7488
J. Phys. Chem. 1994,98, 7488-7491
Monochromatic Nuclear Magnetic Resonance Nutation Spectroscopy: Correlated Fluctuations of Dipolar Couplings and Anisotropic Chemical Shifts in Aromatic Proton Systems R. Konrat,? K. Nutz,* J. Kalchera and H. Sterk'a Institute of Organic and Pharmaceutical Chemistry, Leopold-Franzens University, Innrain 52, A-6020 Innsbruck, Austria, Institute of Organic Chemistry, Karl- Franzens University, Heinrichstrasse 28, A-8010 GRAZ, Austria, and Institute of Theoretical Chemistry, Karl- Franzens University, Mozartgasse 14, A-8010 GRAZ, Austria Received: February 22, 1994; In Final Form: May 23, 1994.
A new method to demonstrate the buildup of longitudinal two-spin order in an AX spin system on account of D-CSA cross-correlation is shown. Two-spin order 21,A Z,X is created by using trains of selective square pulses which nutate only one spin of a two-spin system. Moreover, it is demonstrated, by measuring different aromatic compounds, that aromatic protons are prone to show an anisotropic chemical shift-CSA-term-of roughly 4-8 ppm.
Introduction The effects of cross-correlation between chemical shift anisotropy (CSA) and dipolar coupling (D) have been the subject of detailed investigations over the last three decades.'+ It has been shown that interference terms between the dipolar coupling and the CSA can have significant effects on longitudinal and transverse relaxation or give rise to unusual line shapes.' In the laboratory frame D-CSA cross-correlation leads to a partial conversion of Zeeman order into longitudinal two-spin order. Thus, it was proposed to study this process by double-quantum filtration techniques combined with inversion-recovery or twodimensional exchange spectroscopy (DQF-NOESY).S To improve selectivity and restrict the dissipative evolution of the spin system to certain pathways, a selective spin-locking experiments has been proposed and very successfully applied. Following the idea of spin-locking, we suggest a new technique, which we call a umonochromatic nutation experiment", as an alternative to D-CSA cross-correlation. Although this new method is based on a theoretical concept similar to that of the synchronous nutation9 experiment, it differs significantly from the latter in that only a single spin is nutated selectively and thereby dewupled from its environment. It will be demonstrated that our method is well suited to detect D-CSA cross-correlationeffectsvia the observation of the corresponding longitudinal two-spin order.
Theory For an AX two-spin system in the presence of a radio frequency field selectively applied to, for example, spin A, the coherent Hamiltonian Hah is given by
where QX denotes the offset of nucleus X and Jm is their coupling constant (note that Q* = 0, assuming weak coupling). Provided that the rf amplitude W I = --yB1 >> Jm (rad/s) but still > pi, &,61,pt, the eigenvalues can be further simplified to A,, A, = -1/2[(P, A,,
A4
+ P, + (6, + 6,)) f 2 i q I
= -1/2[(P, + P, - (6, + 61)) f 2 i q I
(7)
In this limit the set of eigenvectors which evolve with exp{-Ad) reduces to
I,, = 1/2(Z+’A + 2Z+’AZzX)
1/ 2 (Z+’A - 21+‘NZx) ZA4 =
1/2(Z-’A - 2Z-’AZ2X)
6.60
These have been expressed in terms of modified (tilted frame) shift operators I*A = ZZA f iZyA and 2 4 A ZZX = 2IzA ZzX f 2iIyAZzX which are eigenoperators of the propagator exp (-iw IxA]. The eigenoperators 1 A 1 and both decay with exp(-1/2(pl (6, al) p,)) while 1 x 3 and Z A decay ~ with exp(-1/2(p1- (6, 6,) +pt )), As we start with a pure longitudinal state at the beginning, u(0) can be formulated in the following way:
+ + + + U(0)
= IzA = 1/2(1Al
+ I,, + 1 ~ +3 1 ~ 4 )= I(0)
I
I
6.46
6.44
(9)
I
I
6.42
6.40
’
6.”
PPH
(8)
Figure3. Two-dimensionalspectrum of Exifone obtained by the sequence in Figure 2,using time-proportional phase increments (TPPI).I2 Thirtytwo experiments were recorded and zero-filled along the tl domain to 5 12 data points. H6 was nutated for 400 ms, and H5 was detected.
