Heteronuclear Hâ€“ nuclear magnetic resonance: Combining

JOURNAL OF CHEMICAL PHYSICS VOLUME 114, NUMBER 13 1 APRIL 2001

Heteronuclear 1H– 13C multiple-spin correlation in solid-statenuclear magnetic resonance: Combining rotational-echodouble-resonance recoupling and multiple-quantum spectroscopy a…

Kay Saalwachter and Hans W. Spiessb)

Max-Planck-Institute for Polymer Research, Postfach 3148, D-55021 Mainz, Germany

~Received 23 October 2000; accepted 11 January 2001!

High-resolution magic-angle spinning~MAS! solid-state nuclear magnetic resonance~NMR!spectroscopy exploiting the dipole–dipole coupling between unlike spins is a powerful tool for thestudy of structure and dynamics. In particular, the rotational-echo double-resonance~REDOR!technique has established itself as a method for probing heteronuclear dipole–dipole couplings inisotopically dilute systems of low-g nuclei. In organic substances it is, however, particularlyadvantageous to consider heteronuclear spin-pairs such as1H–13C, on account of the high naturalabundance of1H and thus a much wider range of possible applications, such as the determinationof order parameters in liquid crystals and polymer melts. We describe the possibility of performing13C-observed REDOR in1H–13C systems, where very-fast MAS with spinning frequencies of up to30 kHz is used to successfully suppress the perturbing homonuclear couplings among the protons,which would usually be expected to hamper a proper data analysis. Simple modifications of theREDOR experiment are presented which lead to a two-dimensional experiment in whichheteronuclear multi-spin multiple-quantum modes are excited, the evolution of which is monitoredin the indirect frequency dimension. The existence of higher quantum orders in the proton subspaceof these heteronuclear coherences is proven by performing a phase-incremented spin-countingexperiment, while a phase cycle can be implemented which allows the observation of specificselected coherence orders in the indirect dimension of two-dimensional shift correlationexperiments. The significance of the heteronuclear approach to spin counting is discussed bycomparison with well-known homonuclear spin-counting strategies. For the shift correlation, thehigh resolution of1H chemical shifts in the indirect dimension is achieved by the use of highB0

fields (vL

1H/2p5700.13 MHz! combined with very-fast MAS, and dipolar coupling information canbe extracted by analyzing either peak intensities or spinning-sideband patterns in the indirectfrequency dimension. The method is termed dipolar heteronuclear multiple-spin correlation~DIP-HMSC!. © 2001 American Institute of Physics.@DOI: 10.1063/1.1352618#

u, his

osed

tus

ely

otinu

in-n

aryct

ast

be

inds,

ad

ole-

ate,

ns.roleof

ay

I. INTRODUCTION

In recent years, the exploitation of dipole–dipole coplings, as determined by magnetic resonance techniquesbecome invaluable for structural studies. By employing dtance constraints from two-dimensional dipole–dipole crrelaxation experiments~i.e., nuclear Overhauser-enhancspectroscopy, NOESY!, nuclear magnetic resonance~NMR!spectroscopy has become the standard tool for strucstudies of small molecules and moderately sized proteintheir natural state, i.e., in solution.1,2 In the solid state,mainly direct dipole–dipole couplings between selectivlabeled spin pairs such as13C–13C ~Ref. 3! or 13C–15N~Refs. 4 and 5! have been investigated so far, on accountthe low natural abundance and the increased site-resoluprovided by the large spread of chemical shifts of theseclei.

A current challenge in solid-state NMR is the harnessof dipolar proximities involving1H, which is the most abundant and sensitive nucleus in NMR experiments on orga

a!This paper is dedicated to Professor Hans Silleseu on his 65th birthdb!Author to whom correspondence should be addressed.

5700021-9606/2001/114(13)/5707/22/$18.00

Downloaded 06 Apr 2001 to 132.230.1.172. Redistribution subjec

-as-s

ralin

fon-

g

ic

compounds, where the chemical-shift information necessfor site selectivity is usually obscured by the strong diredipole–dipole couplings among the protons. Using very-fmagic-angle spinning~MAS!, with spinning frequencies upto 35 kHz, sufficient spectral resolution can indeedachieved even for1H in the solid state.6 Two-dimensional1Hhomonuclear double-quantum~DQ! MAS experiments haveproven to be useful for determining dipolar proximitiesorder to investigate hydrogen bond structures in rigid solifor instance, in benzoxazine dimers.7 However, the use ofsuch methods is limited by a severe overlap of the still broproton lines. In this respect, heteronuclear methods using13Cas the detected spin for the determination of dipole–dipcouplings to1H offer much promise with regards to obtaining more specific distance constraints from solid-stspectra.8,9 Moreover, once1H–13C spin pairs are identifiedthey can be used to study molecular dynamics10–12 in com-plete analogy to2H NMR experiments, which have beeused extensively to study motions on different time scale13

The REDOR method,4,14 is currently the most populamethod for the determination of heteronuclear dipole–dipcouplings in rotating solids. It is based on the application

.

7 © 2001 American Institute of Physics

t to AIP copyright, see http://ojps.aip.org/jcpo/jcpcr.jsp

elya

in

unsentic

t-a

etd

rorolow

nee-lea

gti-rinet-i

e

ao

ing

thara

linnlgs-o

vin

-

al

o-alp, isr re-

estric

sricro-to-

inodel1Dbe

oflear

ering,e, isom-tro-t iser-oni-

ri-ndo-

ofofro-

sible

xi-

ole

l-l

li-er-is

5708 J. Chem. Phys., Vol. 114, No. 13, 1 April 2001 K. Saalwachter and H. W. Spiess

equally spacedp pulses twice per rotor period, which servto recouple the dipole–dipole interaction, which is largeaveraged out under MAS conditions. The coupling informtion is usually extracted by varying the length of thep-pulsetrain applied to the nonobserved spin~henceforth the I-spin!,which results in a coupling-dependent attenuation of thetensity of the observed spin~the S-spin!. However, the one-dimensional nature of the experiment does not allow theraveling of multiple couplings to different I-spins. It itherefore desirable to extend the experiment to two dimsions, where in the second frequency dimension the parpating I-spins can be separated by their chemical shifts.15

Originally designed for the application to isolated heeronuclear two-spin systems, REDOR has never beenplied to 1H–13C systems, on account of the very many heronuclear couplings which render the data analysis modependent, and the strong homonuclear couplings amongprotons which lead to deviations from the simple hetenuclear theory used to analyze the data. To make the plem associated with multi-spin systems tractable, we empthe spectral separation of the I-spins discussed above, asas very-fast MAS, which, as shown previously,6,16 helps inbreaking up the strong homogeneous dipolar couplingwork among the protons into pair correlations. It will bcome apparent that the overall suppression of homonuccouplings by very-fast MAS is efficient enough to treat1H–13C spin system in terms of heteronuclear couplinonly. This results in a dramatic simplification of the mulspin problem present in solids, because multiple hetenuclear dipole–dipole couplings can trivially be treatedterms of individual pair couplings, since they are inhomogneous in nature.17 Consequently, simple concepts from firsorder perturbation theory, on which the theory for REDORbased, can be used to calculate the spin dynamics.

Different authors have claimed that REDOR becominefficient at very high spinning frequencies.18,19 Regardingpotential problems with finite pulses, which then coverconsiderable fraction of the rotation period, Griffin and cworkers only recently showed that complications arisfrom an increased duty cycle are very minor.20 Moreover,our results clearly indicate that problems associated withinterplay of finite pulses and homonuclear couplingssmall. In previous publications, we have already shown th

using high magnetic fields (vL

1H/2p5700.13 MHz! and very-fast MAS with spinning frequencies around 30 kHz,1H–13Ccorrelation experiments based on REDOR-type recoupcan be performed in which the signal intensities are oslightly influenced by the residual homonuclear couplinamong the protons.8,21,22Using these techniques, it was posible to determine order parameters in a new class of discliquid crystals without the need of isotopic labeling.12 In ourearlier work, the pulse sequences were designed to coninitial 1H magnetization directly into heteronuclear two-spmodes, which are monitored during thet1 dimension of a 2Dexperiment, and then converted to13C observable magnetization, which is subsequently detected int2 . These so-calledrecoupled polarization-transfer~REPT! sequences8,22 arethus asymmetric.

The emphasis of this work is on modifying the origin


-

-

-

-i-

p--elthe-b-yell

t-

ar

s

o-

-

s

s

-

eet,

gys

tic

ert

REDOR experiment in order to obtain a similar twdimensional experiment which is symmetric in that initi13C magnetization, as created by a cross-polarization steused to excite heteronuclear coherences, which are lateconverted into detectable13C magnetization. While for theREPT method, only the evolution of two-spin coherencduring t1 is detected as a consequence of the asymmedesign of the pulse sequence,22 multiple-quantum coherenceinvolving many protons can be excited with a symmetsequence. The whole class of symmetric dipolar hetenuclear correlation experiments will generally be referredas DIP-HMSC~dipolar heteronuclear multiple-spin correlation!.

In the following section, the basic theory of the spdynamics will be summarized, and measurements on a msystem will be presented which show that the simpleREDOR experiment under very-fast MAS can indeedused for the quantitative determination of weak1H–13C cou-plings even in the presence of strong1H–1H couplings. InSec. III we will describe in detail how a simple extensionthe REDOR pulse sequence leads to a heteronucmultiple-quantum~HMQ! experiment. Section IV deals withthe experimental verification of the excitation of higher-ordmultiple-quantum coherences: heteronuclear spin-countcarried out using a simple phase-incrementation schemintroduced, and its specific properties are discussed in cparison with homonuclear approaches to spin-counting induced by Pines and co-workers. Section V shows that ipossible to select specific multi-spin modes by their cohence order using an appropriate phase cycle, and thus mtor their chemical-shift evolution in two-dimensional expements. Finally, in the last section, an alternative acompletely different way of extracting dominant heternuclear dipole–dipole couplings is described: the analysisspinning sidebands which appear in the indirect dimensionthe two-dimensional experiment as a consequence of thetor encoding of the recoupling Hamiltonian,23–25 is demon-strated. This method has already been shown to be feawith the REPT techniques.8,12,22

II. REDOR IN 1H–13C SYSTEMS

A. Basic theory of REDOR in I nS-spin systems

The Hamiltonian of a heteronuclear InS-spin system un-der magic-angle spinning conditions in the secular appromation reads

H~vRt !5(i 51

n

dIS( i )~vRt ! 2I z

( i )Sz1(i 51

n

v iso,i I z( i )

1~v iso,S1sS~vRt !! Sz . ~1!

It is composed of the sum of all heteronuclear dipole–dipinteractions~first term!, the isotropic I-spin chemical shifts~second term!, and the S-spin isotropic shift and chemicashift anisotropy~third term!. Throughout this paper, we wilneglect the I-spin (1H) chemical-shift anisotropy~CSA! andthe homonuclear dipole–dipole interaction. In earlier pubcations we have shown that, for evolution times of a modate number of rotation periods, the latter approximation


n

.

c-

se

dra

5709J. Chem. Phys., Vol. 114, No. 13, 1 April 2001 Multiple-spin correlation in solid-state NMR

FIG. 1. Pulse sequences for1H–13CREDOR. Initial 13C magnetization iscreated by a ramped cross-polarizatio~CP! step~Ref. 65!, which is advisableunder the very-fast MAS conditions(nR525– 30 kHz! used to suppress theinfluence of homonuclear couplingsThe matching condition wasv1

S5v1I

2vR , with the ramp varying from0.9v1

I to 1.1v1I . The recoupling

p-pulse trains~open boxes! can be ap-plied to the1H ~a! or 13C ~b! channels,and the pulse phases are cycled acording to the (xy-4) scheme~Ref.33!, in order to avoid signal reductionfrom spectral offsets and to suppresartifacts from pulse imperfections. Thfinal 90° pulses~black bars! on 13Cform az filter ~Ref. 66! of several tensof ms length, which helps to obtaincleaner spectra by purging unwantesignal contributions. Reference spectcan be taken by either omitting theppulses on1H in both sequences, or byapplying an additionalp pulse in se-quence~a!.

steithth

th

to

pi

rle

fu

-y

a

Aa

o

lar

polethe

by

u-

t isratedre-e

or,n,

nalal

excellent even in1H systems, provided that a sufficiently faspinning frequency is employed.8,22 The work presented herapplies the condition of very-fast magic-angle spinning wfrequencies exceeding 20 kHz. Under these conditions,strong homonuclear dipolar coupling network amongprotons breaks up into a sum of pair correlations.6,16 As aresult, the spin system behaves inhomogeneously.17 Evenwhen the heteronuclear coupling is recoupled in a rosynchronized fashion~vide infra!, the homonuclear couplingis essentially averaged out over full rotor cycles of S-stransverse evolution.

The first term representing the time-dependent hetenuclear dipole–dipole coupling contains the coupling ement defined as

dIS( i )~vRt !52D IiS (

m522

2 F (m8522

2

D 02m8(2)

~VPC!

3D 2m82m(2)

~VCR!G d2m0(2) ~bM ! eimvRt. ~2!

