14872
J. Phys. Chem. 1996, 100, 14872-14881
133Cs
Chemical Shielding Anisotropies and Quadrupole Couplings from Magic-Angle Spinning NMR of Cesium Salts† Jørgen Skibsted, Thomas Vosegaard, Henrik Bildsøe, and Hans J. Jakobsen* Department of Chemistry, UniVersity of Aarhus, DK-8000 Aarhus C, Denmark ReceiVed: March 22, 1996; In Final Form: June 24, 1996X
Magnitudes and relative orientations of 133Cs quadrupole coupling and chemical shielding tensors have been accurately determined from 133Cs magic-angle spinning (MAS) NMR spectra of the central and satellite transitions for four powdered cesium salts. Effects of small 133Cs chemical shielding anisotropies on the spectral appearance are observed in highly stabilized low-speed 133Cs MAS NMR spectra and analyzed by iterative fitting and numerical error analysis of the complete manifolds of spinning sidebands. 133Cs MAS NMR spectra of the single Cs site for CsVO3 and CsClO4, recorded at different spinning speeds, give consistent values for the parameters describing the two tensor interactions, while numerical error analysis of the spectra demonstrates that high levels of accuracy can be obtained for all parameters employing low-speed MAS NMR. The performance of the method for powders containing multiple sites is demonstrated by the 133Cs MAS spectra of Cs2CrO4 and Cs2SO4. The error limits for the 133Cs MAS NMR data for Cs2CrO4 are similar to those reported in a recent single-crystal NMR study. Quadrupole coupling parameters and isotropic chemical shifts are reported for Cs2CO3 from a high-speed 133Cs MAS spectrum. A linear correlation between 133Cs quadrupole tensor elements and estimated EFG tensor elements from point-charge calculations, employing effective oxygen charges, is reported and used to assign the NMR parameters for the two different crystallographic sites in Cs2CrO4, Cs2SO4, and Cs2CO3.
Introduction Paralleling the technical innovations of high-speed magicangle spinning (MAS) during the past decade, this method has become of increasingly beneficial use in studying the quadrupole coupling interaction (CQ, ηQ) for half-integer quadrupolar nuclei (in particular 23Na and 27Al) by solid-state NMR of either the central transition1,2 or the manifold of spinning sidebands (ssb’s) for the satellite transitions.3,4 For the heavier quadrupolar nuclei, such as 51V, 59Co, 87Rb, 95Mo, and 133Cs, the chemical shielding anisotropy (CSA) interaction may come into operation in addition to the quadrupole coupling. This was first shown by single-crystal NMR,5,6 a technique still successfully applied in such studies,7,8 and by static-powder NMR methods.9-15 Recently we introduced MAS NMR to the study of the combined effect of the two tensorial interactions including the relative orientation of the two tensors from polycrystalline powders.16 Following this exploratory investigation, 51V and 87Rb MAS studies16-18 of inorganic salts clearly demonstrated the simplicity, accuracy, and usefulness of the method resulting from the increased resolution of spectral features and improved sensitivity due to MAS. However, for most quadrupoles, the CSA interaction is quite small and the effect of the CSA on the spectral appearance is easily suppressed by MAS, even at ordinary or quite low spinning speeds, as is the case for the alkali metal nuclei. For example, determination of the 87Rb CSA in RbClO4 (δσ ) 13.5 ppm) from MAS NMR requires spinning speeds less than about 2-3 kHz even in a magnetic field of 11.7 T,18 i.e., a spinning frequency less than the second-order quadrupolar broadening for the central transition at 11.7 T. Similarly, following the * Corresponding author: Hans J. Jakobsen, Department of Chemistry, University of Aarhus, DK-8000 Aarhus C, Denmark. Phone: +45 8942 3842. FAX: +45 8619 6199. † Presented in part at the 12th International Meeting on NMR Spectroscopy, Manchester, England, July 1995. X Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(96)00874-X CCC: $12.00
