352 1H
J. Phys. Chem. 1996, 100, 352-356
NOESY NMR on Adsorbed Molecules Uwe Schwerk and Dieter Michel* Fakulta¨ t fu¨ r Physik und Geowissenschaften der UniVersita¨ t Leipzig, Linne´ strasse 5, D-04103 Leipzig, Germany ReceiVed: July 26, 1996; In Final Form: September 26, 1995X
First 1H NOESY NMR investigations on adsorbed molecules are presented. Experiments have been carried out on allyl alcohol adsorbed on NaX zeolite with a loading of approximately four molecules per supercage. By application of magic angle spinning (MAS) on the sealed samples, all five magnetically inequivalent protons could be resolved spectroscopically. 1H MAS NMR spectra in the temperature range from 260 to 420 K are reported. Cross peak and diagonal peak intensities of 2D NOESY spectra at room temperature for different mixing times have been measured. Subsequently the matrix of cross relaxation rates has been obtained by a single least mean square deviation fit to all 2D peak intensities. Errors in the determination of cross relaxation rates are discussed. Selected cross relaxation rates could be interpreted by isotropic reorientation of the allyl group with a correlation time τc ) (6.1 ( 0.4) × 10-9 s at a temperature of 300 K.
Introduction NMR spectroscopy has become a versatile tool for the investigation of the state and dynamical behavior of molecules adsorbed on the surface of porous materials, particularly in zeolites.1 Among the various nuclei used to study adsorbed molecules, protons are especially attractive because of their relatively high sensitivity in NMR experiments. Magnetic susceptibility broadening and relaxation due to paramagnetic impurities in the adsorbent, both of which decrease spectral resolution, have been shown to be canceled by application of the magic angle spinning (MAS) technique and utilization of ultrapure zeolites, respectively.2 Thus, 1H NMR line widths remain determined by the restricted mobility of the adsorbed molecule. Depending on the correlation time τc of molecular reorientation, different types of NMR experiments can be carried out. In the approximate range 10-10 s < τc < 10-7 s favorable conditions for 1H 2D NOESY experiments exist. Similar mobilities can be found for molecules of sufficient size in solution. Here the 1H NOESY method provides the basis for very successful conformational studies especially on biomolecules.3 By using the same experiments and strategies as applied to biomolecules, NOESY experiments can contribute to the study of the dynamics and conformation of adsorbed species. Moreover, molecules adsorbed for example in zeolites are of much smaller size, typically hydrocarbons with up to ten carbon atoms. As a consequence proton NMR spectra are much less crowded, leading to new possibilities in the determination and interpretation of cross relaxation rates in comparison with the situation encountered for biomolecules in solution. Hence, adsorbed molecules are potentially suited as a model system for the refined interpretation of 1H NOESY NMR measurements. For instance, variation of adsorbate, adsorbent, loading, and temperature leaves much choice to the experimentalist for methodical investigations of intra- and intermolecular cross relaxation on simple molecules and the influence of internal motions.
