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Triple-quantum NMR spectroscopy in dipolar solids
13 March 1998
Chemical Physics Letters 285 Ž1998. 49–58
Triple-quantum NMR spectroscopy in dipolar solids Ulli Friedrich a , Ingo Schnell a , Dan E. Demco b, Hans W. Spiess a
a,)
Max-Planck-Institut fur ¨ Polymerforschung, Postfach 3148, D-55021 Mainz, Germany b Technical UniÕersity, Physics Department, R-3400 Cluj, Romania Received 15 September 1997; in final form 17 October 1997
Abstract Triple-quantum ŽTQ. NMR spectroscopy in dipolar solids under fast magic-angle spinning is introduced. Proton dipolar connectivities derived from two-dimensional high-resolution TQ NMR spectra are shown for bisphenol-A-polycarbonate, fully protonated and OH-deuterated dimethylglyoxime and acetonitrile trapped in the cages of perdeuterated hydroquinone. For spin-1r2-triads, fast rotating about their threefold symmetry axis, MAS-induced TQ spinning-sideband patterns are evaluated. Analytical treatment of isolated spin-1r2-triads is compared to numerical spin-dynamics simulations including influences of surrounding spins with respect to effects on both the integral intensities of TQ coherences and the signal distribution on TQ sideband patterns. Using the above samples, which contain methyl groups in different surroundings, the perturbing effects of neighboring protons are elucidated. q 1998 Published by Elsevier Science B.V.
1. Introduction Multiple-quantum ŽMQ. NMR is a well established tool for investigating structure and dynamics of molecules in liquids and oriented systems w1–4x. In the past, the emphasis of MQ NMR of solids was placed on the measurement of spin cluster sizes and the understanding of the spatio-temporal growth of MQ coherences in networks of strongly coupled spins Žw3–5x, and references therein.. In recent years a new field of MQ NMR spectroscopy has developed into an important characterization probe. It offers an atomic scale perspective on materials through resolution of structurally distinct sites provided by fast magic-angle sample spinning ŽMAS.. High-resolution MQ MAS NMR spectroscopy in solids was realized for homonuclear )
Corresponding author.
dipolar coupled nuclei such as 1 H w6–9x, 31 P w10–12x and 13 C w13,14x and heteronuclear 13 C– 1 H w15,16x spin systems. In all cases homonuclear dipolar decoupling Žamong 1 H. and reduction of chemical shift anisotropies Žfor 31 P and 13 C. were achieved by fast MAS. Internuclear distances w7,13x, torsional angles w14x and residual dipolar couplings w13x were measured. Moreover, MQ MAS NMR techniques have been developed to increase the resolution of spin I ) 1 spectra, removing second order quadrupolar couplings w17,18x. One of the important features of MQ NMR spectroscopy in rotating solids is the existence of MQ spinning-sideband patterns w6,7,13x. In general, these patterns originate from the rotor encoding of the reconversion Hamiltonian and the evolution of the excited MQ coherences under the dipolar coupling. Only the first mechanism is present in total spin coherences ŽTSC. spectroscopy w7,13x. The simplest
0009-2614r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 7 . 0 1 2 9 2 - X
50
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
example is represented by spin pairs, where doublequantum ŽDQ. spinning-sideband patterns were investigated using a three-pulse sequence w7x and recoupling pulse sequences w13x in inorganic and organic solids with well localized dipolar interactions. Besides the quantitative information on dipolar and quadrupolar couplings, MQ MAS NMR spectroscopy is a valuable tool for providing connectivities in dipolar solids. The use of scalar couplings to determine the through-bond connectivity by total correlation spectroscopy has also been recently reported w19x. Homonuclear and heteronuclear two-dimensional Ž2D. high-resolution DQ spectroscopy establishes dipolar connectivities in proton w7,8x, phosphorus w10–12x and 13 C– 1 H w15x dipolar networks. Therefore, DQ MAS NMR spectroscopy can be used to elucidate the structure of disordered solids w20x or as a dipolar filter for rigid domains w13x. In order to further develop high-resolution MQ MAS spectroscopy of dipolar coupled spins in solids, more complicated spin topologies leading to higher order coherences have to be handled. The simplest example is the methyl group, which is an important functional group for many organic solids including synthetic and biopolymers. Consequently, it is of fundamental as well as practical interest to investigate highly resolved MQ coherences for protons in the CH 3 system under MAS. We shall focus here on the investigation of triple-quantum ŽTQ. spinningsideband patterns involving the maximum spin co-
herence which can be excited in an isolated spin1r2-triad. Moreover, the perturbing effect of a neighboring proton on TQ spinning-sideband patterns is considered.
2. Theory The basic scheme for a homonuclear 2D MQ experiment w1–4x performed on a dipolar solid rotating with angular frequency v R s 2prt R is presented in Fig. 1a. This strategy can be used with different excitationrreconversion pulse sequences w6–13x. We will discuss here only the case of the basic three-pulse sequence symmetrized to a fivepulse sequence by two additional pulses for z-filtering Žcf. Fig. 1b.. This inserts a rotor-synchronized purging period t 0 between reconversion and detection to allow undesired coherences to decay. In the excitation period the phases of the two 908 pulses are orthogonal which is appropriate for the excitation of TQ coherences. High-resolution is achieved solely by MAS. The phases of the radio-frequency ŽRF. pulses for the MQ reconversion period are shifted pr2 relative to the excitation pulses. For an experiment performed under sample spinning, this is not a necessary condition, the reconversion pulse sequence can be identical with the excitation pulse sequence w13x.
Fig. 1. Ža. General scheme for a 2D homonuclear MQ-experiment. During the evolution Ž t1 . and detection periods Ž t 2 . homonuclear decoupling is performed solely by MAS. The spin system is prepared in a form of longitudinal magnetization so that a read pulse has to be applied before detection. Žb. Five-pulse sequence for recording TQ high-resolution spectra under MAS. The excitation period of duration t is flanked by the first two 908 pulses. The third and fourth 908 pulse spaced by the same duration t represent the reconversion period. The delay t 0 is included to allow dephasing of spurious magnetization.
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
2.1. Total spin coherence under MAS
the MQ signals stored along z. Under these circumstances we can rewrite Eq. Ž1., in a simplified form
The effect of sample spinning in the MQ-experiments can be analyzed quantitatively using the density-operator formalism. The normalized NMR observable corresponding to the MQ coherences at the application of the five-pulse sequence presented in Fig. 1b, is given by w13x
1 ² I y Ž t 0 q t q t1 q t . : s Tr Iz2 4 ² I y Ž 0. : p
ˆ
ˆ Ž0.
=Tr I y e i 2 I x eyi H d Ž t 0 q t q t 1 q t ;t q t 1 q t .
½
p
ˆ
ˆ Ž0.
=eyi 2 I x eyi H d Ž t q t 1 q t ;t 1 q t . p
ˆ
p
=e
2
Tr I z2 4
ˆ Ž0.Žtqt 1 q t ;t 1 q t . ip Iˆy yi HˆdŽ0.Žt ;0. i
=Tr I y eyi H d
½
1
e
e
e
p 2
Iˆx
5
Iz .
The TQ MAS free induction decay of an isolated spin-1r2-triad representing TSC can now be evaluated from Eq. Ž2., using the corresponding operator algebra w21,22x. The above equation also describes the spin system response for the three-pulse sequence.
ˆ Ž0.
=e i 2 I y eyi H d Ž t 1 q t ;t . i
S TSC Ž t 1 ;t 2 s 0 . s
Ž 2.
