J. Phys. Chem. B 1997, 101, 8955-8958
Characterization of the Two Rubidium Sites in Rb2CrO4 by
87Rb
8955
Single-Crystal NMR
Thomas Vosegaard, Inger P. Byriel, and Hans J. Jakobsen* Instrument Centre for Solid-State NMR Spectroscopy, Department of Chemistry, UniVersity of Aarhus, DK-8000 Aarhus C, Denmark ReceiVed: June 20, 1997X
The two crystallographically distinct sites in Rb2CrO4 are characterized in terms of their 87Rb quadrupole coupling and chemical shielding anisotropy (CSA) interactions employing 87Rb single-crystal NMR. Accurate values for the quadrupole coupling and CSA parameters are reported for both rubidium sites along with the direction cosines describing the orientation of the tensors for the NMR interactions with respect to the Rb2CrO4 crystal frame. The parameters for site 1 represent the first accurate investigation of this site, while the parameters for site 2 compare excellently with those previously reported. Some remarkable similarities are observed between the present parameters for Rb2CrO4 and the 133Cs parameters determined from recent magicangle spinning and single-crystal 133Cs NMR studies for the isomorphous Cs2CrO4.
Introduction Solid-state 87Rb and 133Cs NMR investigations of rubidium and cesium salts have attracted much interest during the past decade. The reason is that these nuclei possess the potential of exhibiting both quadrupole coupling and anisotropic shielding in the solid state. From spectra showing the combined effect of these interactions, not only the magnitudes of the interactions but also the Euler angles describing the orientation between the corresponding two tensors may be determined. Since the parameters for these interactions all serve to characterize the structural and electronic environment of the observed nucleus, solid-state NMR studies capable of providing this information have become increasingly popular. Spin-echo 87Rb NMR of static powders has allowed the determination of small chemical shielding anisotropies (CSAs) from the combined effect of the two interactions on the lineshape for the quadrupolar broadened central (m ) +1/2, -1/2) transition for a number of rubidium salts.1,2 Similarly, magic-angle spinning (MAS) methods have been successfully employed in two cases (RbClO43 and Rb2SO44) to unravel 87Rb parameters for the interactions with high accuracy. Also, experimentally more demanding two-dimensional (2D) NMR methods such as dynamic-angle spinning (DAS; RbClO4, Rb2SO4, and Rb2CrO4),5 switched-angle spinning (SAS; Rb2SO4 and Rb2CrO4),6 and multiple quantum MAS (MQMAS; Rb2CrO4)7 have been applied for determination of the parameters for the two interactions in rubidium salts. Unfortunately, 87Rb quadrupole coupling constants (CQ) may be quite large in many rubidium salts, whereas the CSA is generally small. Thus, for static spinecho 87Rb spectra showing a width for the central transition in excess of about 200 kHz, the effect of a 87Rb CSA may barely be visible. In 87Rb MAS NMR the applied/required spin rate has in many cases a tendency to average the effect of the small CSAs (e.g., for site 1 in Rb2SO4).4,8 In other cases the 87Rb quadrupole couplings are simply too large for the spinning frequency to even approach the width of the second-order quadrupolar-broadened central transition. In such cases the spinning methods generally become useless. For these reasons state-of-the-art single-crystal NMR9 has become a most valuable * To whom correspondence should be addressed: Hans J. Jakobsen, Instrument Centre for Solid-State NMR Spectroscopy, Department of Chemistry, University of Aarhus, DK-8000 C, Denmark. Tel.: +45 8942 3842. Fax: +45 8619 6199. E-mail:
[email protected]. X Abstract published in AdVance ACS Abstracts, October 1, 1997.