of allyl alcohol (purity > 98%, Fluka Chemie AG) per supercage, the cylindrical sample container has been sealed off in a way which enabled MAS.5 NMR experiments have been carried out on a MSL 500 spectrometer (500 MHz proton resonance frequency; Firma Bruker) under conditions of MAS with rotor frequencies of 4.1 kHz and at variable temperatures. NOESY spectra have been recorded by 256 × 512 time domain points transformed to 512 × 512 points in the 2D spectrum. Time proportional phase incrementation (TPPI) has been used to obtain pure absorption spectra. Suitable phase cycling schemes allowed only zero quantum coherences to survive the mixing period.6 2D peak intensities (peak volumes) have been determined by integration over the corresponding spectral region. Theory In the framework of semiclassical relaxation theory, cross relaxation processes among nuclear spins are described by a linear system of differential equations:
d
has been used as A NaX zeolite prepared by Shdanov et adsorbent. Before adsorption the zeolite has been activated in Vacuo. After being loaded with approximately four molecules
Rij ) Rii )
X
Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-0352$12.00/0
∑j RijIj(t)
(1)
where Ii denotes the deviation of the magnetization of the proton species i from its thermal equilibrium value and Rij are elements of the dynamical matrix R. For a single proton species eq 1 reduces to the description of the usual single-exponential relaxation with R representing the longitudinal relaxation rate. Hence the matrix R can be understood as the generalization of the relaxation rate to the case of a spin system coupled by cross relaxation. The analytical expressions for Rij in the case of dipolar relaxation among protons are based on the Solomon equations for a two-spin system,7 which is generalized to an arbitrary number of participating spins by neglecting cross correlation effects:8,9
Experimental Section al.4
Ii(t) ) -
dt
( )
1 µ0 2 2 γ p [6Jij(2ω0) - Jij(0)]; for i * j 20 4π
( )
1 µ0
(2a)
∑ j*i 20 4π
2
γ2p [6Jij(2ω0) + 3Jij(ω0) + Jij(0)]
© 1996 American Chemical Society
(2b)
1H
NOESY NMR on Adsorbed Molecules
J. Phys. Chem., Vol. 100, No. 1, 1996 353
Here γ and ω0 are the gyromagnetic ratio and the Larmor frequency of the proton spin, respectively. Jij(ω) denotes the generalized spectral density, which characterizes the stochastic time dependence of the vector brij connecting spins i and j. In the simplest case of a fixed distance rij and an isotropic reorientation of brij with a correlation time τc, the generalized spectral density is given by
Jij(ω) )
2τc 1 6 rij 1 + ω2τ2c
(3)
More complex motional models lead to different expressions for Jij(ω)8,10-12 but do not affect the expressions in eq 2. Incorporation of cross correlation results in the necessity to include additional intensities Ik representing multiple spin magnetizations in eq 1 but leaves cross relaxation rates between single spin magnetizations (eq 2) unchanged.8 Cross relaxation rates among all longitudinal (single and multiple) spin magnetizations of a three-spin system caused by dipolar interaction and chemical shift anisotropy have recently been reported by Chaudhry et al.13 The analytical expressions given in ref 13 indicate a dominance of cross relaxation among single-spin magnetizations in a proton spin system for low molecular mobility (ω0τc > 1) since (i) the corresponding rates Rij are the only ones containing a generalized spectral density at zero frequency Jij(0) and (ii) chemical shift anisotropy can be considered to be small compared to dipolar interactions. Therefore we will neglect cross correlation henceforth. Dipolar interaction is the dominant interaction between proton spins (besides negligible scalar J coupling) and thus the only possible contribution to cross relaxation rates Rij. Other relaxation mechanisms, such as originating from paramagnetic impurities or proton chemical shift anisotropy, only affect diagonal elements of R. They can be included in eq 2 by adding an ‘external’ relaxation rate Riext to each diagonal element Rii. Magnetically equivalent protons, frequently occurring in methyl and methylene groups, can be adequately represented by a single index, in which case eq 2 is slightly modified.14 The experimental observation of the matrix R is possible by 1H NOESY NMR spectroscopy. The integrated peak volumes Nij(τ) of a two-dimensional NOESY spectrum with a mixing time τ form the intensity matrix N(τ), which is given by14,15
N(τ) ) [exp(Rτ)]N(0)
(4)
N(0) corresponds to the NOESY spectrum with vanishing mixing period: its diagonal elements Nii(0) contain the magnetizations Ii at the beginning of the mixing period, while all off diagonal elements are zero. To extract Rij from the NOESY spectra, different strategies are possible. If all peak intensities Nij (including diagonal peaks) for two different mixing times are known with sufficient accuracy, R can be calculated by using the matrix logarithm:15,16
R)
1 log[N(τ1) N-1(τ0)] τ1 - τ0
(5)
In case N(τ) has been determined for a series of different mixing times τ, eq 4 can be used to fit R to all Nsin complete analogy to a single-exponential fit of longitudinal relaxation data. A less rigorous approach is needed if some Nij are inaccessible to quantitative measurements, as is often the case for diagonal peak intensities Nii in NOESY spectra of biomolecules. The experimental determination of R as described above is not possible anymore, and the Nij(τ) have to be interpreted directly. In contrast to the entry in the cross relaxation matrix Rij, each
Figure 1. Temperature dependence of 1H NMR spectra of allyl alcohol adsorbed on NaX. One conformer (sp, sc) of allyl alcohol is sketched on top. Peak assignment is indicated on the room temperature spectrum.