S Ž t 1 ;t 2 s 0 . s
51
Iˆy yi HˆdŽ0.Žt ;0. i
e
e
p 2
Iˆx
5
Iz ,
Ž 1.
with the effective Hamiltonians HdŽ0. Ž t X ,t Y . s Y Ž0. Ž . tX Ht Hd t d t, integrated over the time-interval Ž tX , tY .. The time-domain signal is normalized to ² I y Ž0.: which is proportional to the amplitude of the singlequantum ŽSQ. free induction decay. The operators describing radio-frequency pulses and free evolution period propagators are written as Liouville operators w1x. The different entities in Eq. Ž1. are defined, for instance, in Refs. w7,13x, and the time intervals are those of Fig. 1b. The above equation is valid for a dipolar-coupled multi-spin system as well as for nuclei with quadrupolar interactions and can be extended easily including chemical-shielding interactions. It is evident from Eq. Ž1. that the spin system response will show a MQ spinning-sideband pattern, which originates partially from the rotor-modulation of the secular dipolar Hamiltonian Žas well as chemical-shielding interactions. during the evolution time and partially from the rotor-encoding of the Hamiltonian active during the reconversion period. If total spin coherence ŽTSC. w3,4x is excited, all coupled spins are active in respective MQ coherences which, therefore, do not evolve under the multi-spin dipolar Hamiltonian. The free evolution in the purging period t 0 Žcf. Fig. 1. does not change
2.2. Proton triple-quantum spinning-sideband patterns of an isolated CH3 group In a high external magnetic field, three 1 H nuclei in a CH 3 group reorienting fast relative to the NMR linewidth of rigid groups can be described by an energy-level scheme containing eigenstates labeled A " 3r2 , A " 1r2 , E a" 1r2 and E b" 1r2 according to the irreducible representations of the cyclic point group C 3 w23x. The indices "m denote the z-component of the total nuclear spin. The energy levels A " 3r2 are shifted upwards and A " 1r2 levels downwards by the intragroup dipolar interactions whereas E a",b1r2 levels are unperturbed. The responses to RF-pulse sequences in static solids containing isolated reorienting triads of spin1r2-nuclei Že.g. CH 3 or CF3 groups. have been analyzed mainly by treating the three spins as a single spin-3r2-particle subjected to a quasiquadrupolar interaction w24,25x. Therefore, the excitation of TQ coherences of a spin-1r2-triad in a fast internal rotation limit can be described by considering the system as an A spin-isomer of total spin F s 3r2. The fast axial rotation reduces the proton dipolar couplings and makes the angular dependence of the dipolar Hamiltonian the same for all proton pairs. For rapidly rotating methyl groups the rotor-mod-
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
52
ulated secular dipolar Hamiltonian integrated over the Ž tX ,tY . time interval is given by HdŽ0. Ž tX ,tY . s
m0
ž p/ž
"g 2
'6
4
/ž / 3 r HH
4
2
=
Ž2. Ž2. dym ,0 Ž b M . d 0,y m Ž b .
Ý msy2 t
=
Y
Ht e
i mŽ g q v R t .
X
d t P T2,0 ,
Ž 3.
where r HH is the distance between the interacting nuclei. The characteristic irreducible spin tensor-operator is T2,0 s Ž1r™'6 . 3Fz2 y F Ž F q 1 . w21,22x. The spin operator F operates in the reduced Hilbert space corresponding to the A spin-isomer. The significance of all the other quantities in Eq. Ž3. is given in Ref. w7x. Using the Wigner rotation matrices defined in Ref. w21x, the time-integral of the rotormodulated interproton dipolar coupling Hamiltonian can be written as m 0 g 2 " 2 tY Ž0. X Y Hd Ž t ,t . s sin2b cos Ž 2 v R t q 2g . 3 X 4p 8 r HH t
Fig. 2. Rotational sideband patterns of 1 H SQ Ža. and TQ spectra Žb. of isolated methyl groups under MAS for different spinning frequencies. The SQ spectra of methyl groups can be simulated analogously to the TQ spectra w27x.
H
y'2 sin Ž 2 b . cos Ž v R t q g . 4 d t P T2,0 . Ž 4. Thus, the TQ spinning-sideband pattern can be evaluated for the fast rotating methyl group using ™ ™ Eqs. Ž2. and Ž4. with all I replaced by F operators. We finally obtain STQ Ž t 1 ;t 2 s 0 . s 409
¦½ cos '6 v Ž t q t q t ;t q t . = ½ cos '6 v Ž t ;0 . y 1 5; d
1
1
y1
5 Ž 5.
d
with X
Y
vd Ž t ;t . s
m0
'6
4
16
ž p/ž t
g 2"
/ž / 3 r HH
Y
2
Ht sin b cos Ž 2 v
=
X
R t q 2g
.
y'2 sin Ž 2 b . cos Ž v R t q g . 4 d t. Ž 6 . The symbol ² : represents the powder average. 2.3. Simulated spinning-sideband patterns of isolated methyl groups The numerical powder average of Eq. Ž5. was used to simulate TQ spinning-sideband patterns. The
results for an isolated fast rotating CH 3 group Žinterproton distance r HH s 0.19 nm. are displayed in Fig. 2b for different ratios of motionally averaged dipolar 3 . coupling v D s Ž m 0r4p .Žg 2 "r2 r HH to rotor frequency v R . For comparison, the corresponding SQ spectra have also been calculated and are plotted in Fig. 2a. In order to simplify the spectra, we set our preparationrreconversion times to t s t R r2. Considering Eq. Ž6., this makes the integral over the term containing cosŽ2 v R t q 2g . vanish. Inserting the remaining parts of Eq. Ž6. into Eq. Ž5. leads to a tim e -d e p e n d e n t te rm o f th e fo rm cosw D sinŽ2 b .rv R x sinŽ v R t 1 q g .4 , where D contains all prefactors and the dipolar coupling strength Žsee Eqs. Ž5. and Ž6... Expanding this into a series of Bessel functions w26x, we obtain cos
D sin Ž 2 b .
vR
s J0
ž
sin Ž v R t 1 q g .
D sin Ž 2 b .
vR
`
/
q2
Ý J2 k ks1
=cos Ž 2 k v R t 1 q 2 kg . ,
ž
D sin Ž 2 b .
vR
/ Ž 7.
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
where Jn denotes Bessel functions of nth order. This allows us to write the TQ signal in closed form
½ ž
S TQ Ž t 1 ;t 2 s 0 . A 1 y J0
D sin Ž 2 b .
vR
`
y2
Ý J2 k ks1
ž
/
D sin Ž 2 b .
vR
=cos Ž 2 k v R t 1 q 2 kg .
½ ž
= 1 y J0
D sin Ž 2 b .
vR
`
y2
Ý J2 k ks1
ž
D sin Ž 2 b .
vR
5
=cos Ž 2 kg . .
threefold symmetry axis of the CH 3 group interacting with the methyl spin-1r2-triad. The perturbing dipolar interaction introduced by this additional spin is motionally averaged by the methyl protons rotating about their symmetry axis. Therefore, it is given by
/ 3 yH s v CH D
5 /
4p 1 2
Ž 8.
Thus, eÕen order TQ spinning sidebands only occur for each single crystallite. As in SQ MAS spectroscopy in powders, absorptive lines are observed by integration over g . For all MAS regimes, the TQ signal intensity is concentrated in a strong centerband. In the slow MAS regime, i.e. v D rv R 4 1, the spectra show many rotational sidebands of low intensity. With increasing v R , the intensity is concentrated in the central frequency-range of the spectrum and the number of spinning-sidebands is reduced. When preceding towards the limit of fast rotation, i.e. v D rv R < 1, the TQ spectra show spinning-sidebands with an overall pattern not very sensitive to the ratio v D rv R . Contrary to SQ spectra, however, the integral intensity of TQ spectra decreases rapidly for v D rv R ™ 0, because the TQ excitation time t becomes shorter Žt s t R r2 ™ 0. and more and more insufficient to build up TQ coherences. 2.4. Influence of surrounding spins So far, our analytical considerations were limited to isolated spin-1r2-triads. In real spin systems, we will hardly find methyl groups completely isolated from any dipolar interaction with surrounding spins. In order to mimic dipolar coupling to remote nuclei, we add one further identical spin located on the
"g 12H
m0
=
/
53
2 d 2 q Ž r HH r3 .