numerous applications of 133Cs MAS NMR in the literature,19 there has been no documentation of 133Cs CSA’s determined by this method. Despite this fact, 133Cs CSA’s ranging from about δσ ) 20 to 220 ppm have been determined for a few inorganic salts using static-powder11,20 and single-crystal NMR.7 In particular we mention the detailed single-crystal 133Cs NMR study of Cs2CrO47 resulting in the magnitudes and orientations of the CSA and quadrupole coupling tensors for the two distinct Cs sites in the crystal structure. Prompted by these observations we have investigated the possibility of employing 133Cs MAS NMR for determination of the magnitudes and relative orientations (Euler angles ψ, χ, ξ) of the 133Cs CSA (δσ, ησ, δiso) and quadrupole coupling (CQ, ηQ) tensors in cesium salts. Here we report the successful application of highly stabilized low-speed MAS for this purpose to CsVO3, CsClO4, Cs2CrO4, and Cs2SO4. In addition to the determination of the eight parameters (characterizing the two interactions for each site) by least-squares fitting of the experimental spectra, the accuracies of these parameters have been evaluated by numerical error analysis of the spectra. From these results it is concluded that the accuracies of the 133Cs MAS NMR data are similar to those obtained from single-crystal 133Cs NMR (Cs2CrO4).7 Finally, in contrast to the comments7 on spectral resolution of multiple sites in powder spectra as compared to single-crystal NMR spectra, the present results clearly show that 133Cs MAS NMR of powders yields spectral resolution, e.g., for the two sites in Cs2CrO4, that leads to parameters of the same quality as those from single-crystal NMR. Experimental Section CsClO4, Cs2CrO4, Cs2SO4, and Cs2CO3 were purchased from Johnson Matthey GmbH (Karlsruhe, Germany) and used as recieved, while CsVO3 was prepared by reaction of Cs2CO3 with V2O5 according to the procedure described elsewhere.21 133Cs MAS NMR experiments were performed at 39.3 MHz (7.1 T) © 1996 American Chemical Society
133Cs
Quadrupole Coupling and Chemical Shielding Tensors
and 52.4 MHz (9.4 T) on Varian XL-300 and UNITY-400 spectrometers both equipped with home-built MAS probes22 for spinning 7 mm o.d. ceramic rotors in the range 0.5-10 kHz. Highly stabilized spinning frequencies ((1 Hz) were achieved by applying a computer-controlled voltage signal (0-5 V in a feedback loop) to an electropneumatics pressure regulator23 (SMC Pneumatics Inc., Model NIT201-202) using a modification of the Varian pneumatics/rotor controller unit. All experiments were performed at ambient temperature (295 ( 2 K) using exact magic-angle setting, spectral widths of 100-400 kHz, single-pulse excitation with a pulse width of 1 µs and a rf field strength of γH1/2π ≈ 40 kHz, and relaxation delays in the range 60-120 s. Minor baseline distortions were removed by linear prediction of the first few (2-8) data points of the FID followed by baseline correction using the routine of the Varian VNMR software. Isotropic chemical shifts are in parts per million relative to an external sample of solid CsCl, which has an isotropic chemical shift δiso ) 223.2 ppm relative to 0.5 M CsCl in H2O.11 However, for the spectra shown in the figures, except Figures 5a and 6, the kHz scale is given relative to the isotropic peak (determined from spectra employing different spinning speeds) in order to appreciate the asymmetry of the manifolds of ssb’s. Simulations, least-squares fittings, and error analyses of the experimental spectra were performed on the SUN Sparc 10/51 workstation of the UNITY-400 spectrometer using the solidstate NMR software package STARS (SpecTrum Analysis of Rotating Solids) developed in our laboratory2-4,16-18 and incorporated into the Varian VNMR software. A simulation of the ssb intensities for the central and satellite transitions of a 133Cs MAS spectrum requires between 2 and 5 s of CPU time on the SUN Sparc 10/51 computer, and a complete iterative fitting to an experimental spectrum, allowing all seven interaction parameters to vary, typically requires 150-200 simulations. Theory and Error Analysis. The 133Cs MAS NMR spectra of the cesium salts investigated in this work appear as manifolds of ssb’s from all seven 133Cs single-quantum transitions. The ssb patterns cover spectral widths ranging from 55 to 170 kHz, and the individual ssb’s exhibit almost Gaussian line shapes with a full width at half-maximum (fwhm) ) 1.5-3.0 ppm. Because the full width of the complete ssb manifold equals 3CQ/ 2I,4 this demonstrates that the quadrupole couplings for the present cesium salts are quite small (i.e., 130 kHz j CQ j 400 kHz). Thus, the 133Cs MAS spectra can be simulated by considering only the first-order contributions to the average Hamiltonian