Nij(τ) is, however, affected by all spins and not only by the pair of spins i and j. Interpretation of Nij(τ) is usually done by changing the parameters characterizing conformation and dynamics of a hypothetical molecule until maximum agreement between the corresponding simulated (eqs 1-3) and the experimentally obtained cross peak intensities is reached (full matrix approach).3,17-19 Thus, a model for the conformation and dynamics of the complete molecule is necessary in order to interpret the Nij(τ). From this point of view the interpretation of Rij is much easier, since only a model of the time dependence of the distance vector connecting protons i and j is required. Hence, the determination of R amounts to a decomposition of the relaxation network and, therefore, serves as a convenient intermediate step between the determination of NOESY cross peak intensities and their interpretation in terms of model parameters. For NOESY applications on adsorbed molecules this can prove especially useful. Results and Discussion 1H
NMR spectra of allyl alcohol adsorbed on NaX zeolite are shown in Figure 1. At room temperature all five magnetically inequivalent protons in the molecule are resolved. Individual peaks have been assigned by comparison with spectra of liquid allyl alcohol. The position of the OH peak shifts upfield with increasing temperature. While strong line overlap dominates the appearance of the spectrum at 260 K, 1H NMR line widths are reduced with increasing molecular mobility at higher temperatures. Line splitting caused by the strongest proton J couplings can already be observed at 300 K. NOESY spectra have been taken at temperatures of 300 and 370 K (Figure 2), where the hydroxyl group is only to a small
354 J. Phys. Chem., Vol. 100, No. 1, 1996
Schwerk and Michel
Figure 3. Mixing time dependence of NOESY peak intensities at 300 K. Proton labels are indicated at the bottom and left margin of the 5 × 5 ‘matrix’. Each entry represents the mixing time dependence of the corresponding 2D NOESY intensity. A coordinate system has been sketched for N23(τ). The vertical scale for diagonal entries Nii is scaled by a factor of 4 compared to that for off diagonal entries. The closest fit with a cross relaxation rate matrix (which is Rex(300 K) given in the text) is marked by a solid line.
Since all magnetically inequivalent protons are spectroscopically resolved, the mixing time variation of the NOESY peak volumes can be interpreted directly with eq 4. A nonlinear fit procedure20 has been used to find a matrix Rex, the exponential evolution (eq 3) of which shows the minimum quadratic deviation from the experimental data (Figure 3). The symmetry condition njRexij ) niRexji (nk is the number of magnetically equivalent spins in position k)14 reduces the number of independent parameters from 25 to 15. For both temperatures the nonlinear fit procedure led to a unique matrix Rex for a broad range of different starting matrices. Deviations of experimental intensities and their best matrix fit mostly remain within the limits of experimental error (Figure 3). The matrices obtained are
Figure 2. 1H NOESY NMR spectra of adsorbed allyl alcohol: (a, top) T ) 300 K, τ ) 80 ms; (b, bottom) T ) 370 K, τ ) 400 ms.