This result can be derived by using the second-rank(D m8m

(2) (V)) and reduced (dm8m(2) (b)) Wigner matrix

elements26 for the rotation of the dipole–dipole coupling tensor in its spherical representation from its principal axes stem ~P! first into the crystal~or molecular! frame ~C!, theninto the rotor frame~R!, and finally into the laboratory frame~L!. The sets of Euler angles relating the different framesdenoted asV5$a,b,g%. The last rotation from the rotor intothe laboratory frame is rendered time dependent by M(VRL5$vRt,bM,0%), and for a polycrystalline sample,powder average has to be performed overVCR . VPC speci-fies the various relative tensor orientations within one mecule or coupling network:


ee

r-

n

o--

ll

s-

re

S

l-

D IiS5

m0\g IgS

4pr i3

~3!

is the dipole–dipole coupling constant in units of angufrequency. The time-dependent CSA,sS(vRt), can betreated in essentially the same fashion as the dipole–dicoupling, and explicit representations can be taken fromliterature.21,11

The time evolution of the spin system, as representedthe density operatorr, during the interval (ta ;tb) is calcu-lated using the integrated form of the Liouville–Von Nemann equation

r~ tb!5U~ ta ;tb! r~ ta! U21~ ta ;tb!. ~4!

The density operator at the beginning of the experimencomposed of S-spin transverse magnetization, as geneby cross-polarization from the I-spins, and can be repsented asr(0)5Sx . Throughout this paper, we will use thformalism of product operator theory27 for the calculation ofthe time evolution. In the case of MAS, the propagatU(ta ;tb), can be calculated from the average HamiltoniaH(ta ;tb), during this interval as

U~ ta ;tb!5exp$2 iH ~ ta ;tb!3~ tb2ta!%. ~5!

The use of the zeroth-order average Hamiltonian,

H~ ta ;tb!5~ tb2ta!21 Eta

tbH~ t8!dt8, ~6!

is well justified in our case since the Hamiltonian in Eq.~1!commutes with itself at different times.28

Two possible pulse sequences for the conventioREDOR experiment4 are depicted in Fig. 1. The essenti


ge

lsr-A

ncl

-o

aedy

olly

re

in

c-

ue,

,toalren

-

by

i-

di-is

ling

cou-nceareect-illthene-egdr

al-atfac-

astent-

ndion


idea behind REDOR is the recoupling~i.e., reintroduction! ofthe heteronuclear dipole–dipole coupling, which is averaout by MAS. This is achieved by application ofp pulses inthe middle and at the end of each rotor period. These pueffectively invert the dipolar evolution, which can be intepreted as a counter-rotation in spin-space, opposing the Min a synchronized fashion. Thep pulses can be applied oeither channel, because the sign change of the heteronudipole–dipole coupling Hamiltonian (;2I zSz) can beachieved by applying ap rotation to either one of the constituting z angular momentum operators. The placementthe p pulses on the1H channel@Fig. 1~a!# is beneficial inthat the maximum number of pulses is applied on the chnel where only longitudinal components are to be invertwhile the13C chemical shift and CSA are fully refocused bthe centralp pulse on13C. The application of the manyppulses on13C @Fig. 1~b!# and omitting the central one alsleads to13C CSA refocusing, but the pulses more criticainteract with the evolution of transverse coherence.29 Forboth implementations, the only interaction to be consideduring the recoupling period ofNrcpl rotor periods length isthe heteronuclear dipole–dipole coupling@the first term inEq. ~1!#.

The average heteronuclear dipole–dipole couplHamiltonian is most conveniently written as

H IiS~ ta ;tb!5

F ( i )~ ta ;tb!

tb2ta2I z

( i )Sz , ~7!

whereF ( i )(ta ;tb) is the dipolar phase factor, which is aquired during the interval (ta ;tb). From Eqs.~1!, ~6!, and~7!it is given by

F ( i )~ ta ;tb!5Eta

tbdIS

( i )~vRt !dt. ~8!

For REDOR, i.e., when the sign of the dipole–dipole copling Hamiltonian is inverted for every other half rotor cyclthe average REDOR phase factor for a full rotor cycle~asindicated by the bar! reads

F t( i )5E

t

t1tR/2

dIS( i )~vRt8!dt82E

t1tR/2

t1tRdIS

( i )~vRt8!dt8

52F ( i )~ t;t1tR/2!, ~9!

The importance of the lower bound of the time integralt,which merely describes a dependence on the initial rophase,vRt, will become apparent for the two-dimensionextensions discussed below. If only one I-spin is considei.e., when the relative orientation of different coupling tesors does not need to be specified, Eq.~2! can be evaluatedusingVPC5$0,0,0%, which yields the simplified result published by Gullion and Schaefer4

F t52D IS

vR2A2 sin2bCR sin~vRt1gCR!. ~10!

If the REDORp-pulse train is applied at a timet for Nrcpl

rotor cycles, the overall phase factor is simply givenNrcplF t

( i ) .


d

es

S

ear

f

n-,

d

g

-

r

d,-

A calculation of the REDOR-recoupled evolution of intial Sx transverse magnetization, dipolar coupled ton I-spins,yields

Sx ——→Nrcpl( iF0

~ i !2SzI z~ i !

Sx )i

cosNrcplF0( i ) ~11!

1(j

2SyI z( j ) sinNrcplF0

( j ))iÞ j

cosNrcplF0( i )

~12!

2(j ,k

4SxI z( j ) I z

(k) sinNrcplF0( j ) sinNrcplF0

(k)

3 )iÞ j ,k

cosNrcplF0( i ) ~13!

2 (j ,k, l

8SyI z( j ) I z

(k) I z( l )

3sinNrcplF0( j ) sinNrcplF0

(k) sinNrcplF0( l )

3 )iÞ j ,k,l

cosNrcplF0( i ) . ~14!

]

The calculation is simple and straightforward since all invidual couplings can be evaluated independently. Thispossible because the individual heteronuclear coupHamiltonians commute with each other:@H IiS

,H I jS#50. We

see that the density operator at the end of the REDOR repling period is composed of a carbon transverse cohere@Eq. ~11!# and multi-spin antiphase coherences. The latterneither detectable quantities, nor do they evolve into detable magnetization without further recoupling, but they wgain importance in the two-dimensional extensions oftechnique discussed later. The final signal in a odimensional REDOR experiment which passes through thzfilter is thus proportional to the coefficient of the remainintransverse coherence,Sz . The dephased signal is calculateas the powder average overVCR ~as indicated by the angulabrackets!:

S5K )i

cosNrcplF0( i ) L . ~15!

For three isolated methyl protons which couple tosingle carbon atom~this case will be investigated in the folowing! the above formula can be simplified by noting ththe three heteronuclear coupling tensors, thus the phasetors F0

( i )5F0CH3, are identical as a consequence of the f

three-site jumps performed by methyl groups at ambitemperature.22,30 If the 13C in question is located on the rotation axis,F0

CH3 is a function of a modified dipole–dipolecoupling constant31

D ISapp5D IS

12~3 cos2 u21!, ~16!

whereu is the angle between the IS-internuclear vector athe methyl rotation axis. For S-spins located off the rotat


d

hy

sooo

ouo

n-

ge

e-

in,odge

sn

fee-thhe

naut

Cdyda

up

Al

et.red

n

es,

theex-e 2

ofesnt

e

o-a

ofin-tionf

eer-

sityfim-case

then-

encethe

sesas

sent


axis, the individualF0( i ) are still equal, but the average

dipole–dipole tensor will be asymmetric, and hence Eq.~16!is not applicable. The theoretical intensity for a single metgroup is simply

SCH35^cos3 NrcplF0CH3 &. ~17!

This result certainly represents a very unique multi-spin caHowever, the ensuing experimental test provides a very gproof of the negligible influence of the rather strong homnuclear couplings among the three methyl protons inexperiments. For the case of a carbon close to more thanmethyl group, we obtain

SnCH35K )i

cos3 NrcplF0CH3 ,i L . ~18!

The intensities in Eqs.~15!, ~17!, and ~18! can directlybe measured on an absolute scale by normalizing the13Csignal intensity of the REDOR spectrum with the udephased reference intensity ofSx (S0), whereby relaxationeffects are corrected for. Finally, the resultSREDOR5(12S/S0)5DS/S0 is plotted as a function of the recouplintime. The dipole–dipole coupling constants can then betracted from an analysis of this so-called build-up curve. Wwill reinterpret such data in terms of a build-up of multiplquantum coherences in Sec. III.

Using the pulse sequence with only onep pulse on13C,the mentioned reference spectrum is obtained by performan experiment in which the1H p pulses are either left outor a p pulse is added in the middle of the recoupling peri@dashed pulse in Fig. 1~a!#. In the first case, no recouplinoccurs at all, and theSx coherence, subject to evolution duto the Hamiltonian in Eq.~1!, is simply refocused, but sufferthe same relaxation effects as the dephased coherence i~11!. In the second case, the two simultaneousp pulses inthe middle of the sequence cancel each other in their efof inverting the dipolar Hamiltonian. Therefore, the rcoupled dipolar evolution runs backwards in time duringsecond half of the REDOR recoupling, converting all tmulti-spin antiphase coherences@Eqs. ~12!, ~13!, ~14!,...#,which are similarly present afterNrcpl/2, back into observ-able Sx magnetization by the end ofNrcpl . Restricting thediscussion to the Hamiltonian given in Eq.~1!, thus neglect-ing homonuclear couplings, effects of finite rf pulses, aexperimental imperfections, which would all interfere withproper time reversal, the amplitude of this coherence wobe just the same as for the reference experiment withouppulses on1H.

B. Experimental test of REDOR in 1H–13C systems

Partially deuterated methylmalonic acid, DOO–CD~CH3!–COOD, is a useful model compound to sturelatively weak1H–13C couplings. It can be easily preparefrom commercially available methylmalonic acid; the prepration procedure is described in Ref. 22. The methyl groin this substance are fairly isolated, with next CH3 protonneighbors about 4.3 Å away from the methyl carbon.measurements in this publication were performed on


l

e.d

-rne

x-e

g

Eq.

ct

e

d

ld

-s

la

Bruker DRX700 console using a 16.4 T narrow bore magnA 2.5 mm MAS double-resonance probe, also manufactuby Bruker, was used. 90° pulses of 2ms length~correspond-ing to v1/2p5125 kHz! were applied on both channels. Iall experiments, TPPM dipolar decoupling32 was employed,using the same rf field strength, approximately 160° pulsand a modulation angle of 30°.

1. Referencing procedure

At first, we shall investigate the stated equivalence oftwo possible ways of performing the REDOR referenceperiment, as explained in the preceding section. Figurshows normalizedS0 intensities of the CO group in partiallydeuterated methylmalonic acid for the two possibilitiesrecording the reference with and without recoupling pulson 1H, and, additionally, reference intensities for the variawith manyp pulses on13C @Fig. 1~b!# and no1H pulse. Mostnotably, the13C intensity hardly decays at all when only oncentral refocusing pulse on13C and no pulses on1H areapplied ~open squares!. This proves the successful heternuclear decoupling by the very-fast MAS. However, whenfull p-pulse train is applied to the protons, and the signthe recoupled heteronuclear dipole–dipole interaction isverted during the second half of the sequence by applicaof two simultaneousp pulses to both spins in the middle othe sequence, a marked dephasing is observed~solidsquares!. This effect may qualitatively be explained by thunsuccessful conversion of the multi-spin antiphase cohences@Eqs.~12!, ~13!, ~14!,...# into observableSx coherenceduring the second half of the sequence. Numerical denmatrix simulations of SIn spin systems including the effect ohomonuclear couplings, finite pulse durations, and pulseperfections indicated that the dephasing observed in theof the reference experiment with manyp pulses on1H is inpart indeed due to homonuclear couplings, but only whenp pulses are of finite length. Flip angle deviations also cotribute, but these perturbances are not altered by the presor absence of homonuclear couplings. To our knowledge,combined effect of homonuclear couplings and finite pulhas not yet been explored in detail. A similar effect wobserved for the related REPT sequences.22

FIG. 2. 1H–13C REDOR reference intensities~arbitrary units! measured onpartially deuterated methylmalonic acid at 30 kHz MAS. Squares repredata from an experiment with only a singlep pulse on13C @Fig. 1~a!#, withan additional centralp pulse on1H ~j! or no 1H pulses at all (h). Circlesare from experiments with manyp pulses on13C @Fig. 1~b!#, where noppulse was applied to1H (d).


nthbeli

th

trtt

fotiog

o

os-nn

it

e-

lessnced

nic

theteendlingon-

es.rea-

thethanise

twoe-

ae ob-ar-lar

u-

T

le–inu

ak

car-nic

the

dralids

osi-


Pulse imperfections are clearly the reason for the sigdeterioration whenS0 is measured using the experiment wimany p-pulses on13C. Such perturbances can certainlyfurther suppressed by using more elaborate phase cycschemes such as (xy-8) or (xy-16) for thep-pulse trains.33

By contrast, in most of our experiments, that is, whenmajority of thep pulses is applied to1H, the performance of(xy-4) could not be improved significantly~higher-ordercycles necessitate more complicated pulse programs!. Thissupports again the notion that homonuclear effects, as induced by finite pulses, dominate the signal loss in the lacase.