ž
3 1q
2 r HH
3d 2
3r2
y1
/
y1 ,
Ž 9.
where d is the distance between the additional spin and the center of the CH 3 triad. In our numerical spin-dynamics simulations, RFpulses and dipolar interactions act on the spin system according to the pulse sequence given in Fig. 1b. The time axis is divided into propagation periods D t, sufficiently short to restrict calculations to the time independent part of the interactions: UŽ t, t q D t . s expŽyi HD t . with an effective, time independent Hamiltonian H valid during D t. For each period D t a propagator U is evaluated and applied sequentially on the spin system. A more detailed description of the simulation procedure will be given elsewhere w27x. In the spin system considered here, TQ coherences among methyl protons are no longer TSC and, therefore, evolve due to the additional spin during t1. This results in a different intensity distribution in the sideband pattern compared to the isolated CH 3 case. Moreover, in the excitation period, a fourth spin enables spin-cluster growth and build-up of higher order coherences, depending on the product of the strength of the interaction and the time it acts on the system. A weak additional coupling is, therefore, expected to affect first the sideband pattern of the spectrum by TQ evolution during t1 leaving the overall TQ intensity rather unchanged, because t1 is longer by a factor of 10 to 100 compared to the excitation period t . With increasing coupling strength to the fourth spin the changes of the sideband patterns are expected to be accompanied by a significant reduction of TQ intensity.
54
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
Fig. 3. Ža. TQ spinning-sideband patterns of methyl protons perturbed by a fourth proton at a MAS frequency of v R r2p s 14.3 kHz. The intra-methyl proton–proton distance is set to 0.19 nm, d denotes the distance between the fourth spin and center of the methyl group. Žb. Relative intensities of the peaks in the simulated spectra given in Ža.. For weak perturbations, the integral TQ intensity is rather constant, only the pattern shows the characteristic growth of first order sidebands. For stronger dipolar perturbations, the pattern is massively changed, higher order sidebands begin to arise and the integral TQ intensity decreases because four-quantum coherences involving the fourth spin are built up.
Indeed, these features of TQ spectra are borne out by the simulations. Fig. 3a shows TQ MAS spectra Ž v R r2p s 14.3 kHz. of methyl-groups with an intra-methyl proton–proton distance of r HH s 0.19 nm, perturbed by a fourth spin at a distance d from the center of the CH 3-proton triangle. With increasing dipolar coupling strength, the presence of a fourth spin leads to growing signals at frequencies in the spectrum, where no intensity is expected for unperturbed TSC and t s 1r2t R , especially at "v R r2p Žcf. Eq. Ž8... For weak perturbations with 3 yH - 1 v , signal intensity is transferred mainly v CH D D 3 from the centerband and second order sidebands to first order sidebands, leaving the overall TQ intensity and the relative intensities of the ‘‘genuine’’ TSC3 yH ) pattern almost unaffected Žcf. Fig. 3b.. For v CH D 1 3 v D , corresponding to d - 0.30 nm, the loss of integral TQ intensity indicates that the fourth spin is also increasingly involved during the excitation period leading to massive changes in the sideband pattern and, additionally, to TQ coherences including the fourth spin. The perturbing interaction strength of 3 yH f 1 v v CH D D can be roughly identified with a TQ 3
MAS spectrum in which first- and second-order sidebands are of equal intensity. A more precise evaluation with respect to more extended dipolar coupling networks requires chemical shifts, angular dependencies, and, of course, all contributing dipolar couplings to be considered in the spin-dynamics simulations. However, even for more complicated systems, the characteristic features of TQ MAS spectra are similar to those calculated for this simple four-spin topology, in which the fourth spin is then viewed to as mimicing the perturbing influences of the surroundings on the methyl-group. A detailed consideration of particular influences, however, leads to minor modifications of the general effects shown here w27x. 3. Experimental The experiments were performed on a Bruker ASX 500 NMR spectrometer, operating at a 1 H frequency of 500.13 MHz. TQ coherences were excited with the five-pulse sequence shown in Fig. 1b, using a 908 pulse length of about 3 ms. TQ coher-
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
ences were selected by cycling the phases of the excitation pulses relative to the reconversion pulses in steps of 608 and adding the signals of six successive scans with alternating signs. The excitation delay was chosen to be t s prv R , i.e. t s 35 ms for a rotor frequency v R r2p s 14.3 kHz. The 2D experiments are performed with a t 1-increment of about 3 ms, including TPPI. Commercial polycrystalline dimethylglyoxime Žhereafter DMG. was used without further purification. In order to reduce the dipolar coupling amongst protons, in a second sample the OH-groups in dimethylglyoxime were deuterated Žd OH -DMG. by dissolving the compound in d 1-ethanol. After evaporation of the solvent the procedure was repeated three times. The degree of deuteration was about 95%. Largely isolated molecules of acetonitrile in the cavities of deuterated hydroquinone Žhydroquinone-acetonitrile Ž3:1. clathrate, hereafter ANC. were prepared by H. Zimmermann at the Max Planck-Institut fur ¨ Medizinische Forschung in Heidelberg. For perdeuteration, 1,4-hydroquinone-d 4 was recrystallized several times using d 1-ethanol and, after that, dissolved in acetonitrile. Slow evaporation of the solvent gave crystals of the clathrate. The degree of deuteration was about 95% at the aromatic positions and about 80% at OH as measured from the NMR absorption spectra, because the OD groups are subjected to back exchange when exposed to air. These samples were chosen to provide methylgroups in surroundings with different dipolar interactions. In ANC, the methyl-groups of acetonitrile are separated from each other by 0.7 nm w28x. In our case, we had to expect some residual 1 H– 1 H couplings to the matrix, because 20% of the OH-groups of the host-molecule were still protonated. In d OH DMG, inter-methyl dipolar couplings are possible. In case of protonated OH-groups ŽDMG., there are additional 1 H– 1 H dipolar interactions between CH 3and OH-groups w29x. Bisphenol-A-polycarbonate Žhereafter PC., finally, provides methyl groups in a surrounding without structural separation or dilution of the dipolar coupling network. 4. Results and discussion In the following, 1 H TQ MAS spectra shall be discussed first with respect to TQ intensities at dif-
55
ferent resonance positions indicating respective TQ coherences and, therefore, sufficiently strong dipolar connectivities between defined triads of protons. Then, we will focus on characteristic spinning-sideband patterns of TQ MAS spectra including methyl groups. 4.1. Proton connectiÕities by TQ NMR spectroscopy In order to achieve information on dipolar connectivities manifested in TQ coherences, we have to consider TQ intensities in 2D high-resolution spectra which are, in principle, structured in the same manner as 2D DQ spectra published previously w6–13,15x. For this purpose, MQ intensities, in general, have to be integrated over their spinning-sideband patterns to avoid distortions due to different frequency distributions. In TQ MAS spectra, however, the signal is largely concentrated in the centerband Žcf. Fig. 2., so that one can focus on the central region of the 2D spectrum as a good approximation. The central regions of 1 H TQ high-resolution spectra of DMG and d OH -DMG are presented in Fig. 4a and b, respectively. For the fully protonated compound dipolar connectivities lead to three of four possible spin-triples producing TQ coherences Žcf. Fig. 4a.: AAA, AAB, and ABB with A s CH 3-proton and B s OH-proton. A highly intense AAA peak from strong intra-methyl 1 H– 1 H couplings with r HH f 0.19 nm is obvious. All ‘‘mixed’’ coherences are excited with lower efficiency because the shortest proton–proton distances between different functional groups are above 0.2 nm w28x. TQ coherences between OH protons only ŽBBB. are not excited under our experimental conditions because further OHgroups are spaced from BB-pairs by more than 0.4 nm. If the OH-groups are deuterated, only intramethyl TQ coherences are detected as it is evident from Fig. 4b. The functional group connectivities through space are also revealed by the 2D TQ spectrum of PC Žcf. Fig. 4c. showing all four possible spin-triples: TQ coherences involving methyl protons only ŽAAA., phenylene protons only ŽBBB. and those involving protons from both groups ŽAAB and ABB.. The 1 H TQ spectrum of ANC Žnot shown. shows only one peak, which stems from the methyl protons.