extent overlapped with other proton lines. Two-dimensional line shapes reveal a prevailing homogeneous line broadening. The determination of 2D peak volumes is possible by integrating the intensity over appropriately chosen rectangular areas in the 2D spectrum. A mixing time variation including five (at T ) 300 K) and three (at T ) 370 K) different nonzero mixing times τ has been recorded. To obtain a convenient representation, all peak volumes have been arranged in a matrix each entry of which is a plot of the time dependence of the corresponding 2D peak intensity (Figure 3). For vanishing mixing time only diagonal peak intensities Nii(0) differ from zero. In order to obtain their relatiVe intensities a one dimensional single-pulse proton spectrum has been taken with the same repetition time as the NOESY spectra. The integrated 1D intensities correspond to the intensities present at the beginning of the mixing period for a vanishing preparation time (t1 ) 0 in the F1 time domain) and hence to the 2D peak volumes for vanishing mixing time. To achieve the proper absolute intensity, a single scaling factor is necessary, which was adjusted visually to the data obtained from the 2D spectra.
(
H3
H4
H1
H2
H5
) )
-9.5 1.3 1.5 1.7 3.3 H3 1.3 -23.2 4.4 0.4 7.3 H4 Rex(300 K) ) 1.5 4.4 -14.1 8.6 0.5 s-1H1 1.7 0.4 8.6 -14.0 0.1 H2 6.6 14.7 1.0 0.3 -17.9 H5 and
Rex(370 K) )
(
H3
H1
H4
H2
H5
-0.93 0.11 0.11 0.13 0.20 H3 0.11 -1.20 0.34 0.55 0.07 H1 -1 4 0.11 0.34 -1.84 0.08 0.64 s H 0.13 0.55 0.08 -1.27 0.06 H2 0.39 0.14 1.27 0.11 -1.76 H5
Rows and columns are labeled with the corresponding protons (compare Figure 1). Note that the indices always refer to proton labels and not to the position in the matrices given here. The latter has been chosen to match the appearance of the 2D NOESY spectra.
1H
NOESY NMR on Adsorbed Molecules
J. Phys. Chem., Vol. 100, No. 1, 1996 355
TABLE 1: Relaxation Matrix Entries and Corresponding Interproton Distances for the Allyl Group As Determined Experimentally for 300 K and Evaluated by Model Calculations H1-H2
proton pair R ij(τc ) 6.06 × 10 rmodij Rexij (300 K) ∆Rexij rexij rexij ( ∆rexij( mod
-9
s) 8.6 s 1.86 Å 8. 6 s-1 1.1 s-1 1.86 Å 1.82-1.90 Å -1
H1-H3
H2-H3
0.41 s 3.09 Å 1.5 s-1 1.1 s-1 2.66 Å 2.27-3.10 Å
1.53 s-1 2.48 Å 1.7 s-1 1.1 s-1 2.44 Å 2.24-2.90 Å
-1
Until now no assumptions concerning the conformation and dynamics of the molecule have been necessary except some rather general implications ensuring the validity of eq 1. However, models have to be used for the interpretation of entries in Rex. Off diagonal entries Rexij are affected exclusively by the position and motion of spins i and j. Most suitable for interpretation are elements Rexij for i, j ) 1-3, since the allyl group can be approximated to be rigid.23 Further we assume the reorientation of this group to be isotropic and therefore eq 3 to be applicable. The correlation time τc of thermal reorientation remains the only adjustable parameter. Table 1 lists experimental values Rexij and model values Rmodij. Since the highest cross relaxation rate is least influenced by errors, the correlation time τc has been determined by matching values for Rex12 and Rmod12. For room temperature we find τc ) 6.1 × 10-9 s. Thus, NOESY experiments at a single temperature allow the determination of the molecular mobility of adsorbed species. Conventionally this information is obtained from diagonal elements in R, for instance as in the full relaxation analysis based on the temperature dependence of longitudinal relaxation times T1.21 Although easier to measure, longitudinal relaxation times in many cases can be defined only by neglecting cross relaxation. Additionally, they may be affected by all and not just a selected pair of spins (eq 2) and by external relaxation such as relaxation due to paramagnetic impurities. Determination of off diagonal elements in R is more sophisticated; their definition, however, is well founded and their physical interpretation straightforward. The latter is based on the fact that only direct interactions between two spins may give rise to direct magnetization transfer. Therefore, only internuclear dipolar interactions have to be taken into account, leading to a simple and unambiguous interpretation of cross relaxation