We conclude that, in order to partially compensatepulse imperfections and homonuclear effects in conjuncwith finite rf pulses,1H–13C REDOR experiments accordinto the pulse sequences in Figs. 1~a! and 1~b! should be per-formed using reference experiments which rely only upadding or omitting a centralp pulse on1H, respectively,rather than just omitting all1H p pulses. Then, both thedephased and the reference spectra suffer the same lfrom experimental imperfections~at revision stage, we became aware of a very recent publication of Chan aEckert,34 who treat this new and improved referencing cocept in great detail!. From an experimental point of view,may be advisable to use the sequence in Fig. 1~a!, where thepossibility of applying higher radio frequencies, thus evshorter pulses, to1H can be taken advantage of. If sufficiently short pulsescan be applied to the13C channel, it

FIG. 3. Normalized1H–13C REDOR intensities measured on partially deterated methylmalonic acid at 30 kHz MAS. Open circles (s) in the topdiagram represent data for the CH3 carbon, while solid squares~j! are forthe CD and CO carbons in the top and bottom diagrams, respectively.solid lines are REDOR master curves for a rapidly rotating I3S unit @Eq.~17!#, with thex axis scaling adjusted to obtain a fit for the apparent dipodipole coupling constants given in Table I. The normalized differencetensities are on an absolute scale. Dashed lines are from analytical simtions for the CD and CO carbons, based on crystal structure data and tinto account the nine closest CH3 moieties.


al

ng

e

o-er

rn

n

ses

d-

n

might be possible to acquire spectra which are evenperturbed by homonuclear couplings, by using the sequewith the manyp pulses on13C. This has not yet been testeexperimentally.

2. Experimental results

Results from REDOR experiments on the methylmaloacid sample with manyp pulses on1H, referenced using anexperiment with one additionalp pulse on1H, are shown inFig. 3. The signals from all three carbon atoms approachtheoretically predicted plateau of 1.0, indicating compledephasing. Fort rcpl.1500ms, the measured values becomunreliable on account of the increasingly weak signal ahence poor S/N of the reference spectra at longer recouptimes. Results for the apparent dipole–dipole coupling cstants,D IS

app, Eq. ~16!, were obtained by fitting thex scalingof a master curve calculated using Eq.~17! to the measureddata points. The best-fit curves are indicated as solid linThe scaled master curves model the experimental datasonably well, in particular, the data for the CH3 carbon ex-hibits the expected oscillations in the plateau region. ForCD and CO carbons, deviations are nevertheless biggerthe experimental errors which were estimated from the nolevel. However, the coupling constants for the CH3 and CDcarbons are close to the expected values~see Table I!, andthe 1H–13C distances are well reproduced.

The observed discrepancies can be attributed tomain factors. First, multi-spin effects, i.e., couplings to rmote methyl groups, contribute to the build-up, and asconsequence, larger than expected coupling constants artained. This is most pronounced in the data for the CO cbon, which is located quite far away from the intramolecu

he

-la-

ing

TABLE I. Experimentally observed and expected apparent1H–13C dipole–dipole couplings and internuclear distances between the three differentbon atoms and the methyl protons in partially deuterated methylmaloacid, as obtained from the REDOR experiments~Fig. 3! and from the DIP-HDOR spinning sideband analysis~Fig. 16!. The negative signs for thetheoreticalD IS

app obtained from the crystal structure are a consequence ofaveraging process@see Eq.~16!#.

Fits of NMR dataa From crystal structureb

REDOR uD ISappu/2p ~kHz! ⇒r IS ~Å! D IS

app/2p ~kHz!c r IS ~Å!

CH3 7.360.02 1.11d 27.77 1.09CD 2.2360.02 2.08e 21.97 2.165CO 1.8960.02 21.02/20.96

SidebandsCH3 6.6960.07 1.14560.004 27.77 1.09CD 2.1560.04 2.1060.01 21.97 2.165CO 1.9460.07 21.02/20.96e

aError margins are based on the quality of the fits.bDue to the poor proton localization in the available x-ray structure~Ref.35!, the methyl proton positions were adjusted according to a tetrahestructure withr CH51.09 Å, as commonly encountered in, e.g., amino ac~Ref. 51!. For details see Ref. 67.

cCalculated from the average dipole–dipole tensor of the three proton ptions.

dCalculated from Eqs.~3! and ~16!, assumingu5109.5°.eCalculated from Eqs.~3! and ~16!, assumingu528.4°.fTwo inequivalent positions in the crystal.


he twoin 2

lse,


FIG. 4. Pulse sequence for the1H–13C multiple-quantum correlation experiment. Solid and open bars indicate 90° and 180° pulses, respectively. Tblocks of REDOR recoupling~see Fig. 1! are now identified as HMQ excitation and reconversion periods, where the recoupling times can be variedtR

steps by incrementing the indicated loops. Multiple-quantum filtration is achieved by applying a phase cycle to the two1H 90° pulses (f1 andf2) and thereceiver phase,f rec. The dotted box indicates how, fort150 andf256f1 , the two 1H 90° pulses can be regarded as an effective 180° or 0° pucorresponding to sequences used to obtain a 1D REDOR reference or dephased spectrum, respectively.

mm

cistmnialepociso

sfa

rA

nc

onea

ecof

bth

Q-

.

t

ec.

le

ofter-re-r-y

e as

g in

le-

0°n-

be

of

methyl group. In Fig. 3, theoretical curves calculated froEq. ~18! using the tensor parameters of the nine closestthyl proton triplets~based on the crystal structure35! are in-cluded as dashed lines. These curves show no more ostions and match the experimental data better, but theyunderestimate the experimentally observed coupling. Honuclear couplings among the protons, as introduced by fiand imperfect pulses, may account for this additional dephing at intermediate recoupling times. Apart from possibheteronuclear contributions of further remote methyl grouthese deviations are an indication that the referencing prdure cannot fully correct for all homonuclear effects. Thisnot surprising, since, due to the noncommutativity of homnuclear and heteronuclear couplings, homonuclear effectnot manifest themselves as simple additional dephasingtors which cancel upon calculation ofS/S0 . However, theseeffects are still rather small and do not completely hampesimplified data analysis based on a single methyl group.expected, fits to REDOR data normalized to the refereexperiments without any1H pulses~data not shown! yieldsdipole–dipole coupling constants for the CD and CO carbwhich are larger by about 10%, because dephasing duhomonuclear couplings and pulse imperfections is notcounted for at all.

III. REDOR AND MULTIPLE-QUANTUMSPECTROSCOPY

A. Experimental procedure and theory

As in liquids,1 selectivity and versatility of NMR in sol-ids can substantially be improved by multiple-quantum sptroscopy. Therefore, we will now turn to the applicationthe concepts of REDOR recoupling to1H–13C multiple-quantum spectroscopy. An HMQ experiment can easilyderived from the REDOR pulse sequences by dividingcentral1H p pulse@the dashed one in Fig. 1~a!# into two 90°pulses flanking a multiple-quantum (t1) dimension. The firsthalf of the REDOR recoupling is then identified as an HMexcitation period of durationNexc rotor cycles, while the second half serves as a reconversion period of durationNrec

rotor cycles. The basic pulse sequence is shown in Fig. 4


e-

lla-illo-tes-

s,e-

-doc-

ase

sto

c-

-

ee

In

each of the recoupling periods, a centralp pulse is placed on13C, such that the13C chemical shielding is fully refocused athe start oft1 and before the finalz filter. This is not strictlynecessary for the depicted HMQ sequence, which has a13Crefocusing pulse also in the middle oft1 , but will be ofimportance for the variants of the concept presented in SIII C.

For t150, it can easily be rationalized that by a simp180° phase switch of the second 90° pulse (f2) relative tothe first one on alternate transients, effective flip angles180° or 0° can be realized. If the receiver phase also alnates its sign for every other transient, intensities in thesulting spectrum will automatically be the REDOR diffeence intensities,DS. This idea was recently published bSandstro¨m et al.36 in a 13C–2H HMQ experiment. Althoughthere is no experimental advantage in using this sequencopposed to conventional REDOR~the reference spectrumstill has to be acquired in a separate experiment, resultinan effectively longer total experiment time!, the concept em-phasizes the close relationship of REDOR and multipquantum spectroscopy.

HMQ coherences are created by the first of the two 9pulses on1H. The S-spin transverse and the multi-spin atiphase coherences in Eqs.~11!–~14! are converted into vari-ous kinds of HMQ coherences, the evolution of which canprobed duringt1 :

~19!

wherer(NexctR2) denotes the density operator at the end


0ieo-sm

,ero-

sa

fo

nnln

-if

eaed

ohen

bb

he

oveeioof

be-om

urengqs.

0°en-here-

fo-

se

R

al-f

edem-In

toto

tion

al is


the excitation period before the application of the first 9pulse, andsandc refer to the sine and cosine phase factorsEqs. ~11!–~14!. As indicated, the product operators for thI-spins comprise mixtures of different multiple-quantum cherences, coupled to S-spin transverse coherence. The Scontribution can be treated separately, since it can benipulated independently.

The second 90° pulse~with f256f1) again createsantiphase coherences, but with signs depending onf2 and onthe number ofI z multipliers. During the reconversion periodthe individual antiphase coherences evolve back into obsable Sx magnetization with a corresponding phase facte.g., a single two-spin term from Eq.~12! becomes observable as

2SyI z~ j ! sinNexcF0

~ j !)iÞ j

cosNexcF0~ i !

——→reconversion

Sx sinNexcF0~ j ! sinNrecFt1

~ j !

3)iÞ j

cosNexcF0~ i ! cosNrecFt1

~ i ! . ~20!

Note the explicitt1 dependence of the reconversion phafactors, which leads to the appearance of spinning-sidebpatterns ifDt1ÞntR . This will be explained more fully inSec. VI. The trigonometric prefactors ofSx constitute theexpression for the intensity of the detected signal, whichthe special case of an isolated CH group is simply

SMQCH 5^sinNexcF0 sinNrecFt1

&. ~21!

In the following discussions, multiple-quantum filtratiowill be discussed in reference to the I-spin subspace oand a few comments should be made on its independefrom the S-spin subspace: a coherence such as 2SyI x consti-tutes a mixture ofheteronuclearzero- and double-quantumcoherence. The interaction picture~i.e., the secular approximation! demands a description of the I- and S-spins in dferent rotating frames, thus interactions between eachthese spins and some other spin can be evaluated forspin individually. The relative sign of the evolution in thdifferent rotating frames~which defines the zero- andouble-quantum part of the heteronuclear coherence! doesnot affect the modulation frequency due to an interaction tthird spin, which means that HZQ and HDQ, apart from tdirection of their precession, are indistinguishable and dorelax with different rates, as is the case for homonuclear Mcoherences. The principles of coherence order selectionphase cycling1 can thus be applied for the I- and S-spin suspaces individually. Following the simple rules publishedErnst et al. ~see Ref. 37 for a clear description!, the phasecycle in the above-mentioned experiment yielding tREDOR difference intensity can be regarded as amultiple-quantum filterin the I-spin subspace: the 180° phase shiftthe second 90° pulse, along with an inversion of the receiis nothing but anodd-quantumselection on the I-spins. SincS-spins are detected, the I-spin odd-quantum contributmust have been part of an HMQ coherence. Selection


°n

-pina-

v-r,

end

r

y,ce

-ofch

a

otQby-y

fr,

nsa

specific quantum order on the S-spins is not necessarycause the excitation of higher S-spin MQ coherences frtransverse S-magnetization using the Hamiltonian in Eq.~1!is not possible.

The above-mentioned odd-quantum selection procedcan be followed by writing down the detected signal arisifrom all different higher-order antiphase coherences, E~11!–~13!. Following the principle outlined for Eq.~20!, thesignal for a single crystallite for the simple case oft150 andNexc5Nrec5Nrcpl reads

S651)i

cos2 NrcplF0( i ) ~22!

7(j

sin2 NrcplF0( j ))

iÞ jcos2 NrcplF0

( i ) ~23!

1(j ,k

sin2 NrcplF0( j )sin2 NrcplF0

(k) )iÞ j ,k

cos2 NrcplF0( i )

~24!

7 (j ,k, l

sin2 NrcplF0( j )sin2 Nrcpl

3F0(k)sin2 NrcplF0

( l ) )iÞ j ,k,l

cos2 NrcplF0( i ) ~25!

],

where the6 subscript indicates the sign of the second 9pulse or, equivalently, the existence or omission of the ctral p pulse in a conventional REDOR experiment. For treference spectrum, the complete initial magnetization isgained (S05^S2&), whereas the dephased signal,S5^S1&,reduces to Eq.~15! with an effective recoupling time o2Nrcpl . The multiple-quantum signal, as created by the twstep phase cycle isSMQ5^S22S1&/2. Only the terms withan odd number ofI z multipliers change sign and are thuretained by the MQ filter. For a single IS-spin pair thmultiple-quantum signal therefore reads

SMQ5^ sin2 NrcplF0 &5 122 1

2^cos 2NrcplF&. ~26!