56
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
are too weak to excite a detectable ‘‘mixed’’ TQ signal. 4.2. Triple-quantum spinning-sideband patterns for methyl groups Slices of 1 H TQ MAS spectra at the CH 3 proton resonance are presented in Fig. 5 for different compounds. The respective 2D spectra were recorded at room temperature and a MAS frequency of 14.3 kHz. For PC Žcf. Fig. 5a., DMG Žcf. Fig. 5b. and d OH -DMG Žcf. Fig. 5c. the patterns are characterized by intense spinning-sidebands present at "v R r2p and "2 v R r2p as predicted from our simulations for a four-spin system, in which the fourth spin
Fig. 4. 2D high-resolution 1 H TQ spectra recorded using the five-pulse sequence of Fig. 1b with t s 35 ms, i.e. half of the rotor period Ž v R r2p s14.3 kHz.. Ža. For dimethylglyoxime, AAA, AAB and ABB TQ coherences are generated ŽA s methyl– proton, BsOH–proton.. Žb. For OH-deuterated dimethylglyoxime, the AAA TQ peak originating from methyl protons only is solely detected. Žc. For bisphenol-A-polycarbonate, all four possible TQ coherences are present. The ABB-peak is missing at the CH 3 Ž s A.-resonance due to strong dipolar interactions between the TQ coherence and the two remaining CH 3 -protons. The spectral intensity of AAA TQ coherences at the aromatic Ž s B. resonance frequency is probably caused by spin-diffusion during t 0 . These effects are considerably reduced at higher MAS rates w27x.
No TQ cross-peaks indicating dipolar connectivities between methyl protons and the partially protonated hydroquinone are detected in our spectra. This indicates that the number of OH protons surrounding CH 3 groups is too small and the dipolar couplings
Fig. 5. Proton TQ spinning-sideband patterns of CH 3 groups in bisphenol-A- polycarbonate Ža.; dimethylglyoxime Žb.; OH-deuterated dimethylglyoxime Žc. and acetonitrile molecules in perdeuterated hydroquinone Žd.. The patterns correspond to slices through the experimental TQ-spectra recorded using the five-pulse sequence with t st R r2 s 35 ms at a rotor frequency v R r2p s 14.3 kHz.
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
mimics the interactions perturbing the dominating intra-methyl couplings Žcf. Fig. 3a.. Even in the case of ANC Žcf. Fig. 5d., in which the methyl groups are largely isolated, considerable intensity is observed at "v R , indicating perturbing effects of surrounding spins, i.e. residual OH-protons. However, no TQ coherences involving OH protons could be detected. Hence, dipolar couplings which are too weak to build up TQ coherences are, nevertheless, able to modify the spinning-sideband pattern of other TQ coherences considerably. The reduction of the dipolar coupling to remote spins also significantly narrows the TQ spectral lines. In the slice of the d OH -DMG TQ spectrum Žcf. Fig. 5c., intense first order spinning-sidebands and broadened lines indicate inter-methyl dipolar couplings acting additionally to intra-methyl couplings in agreement with the crystalline structure w28x. Replacing the deuterons on the OH groups by protons ŽDMG, cf. Fig. 5b. leads to ‘‘mixed’’ hydroxylmethyl proton TQ coherences at respective frequencies. Furthermore, the spinning-sideband pattern of the methyl-only TQ coherence is considerably changed compared to the OH deuterated case. As expected from our simulations, the presence of additional strong couplings results in increased first and third order sidebands. The slice of the PC TQ spectrum shows a sideband pattern consisting of three different resonances corresponding to the three possible TQ coherences involving at least one methyl proton ŽAAA, AAB and ABB, cf. Fig. 4c.. The methyl-only pattern is quite similar to that of d OH -DMG indicating a dipolar coupling network of comparable effective strength.
5. Conclusions The possibility of exciting TQ coherences under MAS in dipolar solids will enhance the ability to investigate dipolar connectivities and to obtain structural and molecular dynamic information. The TQ spinning-sideband patterns prove to be sensitive to both the topology of the CH 3 unit itself and, notably, to the perturbing influence of additional spins in the surroundings. Even weak interactions cause characteristic changes in the patterns
57
leaving the integral methyl-only TQ intensity essentially unchanged. Thus, TQ patterns of methyl groups can be viewed as sensitive detectors of remote spins. With increasing coupling strengths, TQ coherences involving surrounding spins are excited and can be used to derive dipolar connectivities among proton triads in terms of 2D high-resolution TQ spectroscopy. These techniques allow the handling of methyl groups in solid state NMR and, furthermore, in connection with SQ and DQ MAS NMR spectra, to determine the topology of finite spin-clusters. Hence, TQ spectroscopy and the examination of spin-1r2triads open the field to distance as well as angle determination in non-crystalline solids w27x.
Acknowledgements We would like to thank Prof. U. Haeberlen and H. Zimmermann for providing the dimethylglyoxime and the d 6-hydroquinone-acetonitrile clathrate as well as for stimulating discussions. The authors acknowledge financial support from the Volkswagen-Stiftung and from the Deutsche Forschungsgemeinschaft ŽSFB 262..
References w1x R.R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions, Clarendon Press, Oxford, 1987. w2x G. Bodenhausen, Prog. NMR Spectrosc. 14 Ž1981. 137. w3x D.P. Weitekamp, Adv. Magn. Reson. 11 Ž1983. 111. w4x M. Munowitz, A. Pines, Adv. Chem. Phys. 66 Ž1987. 1. w5x S. Lacelle, Adv. Magn. Opt. Reson. 16 Ž1991. 173. w6x H. Geen, J.J. Titman, J. Gottwald, H.W. Spiess, Chem. Phys. Lett. 227 Ž1994. 79. w7x J. Gottwald, D.E. Demco, R. Graf, H.W. Spiess, Chem. Phys. Lett. 243 Ž1995. 314. w8x S. Ding, C.A. McDowell, J. Magn. Reson. A 120 Ž1996. 261. w9x H.W. Spiess, Ann. Rep. NMR Spectrosc. 34 Ž1997. 1. w10x M. Feike, R. Graf, I. Schnell, C. Jager, H.W. Spiess, J. Am. ¨ Chem. Soc. 118 Ž1996. 9631. w11x M. Feike, D.E. Demco, J. Gottwald, S. Hafner, H.W. Spiess, J. Magn. Reson. 122 Ž1996. 214. w12x H. Geen, J. Gottwald, R. Graf, I. Schnell, H.W. Spiess, J.J. Titman, J. Magn. Reson. 125 Ž1997. 224. w13x R. Graf, D.E. Demco, J. Gottwald, S. Hafner, H.W. Spiess, J. Chem. Phys. 106 Ž1997. 885.