S1089-5647(97)02024-5 CCC: $14.00
additional tool in solid-state 87Rb NMR studies of the two interactions.8 With the much smaller quadrupole moment and thus CQ values for the 133Cs spin I ) 7/2 isotope, static10 and MAS11 133Cs NMR of powders as well as 133Cs single-crystal NMR12 have been very succesful in unraveling the quadrupole coupling and CSA interactions in cesium salts. From these studies it appears that the two Cs sites in Cs2CrO4 have by far the largest CQ for one of the sites and the largest CSA for the other site of all cesium salts studied so far. Rb2CrO4 is isomorphous to Cs2CrO4, but in case of 87Rb NMR of Rb2CrO4 only the Rb site with the smallest quadrupole coupling has been studied in detail. Apparently the CQ value for the other site (CQ ≈ 10 MHz)1 is too large to be handled by spinning methods. For this reason, and because it appears of interest to compare data for the 87Rb quadrupole and CSA interactions for the two Rb sites in Rb2CrO4 with those for the corresponding sites in the isomorphous Cs2CrO4, this work reports a 87Rb single-crystal NMR study of Rb2CrO4 and data of high accuracy for both Rb sites. Experimental Section Single crystals of Rb2CrO4 were obtained from an aqueous solution by slow evaporation at room temperature. The singlecrystal 87Rb NMR experiments were performed on a Varian UNITY-400 spectrometer at 130.8 MHz using a homebuilt single-crystal NMR probe equipped with a new goniometer design as recently described elsewhere.9 A single crystal (∼2 × 3 × 4 mm3) was glued onto a dovetail tenon (T) which fits into three mutually perpendicular mortises of the goniometer. This leads to rotations about the -xT, yT, and -zT axis, respectively.9 The probe is fully automated with respect to rotation of the goniometer and is controlled by the SUN Sparc 10/54 workstation of the spectrometer via a homebuilt interface. This ensures a high accuracy ((0.1°) for the angular setting. For each rotational axis 21 spectra were recorded, each following an incrementation in the rotation angle of 9°. A spectral width of 500 kHz, single-pulse excitation (τp ) 2 µs for γB1/2π ≈ 50 kHz), a relaxation delay of 2 s, and a total of 128 scans has been applied for each angular setting. The total acquisition time for the 63 spectra was 5 h. The isotropic chemical shifts are in ppm relative to an external solution of 1.0 M RbNO3. The assignment of the individual resonances in each spectrum, required for the rotation plots, is greatly facilitated by the © 1997 American Chemical Society
8956 J. Phys. Chem. B, Vol. 101, No. 44, 1997
Vosegaard et al.
Figure 1. Single-crystal 87Rb NMR spectra (9.4 T) of the central transition for Rb2CrO4. Spectra were recorded following a 9° increment for the rotation about the (a) -xT, (b) yT, and (c) -zT axis; however, only every second spectrum for these rotations is shown here.
software package ASICS (analysis of single-crystal spectra) developed in our laboratory. Optimized parameters describing the tensorial NMR interactions along with their error-limits, calculated as 95% confidence intervals,13 are automatically obtained by the software. Results and Discussion The single-crystal 87Rb NMR spectra of Rb2CrO4 resulting from rotation about the (a) -xT, (b) yT, and (c) -zT axis are shown in Figure 1. A maximum of four equally intense resonances is observed for the central transitions for each orientation of the crystal in accordance with the existence of four magnetically nonequivalent Rb+ ions for Rb2CrO4.14 The theory necessary for interpretation of these spectra in terms of the quadrupole coupling and anisotropic shielding interactions has been outlined elsewhere8 and only the relevant definitions are stated here for clarity. The quadrupole coupling and CSA interactions are defined by the parameters
CQ ) 1
eQVzz Vyy-Vxx , ηQ ) ; δiso ) h Vzz
/3(δxx + δyy + δzz), δσ ) δiso - δzz, ησ )
δxx-δyy (1) δσ