for the quadrupole and CSA interactions, i.e., h˜ Q(1)(t) and H h˜ σ(1)(t). Explicit expressions for H h˜ Q(1)(t) and H (1) 4,16 h˜ σ (t) have been presented elsewhere, H and it is seen that these contributions to the simulated 133Cs MAS spectra are orders of magnitude larger than those from the second-order (2) h˜ Q(2)(t), H h˜ σ(2)(t), and H h˜ Q,σ Hamiltonians H (t)) for the cesium salts considered here at magnetic fields of 7.1 and 9.4 T. This approximation may not be valid for other 133Cs spin systems since second-order quadrupolar line shapes for 133Cs central transitions and quadrupole couplings as large as CQ ) 3.1 MHz have been reported from a 133Cs MAS NMR study of dehydrated cesium mordenites.24 The anisotropic parameters are expressed by the principal elements of the chemical shielding (σ) and electric field gradient (V) tensors using the convention25 |λzz 1/ Tr(λ)| g |λ - 1/ Tr(λ)| g |λ - 1/ Tr(λ)| for λ ) σ, V and 3 xx 3 yy 3 the magnitudes of the two interactions are described by
J. Phys. Chem., Vol. 100, No. 36, 1996 14873 the CSA interaction to the quadrupole coupling or electric field gradient tensor are formally defined in the ranges 0 e ψ, ξ e 2π, and 0 e χ e π and correspond to positive rotations around the z axis (ψ), the new y axis (χ), and the final z axis (ξ). However, as pointed out elsewhere,17 the symmetry of the h˜ Q(1)(t) and H h˜ σ(1)(t) and the powder averaging expressions for H over all crystallite orientations imply that the ranges for the Euler angles can be reduced to 0 e ψ e π and 0 e χ, ξ e π/2. Expressions for the sets of orientations that cannot be distinguished were also reported.17 The error limits for the optimized CSA and quadrupole parameters in Tables 1-4 have been determined from numerical analysis of the experimental ssb intensities using the approach outlined in ref 26 and also recently employed in a static-powder NMR study.27 During optimization of the parameters the rootmean-square deviation
rms )
{
1
N
∑(Iie - Isi)2
N i)1
}
1/2
(2)
between simulated (Isi) and experimental (Iie) ssb intensities is minimized for the number (N) of experimental ssb’s. Iie is normalized relative to the intensity for the most intense peak in the spectrum and a direct impression of the goodness of the fit is obtained from the final rms deviation (rmsmin), which gives the mean deviation of the simulated ssb intensities relative to this peak. The χ2 function required for the estimation of the parameter limits, is related to the rms deviation by χ2 ) N(rms2)/ σ2, where it is assumed that all ssb intensities have the same measurement error (σ). Although σ is related to the signal-tonoise level in the spectrum, we find that other effects such as a nonideal baseline and phase anomalies of the ssb’s also contribute to the errors for the integrals of the ssb’s. Therefore, the suggestion in ref 26 of setting σ2 ) χmin2/N () rmsmin2) is adopted. The confidence limits for a parameter (p) can be obtained from the curvature of ∆χ2 ) χp2 - χmin2, which defines a one-dimensional projection of the χ2 hypersurface in the direction of the parameter p. χmin2 and χp2 are the minimum values of χ2 from an M-parameter fit and from (M - 1)parameter fits with fixed (but different) values for the parameter p, respectively. Sufficiently close to the optimized value for p the variation of χ2 can be approximated by a quadratic form, which implies that ∆χ2 is parabolic in the vicinity of the optimized value for p. Thus, the 95% confidence interval for p is obtained as δ(p) ) 2/xa,26 where a is the optimized value for the second-order coefficient in a fit of ∆χ2 to a secondorder polynomial. In practice, the variation of ∆χ2 as function of p is obtained from a series of (M - 1)-parameter least-squares fits employing fixed values for p corresponding to 5-10 equidistant steps on both sides of the optimized value for p. All error estimates for the MAS NMR data listed in Tables 1-4 are 95% confidence limits obtained using this method. The error limits calculated from the 133Cs MAS spectra (9.4 T) at low spinning speeds are of magnitudes similar to those reported for the considerably larger 51V tensor interactions in metavanadates, determined by 51V MAS NMR at 9.4 T and νr ) 7-9 kHz.17 These error limits were estimated from visual comparisons of experimental ssb intensities with simulations in which only one parameter was varied at a time. Results and Discussion