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w14x X. Feng, Y.K. Lee, D. Sandstrom, ¨ M. Eden, ´ H. Maisel, A. Sebald, M.H. Levitt, Chem. Phys. Lett. 257 Ž1996. 314. w15x W. Sommer, J. Gottwald, D.E. Demco, H.W. Spiess, J. Magn. Reson. A 112 Ž1995. 131. w16x M. Hong, J.D. Gross, R.G. Griffin, J. Phys. Chem. B 101 Ž1997. 5869. w17x L. Frydman, J.S. Harwood, J. Am. Chem. Soc. 117 Ž1995. 5367. w18x C. Fernandez, J.P. Amoureux, Solid State Nucl. Magn. Reson. 5 Ž1996. 315. w19x M. Baldus, B.H. Meier, J. Magn. Reson. A 121 Ž1996. 65. w20x M. Feike, C. Jager, H.W. Spiess, J. Non-Cryst. Solids, ¨ submitted. w21x K. Schmidt-Rohr, H.W. Spiess, Multidimensional Solid State NMR and Polymers, Academic Press, New York, 1994.
w22x G.J. Bowden, W.D. Hutchison, J. Khachan, J. Magn. Reson. 67 Ž1986. 415. w23x E.R. Andrew, R. Bersohn, J. Chem. Phys. 18 Ž1950. 159. w24x P.S. Allen, W. Harding, P. Mansfield, J. Phys. C 5 Ž1972. L89. w25x Y.N. Moskvich, N.A. Sergeev, G.I. Dotsenko, Phys. Status Solidi Ža. 30 Ž1975. 409. w26x M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, Dover Publications, New York, 1989. w27x I. Schnell, U. Friedrich, A. Lupulescu, D.E. Demco, H.W. Spiess, to be published. w28x B.M. Craven, C.H. Chang, D. Ghosh, Acta Cryst. B 35 Ž1979. 2962. w29x C.W. Thomas, C.W. Mak, K.-S. Lee, Acta Cryst. B 34 Ž1978. 3631.
Chemical Physics Letters 285 Ž1998. 49–58
Triple-quantum NMR spectroscopy in dipolar solids Ulli Friedrich a , Ingo Schnell a , Dan E. Demco b, Hans W. Spiess a
a,)
Max-Planck-Institut fur ¨ Polymerforschung, Postfach 3148, D-55021 Mainz, Germany b Technical UniÕersity, Physics Department, R-3400 Cluj, Romania Received 15 September 1997; in final form 17 October 1997
Abstract Triple-quantum ŽTQ. NMR spectroscopy in dipolar solids under fast magic-angle spinning is introduced. Proton dipolar connectivities derived from two-dimensional high-resolution TQ NMR spectra are shown for bisphenol-A-polycarbonate, fully protonated and OH-deuterated dimethylglyoxime and acetonitrile trapped in the cages of perdeuterated hydroquinone. For spin-1r2-triads, fast rotating about their threefold symmetry axis, MAS-induced TQ spinning-sideband patterns are evaluated. Analytical treatment of isolated spin-1r2-triads is compared to numerical spin-dynamics simulations including influences of surrounding spins with respect to effects on both the integral intensities of TQ coherences and the signal distribution on TQ sideband patterns. Using the above samples, which contain methyl groups in different surroundings, the perturbing effects of neighboring protons are elucidated. q 1998 Published by Elsevier Science B.V.
1. Introduction Multiple-quantum ŽMQ. NMR is a well established tool for investigating structure and dynamics of molecules in liquids and oriented systems w1–4x. In the past, the emphasis of MQ NMR of solids was placed on the measurement of spin cluster sizes and the understanding of the spatio-temporal growth of MQ coherences in networks of strongly coupled spins Žw3–5x, and references therein.. In recent years a new field of MQ NMR spectroscopy has developed into an important characterization probe. It offers an atomic scale perspective on materials through resolution of structurally distinct sites provided by fast magic-angle sample spinning ŽMAS.. High-resolution MQ MAS NMR spectroscopy in solids was realized for homonuclear )
Corresponding author.
dipolar coupled nuclei such as 1 H w6–9x, 31 P w10–12x and 13 C w13,14x and heteronuclear 13 C– 1 H w15,16x spin systems. In all cases homonuclear dipolar decoupling Žamong 1 H. and reduction of chemical shift anisotropies Žfor 31 P and 13 C. were achieved by fast MAS. Internuclear distances w7,13x, torsional angles w14x and residual dipolar couplings w13x were measured. Moreover, MQ MAS NMR techniques have been developed to increase the resolution of spin I ) 1 spectra, removing second order quadrupolar couplings w17,18x. One of the important features of MQ NMR spectroscopy in rotating solids is the existence of MQ spinning-sideband patterns w6,7,13x. In general, these patterns originate from the rotor encoding of the reconversion Hamiltonian and the evolution of the excited MQ coherences under the dipolar coupling. Only the first mechanism is present in total spin coherences ŽTSC. spectroscopy w7,13x. The simplest
0009-2614r98r$19.00 q 1998 Published by Elsevier Science B.V. All rights reserved. PII S 0 0 0 9 - 2 6 1 4 Ž 9 7 . 0 1 2 9 2 - X
50
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
example is represented by spin pairs, where doublequantum ŽDQ. spinning-sideband patterns were investigated using a three-pulse sequence w7x and recoupling pulse sequences w13x in inorganic and organic solids with well localized dipolar interactions. Besides the quantitative information on dipolar and quadrupolar couplings, MQ MAS NMR spectroscopy is a valuable tool for providing connectivities in dipolar solids. The use of scalar couplings to determine the through-bond connectivity by total correlation spectroscopy has also been recently reported w19x. Homonuclear and heteronuclear two-dimensional Ž2D. high-resolution DQ spectroscopy establishes dipolar connectivities in proton w7,8x, phosphorus w10–12x and 13 C– 1 H w15x dipolar networks. Therefore, DQ MAS NMR spectroscopy can be used to elucidate the structure of disordered solids w20x or as a dipolar filter for rigid domains w13x. In order to further develop high-resolution MQ MAS spectroscopy of dipolar coupled spins in solids, more complicated spin topologies leading to higher order coherences have to be handled. The simplest example is the methyl group, which is an important functional group for many organic solids including synthetic and biopolymers. Consequently, it is of fundamental as well as practical interest to investigate highly resolved MQ coherences for protons in the CH 3 system under MAS. We shall focus here on the investigation of triple-quantum ŽTQ. spinningsideband patterns involving the maximum spin co-
herence which can be excited in an isolated spin1r2-triad. Moreover, the perturbing effect of a neighboring proton on TQ spinning-sideband patterns is considered.
2. Theory The basic scheme for a homonuclear 2D MQ experiment w1–4x performed on a dipolar solid rotating with angular frequency v R s 2prt R is presented in Fig. 1a. This strategy can be used with different excitationrreconversion pulse sequences w6–13x. We will discuss here only the case of the basic three-pulse sequence symmetrized to a fivepulse sequence by two additional pulses for z-filtering Žcf. Fig. 1b.. This inserts a rotor-synchronized purging period t 0 between reconversion and detection to allow undesired coherences to decay. In the excitation period the phases of the two 908 pulses are orthogonal which is appropriate for the excitation of TQ coherences. High-resolution is achieved solely by MAS. The phases of the radio-frequency ŽRF. pulses for the MQ reconversion period are shifted pr2 relative to the excitation pulses. For an experiment performed under sample spinning, this is not a necessary condition, the reconversion pulse sequence can be identical with the excitation pulse sequence w13x.
Fig. 1. Ža. General scheme for a 2D homonuclear MQ-experiment. During the evolution Ž t1 . and detection periods Ž t 2 . homonuclear decoupling is performed solely by MAS. The spin system is prepared in a form of longitudinal magnetization so that a read pulse has to be applied before detection. Žb. Five-pulse sequence for recording TQ high-resolution spectra under MAS. The excitation period of duration t is flanked by the first two 908 pulses. The third and fourth 908 pulse spaced by the same duration t represent the reconversion period. The delay t 0 is included to allow dephasing of spurious magnetization.