We see that this result differs from the conventional REDOdifference signal by a factor of12. Therefore, if REDOR in-tensities are to be interpreted as MQ intensities, the normization to be used is (SN2S0)/2S0 , because the number otransients acquired forDS5SN2S0 is effectively twice aslarge as forS0 only. Note that in the spin-pair case, MQexcitation efficiencies in the plateau region never exce50% only because of destructive interference of signals stming from differently oriented crystallites in the powder.experiments using the isotropic J-coupling as a meanscorrelate different nuclei, transfer efficiencies of close100% are commonly realized@the evolution time is adjustedin such a way that the argument of the cosine in an equaequivalent to~26! is close to 2p]. A drawback of solid-stateexperiments based on J-couplings is that the overall signusually substantially reduced byT2 relaxation during thelong excitation and reconversion intervals.38


wQ

allu

th

s

gngQoi-o

th

con-hes.

ri-

nesandty

isTQ

ifte-

anf thehas

ed-

theide.intorob-the

beion,by

he

f a

R

o


B. The methyl group as an example

As a more specific and instructive example, we will nosketch the derivation of formulae describing the HMbuild-up behavior and thet1 time dependence for the signof an isolated CH3 group, this time including the chemicashift evolution of the I-spins. As mentioned, this is a particlarly simple case since the three integrated phases,FCH3, areequal. Furthermore, the isotropic chemical shifts ofprotons are identical. The regular HMQ~i.e., I-spin odd-order! filtered intensity is the sum of Eqs.~23! and~25! withn53:

SMQCH353^ sin2 NrcplF0

CH3~cos2 NrcplF0CH3!2&

1^~sin2 NrcplF0CH3!3&. ~27!

The build-up of HMQ intensity is depicted in Fig. 5. It inoteworthy that although the 3I-spin contribution@secondterm in Eq. ~27!# grows in more slowly upon increasinNrcpl , it reaches higher intensities for longer recouplitimes and thus contributes more strongly to the final HMfiltered signal. The indicated plateau values for the limitsNrcpl→` can be derived by application of the familiar addtion theorems for trigonometric functions to the productssines and cosines ofF0

CH3, e.g., for the 3I-spin term we

obtain ~with a5NrcplF0CH3)

^sin6 a&5 132^10215 cos 2a16 cos 4a2cos 6a& 5

Nrcpl→`1032.

~28!

By inserting the definition of the shift operators@in the formI x5(1/A2)(I 11 I 2)] into the different terms of Eq.~19!,e.g.,

~29!

the fractions with which the different coherence orders inI-spin subspace contribute to the individualn-spin coher-

FIG. 5. DIP-HMQ build-up curves for three contributions to the signal orotating I3S group@with an averaged apparent coupling constant,Dapp, de-fined in Eq.~16!#. The HMQ-filtered curve is the sum of the 1I-spin@Eq.~23!# and 3I-spin@Eq. ~25!# contributions, and is equivalent to a REDOcurve, described by Eq.~15!. The 2I-spin curve@Eq. ~24!# represents thebuild-up of I–~DQ1ZQ! intensity ~only half of this signal corresponds tthe actual I–DQ-filtered intensity!. The plateau values forNrcpl→` are in-dicated by thin dotted lines.


-

e

-f

f

e

ences can easily be derived. Thus, the 2I-spin coherencesists of DQ and ZQ contributions in equal parts, while t3I-spin coherence has 75% SQ and 25% TQ contribution

The t1 time dependence for the HMQC or HSQC expements~including isotropic chemical shifts,F t1

) is obtainedfrom Eqs. ~23! and ~25! by explicitly taking thet1 depen-dence of the dipolar phases,F t1

CH3, during reconversion into

account. The transverse I-spin contributions pick up cosiand sines of the chemical-shift phases for each I-spin,the x and y components of thet1 signal for an experimenwith equal excitation and reconversion times are given b

SxCH35^cosvCS,It1 sinNrcplF0

CH3 sinNrcplF t1

CH3

3~cosNrcplF0CH3 cosNrcplF t1

CH3!2&

1^cos3 vCS,It1~sinNrcplF0CH3 sinNrcplF t1

CH3!3&,

~30!

SyCH35^sinvCS,It1 sinNrcplF0

CH3 sinNrcplF t1

CH3

3~cosNrcplF0CH3 cosNrcplF t1

CH3!2&

1^sin3 vCS,It1~sinNrcplF0CH3 sinNrcplF t1

CH3!3&.

~31!

The cos3 vCS,It1 and sin3 vCS,It1 terms contain the effectiveevolution frequencies for the 3I-spin coherence, e.g.,

sin3vCS,It15 34 sinvCS,It12 1

4 sin 3vCS,It1 . ~32!

This proves again the 25% contribution of I-spin TQ to thcoherence, and shows that in the HMQ-filtered case, thepart evolves with 3vCS,I but in theoppositedirection to theSQ part@minus sign in Eq.~32!#. If a pure I-TQ signal isselected, sign discrimination of the effective chemical-shevolution int1 is achieved by time-proportional phase incrmentation~TPPI, generalized for MQ experiments39! of thesecond proton pulse (f2 in Fig. 4! by 90°/n, with n53 forTQ coherences. This procedure ensures that forn-quantum coherence, a 90° phase-shifted component ochemical-shift signal is detected on alternate scans, and itthe additional benefit that contributions from unwantlower-order coherences~which may survive due to imperfections in the MQ-filter phase cycling! reside in regions of thespectrum where, due to the artificial offset introduced byTPPI, no signal from the coherence of interest would resUnwanted higher-order coherences might be folded backthe spectrum, but these do not generally pose a serious plem since their intensities are much lower than those ofdesired coherence.

C. Generalized pulse sequences and experimentalaspects

The dipolar HMQC experiment discussed above canused to achieve the final goal presented in the introducti.e., it can be used to record shift-correlation spectrameans of which the contributions of different I-spins to t


-

d-ndf


FIG. 6. Different variants of symmet-ric dipolar HMS correlation experi-ments, and RELM. The HSQC andHDOR experiments, which are modifications of the HMQC sequence inFig. 4, are discussed in Secs. III C anVI, respectively. The bottom pulse sequence generates spinning-sidebapatterns through rotor-encoding olongitudinal magnetization~RELM!~Ref. 41! ~see also Sec. VI!.

b

ac

li-evt irepale

thb

acin-oli-ra

Qin

thesthe

r-ero-n,

theasethe

ngorme.

or-pec-he

conventional REDOR dephasing of a given S-spin canseparated by their chemical shift~Sec. V!. This is done byperforming arotor-synchronizedexperiment, in whichDt1

5ntR . Then, the explicit time dependence of the phase ftors is of no concern (FntR

5F0), and the frequency infor-mation governing thet1 dimension is the isotropic chemicashift of the involved protons. The individual signal intensties can be used to obtain qualitative, and in some casesquantitative, distance constraints. If the 2D experimenconducted with a smallert1 increment, and a thus largespectral width, spinning sidebands appear in the MQ dimsion of the experiment. The analysis of such sidebandterns represents an alternative way of extracting the dipodipole coupling information. See Sec. VI for details.

The HMQC sequence can easily be modified in thatcoherence type monitored in the indirect dimension canchanged. Different variants are depicted in Fig. 6. Oncount of the possibility of exciting multi-spin coherencesvolving two or more nuclei with these techniques, the whclass of experiments will be referred to DIP-HMSC, for dpolar heteronuclear multiple-spin correlation. The geneuse of coherence type selection duringt1 is elsewhere de-


e

-

ens

n-t-–

ee-

e

l

scribed in relation to the REPT techniques,22 where a moredetailed discussion can be found.

In addition to monitoring an actual heteronuclear Mcoherence, the I-spin MQ contribution can also be probedantiphase to the S-spin if a 90° storage pulse is applied toS-spin prior tot1 . This variant of the experiment is shown athe second pulse sequence in Fig. 6. It is analogous tosolution-state HSQC experiment40 and the REPT-HSQCexperiment,8,22 even though, strictly speaking, the coheences probed in the multi-I-spin case need not be hetnuclearsingle-quantum coherences. With this modificatiothe influence of the S-spin CSA duringt1 ~if Dt1Þ2ntR)and, more importantly, homonuclear couplings amongS-spins, which lead to additional line broadening in the cof fully labeled samples, are suppressed. The evolution ofIMQSantiphasecoherence under the IS-dipole–dipole couplimust then be considered by adding cosine factors of the fcosFDIS

( i ) (t1) for all I-spins which are part of the coherenc

However, since this factor is periodic with respect totR , itseffect does not appear in rotor-synchronized HSQ shift crelation spectra. These can be recorded with twice the stral width of the corresponding HMQC experiment, since t


gib

oecs,

ltooa

is

m

eacl

h

ei.e

lere

s‘rentin

rda

-

th

ndup-sc-

ede

otnou

erringit-cesut

thercre-umt is.rr-der,ivity-

ed

all

ofsinen-

ne-

or,

e-

sed.x-lef a. Ach aond

the

lece,by

thethe

an

nd

od-in-viorurs


p pulse in the middle oft1 necessitates at1 increment of 2tR for HMQC, if artifacts from incomplete CSA refocusinare to be avoided. Note that all of these effects are negligweak when very high spinning frequencies are used.

The third pulse sequence probes longitudinal dipolarder duringt1 , which does not undergo time evolution. ThHDOR ~heteronuclear dipolar-order rotor-encoding approawas also introduced in the context of the REPT technique22

and is particularly useful to study spinning sidebands int1 inan isolated fashion. The RELM~rotor-encoded longitudinamagnetization! sequence on the bottom is very similarHDOR in that the coherence state int1 does also not undergtime evolution, and is rotor-encoded. In this case, a phcycle and a dephasing delay are used to selectSz @as obtainedfrom the transverse state in Eq.~11! by a 90° storage pulse#.The modulation function for an IS-pair signal

^cosNF0 cosNFt1& as opposed to sinNF0 sinNFt1

& @Eq.~21!#, which yields different sideband patterns, yet the sadipole–dipole coupling information as in HDOR.41

The phase cycle for the S-spin part of all sequences gerally consists of SQ selection, along with 180°-pulse artifsuppression~EXORCYCLE! and quadrature artifact remova~CYCLOPS!. As a supercycle, a multiple-quantum filter isimplemented on the I-spins, the simplest example of whicthe 6x phase inversion of the I-spin 90° pulse aftert1 (f2

in Fig. 6! along with a receiver phase inversion. This 2-stcycle selects all odd-order coherences of the I-spins,. . . 23 ~22! 21 ~0!11 ~12! 13 . . . It will be henceforthreferred to as theHMQ filter. It yields the conventionaREDOR intensities, and it is of interest in how far highthan just first-order coherences in the I-spin subspace arimportance.

For the design of selective higher-order filters, one habear in mind that the S-spins act as a single-channel ‘ceiver.’’ No phase information can be transferred from ospin species to the other as a result of the different rotaframes.42 Therefore, the ‘‘filter-width,’’ i.e., the specificity ofthe desired quantum order, depends on the quantum oitself. Since ann-quantum coherence inverts its sign uponrelative phase change of 180°/n, only 2n-step-cycles are possible. The coherences subject to sign-change are thenlected by simply alternating the receiver phase. This isreason why, if I-spin SQ selection is wanted (n51, i.e., theREDOR signal is selected!, the phase cycle has 2 steps, aI-spin TQ and higher odd order contributions cannot be spressed. I-spin DQ coherences are thus selected by a 4phase cycle off2 , a six-step cycle is needed for TQ seletion, and so on.

IV. HETERONUCLEAR SPIN COUNTING

A. Principles of spin counting

The concept of spin counting was introduced by Pinand co-workers, who in the early 1980’s pioneered thevelopment of MQ spectroscopy in the solid state.43 Unlike insolution, where the localized J-coupling limits the numbercoupled partners within a cluster of spins, it is possibleexcite ~homonuclear! MQ coherences comprising more tha100 spins by using the through-space dipole–dipole c


ly

r-

h

se

e

n-t

is

p.,

of

to-

eg

er

se-e

-tep

s-

fo

-

pling. Monitoring the build-up behavior of such high-ordcoherences gives valuable information about spin clustein solids. Baumet al. developed pulse sequences with suable MQ Hamiltonians capable of exciting such coherenunder static conditions. Spin counting involves carrying oan MQ experiment where a TPPI scheme is applied to eithe excitation or reconversion pulse sequence in order toate an artificial offset which separates the different quantorders excited by the sequence. This frequency offsegiven byDv5Df/Dt1 , whereDf is the phase incrementA coherence of ordern is then offset from the spectral centeby nDv, resulting in a spectrum in which all excited coheence orders can be observed. Since with increasing orcoherences suffer increased line broadening and sensitto B0 inhomogeneity duringt1 , the sensitivity for the observation of higher-order coherences diminishes rapidly.

An improved experimental scheme was publishlater,44 in which t1 is kept constant (t150 is the most sen-sible choice! and only the phase is incremented in smsteps. The phase is varied in 2n steps ranging from 0° to360° in order to observe a maximum ofn quantum orders.The signal in the indirect, phase-incremented dimensionsuch a 2D experiment is then catenated, and after a coFourier transform, an MQ spectrum is obtained which cosists of an array of up ton equally spaced peaks with aarbitrarily small linewidth and with intensities reflecting thcontribution of thenth quantum order to the integral intensity. This scheme was recently applied in an1H NMR MASexperiment on adamantane45 using C746 as the MQ excita-tion scheme. It was shown that the MQ build-up behavimeasured as a function of a scaled excitation time~whichtakes the different MQ excitation efficiencies of different squences into account!, is similar in the static and the MAScase, where spinning frequencies of 8 and 16 kHz were u

As noted in the preceding sections, the DIP-HMSC eperiments are theoretically capable of exciting multiphigher-order coherences in the proton subspace oInS-coherence, and I-spin counting should be possiblephase-incrementation scheme can be implemented in susequence simply by incrementing the phase to the secproton 90° pulse (f2 in Fig. 6!. If the DIP-HMQC sequenceis used for this experiment, one has to make sure thatundephasedreferenceintensity is measured forDf50 ~firstslice!, i.e., that no effective inversion of the dipole-dipocoupling Hamiltonian occurs in the middle of the sequenand that the full echo is measured. This is achievedchoosing equal initial phases forf1 andf2 .