δσ ) σzz - 1/3Tr(σ), ησ ) (σyy - σxx)/δσ, CQ ) (eQ/h)Vzz, ηQ ) (Vyy - Vxx)/Vzz (1) The Euler angles (ψ, χ, ξ) relating the principal axis system of
133Cs (I ) 7/ , 100% natural abundance) has a small 2 quadrupole moment (Q ) -3 × 10-31 m2) which is responsible for the generally small 133Cs quadrupole couplings observed for cesium salts. 133Cs MAS NMR spectra for CsVO3, CsClO4,
14874 J. Phys. Chem., Vol. 100, No. 36, 1996 Cs2CrO4, and Cs2SO4 are shown in Figures 1 and 3-8, and the optimized interaction parameters, resulting from least-squares fitting to these spectra, are summarized in Tables 1-4. CsVO3 and CsClO4 both contain a single 133Cs site in the asymmetric unit, and their 133Cs MAS NMR spectra (Figures 1 and 4) illustrate the effect of the spinning speed on the appearance of the ssb manifolds for moderate (CsVO3) and small (CsClO4) tensorial interactions. The necessity of employing stable, lowspeed spinning for an accurate determination of the CSA and quadrupole coupling parameters for these salts is evident from the spectra in Figures 1, 3, and 4 and from the data in Tables 1 and 2. The high performance of the MAS method for unraveling the parameters of the individual sites in powders with multiple sites is demonstrated by the 133Cs MAS spectra of Cs2CrO4 and Cs2SO4 in Figures 5-8. A comparison is made of our MAS data for Cs2CrO4 (Table 3) with results obtained from the more traditionally used methods of static-powder11 and single-crystal NMR.7 Finally, relations between the relative orientation of the CSA and quadrupole tensors and the 133Cs point symmetries in the crystal structure are discussed for all salts. CsVO3. 133Cs MAS NMR spectra (9.4 T) of all transitions for CsVO3 and with spinning speeds from 5 to 0.8 kHz are shown in Figure 1a-d. For the highest speed (Figure 1a) the ssb manifold is almost symmetrical around the central transition, which indicates that the effect of the CSA is averaged at this spinning speed. Optimization and error analysis of simulated to experimental ssb intensities, considering the quadrupole interaction only, gives CQ ) 229 ( 7 kHz and ηQ ) 0.42 ( 0.12 corresponding to the simulation in Figure 1e. The fairly large rms deviation and error limits in this case may reflect that the effect from the CSA is not completely averaged at νr ) 5 kHz. At lower spinning speeds (Figure 1b-d), an asymmetry for the envelope of the ssb manifolds becomes increasingly apparent and demonstrates the importance of the CSA interaction in addition to the quadrupole coupling. Seven-parameter fits of experimental spectra recorded at lowspeed spinning give the parameters (Table 1) characterizing the anisotropic parts of the two tensorial interactions. The goodness of these fits, and thereby the high quality of the experimental spectra, is evident from comparison with the simulations (Figures 1f-h) shown for some of the spectra. Also, this is clearly reflected by the best rms errors for the ssb intensities (Table 1), which are on the order of 1%, and by the consistency of the parameters (including errors) determined from the individual spectra. The results of the error analyses (95% confidence limits), determined for the individual parameters in Table 1, clearly show that the accuracies of all seven parameters (CQ, ηQ, δσ, ησ, ψ, χ, and ξ) significantly improve for spinning frequencies below about νr ) 2 kHz (at 9.4 T). Further improvements for some of the parameters (ησ, ψ, and ξ) are obtained at still lower spinning speeds. Generally the error limits for the parameters improve by about 50-70% on going from νr ) 3 kHz to νr < 1.5 kHz. In particular we note the improved accuracy for the two Euler angles ψ and ξ, while the angle χ, relating the principal axes for the unique elements (σzz and Vzz) of the two tensors, is obtained with by far the best accuracy of all Euler angles at all spinning speeds. The possibility of the least-squares optimization routine getting trapped in a local minimum increases when the number of parameters increases, as recently indicated in a static-powder NMR study.27 In the case of CsVO3 an impression of the reliability of results from the least-squares fitting of the parameters may be gained from the contour plots in Figure 2. These show two-dimensional cross sections (at minimum rms)
Skibsted et al.