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
2.1. Total spin coherence under MAS
the MQ signals stored along z. Under these circumstances we can rewrite Eq. Ž1., in a simplified form
The effect of sample spinning in the MQ-experiments can be analyzed quantitatively using the density-operator formalism. The normalized NMR observable corresponding to the MQ coherences at the application of the five-pulse sequence presented in Fig. 1b, is given by w13x
1 ² I y Ž t 0 q t q t1 q t . : s Tr Iz2 4 ² I y Ž 0. : p
ˆ
ˆ Ž0.
=Tr I y e i 2 I x eyi H d Ž t 0 q t q t 1 q t ;t q t 1 q t .
½
p
ˆ
ˆ Ž0.
=eyi 2 I x eyi H d Ž t q t 1 q t ;t 1 q t . p
ˆ
p
=e
2
Tr I z2 4
ˆ Ž0.Žtqt 1 q t ;t 1 q t . ip Iˆy yi HˆdŽ0.Žt ;0. i
=Tr I y eyi H d
½
1
e
e
e
p 2
Iˆx
5
Iz .
The TQ MAS free induction decay of an isolated spin-1r2-triad representing TSC can now be evaluated from Eq. Ž2., using the corresponding operator algebra w21,22x. The above equation also describes the spin system response for the three-pulse sequence.
ˆ Ž0.
=e i 2 I y eyi H d Ž t 1 q t ;t . i
S TSC Ž t 1 ;t 2 s 0 . s
Ž 2.
S Ž t 1 ;t 2 s 0 . s
51
Iˆy yi HˆdŽ0.Žt ;0. i
e
e
p 2
Iˆx
5
Iz ,
Ž 1.
with the effective Hamiltonians HdŽ0. Ž t X ,t Y . s Y Ž0. Ž . tX Ht Hd t d t, integrated over the time-interval Ž tX , tY .. The time-domain signal is normalized to ² I y Ž0.: which is proportional to the amplitude of the singlequantum ŽSQ. free induction decay. The operators describing radio-frequency pulses and free evolution period propagators are written as Liouville operators w1x. The different entities in Eq. Ž1. are defined, for instance, in Refs. w7,13x, and the time intervals are those of Fig. 1b. The above equation is valid for a dipolar-coupled multi-spin system as well as for nuclei with quadrupolar interactions and can be extended easily including chemical-shielding interactions. It is evident from Eq. Ž1. that the spin system response will show a MQ spinning-sideband pattern, which originates partially from the rotor-modulation of the secular dipolar Hamiltonian Žas well as chemical-shielding interactions. during the evolution time and partially from the rotor-encoding of the Hamiltonian active during the reconversion period. If total spin coherence ŽTSC. w3,4x is excited, all coupled spins are active in respective MQ coherences which, therefore, do not evolve under the multi-spin dipolar Hamiltonian. The free evolution in the purging period t 0 Žcf. Fig. 1. does not change
2.2. Proton triple-quantum spinning-sideband patterns of an isolated CH3 group In a high external magnetic field, three 1 H nuclei in a CH 3 group reorienting fast relative to the NMR linewidth of rigid groups can be described by an energy-level scheme containing eigenstates labeled A " 3r2 , A " 1r2 , E a" 1r2 and E b" 1r2 according to the irreducible representations of the cyclic point group C 3 w23x. The indices "m denote the z-component of the total nuclear spin. The energy levels A " 3r2 are shifted upwards and A " 1r2 levels downwards by the intragroup dipolar interactions whereas E a",b1r2 levels are unperturbed. The responses to RF-pulse sequences in static solids containing isolated reorienting triads of spin1r2-nuclei Že.g. CH 3 or CF3 groups. have been analyzed mainly by treating the three spins as a single spin-3r2-particle subjected to a quasiquadrupolar interaction w24,25x. Therefore, the excitation of TQ coherences of a spin-1r2-triad in a fast internal rotation limit can be described by considering the system as an A spin-isomer of total spin F s 3r2. The fast axial rotation reduces the proton dipolar couplings and makes the angular dependence of the dipolar Hamiltonian the same for all proton pairs. For rapidly rotating methyl groups the rotor-mod-
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
52
ulated secular dipolar Hamiltonian integrated over the Ž tX ,tY . time interval is given by HdŽ0. Ž tX ,tY . s
m0
ž p/ž
"g 2
'6
4
/ž / 3 r HH
4
2
=
Ž2. Ž2. dym ,0 Ž b M . d 0,y m Ž b .
Ý msy2 t
=
Y
Ht e
i mŽ g q v R t .
X
d t P T2,0 ,
Ž 3.
where r HH is the distance between the interacting nuclei. The characteristic irreducible spin tensor-operator is T2,0 s Ž1r™'6 . 3Fz2 y F Ž F q 1 . w21,22x. The spin operator F operates in the reduced Hilbert space corresponding to the A spin-isomer. The significance of all the other quantities in Eq. Ž3. is given in Ref. w7x. Using the Wigner rotation matrices defined in Ref. w21x, the time-integral of the rotormodulated interproton dipolar coupling Hamiltonian can be written as m 0 g 2 " 2 tY Ž0. X Y Hd Ž t ,t . s sin2b cos Ž 2 v R t q 2g . 3 X 4p 8 r HH t
Fig. 2. Rotational sideband patterns of 1 H SQ Ža. and TQ spectra Žb. of isolated methyl groups under MAS for different spinning frequencies. The SQ spectra of methyl groups can be simulated analogously to the TQ spectra w27x.
H
y'2 sin Ž 2 b . cos Ž v R t q g . 4 d t P T2,0 . Ž 4. Thus, the TQ spinning-sideband pattern can be evaluated for the fast rotating methyl group using ™ ™ Eqs. Ž2. and Ž4. with all I replaced by F operators. We finally obtain STQ Ž t 1 ;t 2 s 0 . s 409
¦½ cos '6 v Ž t q t q t ;t q t . = ½ cos '6 v Ž t ;0 . y 1 5; d
1
1
y1
5 Ž 5.
d
with X
Y
vd Ž t ;t . s
m0
'6
4
16
ž p/ž t
g 2"
/ž / 3 r HH
Y
2
Ht sin b cos Ž 2 v
=
X
R t q 2g
.
y'2 sin Ž 2 b . cos Ž v R t q g . 4 d t. Ž 6 . The symbol ² : represents the powder average. 2.3. Simulated spinning-sideband patterns of isolated methyl groups The numerical powder average of Eq. Ž5. was used to simulate TQ spinning-sideband patterns. The
results for an isolated fast rotating CH 3 group Žinterproton distance r HH s 0.19 nm. are displayed in Fig. 2b for different ratios of motionally averaged dipolar 3 . coupling v D s Ž m 0r4p .Žg 2 "r2 r HH to rotor frequency v R . For comparison, the corresponding SQ spectra have also been calculated and are plotted in Fig. 2a. In order to simplify the spectra, we set our preparationrreconversion times to t s t R r2. Considering Eq. Ž6., this makes the integral over the term containing cosŽ2 v R t q 2g . vanish. Inserting the remaining parts of Eq. Ž6. into Eq. Ž5. leads to a tim e -d e p e n d e n t te rm o f th e fo rm cosw D sinŽ2 b .rv R x sinŽ v R t 1 q g .4 , where D contains all prefactors and the dipolar coupling strength Žsee Eqs. Ž5. and Ž6... Expanding this into a series of Bessel functions w26x, we obtain cos
D sin Ž 2 b .
vR
s J0
ž
sin Ž v R t 1 q g .
D sin Ž 2 b .
vR
`
/
q2
Ý J2 k ks1
=cos Ž 2 k v R t 1 q 2 kg . ,
ž
D sin Ž 2 b .
vR
/ Ž 7.