Important differences are, however, to be expected inbehavior of the build-up of higher-order coherences inhomonuclear and the heteronuclear cases. Inhomonuclearspin-counting experiments, the growth of a spin cluster cbe described by a statistical model.43,47 The development ofthis model was inspired by the observation that in large ahomogeneous coupling networks~e.g., adamantane!, the in-tensity distribution among the coherence orders can be meled with a Gaussian function, the variance of whichcreases with increasing excitation time. Such a behasuggests that the build-up of homonuclear MQ modes occin a fashion similar to arandom walkor a diffusion process.


thaeshena

thsli

ro

ssthetig

so

a-

am

ia

ver,is

edoreess-

ei-

on-cesosen

ouldthes thece-

y

gtoby aPTerled

us

arco-

2Dni-

ing

rlyith

er-an-

velhede-eakfor

oensitiv-

re-ely

i-


As more and more spins are correlated, the growth ofspin cluster proceeds from newly incorporated spins intodirections. The ‘‘diffusion’’ constant is dominated by th~rather strong! interaction of adjacent homonuclear spinThis notion is illustrated on the left-hand side of Fig. 7. Tdifferent indicated pathways represent the nonlocalizedture of the growth process of the spin cluster which is chacteristic for a random walk.

On the other hand, the multiple-quantum modes inI-spin subspace of aheteronuclearexperiment are excited aa consequence of the heteronuclear dipole–dipole coupof all of these spins to a single heteroatom. For this hetetom, the multitude of surrounding I-spins creates alocalfield. This local field is probed by the spin counting proceand the number of proton spins that are incorporated intoheteronuclear MQ coherence grows as a function of thdistance from the central heteroatom. This means thathigher the coherence order becomes, the more slowly itstensity builds up, as a consequence of the increasinsmaller coupling constants~Fig. 7, right!.

The differences are a direct consequence of the formthe average Hamiltonians responsible for the excitationthe MQ modes and their action on the spin states they creThe homonuclearsituation is characterized by the noncommutativity of the single MQ operators connecting individupairs with the total excitation Hamiltonian, which is a suover all possible pairs, for instance,

HDQ;(i , j

~ T22( i j )1T222

( i j ) !. ~33!

Usually, pulse sequences with an effective DQ Hamilton

FIG. 7. Growth of a spin cluster in homonuclear~left! and heteronuclear~right! MQ spectroscopy.


ell

.

a-r-

e

nga-

,eirhen-ly

off

te.

l

n

which can excite only even orders have been used. Howespin counting using an odd-order selective Hamiltonianalso possible.48 The noncommutativity leads to the observspreading of the correlated spin cluster over more and mspins. The process can be viewed as a random walk accing all possible product operator states~where the possiblestates are, for instance, only product operators describingther even- or odd-order MQ coherences!.

In the heteronuclearcase, all individual dipole–dipolecoupling pair operators commute, and the experiment is cducted in such a way that multi-spin antiphase coherenare created, where the S-spin species is deliberately chas the transverse component of these coherences@Eqs.~11!–~14!#. The spins arefixed in spacerelative to a given pointrepresented by the S-spin. Coherence transfer, which clead to a propagation of the build-up process throughcombined I- and S-spin subspaces, does not occur unlesexperimenter chooses to include an INEPT-type coherentransfer step~which is an essential building block in mansolution-state heteronuclear correlation techniques49!. Suchsteps would correspond to the so-called ‘‘relay’’ buildinblocks, which are commonly used in solution-state NMRestablish correlations between spins which are separatedwell-defined number of chemical bonds. Using such INEtransfer steps, a ‘‘random walk’’ with a well-defined numbof steps could thus be selectively reintroduced in a labesample.

B. Experimental results

In order to demonstrate the existence of the variomulti-spin antiphase coherences described by Eqs.~11!–~14!, the possibility of converting them into heteronucleMQ coherences, as well as the possibility of separatingherence orders upon reconversion, phase-incrementedDIP-HMQC spectra were measured for a sample of uformly labeled L-alanine @NH3

1 – CH(CH3) – COO2#. Theresults of several experiments with increasing recoupltimes are summarized in Figs. 8 and 9.

The build-up of higher-order coherences is cleaproven by the spectra displayed in Fig. 8. Starting wmainly 1H zero-quantum signal~most of which simply rep-resents13C transverse magnetization!, the CO signal showsthe increasing participation of higher-order proton cohences upon increasing the recoupling time. The highest qutum order in the1H subspace apparent above the noise leis five, detected at the CH position of the molecule. Tsignal-to-noise ratio was, however, not good enough totect even higher coherence orders. The inherently very wrelative intensities of higher-order coherences arise, first,statistical reasons~e.g., a1H 5-spin coherence contains1H1Q, 3Q, and 5Q in decreasing parts!, and second are due tincreasingly small prefactors. The failure to detect evhigher coherence orders is also due to the increased senity of higher-order coherences~by mere probability! to ef-fects of homonuclear couplings among the protons, as asult of the finite pulses. A proper reconversion is severhampered in such cases.

The full set of data is shown in Fig. 9. The MQ intens


itis

f

thatmerigon

ela

chrinla

cifiea

on

is

s,--

tedisitenf

reHns

gerto

be-ed

nge

ea-in-upIofe ority.of

, asr,

ispa-is

nthedes

eC

diulor


ties are normalized with respect to the full spectral intensof the signals at the individual carbon positions, whichequivalent to the intensity of the13C peaks in the first slice othe 2D data set~the REDOR reference intensities!. This nor-malization assumes that the~heteronuclear! dipolar evolutionis completely reversed during the reconversion period ofreference experiment. Processes such as different relaxbehavior of higher-order antiphase coherences and honuclear effects were shown to interfere with this time revsal. However, for moderate recoupling times and very hspinning frequencies, such adverse effects were seen tweak, yielding at least semiquantitative results. Since o1H I z-operators are involved, different protonT18s couldstill lead to differences in the relaxation of the higher-ordantiphase coherences, but these effects should also not psignificant role on the time scale of these experiments.

It should be mentioned that the normalization is mumore problematic in homonuclear systems, where, in pciple, separate experiments to measure the influence of reation phenomena would be needed. In practice, one cansort to separately measuring spectra filtered for a spequantum order~e.g., DQ! and using these to normalize thspin counting data.45 Then50 peak is usually not used forquantitative analysis, owing to the fact that a separationZQ coherences and residual longitudinal magnetization ispossible. In the homonuclear case, theT2 relaxation timesinvolved in the creation of these types of coherences canexpected to differ significantly. These problems do not arin the heteronuclear case. Even though then50 peak iscomposed of I-ZQ [email protected]., half of the 2I-spin coherenceEq. ~13!# and pure, cosine-modulated13C transverse magnetization @Eq. ~11!#, the effects of13C relaxation on these contributions ~mainly T2) can be assumed to be equal.

As discussed above, the data in Fig. 9 cannot be inpreted in terms of a Gaussian growth process. Distinctferences are apparent in the distribution of the intenamong the different quantum orders for the three differ13C atoms. While for the CO, the1H 1Q is less than 20% o

FIG. 8. Spin-counting experiments on U–13C L-alanine. The spectra arslices from phase-incremented DIP-HMQC experiments at the CH andpositions obtained at 30 kHz MAS with different recoupling times as incated.f2 was incremented in 128 steps of 360°/32, resulting in four f360° cycles in the indirect dimension, over which a cosine Fourier transfwas performed to obtain the MQ spectra.


y

eiono--hbe

ly

ry a

-x-

re-c

fot

bee

r-f-yt

the total signal for the shortest recoupling time, it is mothan twice as high for the protonated carbons. The C3

group, in particular, has significant 2Q and 3Q contributioalready at the same recoupling time of 66.7ms. Clearly, thedifferent short-range local fields of the individual13C atomsare responsible for these differences. However, for lonrecoupling times, the contributions of the different ordersthe signal is very similar for all three13C positions. This isnot unexpected, since the longer the recoupling timescome, the less does it matter from which of the three fixpoints, which are relatively close in space, the longer-ralocal dipolar field is probed.

The question remains as to how far the intensities msured at moderate recoupling times are quantitative. Ansight can be gained by looking at the theoretical build-curves for the different higher-spin coherences in an3Sgroup~Fig. 5!. It becomes clear that for a specific numberspins in a subsystem, any type of higher-spin coherencn-quantum order reaches a plateau value for its intens~Note that these curves do not represent the build-uphigher coherenceorders, rather, the different higher-spinmodes contain higher-order coherences in different ratiosexplained in Sec. IV B.! This plateau value can, howeveonly be measured accurately when the local spin systemseparated well enough from its environment. When the seration by the relative magnitude of the coupling constants

FIG. 9. Spin-counting data on U–13C L-alanine obtained from the spectra iFig. 8. The individual signal intensities are normalized with respect tototal integral intensity of the individual spectra. The lines are simply guito the eye, and the labels indicate the quantum order in the1H subspace.

O-lm


anth

giopleuro

torit

blct

ontioheto

rScoeD

rable

ing

vee

e--le-tor-n a

thear-nch-

-en-Tfastbe

IP-

o-ngs aoesegralD

hisea islti-up

ient

TQthe

-

sear

ionns,hreethe

et-e

deada


good enough, the distribution of intensity among the qutum orders should provide valuable information aboutlocal environment.

A rigorous quantification of this aspect, properly takinthe dependence of the results of relative tensor orientatinto account, is beyond the scope of this paper. A simexperimental test, however, performed on the partially dterated methylmalonic acid sample, yields encouragingsults ~Fig. 10!. Assuming an apparent coupling constantD IS

app/2p57.8 kHz ~see Table I! for the methyl carbon, weobtainNrcplD IS

app/vR52.08, from which theoretical values~insquare brackets in Fig. 10! can be obtained by referencethe data presented in Fig. 5. These values are in good agment with the experimental data. For the CD carbon, wD IS

app/2p52 kHz, the theoretical values are still in reasonaagreement with the experiment. Deviations must be expe~and are quite large for the CO carbon! since the individualmethyl groups are not completely isolated, and contributifrom neighboring molecules change the measured raNevertheless, the experimental evidence indicates thateronuclear spin counting, with its property of probing a slected local environment, represents an interesting newfor the investigation of chemical structures.

V. HETERONUCLEAR MULTIPLE-SPIN CORRELATION

Having demonstrated the possiblity of exciting highequantum coherences among the I-spins with the DIP-HMsequences, we will now monitor the evolution of theseherences in 2D correlation experiments, where the differcoherence orders are selected by a phase cycle. The

FIG. 10. Slices from the phase-incremented spin-counting data at theferent13C signal positions of partially deuterated methylmalonic acid, msured at 30 kHz MAS witht rcpl58, tR5266.7ms. Theoretical values baseon the coupling to a single intramolecular methyl group are given in squbrackets.


-e

nse-

e-f

ee-heed

ss.et--ol

-C-ntIP-

HSQC pulse sequence~Fig. 6! gives the best resolution fomeasurements on a fully labeled sample, and is most suitfor rotor-synchronized applications sincet1 can be incre-mented in steps of one rotor cycle without artifacts arisfrom a refocusingp pulse present in the HMQC variant~seeSec. III C!. The states-TPPI method was used to achiesign-sensitive detection int1 . The same pulse sequenc~termed ‘‘REDOR 3D’’! was already applied to distance dterminations in a13C–15N system,15 where the authors, however, did not give an account on multi-spin and multipquantum aspects, and did not mention the effect of roencoding~i.e., the necessity of measuring such spectra irotor-synchronized fashion!.

Figure 11 shows spectra measured on a fully13C-labeledL-alanine sample. The spectrum in Fig. 11~a! is an HMQ-filtered ~i.e., regular I-spin odd-order selective filtered! spec-trum. Note that the observed residual line broadening in1H dimension of less than 2 ppm is solely due to line nrowing by ultrafast MAS. Narrower lines have only beeobserved using sophisticated coherent line-narrowing teniques in the F1 dimension.38,50 The resolution in this spectrum is comparable to the one obtained with the aforemtioned REPT techniques.22 An advantage on behalf of REPis the higher S/N, since losses due to inefficient CP atspinning frequencies in the case of DIP-HMSC cannotavoided.