Q,P and the tensor elements Aσ,P RR ) -δRR and ARR ) eQVRR/2I(2I - 1)h) in the principal axis frame (Pλ) are defined in the order
λ,P 1 λ 1 λ |Aλ,P zz - /3 Tr(A )| g |Axx - /3 Tr(A )| g 1 λ |Aλ,P yy - /3 Tr(A )| (2)
The relative orientation of the CSA and quadrupole coupling tensors follows our earlier definition3,8 and is described by the Euler angles (ψ,χ,ξ). The resonance frequency for the central
transition is given by8 (R) ν1/2,-1/2 (θ) ) A(R) + B(R) cos 2θ + C(R) sin 2θ +
D(R) cos 4θ + E(R) sin 4θ (3) where R ) -xT, yT, and -zT and the coefficients M(R) are functions of the quadrupole-coupling and CSA tensors in the tenon frame according to the expressions given elsewhere.8 A preliminary analysis of the four individual resonances gives two sets of quadrupole coupling and CSA parameters which indicate the presence of only two crystallographically nonequivalent Rb sites. The rotation plots for the experimental resonance frequencies of Rb(1) and Rb(2) are shown in Figures 2 and 3, respectively, where the symbols (4,O) represent the two magnetically nonequivalent Rb+ ions for each site. The solid lines correspond to the optimized quadrupole coupling and CSA parameters and are calculated employing eq 3. The optimized parameters are summarized in Table 1 along with their error limits (95% confidence intervals). Rb2CrO4 has an orthorhombic crystal structure (space group 15 Pmcn (D16 2h, no. 62) ) with two crystallographically distinct Rb sites located in the mirror plane perpendicular to the a axis.14 As usual,3,4,8,10-12 this implies that the quadrupole coupling and CSA tensor for each of the four magnetically nonequivalent Rb+ ions have one principal element parallel to a.16 The direction cosines describing PQ in the tenon frame show that (i) V(i) xx for Rb(1) and Vyy for Rb(2) (i ) 1, 2 represent the two magnetically nonequivalent Rb+ ions of each site) are all parallel and therefore define the orientation of the a axis in the tenon frame. Moreover, the Euler angles (ψ, ξ ≈ 90°, 0°) for Rb(2) show that δxx and Vyy are parallel within the error limits in accordance with the crystal symmetry. For Rb(1) it is found that χ ≈ 0° which implies that only the sum of the two Euler angles ψ and ξ is defined. The requirement of one CSA principal element being parallel to Vxx for this site may be expressed as (ψ + ξ) ) n 90°. An initial optimization gave a result inconsistent with the crystal symmetry, and therefore (ψ
87Rb
Single-Crystal NMR of Rb2CrO4
J. Phys. Chem. B, Vol. 101, No. 44, 1997 8957
TABLE 1: 87Rb Quadrupole Couplings (CQ, ηQ), Chemical Shielding Anisotropies (δσ, ησ), Relative Orientations (ψ, χ, ξ), and Isotropic Chemical Shifts (δiso) for Rb2CrO4 site Rb(1) Rb(2)
CQ (MHz) 9.43 ( 0.06 11.53 3.549 ( 0.014 5.23 3.5 ( 0.2
ηQ 0.700 ( 0.014 0.75 0.362 ( 0.012 0.48 0.3 ( 0.1
δσ (ppm) -80 ( 7 -13.14b 109.7 ( 0.6 149.19b 110 ( 15
ησ 0.19 ( 0.14 0.16 0.037 ( 0.010 0.25 0 ( 0.15
δiso (ppm) -60 ( 3 -52.8 -8.7 ( 0.2 47.4 -7
ψ (deg) a
90 77c 93 ( 11 -37c d
χ (deg) -0.9 ( 1.9 -74c 68.88 ( 0.16 15c 70 ( 5
ξ (deg)
ref
0 0c -0.3 ( 1.6 -28c 0 ( 15
this work 1 this work 1 5
a
a Parameter fixed during optimization (see text). b δ is calculated from ∆σ in ref 1 using the definition δ ) 2/3∆σ. c Euler angles are in σ σ accordance with the definition used in ref 1. d ψ is undefined when ησ ) 0.
Figure 2. Rotation plots for Rb(1) in Rb2CrO4 showing the experimental resonance frequencies for the two magnetically nonequivalent Rb+ ions marked with 4 and O. The solid lines are calculated employing the optimized-quadrupole coupling and CSA parameters. The three rotation plots correspond to rotation about the (a) -xT, (b) yT, and (c) -zT axis.
Figure 3. Rotation plots for Rb(2) in Rb2CrO4 showing the experimental resonance frequencies for the two magnetically nonequivalent Rb+ ions marked with 4 and O. The solid lines are calculated employing the optimized quadrupole-coupling and CSA parameters. The three rotation plots correspond to rotation about the (a) -xT, (b) yT, and (c) -zT axis.