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
where Jn denotes Bessel functions of nth order. This allows us to write the TQ signal in closed form
½ ž
S TQ Ž t 1 ;t 2 s 0 . A 1 y J0
D sin Ž 2 b .
vR
`
y2
Ý J2 k ks1
ž
/
D sin Ž 2 b .
vR
=cos Ž 2 k v R t 1 q 2 kg .
½ ž
= 1 y J0
D sin Ž 2 b .
vR
`
y2
Ý J2 k ks1
ž
D sin Ž 2 b .
vR
5
=cos Ž 2 kg . .
threefold symmetry axis of the CH 3 group interacting with the methyl spin-1r2-triad. The perturbing dipolar interaction introduced by this additional spin is motionally averaged by the methyl protons rotating about their symmetry axis. Therefore, it is given by
/ 3 yH s v CH D
5 /
4p 1 2
Ž 8.
Thus, eÕen order TQ spinning sidebands only occur for each single crystallite. As in SQ MAS spectroscopy in powders, absorptive lines are observed by integration over g . For all MAS regimes, the TQ signal intensity is concentrated in a strong centerband. In the slow MAS regime, i.e. v D rv R 4 1, the spectra show many rotational sidebands of low intensity. With increasing v R , the intensity is concentrated in the central frequency-range of the spectrum and the number of spinning-sidebands is reduced. When preceding towards the limit of fast rotation, i.e. v D rv R < 1, the TQ spectra show spinning-sidebands with an overall pattern not very sensitive to the ratio v D rv R . Contrary to SQ spectra, however, the integral intensity of TQ spectra decreases rapidly for v D rv R ™ 0, because the TQ excitation time t becomes shorter Žt s t R r2 ™ 0. and more and more insufficient to build up TQ coherences. 2.4. Influence of surrounding spins So far, our analytical considerations were limited to isolated spin-1r2-triads. In real spin systems, we will hardly find methyl groups completely isolated from any dipolar interaction with surrounding spins. In order to mimic dipolar coupling to remote nuclei, we add one further identical spin located on the
"g 12H
m0
=
/
53
2 d 2 q Ž r HH r3 .
ž
3 1q
2 r HH
3d 2
3r2
y1
/
y1 ,
Ž 9.
where d is the distance between the additional spin and the center of the CH 3 triad. In our numerical spin-dynamics simulations, RFpulses and dipolar interactions act on the spin system according to the pulse sequence given in Fig. 1b. The time axis is divided into propagation periods D t, sufficiently short to restrict calculations to the time independent part of the interactions: UŽ t, t q D t . s expŽyi HD t . with an effective, time independent Hamiltonian H valid during D t. For each period D t a propagator U is evaluated and applied sequentially on the spin system. A more detailed description of the simulation procedure will be given elsewhere w27x. In the spin system considered here, TQ coherences among methyl protons are no longer TSC and, therefore, evolve due to the additional spin during t1. This results in a different intensity distribution in the sideband pattern compared to the isolated CH 3 case. Moreover, in the excitation period, a fourth spin enables spin-cluster growth and build-up of higher order coherences, depending on the product of the strength of the interaction and the time it acts on the system. A weak additional coupling is, therefore, expected to affect first the sideband pattern of the spectrum by TQ evolution during t1 leaving the overall TQ intensity rather unchanged, because t1 is longer by a factor of 10 to 100 compared to the excitation period t . With increasing coupling strength to the fourth spin the changes of the sideband patterns are expected to be accompanied by a significant reduction of TQ intensity.
54
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
Fig. 3. Ža. TQ spinning-sideband patterns of methyl protons perturbed by a fourth proton at a MAS frequency of v R r2p s 14.3 kHz. The intra-methyl proton–proton distance is set to 0.19 nm, d denotes the distance between the fourth spin and center of the methyl group. Žb. Relative intensities of the peaks in the simulated spectra given in Ža.. For weak perturbations, the integral TQ intensity is rather constant, only the pattern shows the characteristic growth of first order sidebands. For stronger dipolar perturbations, the pattern is massively changed, higher order sidebands begin to arise and the integral TQ intensity decreases because four-quantum coherences involving the fourth spin are built up.
Indeed, these features of TQ spectra are borne out by the simulations. Fig. 3a shows TQ MAS spectra Ž v R r2p s 14.3 kHz. of methyl-groups with an intra-methyl proton–proton distance of r HH s 0.19 nm, perturbed by a fourth spin at a distance d from the center of the CH 3-proton triangle. With increasing dipolar coupling strength, the presence of a fourth spin leads to growing signals at frequencies in the spectrum, where no intensity is expected for unperturbed TSC and t s 1r2t R , especially at "v R r2p Žcf. Eq. Ž8... For weak perturbations with 3 yH - 1 v , signal intensity is transferred mainly v CH D D 3 from the centerband and second order sidebands to first order sidebands, leaving the overall TQ intensity and the relative intensities of the ‘‘genuine’’ TSC3 yH ) pattern almost unaffected Žcf. Fig. 3b.. For v CH D 1 3 v D , corresponding to d - 0.30 nm, the loss of integral TQ intensity indicates that the fourth spin is also increasingly involved during the excitation period leading to massive changes in the sideband pattern and, additionally, to TQ coherences including the fourth spin. The perturbing interaction strength of 3 yH f 1 v v CH D D can be roughly identified with a TQ 3
MAS spectrum in which first- and second-order sidebands are of equal intensity. A more precise evaluation with respect to more extended dipolar coupling networks requires chemical shifts, angular dependencies, and, of course, all contributing dipolar couplings to be considered in the spin-dynamics simulations. However, even for more complicated systems, the characteristic features of TQ MAS spectra are similar to those calculated for this simple four-spin topology, in which the fourth spin is then viewed to as mimicing the perturbing influences of the surroundings on the methyl-group. A detailed consideration of particular influences, however, leads to minor modifications of the general effects shown here w27x. 3. Experimental The experiments were performed on a Bruker ASX 500 NMR spectrometer, operating at a 1 H frequency of 500.13 MHz. TQ coherences were excited with the five-pulse sequence shown in Fig. 1b, using a 908 pulse length of about 3 ms. TQ coher-
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
ences were selected by cycling the phases of the excitation pulses relative to the reconversion pulses in steps of 608 and adding the signals of six successive scans with alternating signs. The excitation delay was chosen to be t s prv R , i.e. t s 35 ms for a rotor frequency v R r2p s 14.3 kHz. The 2D experiments are performed with a t 1-increment of about 3 ms, including TPPI. Commercial polycrystalline dimethylglyoxime Žhereafter DMG. was used without further purification. In order to reduce the dipolar coupling amongst protons, in a second sample the OH-groups in dimethylglyoxime were deuterated Žd OH -DMG. by dissolving the compound in d 1-ethanol. After evaporation of the solvent the procedure was repeated three times. The degree of deuteration was about 95%. Largely isolated molecules of acetonitrile in the cavities of deuterated hydroquinone Žhydroquinone-acetonitrile Ž3:1. clathrate, hereafter ANC. were prepared by H. Zimmermann at the Max Planck-Institut fur ¨ Medizinische Forschung in Heidelberg. For perdeuteration, 1,4-hydroquinone-d 4 was recrystallized several times using d 1-ethanol and, after that, dissolved in acetonitrile. Slow evaporation of the solvent gave crystals of the clathrate. The degree of deuteration was about 95% at the aromatic positions and about 80% at OH as measured from the NMR absorption spectra, because the OD groups are subjected to back exchange when exposed to air. These samples were chosen to provide methylgroups in surroundings with different dipolar interactions. In ANC, the methyl-groups of acetonitrile are separated from each other by 0.7 nm w28x. In our case, we had to expect some residual 1 H– 1 H couplings to the matrix, because 20% of the OH-groups of the host-molecule were still protonated. In d OH DMG, inter-methyl dipolar couplings are possible. In case of protonated OH-groups ŽDMG., there are additional 1 H– 1 H dipolar interactions between CH 3and OH-groups w29x. Bisphenol-A-polycarbonate Žhereafter PC., finally, provides methyl groups in a surrounding without structural separation or dilution of the dipolar coupling network. 4. Results and discussion In the following, 1 H TQ MAS spectra shall be discussed first with respect to TQ intensities at dif-