Figure 1. Experimental (a-d) and simulated (e-h) 133Cs MAS NMR spectra (9.4 T) of the central and satellite transitions for CsVO3 using spinning speeds of 5.0 kHz (a and e), 1985 Hz (b and f), 1365 Hz (c and g), and 830 Hz (d and h). The simulations correspond to the individual sets of optimized parameters given in Table 1 and are determined from the experimental spectra in (a-d). The the simulation in e includes the parameters for the quadrupole coupling only. A combination of 50 Hz Lorentzian and 120 Hz Gaussian line broadening has been employed for the simulations. In c and d the isotropic peak is marked with an asterisk while it corresponds to the most intense peak in a and b.
through the seven-dimensional parameter space of the rms function for the 133Cs MAS spectrum recorded at νr ) 1365 Hz (Figure 1c). The plots illustrate that a well-defined minimum is observed in the direction of each parameter and that no local minima are apparent in the vicinity of the values for the optimized parameters. Obviously the above results indicate that, for quadrupoles with tensorial interactions of this order of magnitude or even smaller, such studies are preferably performed at the highest possible magnetic field strength. The reason is that somewhat higher spinning speeds (which may be easier to stabilize within (1 Hz on modern high-speed spinner systems) may be applied in order to improve resolution. Despite this fact we have studied 133Cs MAS NMR spectra of CsVO at the lower magnetic field 3 strength of 7.1 T, e.g., for νr ) 1.47 kHz in Figure 3, to investigate the possibility of obtaining accurate parameters at this field strength. The optimized simulation (Figure 3b) and corresponding parameters (Table 1) show that data of fair accuracy (poorer error limits by a factor of about 2.5) may be obtained at the lower magnetic field strength. For all experiments the values ψ ) ξ ) 90° for the Euler angles are within experimental error, which shows that one each of the principal axes (σxx and Vxx) for the two tensors are parallel.
133Cs
Quadrupole Coupling and Chemical Shielding Tensors
J. Phys. Chem., Vol. 100, No. 36, 1996 14875
TABLE 1: 133Cs Quadrupole Couplings (CQ, ηQ), Chemical Shielding Anisotropies (δσ, ησ), and Relative Orientations (ψ, χ, and ξ) for the Two Tensional Interactions for CsVO3 from 133Cs MAS NMR at 9.4 and 7.1 Ta νL (MHz) 52.45
39.34 mean datac a
νr (Hz)
no. of ssb’sb
rmsmin
CQ (kHz)
ηQ
δσ (ppm)
ησ
ψ (deg)
χ (deg)
ξ (deg)
5000 3000 1985 1365 830 1470
18 30 45 65 95 63
0.0136 0.0067 0.0053 0.0072 0.0105 0.0151
229 ( 7 222 ( 4 225 ( 2 224 ( 2 226 ( 2 224 ( 5
0.42 ( 0.12 0.49 ( 0.05 0.48 ( 0.02 0.47 ( 0.03 0.45 ( 0.03 0.48 ( 0.05
-95.0 ( 4.0 -92.0 ( 1.3 -87.5 ( 1.3 -89.7 ( 1.3 -90.9 ( 2.7
0.40 ( 0.15 0.44 ( 0.06 0.46 ( 0.04 0.44 ( 0.03 0.40 ( 0.11
85 ( 38 89 ( 29 90 ( 13 89 ( 15 88 ( 37
28 ( 5 22 ( 3 24 ( 3 23 ( 3 22 ( 8
89 ( 31 82 ( 29 90 ( 10 89 ( 10 89 ( 30
0.47 ( 0.02
-90.0 ( 1.3
0.44 ( 0.03
89 ( 13
23 ( 3
89 ( 10
225 ( 2 b
c
The error estimates are 95% confidence limits (see text). Number of spinning sidebands (ssb’s) used in the optimization. Mean values obtained as weighted average of the optimized data for the different spinning speeds at 7.1 and 9.4 T.
Figure 2. Contour plots of the root-mean-square (rms) deviation between experimental and simulated intensities for the 65 ssb’s in the 133Cs MAS NMR spectrum of CsVO3 in Figure 1c (νr ) 1365 Hz). The plots illustrate two-dimensional cross sections through the seven-dimensional parameter space of the rms function in the directions of CQ (a), δσ (b), ησ (c), ψ (d), χ (e), and ξ (f) versus ηQ at minimum rms. For each plot the best rms deviation (rmsmin ) 0.0072) is indicated by a dot, while the first and second contours correspond to rms ) 0.0075 and rms ) 0.008. The subsequent contours correspond to an increase in rms deviation by 0.001.