rates (eq 2a). We therefore think the determination and interpretation of cross relaxation rates to be a valuable extension in the capabilities of NMR to investigate molecular mobilities. The two remaining experimentally obtained cross relaxation rates within the allyl group have to follow the same model and correlation time. Hence, they can be translated into internuclear distances rexij, which can be compared to distances rmodij taken from ref 23. While the experimental cross relaxation rate for proton pair 2-3 shows good agreement with the model value, for proton pair 1-3, with the longest internuclear distance, a deviation by a factor of almost four is observed (Table 1). Due to the inverse sixth power dependence of the cross relaxation rate on the internuclear distance r13 (eq 3), the experimental and model values for r13 differ only by less than 20%. To specify the accuracy of the experimental cross relaxation rates Rij, an analysis of the error propagation from the 2D peak volumes Nij(τ) into the rates Rij is necessary. An adequate treatment of this problem has recently been given by Macura.22 He assumes equal and uncorrelated volume errors ∆Nij ) ∆a. Errors in the cross relaxation rates are characterized by the relative error propagator ij defined by ij∆a )∆Rij/Rij. On the basis of eq 5 with N(τ0) being the unity matrix, Macura derives
Figure 4. Relative error propagator ij for the proton pairs of the allyl group calculated using the experimental and the model values for R. Optimum mixing times, corresponding to the smallest experimental error, range from 50 to 100 ms. The presence of more protons (six compared to three for the model matrix) leads to an increase of relative error rates calculated with the experimental matrix and a shortening of the optimum mixing time.
an analytical expression for ij which depends on the mixing time τ and the cross relaxation network, characterized by the matrix R. The relative error propagator ij for the allyl group obtained with the experimental as well as with the model values of Rij is depicted in Figure 4 for varying mixing time. As has already been pointed out by Macura for model geometries, error propagation within the cross relaxation network leads to highly inaccurate values for small cross relaxation rates (such as R13) due to the presence of high rates (R12). Absolute errors ∆Rexij, determined according to Macura with the experimental matrix Rex(300 K) for a mixing time of τ ) 50 ms, and the corresponding error limits for the distance rexij ( ∆rexij( are included in Table 1. On the basis of ∆Rex12 the error for the correlation time τc has been estimated to be ∆τc ) 0.4 × 10-9 s. Due to the determination of R by a fit to a whole mixing time dependence, the real experimental error of the relaxation rates Rexij is expected to be smaller. Hence, the discrepancy between the R13 values obtained experimentally and with the model cannot only be attributed to experimental errors. Some other possible explanations are (i) contributions from intermolecular cross relaxation, (ii) a change of molecular geometry due to adsorption of the molecule, or (iii) invalidity of the chosen model assuming the isotropic tumbling of a rigid molecular fragment. Measurements on a system with smaller loading to estimate influences of intermolecular relaxation are complicated by strong 1H NMR line overlapping due to modified 1H NMR chemical shifts. Considering variations of internuclear distances or models describing anisotropic reorientation will introduce new parameters, the determination of which can in our opinion not be accomplished at the present stage considering accuracy and availability of experimental data. Additional difficulties obstruct the interpretation of the remaining cross relaxation rates. Two conformers of allyl alcohol coexist at 300 K in the liquid state.23 Their interconversion, which is fast on the NMR time scale, leads to time dependent internuclear distances. For adsorbed allyl alcohol the situation is expected to be even more complex. A meaningful modeling of the behavior of allyl alcohol adsorbed in NaX and thus an interpretation of the remaining off diagonal entries in Rex therefore requires inclusion of internal motions and is outside the scope of this publication.