55
ferent resonance positions indicating respective TQ coherences and, therefore, sufficiently strong dipolar connectivities between defined triads of protons. Then, we will focus on characteristic spinning-sideband patterns of TQ MAS spectra including methyl groups. 4.1. Proton connectiÕities by TQ NMR spectroscopy In order to achieve information on dipolar connectivities manifested in TQ coherences, we have to consider TQ intensities in 2D high-resolution spectra which are, in principle, structured in the same manner as 2D DQ spectra published previously w6–13,15x. For this purpose, MQ intensities, in general, have to be integrated over their spinning-sideband patterns to avoid distortions due to different frequency distributions. In TQ MAS spectra, however, the signal is largely concentrated in the centerband Žcf. Fig. 2., so that one can focus on the central region of the 2D spectrum as a good approximation. The central regions of 1 H TQ high-resolution spectra of DMG and d OH -DMG are presented in Fig. 4a and b, respectively. For the fully protonated compound dipolar connectivities lead to three of four possible spin-triples producing TQ coherences Žcf. Fig. 4a.: AAA, AAB, and ABB with A s CH 3-proton and B s OH-proton. A highly intense AAA peak from strong intra-methyl 1 H– 1 H couplings with r HH f 0.19 nm is obvious. All ‘‘mixed’’ coherences are excited with lower efficiency because the shortest proton–proton distances between different functional groups are above 0.2 nm w28x. TQ coherences between OH protons only ŽBBB. are not excited under our experimental conditions because further OHgroups are spaced from BB-pairs by more than 0.4 nm. If the OH-groups are deuterated, only intramethyl TQ coherences are detected as it is evident from Fig. 4b. The functional group connectivities through space are also revealed by the 2D TQ spectrum of PC Žcf. Fig. 4c. showing all four possible spin-triples: TQ coherences involving methyl protons only ŽAAA., phenylene protons only ŽBBB. and those involving protons from both groups ŽAAB and ABB.. The 1 H TQ spectrum of ANC Žnot shown. shows only one peak, which stems from the methyl protons.
56
U. Friedrich et al.r Chemical Physics Letters 285 (1998) 49–58
are too weak to excite a detectable ‘‘mixed’’ TQ signal. 4.2. Triple-quantum spinning-sideband patterns for methyl groups Slices of 1 H TQ MAS spectra at the CH 3 proton resonance are presented in Fig. 5 for different compounds. The respective 2D spectra were recorded at room temperature and a MAS frequency of 14.3 kHz. For PC Žcf. Fig. 5a., DMG Žcf. Fig. 5b. and d OH -DMG Žcf. Fig. 5c. the patterns are characterized by intense spinning-sidebands present at "v R r2p and "2 v R r2p as predicted from our simulations for a four-spin system, in which the fourth spin
Fig. 4. 2D high-resolution 1 H TQ spectra recorded using the five-pulse sequence of Fig. 1b with t s 35 ms, i.e. half of the rotor period Ž v R r2p s14.3 kHz.. Ža. For dimethylglyoxime, AAA, AAB and ABB TQ coherences are generated ŽA s methyl– proton, BsOH–proton.. Žb. For OH-deuterated dimethylglyoxime, the AAA TQ peak originating from methyl protons only is solely detected. Žc. For bisphenol-A-polycarbonate, all four possible TQ coherences are present. The ABB-peak is missing at the CH 3 Ž s A.-resonance due to strong dipolar interactions between the TQ coherence and the two remaining CH 3 -protons. The spectral intensity of AAA TQ coherences at the aromatic Ž s B. resonance frequency is probably caused by spin-diffusion during t 0 . These effects are considerably reduced at higher MAS rates w27x.
No TQ cross-peaks indicating dipolar connectivities between methyl protons and the partially protonated hydroquinone are detected in our spectra. This indicates that the number of OH protons surrounding CH 3 groups is too small and the dipolar couplings
Fig. 5. Proton TQ spinning-sideband patterns of CH 3 groups in bisphenol-A- polycarbonate Ža.; dimethylglyoxime Žb.; OH-deuterated dimethylglyoxime Žc. and acetonitrile molecules in perdeuterated hydroquinone Žd.. The patterns correspond to slices through the experimental TQ-spectra recorded using the five-pulse sequence with t st R r2 s 35 ms at a rotor frequency v R r2p s 14.3 kHz.
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mimics the interactions perturbing the dominating intra-methyl couplings Žcf. Fig. 3a.. Even in the case of ANC Žcf. Fig. 5d., in which the methyl groups are largely isolated, considerable intensity is observed at "v R , indicating perturbing effects of surrounding spins, i.e. residual OH-protons. However, no TQ coherences involving OH protons could be detected. Hence, dipolar couplings which are too weak to build up TQ coherences are, nevertheless, able to modify the spinning-sideband pattern of other TQ coherences considerably. The reduction of the dipolar coupling to remote spins also significantly narrows the TQ spectral lines. In the slice of the d OH -DMG TQ spectrum Žcf. Fig. 5c., intense first order spinning-sidebands and broadened lines indicate inter-methyl dipolar couplings acting additionally to intra-methyl couplings in agreement with the crystalline structure w28x. Replacing the deuterons on the OH groups by protons ŽDMG, cf. Fig. 5b. leads to ‘‘mixed’’ hydroxylmethyl proton TQ coherences at respective frequencies. Furthermore, the spinning-sideband pattern of the methyl-only TQ coherence is considerably changed compared to the OH deuterated case. As expected from our simulations, the presence of additional strong couplings results in increased first and third order sidebands. The slice of the PC TQ spectrum shows a sideband pattern consisting of three different resonances corresponding to the three possible TQ coherences involving at least one methyl proton ŽAAA, AAB and ABB, cf. Fig. 4c.. The methyl-only pattern is quite similar to that of d OH -DMG indicating a dipolar coupling network of comparable effective strength.
5. Conclusions The possibility of exciting TQ coherences under MAS in dipolar solids will enhance the ability to investigate dipolar connectivities and to obtain structural and molecular dynamic information. The TQ spinning-sideband patterns prove to be sensitive to both the topology of the CH 3 unit itself and, notably, to the perturbing influence of additional spins in the surroundings. Even weak interactions cause characteristic changes in the patterns
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leaving the integral methyl-only TQ intensity essentially unchanged. Thus, TQ patterns of methyl groups can be viewed as sensitive detectors of remote spins. With increasing coupling strengths, TQ coherences involving surrounding spins are excited and can be used to derive dipolar connectivities among proton triads in terms of 2D high-resolution TQ spectroscopy. These techniques allow the handling of methyl groups in solid state NMR and, furthermore, in connection with SQ and DQ MAS NMR spectra, to determine the topology of finite spin-clusters. Hence, TQ spectroscopy and the examination of spin-1r2triads open the field to distance as well as angle determination in non-crystalline solids w27x.
Acknowledgements We would like to thank Prof. U. Haeberlen and H. Zimmermann for providing the dimethylglyoxime and the d 6-hydroquinone-acetonitrile clathrate as well as for stimulating discussions. The authors acknowledge financial support from the Volkswagen-Stiftung and from the Deutsche Forschungsgemeinschaft ŽSFB 262..
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