This agrees with the orthorhombic crystal structure for CsVO3 (space group Pbcm),28 where each Cs is located on a mirror plane, implying that one principal axis from each tensor is perpendicular to the mirror plane. Thus, determination of the three Euler angles (ψ, χ, and ξ) by 133Cs MAS NMR of CsVO3 represents an excellent example where the orientation for some of the tensor elements within the crystal structure may be obtained from powder samples, an information which usually requires single-crystal NMR. CsClO4. The 133Cs MAS NMR spectra (9.4 T) of CsClO4 for νr ) 2.5-0.5 kHz (Figure 4a-c) reveal a transition from symmetric to asymmetric features for the ssb manifold on lowering νr, similar to the observation for CsVO3 (Figure 1). However, the observation of the asymmetric features for CsClO4 requires considerably lower spinning frequencies as seen for example by a comparison of the spectra in Figure 1a,b and Figure 4a. This shows that both the quadrupole coupling and
CSA interaction are smaller than for CsVO3. Assuming the presence of only the quadrupole coupling for the spectrum in Figure 4a, a two-parameter fit gives fairly accurate values for CQ and ηQ (Table 2) and the simulated spectrum in Figure 4d. Seven-parameter fits for the ssb intensities recorded at lowspeed spinning (νr j 1.5 kHz) and the associated error analyses show that reliable values for the angles ψ and ξ cannot be obtained from any of the spectra. This is ascribed to the small CSA (δσ ≈ 23 ppm) and low values for the two asymmetry parameters, ησ ≈ 0.3 and ηQ ≈ 0.1, since the accuracies for ψ and ξ decrease for small values of ησ and ηQ, respectively, as pointed out elsewhere.16,18 However, the orthorhombic crystal structure of CsClO4 (space group Pnma)29 shows that the Cs+ ion is located in a mirror plane, which requires one principal axis for each tensor to be perpendicular to this plane. This constraint is fulfilled when two of the Euler angles (ψ, χ, ξ) equal 0° modulo 90°. Five-parameter fits to the spectra using
14876 J. Phys. Chem., Vol. 100, No. 36, 1996
Figure 3. Experimental 133Cs MAS NMR spectra at 7.1 T of the central and satellite transitions for (a) CsVO3 (νr ) 1470 Hz) and (c) CsClO4 (νr ) 590 Hz). Simulated spectra employing the optimized parameters at 7.1 T for CsVO3 (Table 1) and CsClO4 (Table 2) are shown in b and d, respectively. The simulations employ a combination of Lorentzian and Gaussian line broadening (175 Hz for CsVO3 and 105 Hz for CsClO4) to reproduce the line width (and shape) for the ssb's observed in the experimental spectra. The isotropic peak is cut off at half-height in c and d.
the different combinations of these values for two of the Euler angles show that the minimum rms deviations are obtained for ψ ) ξ ) 0°. This corresponds to Vyy and σyy being perpendicular to the mirror plane. The optimized simulations resulting from the five-parameter fits employing ψ ) ξ ) 0° are illustrated in Figure 4e,f. and the corresponding values for the magnitudes of the two tensors and for the angle χ, between the σzz and Vzz elements within the crystallographic mirror plane, are summarized in Table 2. The importance of stabilized low-speed spinning for the accurate determination of small quadrupole coupling and CSA interaction, when combined as in 133Cs MAS NMR of cesium salts, is clearly manifested by the high-quality experimental spectra (Figure 4) and reflected by the improved accuracies of the parameters for CsClO4 (Table 2), obtained by lowering the spinning speed. A rather poor accuracy is obtained for ησ, a feature also observed for small CSA’s in line shape analysis of the combined effect of the two interactions for the central transition in 87Rb MAS18,30 and static-powder NMR.15 As observed for CsVO3 we find that 7.1 T low-speed MAS 133Cs spectra of CsClO4 (Figure 3c) also allow determination of the tensorial interactions, although with slightly reduced accuracies compared to the 9.4 T results. Values for CQ, ηQ, and δσ in CsClO4 have earlier been determined from static-powder NMR spectra of the satellite
Skibsted et al.