However, it should again be emphasized that the DHMQC experiments can bereferencedby performing an ex-periment witht150 and a modified phase cycle which prduces an effective inversion of the dipolar evolution durithe reconversion rather than an HMQ selection. This yieldreference intensityS0 . Therefore, in marked contrast tREPT, absolute MQ intensities are accessible with thmethods. This has been shown to be feasible for the inteREDOR build-up in1H–13C systems in Sec. II, and using 2spectra, more specific build-up data can be extracted. Taspect is beyond the scope of this paper. The general idto introduce the underlying concept and highlight the muspin aspects. In practice, an analysis of the initial build-data in terms of a sum of heteronuclearpair coherences,neglecting the higher-order ones, was shown to be sufficin the above-mentioned paper by Michal and Jelinsky.15

The spectra in Figs. 11~b! and 11~c! were acquired withthe same DIP-HSQC pulse sequence, but with DQ andfiltering schemes and a corresponding adjustment ofTPPI scheme for sign-sensitive detection int1 . These spectraare somewhat unusual since a13C SQ dimension is correlated with either a1H–DQ or a1H–TQ dimension, where thechemical-shift information is the sum of 2- or 3-spin1Hcorrelations, respectively. The information content in thespectra is entirely different from that of the more familihomonuclear1H DQ and TQ correlation spectra.6 While inthe homonuclear case a peak in the DQ or TQ dimensindicates a correlation of two or three spatially close I-spia peak in the heteronuclear spectrum means that two or tconstituent I-spins, respectively, are close to an S-spin,one at which the coherence is detected in thet2 dimension~the HMQ coherence is created solely by the action of heronuclear dipole–dipole couplings!. These protons can b

if--

re


nou-le.

g

pro


FIG. 11. 1H~SQ!–13C ~a!, 1H~DQ!–13C ~b!, and1H~TQ!–13C ~c! DIP-HSQshift correlation spectra of U–13C L-alanine, measured at 30 kHz MAS usinthe second pulse sequence~HSQC! in Fig. 6 with recoupling times as indi-cated. Additional line broadening was applied in the13C dimensions of themiddle and right spectrum to produce more visible contour lines. Thejections are skyline projections. The assignments of the protons areA: CH3 ,B: CH, andC: NH3

1 .


FIG. 12. Slices from1H~DQ!–13C ~a!,~b! and 1H~TQ!–13C ~c! DIP–HSQshift correlation spectra of U–13C L-alanine, measured at 30 kHz MAS. I~a! and~b!, the signals from the three carbon positions are shown for recpling times of 4 and 8tR , respectively. The relative intensities are to scaIn ~c!, the slices at the CH3 position in1H–TQ spectra att rcpl54 and 8tR

are compared. For the assignments see Fig. 11. The gray traces in~a! arefrom simulations, as explained in the text.

-


n

veherebyawn-

tiorri-

yrb

cufoe

asndthg

sagulnp

ret

achypbo

2Da

h

isctw

ases

desp

hra

en-ncee-fforingareerref-

yl-

-in

thean-iesed

tionthsd at

arC

se

ian

iorn,tor

for

ingiar

is

-en-r

l


located on either side of the carbon atom, and the distabetween them can thus be rather long.

Details can be seen in Fig. 12, where projections oindividual carbon positions are shown. Data in t1H~DQ!–13C spectrum measured with a relatively shortcoupling time@Fig. 12~a!# can be expected to be governedintramolecular correlations. The gray background tracescalculated spectra based on a single alanine molecule,intensities given by Eq.~24!, and the chemical shifts takefrom a conventional~SQ! MAS spectrum. The tensor param

eters used for the calculation of the phase factors,NrcplF0( i ) ,

are based on crystal structure data from a neutron diffracstudy.51 The calculated spectra~considering heteronucleacouplings only! indeed yield a good prediction of the expemental intensities. The deviation of theAA andAB signalsfrom the simulations in the CH3 slice may be due to the verlarge and possibly different linewidths of these signals. Fomore quantitative analysis, a proper deconvolution wouldnecessary.

At longer recoupling times@Fig. 12~b!#, the appearanceof the spectra changes because protons in adjacent moleare now included in the MQ modes. This is most obviousthe BB signal, which is clearly present in the CO slic~marked with a gray box!. Since each alanine molecule honly one CH group, this is necessarily a correlation exteing over two molecules. This peak is a good example ofvaluable information inherent in such spectra. Even thouthe two correlated protons are 3.55 Å apart, which givehomonuclear coupling constant which is of comparable mnitude to the involved heteronuclear couplings, it shoagain be emphasized that this homonuclear coupling isinvolved in the generation of the probed heteronuclear 3-scoherence. Rather, it is averaged out by the MAS (vR /D II

'10) while the heteronuclear couplings are selectivelycoupled. The carbon atom acts as a well-defined poinreference, from which the local environment is probed invery selective fashion, through the chemical-shift informtion in the 1H-DQ dimension. The mere existence of supeaks has important structural implications. Thus, this tof experiment represents a valuable addition to our toolof correlation techniques for structural studies.

Similar information is accessible using homonuclear1H TQ MAS spectroscopy,52 which can be performed usingmodified BABA sequence.53 Spectra obtained forL-alanineat 35 kHz MAS and an excitation time of 2tR exhibited astrong signal from theBBC proton triad, detectable at botthe NH3

1 and CH signal positions in the direct1H SQ dimen-sion. The type of connectivity derived from such spectrahowever, less specific than a 3-spin heteronuclear conneity, since in the heteronuclear case, it is clear that only theteronuclear couplings contribute to the build-up of1H~DQ!–13C coherence, while in the homonuclear cathree homonuclear couplings can be involved. Moreover,lective isotopic labeling with13C building blocks can be useto introduce ‘‘spin probes,’’ for instance, in specific residuof larger molecules such as proteins, in order to detect scific conformations locally.

The 1H~TQ!–13C spectra have a much lower S/N, whicis to be expected from the relative distribution of spect


ce

r

-

reith

n

ae

lesr

-eha-

dotin

-ofa-

ex

,iv-o

,e-

e-

l

intensity among the quantum orders. In addition, the intsity is spread out over an even larger spectral width simore cross signals are possible~10 as opposed to 6 in thDQ spectrum!. Moreover, the linewidth of MQ signals increases with increasing quantum order6 as a consequence othe fact that more spins represent more points of attackperturbing couplings to other spins, which leads to dephas~i.e.,T2 relaxation!. As a consequence, the circumstancesnot too favorable for the exploitation of such higher-ordcoherences. One interesting observation can be made byerence to Fig. 12~c!. While, as expected, the intrameth1H~TQ!–13C signal ~AAA ! dominates the spectrum completely for t rcpl54 tR , it is merely a shoulder of theAABcross signal at 8tR . This indicates the complications in interpreting long-recoupling time dipolar correlation spectrageneral. For short recoupling times, information aboutstrongest couplings dominate, permitting at least semiqutitative interpretation of the spectra. However, the intensitalways depend on the relative orientations of the involvdipole–dipole coupling tensors, and a careful consideraof the effects of relative orientations and coupling strengis necessary to ensure the validity of the results obtainelonger recoupling times.

VI. HETERONUCLEAR DIPOLE–DIPOLE COUPLINGSFROM SPINNING-SIDEBAND PATTERNS

A. Rotor-encoding as a mechanism for sidebandgeneration

In Sec. III A it has been pointed out that the dipolphase factor for the reconversion period of a 2D DIP-HMSspectrum,F t1

( i ) , has an explicit dependence on thet1 evolu-

tion time, merely as a result of the sample rotation (vRt1).Equation~10! shows the intimate connection of this phachange and the Euler anglegCR describing the initial rotorphase of a specific crystallite. The reconversion Hamiltonis thereforeencodedby the t1 evolution, and the amplitudemodulation thus introduced leads to an oscillatory behavof the time-domain signal. Upon Fourier transformatiospinning sidebands appear at integer multiples of the rofrequency.

This phenomenon was first observed and explainedthe case of homonuclear DQ MAS experiments,23,24and alsoemployed in heteronuclear experiments.8,22 The generalmechanism was termed reconversion rotor encod~RRE!,25 and should be distinguished from the more familmodulations of the coherences evolving int1 as a result oftensorial interactions involving the participating spins. Thso-called evolution rotor modulation~ERM! leads to spin-ning sidebands as well~it is in fact the mechanism responsible for the generation of spinning sidebands in convtional MAS spectra!, and is of minor importance undeconditions of very-fast MAS.

As a specific example, Eq.~21! describes the signafor an isolated heteronuclear spin pair,SMQ

5^sinNexcF0 sinNrecF t1&. By inserting Eq.~10!, and using

the relation54


st

r-

s

o

th

olb

ngin

ide-les,er-ethe,h aerndslti-ted

g-nts.rns

isandictedthe

pec-

ledverceim-es

m-on

ari-ific

reetores-

ctednandthe

-ent

n

thethan

-Qted

theare

ob

sQairth


sin~x sin~vRt11g!!52 (n50

`

J2n11~x! sin~~2n11! vRt1

1~2n11! g!), ~34!

it can be seen that the patterns are symmetric and consiodd-order sidebands only, due to the (2n11) prefactor ofvRt1 . In the course of an explicit calculation, the powdeaverage over theg angle can be performed analytically,41

and one is left with sideband intensities

I 2n1151

2Eb50

p

J2n11S Nexc

D IS

vR2A2sin 2b D

3J2n11S Nrec

D IS

vR2A2sin 2b D sinb db. ~35!

This integral over a product of Bessel functions,Jn(x), canbe evaluated on a computer. ForNexc5Nrec ~equal argumentsof the two Bessel functions!, it is apparent that all sidebandmust be positive.

At short recoupling times, the spectrum is composedfirst-order sidebands only, while the higher-order (n53)sidebands start appearing only after the first maximum ofbuild-up curve has been reached~Fig. 13!. Clearly, the side-bands do not map out the anisotropy of the dipole–dipinteraction, as is common in SQ MAS spectra but can‘‘pumped’’ to cover arbitrary frequency ranges by increasithe recoupling time. Even though the dipole–dipole coupl

FIG. 13. HMQ spinning-sideband patterns for a single IS-spin pair, astained by Fourier transformation of the powder-averagedt1 time-domainsignal@Eq. ~21!, with Nexc5Nrec5Nrcpl], as a function of the dimensionlesparameterNrcplD IS /vR . The position of the specific values on the HMbuild-up ~i.e., REDOR! master curve is indicated in the inset. The spin-pcase depicted here applies equally well to sideband spectra obtained wiREPT techniques~Ref. 22!.


of

f

e

ee

g

constant can be determined more accurately when more sbands are present, the number of recoupling rotor cycNrcpl , is limited because of increasing effects of pulse impfections,T2 relaxation, etc. Also, the distribution of the samspectral intensity over more and more sidebands affectssignal-to-noise~S/N! ratio. Therefore, for actual applicationswe usually choose the experimental parameters in sucway thatNrcplD IS /vR ranges between 1.0 and 2.0. For highvalues, the resulting patterns, which then comprise sidebaof very high orders, become increasingly sensitive to muspin effects. The exploration of this regime is thus restricto well-isolated and well-defined spin multiplets.

B. Features of DIP-HMS spinning-sideband spectra

We will now explore the specific properties of spinninsideband patterns generated by the DIP-HMSC experimeFor this purpose, chemical-shift resolved sideband pattewere measured on uniformly labeledL-alanine, where up to768 slices int1 were needed for high resolution spectra. Thwas done mainly in order to show the features of sidebpatterns generated by the different pulse sequences depin Fig. 6. Quantitative analyses should be performed withHDOR technique, where the chemical-shift information int1

is lost and very few slices suffice to generate sideband stra. On account of the absence of evolution duringt1 , it isonly necessary to acquire for one rotor period. A detaidiscussion of the advantages of the HDOR approach oHMQC or HSQC can be found in Ref. 22. The sequenused here is derived from the DIP-HSQC experiment by sply keeping the two proton 90° pulses together for all valuof t1 , thus using them as an HMQ filter. To avoid spectroeter timing problems, it is useful to acquire the first slicetop of the first rotor echo, witht151 tR . The resulting pat-terns are virtually free of first-order phase errors.

In Fig. 14, sideband patterns obtained for the three vants of the DIP-HMSC method are compared. For a speccarbon, the overall patterns are very similar for the thvariants. The HDOR patterns were numerically fittedspectra generated using the appropriate theoretical expsions @Eqs. ~21! and ~30! with vCS50] to obtain couplingconstants which are in good agreement with values expefor isolated CH and CH3 groups. In the DIP-HSQC patterof the CH group, the unexpected even-order sidebandsweak centerbands are introduced by dipolar evolution ofantiphase coherence duringt1 . A more detailed explanationof this issue is given in Ref. 22. Distortions of the DIPHMQC patterns due to CSA and ERM are not apparabove the noise level.

From Eqs.~30! and~31! it can be inferred that a1H–TQcontribution should be visible in DIP-HMQ spectra, whethe usual~odd-order selective! HMQ filter is applied on theprotons. This contribution is expected to be weak, andsidebands are also spread over a larger spectral rangethe primary1H–SQ pattern. In the CH3 spectra, weak negative artifacts of unknown origin are stronger than the Tcontributions, which are not visible in the spectra presenhere.