+ ξ) ) 90° has been fixed during the optimization (corresponding to Vxx||δyy) since this gives the best result of the possible values for n. The glide planes (c and n perpendicular to the b and c axis, respectively) of Pmcn relate the two magnetically nonequivalent Rb+ ions for each crystallographic Rb site. The two different tensor orientations for each crystallographic site may therefore be used to determine the orientation of the b and c axis with respect to the tenon frame.8 However, an unambiguous assignment of these two axes is not possible solely from NMR and thus an XRD analysis was performed with the same crystal/tenon setup as for the NMR experiments9 in order to assign the b and c axes. The direction cosines of the quadrupole coupling and CSA principal elements expressed in the crystal frame are given in Table 2. The CSA and quadrupole coupling parameters have been assigned to the four magnetically nonequivalent Rb+ ions by comparing the principal elements of the quadrupole tensor with the EFG tensor elements calculated by an electrostatic point-monopole model.17 This calculation includes oxygen atoms of the first coordination sphere to rubidium where the oxygen charges are calculated from the Cr-O bond valences.18,19 The orientation of PQ and Pσ with respect to the crystal frame is shown in Figure 4 for one of the
two magnetically nonequivalent Rb+ ions of Rb(1) and Rb(2). These Rb+ ions correspond to the symbols O in Figures 2 and 3 and the direction cosines in Table 2. It is noted that the CSA principal elements for the two Rb sites are aligned with the crystal axes as also observed for 87Rb and 133Cs CSA tensors in other rubidium and cesium salts.8,12 The 87Rb quadrupole-coupling and CSA parameters for Rb2CrO4 previously determined from static1 and 2D switched-angle spinning (SAS)6 experiments are listed in Table 1. However, the parameters determined for Rb(1) in this study represent the first proper characterization of this site by its quadrupole coupling and CSA interactions, as other methods have been uncapable of handling the large quadrupole coupling interaction along with the small CSA. The quadrupole coupling constant (CQ ) 9.43 ( 0.06 MHz) for Rb(1) is the largest yet reported for any rubidium salt. The parameters for the two Rb sites reported by Cheng et al.,1 obtained from simultaneous fitting of the two overlapping patterns in a static spectrum, differ significantly from the present data. However, this has recently been accounted for.2 On the other hand, all parameters for Rb(2) determined by Shore et al.6 are in excellent agreement with the present single-crystal NMR results. Moreover, employing
8958 J. Phys. Chem. B, Vol. 101, No. 44, 1997
Vosegaard et al.
TABLE 2: Direction Cosines for the Principal Elements of the Quadrupole Coupling and CSA Tensors for the Two Rb Sites in Rb2CrO4a a
b
c
0.000 0.993 0.120 -0.994 -0.001 0.109
0.004 0.120 -0.993 -0.109 0.015 -0.994
0.363 -0.001 0.932 0.046 -0.999 -0.003
0.932 0.008 -0.363 0.003 0.003 -1.000
Rb(1) Vxx Vyy Vzz δxx δyy δzz
-1.000 0.004 -0.004 -0.004 -1.000 -0.014
Vxx Vyy Vzz δxx δyy δzz
-0.006 1.000 0.007 0.999 0.043 0.004
Rb(2)
a The direction cosines correspond to the magnetically nonequivalent ions represented by the symbol (O) in Figures 2 and 3 and are illustrated in Figure 4.
of the 133Cs quadrupole couplings for Cs2CrO4 are about a factor of 30 smaller than the corresponding 87Rb quadrupole couplings in Rb2CrO4. The ratios CQ(site 1)/CQ(site 2) ≈ 2.6 and δσ(site 1)/δσ(site 2) ≈ -0.73 are found for both compounds. However, it has earlier been noted11 that the assignment for the two sites is reversed in the 133Cs single-crystal study of Cs2CrO4.12 The asymmetry parameters and relative orientations of the CSA and quadrupole coupling tensors are also similar for the Rb2CrO4 and Cs2CrO4 (e.g., the 87Rb and 133Cs CSA tensors for site 2 are nearly axially symmetric, and for site 1 the unique principal elements Vzz and δzz are almost parallel). Conclusion Parameters for the 87Rb quadrupole coupling and CSA have been determined for the two crystallographically distinct Rb sites in Rb2CrO4 with high accuracy from 87Rb single-crystal NMR. For Rb(1) this study presents the first reliable parameters for this site, and thus demonstrates the high-resolution excellence of single-crystal NMR when powder methods (spinning and static) fail for different reasons. Remarkable similarities are found for the EFG and CSA tensors of the two Rb sites and the corresponding Cs sites in the isomorphous Cs2CrO4. Acknowledgment. The use of facilities at the Instrument Centre for Solid-State NMR Spectroscopy, University of Aarhus, sponsored by the Danish Research Councils (SNF and STVF), Teknologistyrelsen, Carlsbergfondet, and Direktør Ib Henriksens Fond, is acknowledged. We thank Aarhus University Research Foundation for equipment grants. References and Notes
Figure 4. Projection of the crystal structure of Rb2CrO4 onto the bc plane (i.e., the mirror plane in which the Rb+ ions are located coincides with the plane of the paper) for illustration of the orientation of the quadrupole-coupling and CSA principal elements for Rb(1) and Rb(2) with respect to the crystal frame. For each site the principal elements are shown only for the magnetically nonequivalent Rb+ ions which correspond to the symbol (O) in Figures 2 and 3 and the direction cosines in Table 2.
