–1H DQC amongst the NH3 and

DQC in the indirect dimension (t2) is correlated via CP with detected 15Nof [2H, 15N]-N-Ac-Val-Leu-OH recorded at 500 MHz and 8.9 kHz MAS

f deuteration achieves high resolution in the 1H dimension for the residual

Fig. 70. Two-dimensional correlation spectra recorded for the microcrystalline deuterated 85-residue protein Crh at 500 MHz and 10 kHz MAS. Theregions corresponding to the Ca and Cb 13C Thr resonances are shown. The spectra were recorded with (a) a DQ-filtered 1H–13C HETCOR, (b) a1H(DQ)–13C and (c) a 13C–13C rf assisted diffusion experiment. The 1H DQ resonances associated with the Thr12 and Thr57 residues at 12.3 and 13.1 ppm,respectively, due to a DQ coherence between the Hc1 and HN protons are indicated. (Reprinted with permission from Ref. [264].)

Co

pyr

igh

t(2

006)

Am

eric

anC

hem

ical

So

ciet

y.


CH3 protons. In addition, strong cross peaks are observedcorresponding to the close (<2.5 A) intramolecular proxim-ities between the NH3–CH (AB), NH3–CH3 (AC) and CH–CH3 (AB) protons. Only weak BB intensity is observed inagreement with the shortest CH–CH distance in the crystalstructure [266] being an intermolecular distance of 3.6 A.

In the 1H TQ MAS spectrum (Fig. 71b), the strongestpeaks correspond to the three protons in the NH3 (AAA)and CH3 (CCC) moieties. In addition, there is clearAAB, AAC, ABB and ACC cross peak intensity (notethe use of a longer recoupling time in the TQ as comparedto the DQ experiment). As commented on in the originalpaper [6], there is a marked asymmetry in the cross peaksdue to both the 2:1 ratio of signals as well as different relax-ation behaviour. 1H (500 MHz) TQ MAS spectra have alsobeen recorded for dimethylglyoxime (with and without OHdeuteration) [265], bisphenol-A-polycarbonate [265] andacetonitrile in hydroquinone [24], using simple 90 sR/2 90pulse sequences for the excitation and reconversion ofTQ coherence at 14 kHz MAS.

1H TQ MAS spectra, in particular when presented incombination with 1H DQ MAS spectra, are able to identifythe clustering of three or more protons. In Ref. [237], a 1H(500 MHz) TQ MAS spectrum is presented for all-silicaZSM-12 zeolite; C7 [130] was employed for TQ excitation(applied to a state of single-quantum coherence createdby a 90� pulse) and reconversion at 10 kHz MAS. The spec-trum contains only a single peak, which lies on the F1

= 3F2 diagonal at a SQ frequency of 10 ppm correspondingto three silanol protons involved in hydrogen bonding atthe defect site, thus demonstrating that the defect silanolgroups have clusters of three protons in close proximity.Fig. 72 compares 1H (500 MHz) TQ MAS (c) and 1HDQ MAS (b) spectra of the amido surface complexesformed by the room-temperature addition of ammonia tosilica- and MCM-41-supported siloxy tantalum hydrides[267]. A 1H–15N heteronuclear correlation spectrum is alsoshown in Fig. 72a. All experiments were performed at12.5 kHz MAS, with DUMBO-1 [33] (a) or eDUMBO-122 [66] (b, c) homonuclear decoupling being applied in

a

b

Fig. 71. Two-dimensional 1H (500 MHz) (a) DQ MAS and (b) TQ MASspectra together with skyline projections recorded for L-alanine at a MASfrequency of 35 kHz. The displayed spectral regions correspond to thefirst-order sideband (DQ) and the centreband (TQ). DQ and TQ excitationand reconversion was achieved using one and two rotor periods of theBABA sequence, respectively. (For TQ excitation, bracketing pulses wereincluded to prepare an initial state of SQ coherence). The F1 = 2F2 andF1 = 3F2 diagonals are indicated as dashed lines. (Reproduced bypermission of Elsevier from Ref. [24]).