The most surprising observation can be taken fromenlarged insets, where correlations with protons that

-

the


.iment tim


FIG. 14. Sideband patterns from symmetric dipolar HMQ experiments, measured on U–13C L-alanine at 30 kHz MAS andt rcpl56 tR , with a 1H offset ofabout16 kHz from the CH signal position in the1H SQ MAS spectrum. In~a! and~b!, patterns from the CH and the CH3 carbons, respectively, are shownThe DIP-HSQC and -HMQC patterns exhibit folded-back sidebands, due to the fact that a smaller spectral width was chosen in order to save expere.The gray background traces are best-fit patterns with the indicated coupling constants.

tn

tioa

nt

anhethplu

om

-

rtee

n

re

hisse ofcesiod,

-

u-

lo-

ed

of

ent-up-isndsgvedlinger-

don-ants,thus

dsquesH

ds

remoteto the respective13C atoms are seen to appear inallsideband orders. This is contrary to the intuitive notion thathe couplings to these protons are weak and consequeonly first-order sidebands should be visible. The observamade here is therefore in marked contrast with similar pterns measured with the REPT sequences,22 which meet theexpectation that contributions from remote spins are fouthere to reside in the first-order sidebands, leaving the resthe pattern virtually unchanged. Even though surprisingsomewhat counter-intuitive, the different behavior in tpresent case can be accounted for on the basis of theretical treatment presented in Sec. III A. In terms of a simI2S 3-spin system, the time-domain corresponding to the spattern contributed by the weakly coupled spin, derived frEq. ~23! with i 51, is

S;^sinNrcplF0w sinNrcplF t1

w cosNrcplF0s cosNrcplF t1

s &,~36!

where the familiar~sin...sin...! term containing the weak coupling phase factor~superscriptw) is ~cos...cos...! modulatedby the strong (s) coupling. For simplicity, the prefactors fothe chemical-shift evolution are omitted. A pattern calculafrom this expression extends over the same spectral rangone calculated with switchedFw and Fs ~which describesthe primary pattern!. This can be rationalized by applying aaddition theorem to Eq.~36!:

^sinNrcplF0w sinNrcplF t1

w cosNrcplF0s cosNrcplF t1

s &

5^@ 12 sinNrcpl~F0

w1F0s!1 1

2 sinNrcpl~F0w2F0

s!#

3@ 12 sinNrcpl~F t1

w1F t1s !1 1

2 sinNrcpl~F t1w2F t1

s !#&.

~37!

As a result, the pattern can be written in terms of pure~sin-...sin...! contributions, where the strong coupling, as rep


tlynt-

dofd

eo-eb-

das

-

sented byFs, dominates the arguments of the sines. Targument does not hold for the REPT sequences becautheir asymmetry, i.e., a cosine modulation of the coherendue to remote spins occurs only in the reconversion per

and the cosF0 term is missing in the corresponding formu

lae. In the REPT case, the cosNrcplF t1term~s! perturbing the

primary pattern mainly lead to signal loss at longer recopling times.

Simulations for several multispin cases~data not shown!indicated that spinning-sideband patterns from spin topogies which are dominated by a strong primary coupling~e.g.,a CH group surrounded by several protons!, when fitted to asimple spin-pair solution, correspond to slightly increasdipole–dipole coupling constants. Equation~37! also pro-vides an intuitive way of understanding this result: a partthe time-domain signal can be written as~sin...sin...! patternwith the sum of the coupling terms as arguments. In a recpaper on the geometry dependence of REDOR buildcurves in InS systems55 it was pointed out that in the multispin case the initial-rise behavior of the REDOR build-upgoverned by the dipolar second moment, which correspoto the observation of an ‘‘effective’’ dipole–dipole couplinconstant. This is in close analogy to the behavior obserhere, where an apparently increased dipole–dipole coupconstant is obtained when one strongly coupled pair is pturbed by several weak couplings~for which the productNrcplD IS /vR is small!. Therefore, simple HDOR sidebananalysis is feasible to determine the dominant coupling cstant. For the case of several comparable coupling constthe results become increasingly geometry dependent,hampering a simple model-free analysis of the data.

A general observation concerning DIP-HMSC sidebanas compared to patterns measured with the REPT techniunder the same conditions is that in the multi-spin case (C3

in particular!, DIP-HMSC spectra exhibit stronger sideban


e-Pntri

n

nslo

i

-mtotrrs

pth

uicthdethrdIr

rs,

nde-

o-andlear

t the

rands

to ae ing-

e,theec-ceiong.

eCHthe

ultsatathe

it-to

u-andou-ex-cesredeli-O

ure-r

onesghof

van-pen-inghat

H

ni

tic


of higher orders. For instance, the patterns in Fig. 14~b! ex-hibits significant intensity in the fifth- and higher-order sidbands, which is not observed for the analogous REexperiment.22 This can be explained in a qualitative fashioA factor of 3 appears in the argument of the trigonomefunctions describing such patterns: sin3 a53

4 sina214sin3a.

The sketched property of products of trigonometric functiohas a direct quantum-mechanical implication: when13Cseparated local field spectra of CH3 groups are discussed iterms of perturbation theory,31 the spectra are calculated aconsisting of two contributions. One associated with thecal field exerted by the three protons inu↑↑↓& or u↑↓↓&configuration~and four further permutations thereof!, and theother with the protons in theu↑↑↑& and u↓↓↓& configura-tions. The local field exerted by the latter configurationsthree times as large, and these yield a 25% contributionthe overall spectral intensity~simply by counting of the possible spin states!. This is reflected in the addition theoreused above for the result obtained from product operatheory. These considerations do not apply for the asymmeREPT, since there the excitation period involves transve1H evolution in the13C local field, leading to a methyl grouformula lacking the above-mentioned power of three incorresponding phase factor.

So far, the spinning sideband patterns were acquireding the regular odd-order selective HMQ phase cycle, whselects the REDOR intensities. In complete analogy toshift correlation spectra discussed in Sec. V, higher-orfilters can also be implemented here in order to observespinning sideband patterns corresponding to the higher-ocoherences in the I-spin subspace. Figure 15 shows DHDOR sideband patterns of a methyl group, also measu

FIG. 15. Higher-order filtered DIP-HDOR sideband patterns of the C3

signal of U–13C L-alanine at 30 kHz MAS andt rcpl54 tR . The gray tracesare from analytical simulations based on the geometry of a single alamolecule taken from a neutron diffraction study~Ref. 51!. Apart from ex-perimental imperfections, deviations between experimental and theorepatterns reflect effects of fast vibrational averaging of distances.


T.c

s

-

sto

rice

e

s-hereerP-ed

on the fully labeledL-alanine sample. Although the regulaheteronuclear1H-MQF pattern has only odd-order sidebandthe heteronuclear1H–DQF pattern consists of a centerbaand even-order sidebands. It is simply described by a timdomain signal;^sin2 . . . sin2 . . . &, which accounts for thisobservation. An analogous effect was investigated in homnuclear systems, where homonuclear DQ spinning-sidebpatterns have only odd-order sidebands, while homonucTQ patterns in turn exhibit only even orders.25 The homo-nuclear and heteronuclear cases are analogous in tharotor encoding of 2-spin coherences~now including theS-spin in the heteronuclear case! generally leads to odd-ordesidebands, while for 3-spin coherences, even-order sideband a centerband are observed.

It is thus not surprising that the heteronuclear1H–TQpattern again has odd-order sidebands: it correspondsrotor-encoded 4-spin coherence. For the methyl examplSec. III B it was shown that the odd-order HMQ-filtered sinal is the sum of 1- and 3-1H contributions. The1H–TQFpattern is naturally a pure 3-1H pattern. It also has the samshape as the 3-1H SQ contribution to the MQF patternwhich has a weighting factor of 3/4 as opposed to 1/4 forpure TQF signal. Note that in the experimental HDOR sptra the MQF pattern is the sum of both contributions, sinthey are not separated by different chemical-shift evolut@Eq. ~30!, with vCS,I50], as opposed to the spectra in Fi14~b!.

C. Quantitative dipole–dipole couplings fromsideband patterns

In order to get a closer insight into the feasibility of thsideband approach with regards to measuring weakdipole–dipole couplings, we performed measurements onpartially deuterated methylmalonic acid sample. The resshould be compared with the corresponding REDOR dpresented in Sec. II B. The patterns were obtained usingDIP-HDOR sequence~see Fig. 6!.

The results are depicted in Fig. 16. All patterns exhibing more than just the first-order sidebands could be fittedthe analytical solution for a single methyl group, Eq.~30!with vCS,I50. Even though this result does not include coplings to remote protons, deviations between experimenttheory are very small and may, apart from these remote cplings, be explained by experimental imperfections. Thetracted dipole–dipole couplings and corresponding distanare also listed in Table I. In contrast to patterns measuwith REPT, even the first-order sideband intensities are rable. Therefore, the weak couplings from the CD and Ccarbons to the methyl protons could be fitted to the measments witht rcpl516tR5533ms. The measurement time fothese patterns was about 12 hours, using a13C naturallyabundant sample. The results are more reliable than thefrom REPT patterns at long recoupling times. Even thouthe DIP-HMS techniques are less sensitive, the reliabilitythe first-order sideband intensities represents a major adtage since the losses due to the CP are more than comsated by the possibility of choosing a shorter recoupltime, thus having fewer losses due to relaxation. Note t

ne

al



FIG. 16. DIP-HDOR spinning sideband patterns of partially deuterated methylmalonic acid, measured at 30 kHz MAS witht rcpl56 tR ~a! and 16tR ~b!,along with best-fit patterns~gray background traces!. TheD IS

app/2p obtained from the fits are indicated.

efth

thO

co

ueletlt

teceb-

o

cieitaning

la

n

lit-gin

oft

nea

oti-tieseub-l thent.o-haser-er-

ple-

s

er

sti-o-rsxci-theer,

are

s areou-Q

spine

,usrleara

bu-elyery-ns.ts a

recoupling times of 24 and 26tR were necessary for thREPT experiments, to have appreciable intensity in the fiorder sidebands.

As is also the case for the simple REDOR results,coupling constants for the CD, and in particular for the Cgroup, deviate towards higher values because of remoteplings, as already discussed above. The value obtainedthe CH3 group is in very good agreement with the valobtained from REPT measurements on the same samp22

indicating that, even though both methods differ significanin the influence of remote spins, this result is very closewhat would be measured in a sample with a fully isolamethyl group. A disagreement of the resulting CH distanwith x-ray or neutron diffraction results is commonly oserved and must be attributed to the different influencefast vibrational motions on the two techniques.56 Therefore,not only does the sideband approach yield the more preresults for dipole–dipole couplings, they are also obtainindependent of the knowledge of correct reference intensS0 , in the case of REDOR. This represents the centralvantage of spinning sideband analysis, because whesample is isotopically dilute in one of the two involved spspecies, the REDOR results must be corrected accordinthe fraction of labeled molecules.14 This information is oftennot easy to assess, in particular when measurements inmolecules with considerable overlap of13C signals such asproteins are performed, where an additional deconvolutiospectral lines must be performed.

VII. CONCLUSIONS

In this publication, we have demonstrated the feasibiof performing REDOR in1H–13C systems. This is essentially made possible by using very-fast MAS with spinninfrequencies exceeding 20 kHz, where clearly, higher spning speeds give even better results, as a consequencesuccessful suppression of homonuclear couplings amongprotons. In addition, we have described a simple extensiothe original REDOR pulse sequence which allows the m


-

e

u-for

,yods

f

sedy,d-

a

to

rge

of

y

-theheof-

suring heteronuclear multiple-quantum spectra, and mvates the reinterpretation of conventional REDOR intensiin terms of HMQ excitation efficiency. The treatment of thspin dynamics shows that the whole product-operator sspace of MQ states encompassing a single S-spin and alI-spins being coupled to it is explored in such an experimeSpin counting is possible, and it was shown that, for twdimensional HMS correlation spectra, the experimenterconsiderable freedom in choosing not only odd-order cohences in the I-spin subspace, but also I-DQ and I-TQ cohences, which can be probed as heteronuclear multi

quantum coherences (Sx) i I x( i )), as antiphase term

(Sz) i I x( i )), or as rotor-encoded heteronuclear dipolar ord

(Sz) i I z( i )) during t1 .

Many possible advantages of the spectroscopic invegation of the above-mentioned type of multi-spin HMQ cherences were already pointed out by Pines and co-worke57

for the case of static samples. In this reference, several etation schemes were discussed. They all have in commonfact that, unlike in the experiments described in this papinitial I-spin magnetization is used, and that the I-spinsalso the detected nuclei~due to sensitivity considerations!. Inthe pulse sequences discussed there, HMQ coherenceexcited in two steps. During the first step, homonuclear cplings among the I-spins lead to I-spin homonuclear Mmodes, which are subsequently coupled to the S-heteroto obtain the final HMQ coherence. The feasibility of thapproach was demonstrated on singly13C-labeled benzeneoriented in a liquid crystal. However, most of the ingenioideas mentioned by Weitekampet al.were never pursued foactual applications, mainly because the strong homonucdipole–dipole couplings in the static case interfere withcontrolled manipulation of the spin system.

With respect to the concepts presented in this contrition, however, the simplicity and robustness of the purheteronuclear approach to HMQ spectroscopy under vfast MAS might open up a number of possible applicatioThe class of techniques introduced in this paper represen


le.e

leh

usb

--e-

puleess.c

o-atth

alnty

Iso

ncthmraer

acI

me-k.edn

rewiSRta

eriosomge

rtfoa.ecusp

tin

ysis,once

ge

d’’ inearveryg-iblearethellyd

-beeid

si-orn

to

ntnsy

he

ngfor

-

M.on.

m.