356 J. Phys. Chem., Vol. 100, No. 1, 1996 Conclusions We demonstrated the possibility of 1H NOESY NMR experiments on adsorbed molecules by presenting NOESY spectra of allyl alcohol adsorbed on NaX recorded for different mixing times. The simplicity of the spectra compared to NOESY spectra of biomolecules allowed the determination of the cross relaxation rate matrix by a direct fit to the mixing time dependence of 2D peak volumes. Errors in the values for individual cross relaxation rates have been estimated. Selected cross relaxation rates have been interpreted in terms of molecular mobility and internuclear distances, suggesting a correlation time for isotropic reorientation of the allyl group of τc ) (6.1 ( 0.4) × 10-9 s at 300 K. Acknowledgment. This work was supported by the Deutsche Forschungsgemeinschaft (SFB 294). References and Notes (1) Engelhardt, G.; Michel, D. High Resolution Solid State NMR of Silicates and Zeolites; John Wiley & Sons: Chichester/New York/Brisbane/ Toronto/Singapore, 1987. (2) Schwerk, U.; Michel, D. Z. Phys. Chem. 1995, 189, 29. (3) Wu¨thrich, K. NMR of Proteins and Nucleic Acids; John Wiley & Sons: Chichester/New York/Brisbane/Toronto/Singapore, 1986. (4) Shdanov, S. P.; Khvoshchov, S. S.; Samulevich, N. N. Synthetic Zeolites; Khimia, Moscow, 1981.
Schwerk and Michel (5) Freude, D.; Hunger, M.; Pfeifer, H. Chem. Phys. Lett. 1982, 91, 307. (6) Ernst, R. R.; Bodenhausen, G.; Wokaun, A. Principles of Nuclear Magnetic Resonance in One and Two Dimensions; Clarendon Press, Oxford, 1987. (7) Solomon, I. Phys. ReV. 1955, 99, 559. (8) Tropp, J. J. Chem. Phys. 1980, 72, 6035. (9) Canet, D.; Robert, J. B. NMR Basic Principles and Progress; Springer Verlag: Berlin/Heidelberg, 1990; Vol. 25, p 45. (10) Woessner, D. E. J. Chem. Phys. 1965, 42 (6), 1855. (11) Woessner, D. E. J. Chem. Phys. 1962, 36 (1), 1. (12) Lipari, G.; Szabo, A. J. Am. Chem. Soc. 1982, 104, 546. (13) Chaudhry, A.; Pereira, J.; Norwood, T. J. J. Magn. Reson. A 1994, 111, 215. (14) Macura, S.; Ernst, R. R. Mol. Phys. 1980, 41, 95. (15) Olejniczak, E. T.; Gampe, R. T.; Fesik, S. W. J. Magn. Reson. 1986, 67, 28. (16) Mirau, P. A. J. Magn. Reson. 1988, 80, 439. (17) Borgias, B. A.; James, T. L. J. Magn. Reson. 1988, 79, 493. (18) Edmondson, S. P. J. Magn. Reson. 1992, 98, 283. (19) Baleja, J. D. J. Magn. Reson. 1992, 96, 619. (20) Press, W. H. Numerical Recipes in Pascal: The Art of Scientific Computing; Cambridge University Press: Cambridge, 1989. (21) Pfeifer, H. NMR Basic Principles and Progress; Springer Verlag: Berlin/Heidelberg/New York, 1972; Vol. 7, p 53. (22) Macura, S. J. Magn. Reson. A 1995, 112, 152. (23) Landolt-Bo¨rnstein New Series II/21; Springer Verlag: Berlin/ Heidelberg/New York/London/Paris/Tokyo, 1992; p 248.
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