(Z2)(t) = exp(R,t) cos(2w1t)
(1 1)
with the decay rates R1 = -1/2(~1+ (bt + 61) + pt) and RZ = -1/2(pl- (St + SI) pt). The time evolution of two-spin order can now be written as
+
Since wI>> p and 6, it is justified to assume the steady statevalues of the density matrix u(=) to be zero. Substituting u(0) back into eq 4 yields a simple time dependence ~ ( t =) exp(-1/2(pl
+ (6, + 6,) + p,)t) [exp(-2iw,tjZAl +
exp(2iqWA21+ e x ~ ( - 1 / 2 ( ~-, (6,+ 61) + p,M X [exp(-2iolt)ZA3 exp(2iw1t)ZA4](10)
+
which describes a damped oscillation of the eigenoperators in the y-r-plane. We define the operators I , = 1 / 4 2 (1x1 + I d and 1 2 = 1 / 4 2 ( Z A ~+ 1~4).Their expectation values are evaluated as (Zl)(t) = exp(Rlt}cos(2wlt)
The difference of the decay rates RI - R2 = 6t + 61 can be seen to be responsible for a buildup and a subsequent decay of twospin order during the nutation period (compare Figure 1). Method and Experiment
Figure 2 shows the pulse sequence. Transverse magnetization Z,A is excited by a self-refocusing 270° Gaussian pulse.1° The evolution under the scalar coupling is refocused by a G3Gaussian cascade11 applied at the chemical shift QA. At the end of the tl-period we thus have pure in-phase magnetization. This transverse magnetization is turned back to the z-axis and
Konrat et al.
7490 The Journal of Physical Chemistry, Vol. 98, No. 31, 1994
I I
6.40
”
”
I
6.30
2dO
40
PPM
Figure 4. Experimental results (2-dimensional)for the aromatic protons H6 (observed) and H5 (nutated) of 2,3,4-trihydroxybenzoicacid. The chemical = 289.8 Hz, and J H ~ =H8.2 ~ Hz. (a) Experimental results for the aromatic protons H4 (observed) and H3 (nutated) shift difference is ASlHSH6/2r of 2-hydroxy-1-naphthaldehyde.(b) The chemical shift difference is AOH’H4/2r = 322.2 Hz, and J W H = ~ 8.7 Hz. For the bars and the right-hand signal; compare Figure 1.
subsequently driven to nutate in the y-z-plane by square pulses. During the nutation period, Zeeman order converts into two-spin order under the influence of D-CSA crosscorrelation. This spin-ordered state can be detected directly by applying a 270° Gaussian pulse to spin X, leading to an antiphase multiplet. The detection of in-phase magnetization of spin X is prevented by cycling the phases of the three Gaussian pulses independently, together with the receiver. There is also the possibility of incrementing tl like a 2-dimensional spectrum (Figure 3), where phase sensitivity is achieved by using timeproportional phase increments (TPPI.)IZ As was shown previously,”” a 2-dimensional presentation is often, via reduction of phasing problems, of advantage. To have at least some very qualitativemeasureof theobtainedeffect, e.g. in the l-dimensional spectra, the peak height of the antiphase signal, obtained by applying a 270° Gaussian pulse and a delay 1/2J, is’shown for comparison. The spectra were acquired on a Bruker AM 360 spectrometer, equipped with a selective excitation unit. The Gaussian pulses were set to a length of 30 ms and an amplitude of 55 Hz; the length of the G3-cascade was 100 ms and its amplitude 24 Hz. The nutation pulses were either 5 or 20 ms long, according to an amplitude of 100 or 25 Hz, respectively.
-1
0
800
11 IO
ms
Figure 5. Simulated time dependency of the longitudinaltwo-spin order (based on the numerical solution of the density matrix); the CSA term is assumed to be 4 ppm. Note that the calculatedtrend is nicely reproduced in Figure 1, 4, and 6 as a sort of envelope.
I
Results To have our method tested, experiments have been performed using a 0.1 M solution of 2,3,4,3’,4’,5/ -hexahydroxybenzophenone (Exifone) in MezSO-d6 (Figure 1 and Figure 6). We employed this molecule since, as it has been reported recently by the group of Bodenhausen,*J3the aromatic protons detectable in Exifone show a reasonable chemical shift anisotropy. In order to show the general applicability of our method, we studied two further compounds, namely 2,3,4-trihydroxybenzoic acid, which is structurally similar to Exifone, and 2-hydroxy-1-naphthaldehyde, which exhibits a totally different structure. Figure 1 and Figure 4 show the magnitude of the longitudinal two-spin order 21,A I,X generated during the nutation pulses. The time dependence of 21,A I,X is obtained by applying a pulse string which consists of an increasing number of pulses. In most cases 16-20 of such “nutation sandwiches” have been used, and their result, which reflects the time-dependent increase and decrease of 21,A I,X, is plotted. From inspection of the data one can unambiguously conclude that all these compounds possess anisotropies of the CSA term of more or less similar strengths (4-8 ppm). To derive a rough estimation of the CSA term, simulations, based on the treatment of the density matrix (exclusively dipolar interactions and rotation in the extreme narrowing limit as well as the axes of the rotational tensor and chemical shift tensor are assumed) and variations of the CSA term strengths, have been done and are compared with the measured values. Thereby, the coherent behavior of the AX spin system is obtained by calculating the influence of square nutation pulses on the density matrix. The relaxation behavior is governed by T ~the , rotational correlation
-li‘ 1
0
I
800
I
1600
ms
Figure 6. Experimental results for the observed aromatic proton H6 and the nutated proton H5 of 2,3,4-3’,4’,5’-hexahydroxybenzophenone
(Exifone), however, yB1 = 25 Hz,corresponding to a 20 ms duration of the square pulse (40-1600 ms (40 echoes)). On the left-hand side, for purposes of comparison,the antiphase signal obtained by applyinga 270’ Gaussian pulse and a 1 / 2 1 delay is shown.