. M.


valuable extension of already well-established homonucand heteronuclear correlation methods in the solid state7,58

Similar experiments using REDOR recoupling have beperformed before by other groups, primarily using tripresonance spectroscopy in labeled systems with isolatederonuclear spin pairs, where the abundant protons wereto enhance the initial polarization of the observed nucleusmeans of a cross polarization~CP!. The published applications comprise, for example, the13C/15N resonance assignment in tripeptides,5 the site-resolved determination of thpeptide torsion anglef,59 or the13C site-resolved investigation of mobility in peptides with deuterated residues.36 Webelieve that the reinterpretation of the very simple and polar concept of REDOR in terms of heternuclear multipquantum spectroscopy will contribute significantly to thetablishment of new techniques aiding in structural studie

A remaining challenge is still the geometry dependenof multi-spin data measured in REDOR and its twdimensional extensions, as represented by the complicdependence of the individual sine and cosine factors of

time-domain signals on the dipolar phase,F t @Eq. ~9!#,which contains information on the relative orientation ofinvolved tensors. In a recent paper on the disentanglememultiple couplings in REDOR,60 the authors successfullmeasured the two heteronuclear coupling constants in an2Sspin system in a model-free approach by performingcalled u-REDOR experiments,61 where a 90° instead of a180° degree pulse was applied in the middle of the sequeA clever combination of the so-obtained data enabledextraction of the two coupling constants. Using data froour two-dimensional extensions of REDOR, with a sepation of different contributions either by I-spin quantum ord~Sec. IV!, or by I-spin chemical shifts~Sec. V!, similar pro-tocols can be envisioned to achieve the final goal of extring model-free heteronuclear dipole–dipole distances.their conclusions section, Liivak and Zax already give sopreliminary hints of how to extend REDOR to the multiplquantum dimension, in close analogy to our present wor

The complications arising from the above-mentionmulti-spin problem, and the limitations set by the instrumetation, are certainly serious enough to conclude that didistance measurements on the order of 10 to 100 Åalmost certainly be better achieved by use of Espectroscopy.62 Focusing direct measurements, however,the 5 Å range and a moderate number of heterospins,using the new extensions of REDOR such as the hetnuclear spin counting or DIP-HMSC techniques, we envisto transgress the intrinsic distance limits of NMR by focuing on specific reporter groups, or points of reference, frwhich the local surrounding is explored, and to probe lardistances in space in a stepwise fashion.

The application of the presented methods to structustudies in rigid heteronuclear rare-spin systems is straighward. There, slower spinning speeds can be employed,homonuclear couplings do not present a serious problem1Hwill then just serve as a source for polarization. We expfruitful applications to structural investigations of amorphosubstances and small proteins in particular, where isotolabeling has already entered a state of experimental rou


ar

n-et-edy

---

e

ede

lof

-

e.e

-

t-ne

-ctll

ondo-n-

r

alr-nd

t

ice.

We should again emphasize the use of sideband analwhich can help to obtain quantitative structural informatiwithout exact knowledge of the correct REDOR referenintensity,S0 , which is hard to estimate in the case of larmultiply labeled molecules.

The natural abundance1H–13C applications presentehere certainly represent in some sense the ‘‘worst casethat, even under very-fast MAS, the strong homonuclcouplings among the protons hamper experiments usinglong recoupling times and, thus, the determination of lonrange couplings. Such experiments are, however, feaswhen dynamic and order phenomena in mobile systemsto be investigated. We have already successfully usedrelated REPT techniques to the determination of motionaaveraged1H–13C dipole–dipole coupling constants, anhence order parameters, in13C naturally abundant discoticmesophases.12

The possibility of applying REDOR and the new DIPHMSC experiments, in which the spectral intensity cannormalized, to1H–13C systems is very promising for thstudy of confined molecular motion in polymers or liqucrystals, where the increased chemical-shift resolution of13Cmight help to correlate order parameters with different potions in the molecule, or different configurationsconformations.63 We have obtained preliminary results opoly~styrene-co-butadiene! block copolymers, where thecis/trans dyads in the butadiene block, which are difficultresolve in homonuclear DQ NMR,64 were indeed seen tohave a different HMQ build-up behavior, hinting at differeresidual dipole–dipole couplings. Extensive investigatioalong these lines are currently underway in our laborator

ACKNOWLEDGMENTS

The authors acknowledge financial support from tDeutsche Forschungsgemeinschaft~SFB 262!. We thankKlaus Schmidt-Rohr for contributing numerous stimulatiideas, and Jerry Chun Chung Chan and Steven P. Browninsightful comments on the paper.

1R. R. Ernst, G. Bodenhausen, and A. Wokaun,Principles of NuclearMagnetic Resonance in One and Two Dimensions~Clarendon, Oxford,1997!.

2D. Neuhaus and M. Williamson,The Nuclear Overhauser Effect in Structural and Conformational Analysis~VCH, Weinheim, 1989!.

3X. Feng, P. J. E. Verdegem, Y. K. Lee, M. Helmle, S. C. Shekar, H. J.de Groot, J. Lugtenburg, and M. H. Levitt, Solid State Nucl. Magn. Res14, 81 ~1999!.

4T. Gullion and J. Schaefer, Adv. Magn. Reson.13, 57 ~1989!.5M. Hong and R. G. Griffin, J. Am. Chem. Soc.120, 7113~1998!.6I. Schnell and H. W. Spiess, Adv. Magn. Opt. Reson.~accepted!.7I. Schnell, S. P. Brown, H. Y. Low, H. Ishida, and H. W. Spiess, J. AChem. Soc.120, 11784~1998!.

8K. Saalwacther, R. Graf, and H. W. Spiess, J. Magn. Reson.140, 471~1999!.

9B.-J. van Rossum, C. P. de Groot, V. Ladizhansky, S. Vega, and H. Jde Groot, J. Am. Chem. Soc.122, 3465~2000!.

10H. Sillescu, J. Chem. Phys.54, 2110~1971!.11K. Schmidt-Rohr and H. W. Spiess,Multidimensional Solid-State NMR

and Polymers~Academic, London, 1994!.12A. Fechtenko¨tter, K. Saalwa¨chter, M. A. Harbison, K. Mu¨llen, and H. W.

Spiess, Angew. Chem. Int. Ed. Engl.38, 3039~1999!.13H. W. Spiess and H. Sillescu, J. Magn. Reson.42, 381 ~1981!.


em

H

G

on

o

e

H

. R

.

.

st

em

n.

.

nd

oc.

ys.

, J.

, A.ot,

Lett.


14T. Gullion, Magn. Reson. Rev.17, 83 ~1997!.15C. A. Michal and L. W. Jelinski, J. Am. Chem. Soc.119, 9059~1997!.16C. Filip, S. Hafner, I. Schnell, D. E. Demco, and H. W. Spiess, J. Ch

Phys.110, 423 ~1999!.17M. M. Maricq and J. S. Waugh, J. Chem. Phys.70, 3300~1979!.18R. Fu, S. A. Smith, and G. Bodenhausen, Chem. Phys. Lett.272, 361

~1997!.19P. Bertani, J. Raya, P. Reinheimer, R. Gougeon, L. Delmotte, and J.

schinger, Solid State Nucl. Magn. Reson.13, 219 ~1999!.20C. P. Jaroniec, B. A. Tounge, C. M. Rienstra, J. Herzfeld, and R.

Griffin, J. Chem. Phys.146, 132 ~2000!.21K. Saalwacher, R. Graf, D. E. Demco, and H. W. Spiess, J. Magn. Res

139, 287 ~1999!.22K. Saalwachter, R. Graf, and H. W. Spiess, J. Magn. Reson.~to be pub-

lished!.23H. Geen, J. J. Titman, J. Gottwald, and H. W. Spiess, J. Magn. Res

Ser. A114, 264 ~1995!.24J. Gottwald, D. E. Demco, R. Graf, and H. W. Spiess, Chem. Phys. L

243, 314 ~1995!.25U. Friedrich, I. Schnell, S. P. Brown, A. Lupulescu, D. E. Demco, and

W. Spiess, Mol. Phys.95, 1209~1998!.26H. W. Spiess, inNMR Basic Principles and Progress, edited by P. Diehl,

E. Fluck, and R. Kosfeld~Springer-Verlag, Berlin, 1978!, Vol. 15, pp.55–214.

27O. W. Sørensen, G. W. Eich, M. H. Levitt, G. Bodenhausen, and RErnst, Prog. Nucl. Magn. Reson. Spectrosc.16, 163 ~1983!.

28U. Haeberlen,High Resolution NMR of Solids, Adv. Magn. Reson., Suppl1 ~Academic, London, 1976!.

29J. R. Garbow and T. Gullion, J. Magn. Reson.95, 442 ~1991!.30C. Schmidt, K. J. Kuhn, and H. W. Spiess, Prog. Colloid Polym. Sci.71,

71 ~1985!.31T. Terao, H. Miura, and A. Saika, J. Chem. Phys.85, 3816~1986!.32A. E. Bennett, C. M. Rienstra, M. Auger, K. V. Lakshmi, and R. G

Griffin, J. Chem. Phys.103, 6951~1995!.33T. Gullion, D. B. Baker, and M. S. Conradi, J. Magn. Reson.89, 479

~1990!.34J. C. C. Chan and H. Eckert, J. Magn. Reson.147, 170 ~2000!.35J. L. Derissen, Acta Crystallogr., Sect. B: Struct. Crystallogr. Cry

Chem.26, 901 ~1970!.36D. Sandstro¨m, M. Hong, and K. Schmidt-Rohr, Chem. Phys. Lett.300,

213 ~1999!.37P. J. Hore, J. A. Jones, and S. Wimperis,NMR: The Toolkit~Oxford

University Press, Oxford, 2000!.38A. Lesage, D. Sakellariou, S. Steuernagel, and L. Emsley, J. Am. Ch

Soc.120, 13194~1998!.39M. Munowitz and A. Pines, Adv. Chem. Phys.66, 1 ~1987!.


.

ir-

.

.

n.,

tt.

.

.

.

.

40G. Bodenhausen and D. J. Ruben, Chem. Phys. Lett.69, 185 ~1980!.41S. M. De Paul, K. Saalwa¨chter, R. Graf, and H. W. Spiess, J. Mag

Reson.146, 140 ~2000!.42A. A. Maudsley and R. R. Ernst, Chem. Phys. Lett.50, 368 ~1977!.43J. Baum, M. Munowitz, A. N. Garroway, and A. Pines, J. Chem. Phys.83,

2015 ~1985!.44D. N. Shykind, J. Baum, S. B. Liu, and A. Pines, J. Magn. Reson.76, 149

~1988!.45H. Geen, R. Graf, A. S. D. Heindrichs, B. S. Hickman, I. Schnell, H. W

Spiess, and J. J. Titman, J. Magn. Reson.138, 167 ~1999!.46Y. K. Lee, N. D. Kurur, M. Helmle, O. G. Johannessen, N. C. Nielsen, a

M. H. Levitt, Chem. Phys. Lett.242, 304 ~1995!.47M. Munowitz, A. Pines, and M. Mehring, J. Chem. Phys.86, 3172~1987!.48D. Suter, S. B. Liu, J. Baum, and A. Pines, Chem. Phys.114, 103~1987!.49G. A. Morris and R. Freeman, J. Am. Chem. Soc.101, 760 ~1979!.50B.-J. van Rossum, H. Fo¨rster, and H. J. M. de Groot, J. Magn. Reson.124,

516 ~1997!.51M. S. Lehmann, T. S. Koetzle, and W. C. Hamilton, J. Am. Chem. S

94, 2657~1972!.52U. Friedrich, I. Schnell, D. E. Demco, and H. W. Spiess, Chem. Ph

Lett. 285, 49 ~1998!.53I. Schnell, A. Lupulescu, S. Hafner, D. E. Demco, and H. W. Spiess

Magn. Reson.133, 61 ~1998!.54M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions

~Dover, New York, 1972!.55M. Bertmer and H. Eckert, Solid State Nucl. Magn. Reson.15, 139

~1999!.56E. R. Henry and A. Szabo, J. Chem. Phys.82, 4753~1985!.57D. P. Weitekamp, J. R. Garbow, and A. Pines, J. Chem. Phys.77, 2870

~1982!.58B. J. van Rossum, G. J. Boender, F. M. Mulder, J. Raap, T. S. Balaban

Holzwarth, K. Schaffner, S. Prytulla, H. Oschkinat, and H. J. M. de GroSpectrochim. Acta, Part A54, 1167~1998!.

59M. Hong, J. D. Gross, and R. G. Griffin, J. Phys. Chem. B101, 5869~1997!.

60O. Liivak and D. B. Zax, J. Chem. Phys.113, 1088~2000!.61T. Gullion and C. H. Pennington, Chem. Phys. Lett.290, 88 ~1998!.62G. Jeschke, M. Pannier, A. Godt, and H. W. Spiess, Chem. Phys.

331, 243 ~2000!.63R. Graf and M. Neidho¨fer ~unpublished!.64R. Graf, A. Heuer, and H. W. Spiess, Phys. Rev. Lett.80, 5738~1998!.65G. Metz, X. Wu, and S. O. Smith, J. Magn. Reson., Ser. A110, 219

~1994!.66O. W. Sørensen, M. Rance, and R. R. Ernst, J. Magn. Reson.56, 527

~1984!.67K. Saalwachter and K. Schmidt-Rohr, J. Magn. Reson.145, 161 ~2000!.


Heteronuclear Hâ€“ nuclear magnetic resonance: Combining

Documents

Transcript of Heteronuclear Hâ€“ nuclear magnetic resonance: Combining