15

10

5

0

-5

Prot

on D

oubl

e Q

uant

um F

requ

ency

(pp

m)

Prot

on T

ripl

e Q

uant

um F

requ

ency

(pp

m)

-300

-200

-100

-400

Nitr

ogen

-15

Che

mic

al S

hift

(pp

m)

Proton Chemical Shift (ppm)8 6 4 2 0

14

10

6

2

-2

101214 -4-2

a

b

c

Ta=NHTa-NH2

Si-NH2

OH

Ta-NH3(NH3)adsO

Ta

Si

NHH2N

O

Si

NH2

SiO

OO

Fig. 72. (a) 1H (500 MHz)–15N heteronuclear correlation, (b) 1H DQMAS and (c) 1H TQ MAS spectra of the amido surface complexes formedby the room-temperature addition of ammonia to silica- and MCM-41-supported siloxy tantalum hydrides (note that the Ta complex shown is inequilibrium with its ammonia adduct [(”SiO)2Ta(=NH)(NH2)(NH3)]). Allexperiments were performed at 12.5 kHz MAS, with DUMBO-1 [33] (a) oreDUMBO-122 [66] (b,c) homonuclear decoupling being applied in theindirect dimension. A change of coherence order of ±2 was achieved usingone full cycle (seven basic elements) of POST-C7 [131] recoupling, withTQ coherence being created following an initial 90� pulse. The resonancesof the tantalum NH, NH2, and NH3 protons are indicated by dotted greyvertical lines. The dotted circles emphasise the expected absence of auto-correlation peaks for the imido proton in the DQ spectrum (b) and for theamido proton in the TQ spectrum (c). (Reprinted with permission fromRef. [267].)

Co

pyr

igh

t(2

006)

Am

eric

anC

hem

ical

So

ciet

y.


the indirect dimension. The resonances of the tantalumNH, NH2, and NH3 protons are indicated by dotted greyvertical lines. The dotted circles emphasise the expectedabsence of auto-correlation peaks for the imido proton inthe DQ spectrum (b) and for the amido proton in the TQspectrum (c).

The same reconversion rotor encoding mechanism[146] discussed above in Section 4 for 1H DQ MAS isalso responsible for the generation of spinning-sidebandpatterns in the TQ dimension of 1H TQ MAS spectra.The appearance and dependence on structural anddynamic parameters of 1H TQ MAS spinning-sidebandpatterns is discussed in Refs. [6,24,146,265]. For acetoni-


trile in hydroquinone [24], an analysis of such spinning-sideband patterns allows the determination of the rela-tive geometry (distance and angle) of the CH3 andOH groups.

6. Outlook

This review has demonstrated the wide applicability of1H solid-state NMR experiments that directly probe pro-ton–proton proximities. Moreover, technological advancessuch as ever faster MAS (P60 kHz is becoming available)as well as modern rf consoles that allow the straightfor-ward implementation and robust and reliable performanceof homonuclear decoupling sequences mean that high-res-olution 1H solid-state NMR spectra are appearing fre-quently in the literature. It is thus envisaged that 1H–1Hspin diffusion and 1H multiple-quantum experiments willbecome increasingly more routine, with application to evermore complex and larger systems.

Acknowledgements

S.P.B. thanks the EPSRC for the award of an AdvancedResearch Fellowship. The author thanks the many fellowNMR spectroscopists who have contributed figures fromtheir work to this review.

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Glossary

BABA: BAck-to-BAckCOSY: COrrelation SpectroscopYCP: Cross PolarisationCSA: Chemical Shift AnisotropyCRAMPS: Combined Rotation and Multiple-Pulse SpectroscopyD: Spin-diffusion coefficientdjk: Dipolar coupling constant (in Hz) (Eq.(2))drss: Root sum square dipolar coupling (Eq.(1))DQ: Double QuantumDQC: Double-Quantum CoherenceDQF: Double-Quantum FilteredDRAMA: Dipolar Recoupling At the Magic AngleDRAWS: Dipolar Recovery with A Windowless SequenceDUMBO: Decoupling Using Mind-Boggling OptimisationFSLG: Frequency-Switched Lee GoldburgFWHM: Full Width at Half MaximumHETCOR: HETeronuclear CORrelationHORROR: HOmonucleaR ROtary Resonance


HSQC: Heteronuclear Single-Quantum CorrelationINADEQUATE: Incredible Natural Abundance DoublE QUAntum

Transfer ExperimentLC: Liquid-CrystallineMAS: Magic-Angle SpinningMQ: Multiple-QuantumNOESY: Nuclear Overhauser Effect SpectroscopYPMLG: Phase-Modulated Lee GoldburgPOST-C7: Permutationally Offset STabilised C7REPT: Recoupled Polarisation TransferRRE: Reconversion Rotor Encoding

SQ: Single QuantumSQC: Single-Quantum CoherenceTPPI: Time-Proportional Phase IncrementationTSD: Spin-diffusion time constantTQ: Triple QuantumDt1: t1 Increment

sm, smix, sSD, tm, tmix: Spin-diffusion mixing timesR: MAS rotation periodsrcpl: Recoupling timemR: MAS rotation frequency (in Hz)xR: MAS rotation frequency (in rad/s)

probing proton–proton proximities in the solid state

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