DAS NMR Baltisberger et al.5 reported a value CQ(1 + η2Q/3)1/2 ) 3.3 ( 0.3 MHz for the second-order quadrupole effect (SOQE) parameter for Rb(2) which is in agreement with the value (3.63 ( 0.03 MHz) calculated from the parameters determined in this study. Most recently the CSA parameters (δσ ) 110 ppm, ησ ) 0.0) have been determined for Rb(2) from the spinning sideband intensities in the ω1 dimension of a 2D MQMAS experiment.7 These values are in excellent agreement with the parameters resulting from this study. Rb2CrO4 is isomorphous to Cs2CrO4,14,20 and therefore some similarities for the EFG and CSA tensors are expected for these two compounds. Comparison of the present values for the 87Rb quadrupole coupling and CSA tensors of Rb2CrO4 with recent MAS11 and single-crystal12 133Cs NMR studies of Cs2CrO4 shows remarkable similarities although the magnitudes
(1) Cheng, J. T.; Edwards, J. C.; Ellis, P. D. J. Phys. Chem. 1990, 94, 553. (2) Koons, J. M.; Hughes, E.; Cho, H. M.; Ellis, P. D. J. Magn. Reson. 1995, A114, 12. (3) Vosegaard, T.; Skibsted, J.; Bildsøe, H.; Jakobsen, H. J. J. Phys. Chem. 1995, 99, 10731. (4) Fernandez, C.; Amoureux, J. P.; Bodart, P.; Maijanen, A. J. Magn. Reson. 1995, A113, 205. (5) Baltisberger, J. H.; Gann, S. L.; Wooten, E. W.; Chang, T. H.; Mueller, K. T.; Pines, A. J. Am. Chem. Soc. 1992, 114, 7489. (6) Shore, J. S.; Wang, S. H.; Taylor, R. E.; Bell, A. T.; Pines, A. J. Chem. Phys. 1996, 105, 9412. (7) Wang, S. H.; Xu, Z.; Baltisberger, J. H.; Bull, L. M.; Stebbins, J. F.; Pines, A. Solid State Nucl. Magn. Reson. 1997, 8, 1. (8) Vosegaard, T.; Skibsted, J.; Bildsøe, H.; Jakobsen, H. J. J. Magn. Reson. 1996, A122, 111. (9) Vosegaard, T.; Langer, V.; Daugaard, P.; Hald, E.; Bildsøe, H.; Jakobsen, H. J. ReV. Sci. Instrum. 1996, 67, 2130. (10) Power, W. P.; Wasylishen, R. E.; Mooibroek, S.; Pettitt, B. A.; Danchura, W. J. Phys. Chem. 1990, 94, 591. (11) Skibsted, J.; Vosegaard, T.; Bildsøe, H.; Jakobsen, H. J. J. Phys. Chem. 1996, 100, 14872. (12) Power, W. P.; Mooibroek, S.; Wasylishen, R. E.; Cameron, T. S. J. Phys. Chem. 1994, 98, 1552. (13) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Wetterling, W. T. Numerical Recipes; Cambridge University Press: Cambridge, 1989; Chapter 14.5. (14) Smith, Jr., H. W.; Colby, M. Y. Z. Kristallogr. 1940, 103, 90. (15) International Tables for Crystallography; Hahn, T. D., Ed., Reidel Publishing Company: Dodrecht, Holland, 1983; Vol. A, p 288. (16) Weil, J. A.; Buch, T.; Clapp, J. E. AdV. Magn. Reson. 1973, 8, 183. (17) Koller, H.; Englehardt, G.; Kentgens, A. P. M.; Sauer, J. J. Phys. Chem. 1994, 98, 1544. (18) Brown, I. D.; Shannon, R. D. Acta Crystallogr. 1973, A29, 266. (19) Brown, I. D.; Altermatt, D. Acta Crystallogr. 1985, B41, 244. (20) Morris, A. J.; Kennard, C. H. L.; Moore, F. H.; Smith, G.; Montgomery, H. Cryst. Struct. Comm. 1981, 10, 529.