time (for simplicity an isotropic reorientation is assumed), and the interatomic HA-HX distances. In our investigation we adopted corresponding values as given in Ref 13 for Exifone (sC = 500 ps) (Figure 5). It is worth noting that Exifone and 2,3,4trihydroxybenzoic acid for both protons HSand H6 as well as the
Monochromatic NMR Nutation Spectroscopy
The Journal of Physical Chemistry, Vol. 98, No. 31, 1994 7491 frequency(Figure 7). We believe this to becorrect, as thenutation pulses act only on the pure state of Zeeman order and all other effects are refocused by the 180' G3-pulse. The intensity of the line is determined by the sum of the weighting factors Ai,whereas the cross-correlations 6, 6, define the line width according to R1 - R2 = 6t + 61, In principle this offers an additional way to detect a CSA contribution, as the width of such lines are defined by at + 61, whereas a line without a CSA term is defined by 6, solely. Unfortunately, in all compounds under investigation in this study, both aromatic protons possess a reasonable CSA term so that a direct comparison of their line widths is not informative.
+
0.00 0
5
10
Hz Figure 7. Spectrum obtained by Fourier transformation of an interferogram corresponding to the signal intensities shown in Figure 6. There is no scaling of the coupling.
protons H3 and H4 in 2-hydroxy-1-naphthaldehydeshow a CSA term. As the timedependenceis less pronounced for thoseprotons in the neighbourhoodof the carbonylfunction, which is according to our simulations characteristic for a larger CSA term, we argue that H3 in 2-hydroxy-1-naphthaldehydeas well as H6 in Exifone and 2,3,4-trihydroxybenzoic acid shows the stronger CSA term (6-8 ppm). In Figure 6 we show the pattern for the case where yBI >> JAXis not fulfilled. It is seen that now the increase in nutation duration leads to an oscillatory behavior, with respect to both intensity and sign, of the observed antiphase magnetization. The reason for this is that the evolution under the scalar coupling Hamiltonian cannot be completely suppressed,for low amplitudes of the nutation field. Therefore an ideal return to the north pole is prevented, equivalent to a certain loss of z-magnetization. Toobtain greater insight,one can measure the plotted intensities of the antiphase magnetization which are obtained by varying the length of the nutation period stepwise (Figure 7) and treat them like an interferogram. This interferogram can be Fouriertransformed according to
+
S(w) = ~,,4,Re[X,]/(Re2[Xi] im2[A,])
(13)
and leads to a one-dimensionalspectrum. This is to some extent comparable to the 2D solid state nutation spectroscopy developed by Samoson and LippmaaI4where two or four lines are observed. We, however, are only able to detect a single signal at a single
Conclusion The proposed "monochromatic nutation experiment", which is based on selective nutation of a single spin, can be applied very effectively for qualitative characterization of the interference terms between dipolar couplings and anisotropic chemical shifts in homonuclear spin systems. Acknowledgment. We are grateful to G. Bodenhausen for enlightening discussions and many helpful comments. We are indebted to J. M. Maurette (Laboratoire Pharmascience, 92400 Courbevoie-France) for a sample of Exifone, and to L. Werbelow for reading the manuscript.
References and Notes (1) Shimizu, H.J. Chem. Phys. 1964,40,3357. (2) Mackor, E. L.; M s c h n , C. J. Chem. Phys. 1966,44, 64. (3) Goldman, M.J. Magn. Reson. 1984, 60, 437. (4) Jaccard, G.; Wimperis S.;Bodenhausen, G. Chem. P h p . Le??.1987, 138,601. (5) Dalvit, C.; Bodenhausen, G. Chem. Phys. Lett. 1989,161, 554. (6) Khigsberger, E.; Sterk, H. J. Chem. Phys. 1985,83,2723. (7) Konrat, R.;Sterk, H. Chem. Phys. Leu. 1993,203, 75. (8) Burghardt, I.; Konrat, R.; Bodenhausen, G. Mol. Phys. 1992,75, 461. (9) Burghardt, I.; Konrat, R.; Boulat, B.; Vincent, S.; Bodenhausen, G. J. Chem. Phys. 1993,1721,98. (10) Emsley, L.; Bodenhausen, G. J. Magn. Reson. 1989,82, 211. (11) Emsley. L.; Bodenhausen, G. Chem. Phys. Let?. 1990,165, 469. (12)Ernst, R.R.; Bodenhausen, G.; Wokaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions; Clarendon Press: Oxford, u.K., 1987. (13) DiBari, L.; Kowalewski, J.; Bodenhausen, G. J. Chem. Phys. 1990, 93,7698. (14) Samoson, A.; Lippmaa, E. J. Magn. Reson. 1988,79, 255.