Figure 4. 133Cs MAS NMR spectra (9.4 T) of the central and satellite transitions for CsClO4. (a-c). Experimental spectra for spinning speeds of 2500 Hz (a), 940 Hz (b), and 500 Hz (c) with the corresponding simulations are shown in d-f, respectively. The simulations employ the individual sets of optimized parameters in Table 2 for the combined effect of the CSA and quadrupole coupling (e and f) and the quadrupole coupling only (d). A combination of Lorentzian and Gaussian line broadening giving ssb line widths of 100 Hz is used for all simulations.
transitions at 4.7 T (CQ and ηQ) and the central transition at 8.5 T (δσ) utilizing the field dependence of the CSA on the spectral appearance.20 Excellent agreement is observed between the magnitudes of these three parameters (see Table 2) and those obtained here from the five-parameter fits of the MAS NMR spectra. Cs2CrO4. The low-speed spinning 133Cs MAS NMR spectra (9.4 T) of Cs2CrO4 in Figures 5 and 6 offer a unique opportunity for a comparison of the quality of the parameter for the two tensor interactions when determined using today’s technology of MAS and single-crystal NMR.7 In both figures two wellseparated manifolds of ssb’s, with a 1:1 ratio for their total intensities, are observed. This agrees with the observation of two Cs sites in the asymmetric unit for the orthorhombic crystal structure (Pnma) determined by X-ray31 and neutron32 diffraction. Stick plots of the integrated intensities for the two manifolds of ssb’s (Figure 5b,c) exhibit highly asymmetric envelopes for both sites. These plots show that the site designated Cs(2) (Figure 5b) has a larger ratio for the CSA to quadrupole coupling interaction as compared to the Cs(1) site (Figure 5c). Although the two 133Cs sites have larger CSA’s and quadrupole couplings compared to CsClO4, least-squares sevenparameter fits (inclusion error analysis) of experimental spectra for νr e 3 kHz give excessive error limits and weak dependencies on the two Euler angles ψ and ξ for both sites. Thus, we utilize that each 133Cs site exhibits the effects of the mirror plane on which it lies,31,32 i.e., two of the Euler angles ψ, χ, and ξ equal 0° or 90°, as was also done in the recent singlecrystal NMR study at 4.7 T.7 For the different combinations
133Cs
Quadrupole Coupling and Chemical Shielding Tensors
J. Phys. Chem., Vol. 100, No. 36, 1996 14877
TABLE 2: Optimized 13Cs Parameters for the Quadrupole Coupling and Chemical Shielding Anisotropy Tensors for CsClO4 from 133Cs MAS NMR at 9.4 and 7.1 Ta νL (MHz)
νr (Hz)
no. of ssb’sb
rmsmin
CQ (kHz)
ηQ
δσ (ppm)
ησ
χ (deg)
52.45
2500 1335 950 500 590
22 42 55 89 62
0.0066 0.0037 0.0027 0.0041 0.0046
132.8 ( 1.9 132.8 ( 1.1 133.4 ( 0.7 134.3 ( 0.6 132.7 ( 1.0
0.09 ( 0.09 0.15 ( 0.04 0.14 ( 0.02 0.11 ( 0.01 0.11 ( 0.01
24.9 ( 2.4 23.9 ( 1.0 22.4 ( 0.6 23.0 ( 1.2
0.24 ( 0.24 0.24 ( 0.14 0.36 ( 0.08 0.29 ( 0.12
19 ( 5 14 ( 5 11 ( 3 13 ( 5
133.6 ( 0.6 135 ( 1
0.11 ( 0.01 0.09 ( 0.01
22.9 ( 0.6 24 ( 2
0.32 ( 0.08
13 ( 3
39.34 mean data from MA S NMRc static-powder NMRd
a Optimized data from five-parameter fits to the experimental MAS spectra assuming ψ ) ξ ) 0°. The error estimates are 95% confindence limits (see text). b Number of spinning sidebands (ssb’s) used in the optimization. c The mean values are weighted averages of the optimized data for the different spinning speeds at 7.1 and 9.4 T. d Reported data from static-powder NMR spectra of the central transition at 8.5 T (δσ) and of the satellite transitions (CQ and ηQ) at 4.7 T.20
Figure 5. 133Cs MAS NMR spectra (9.4 T) of the central and satellite transitions for Cs2CrO4 using νr ) 1255 Hz. (a) Experimental spectrum showing the overlap of two manifolds of ssb's from two 133Cs sites in Cs2CrO4. The spectrum is referenced to solid CsCl, and the inset shows the region for the isotropic peaks from the two Cs sites. (b and c) Normalized stick plots of integrated ssb intensities for the 133Cs sites designated Cs(2) and Cs(1), respectively. (d and e) Simulations of the ssb manifolds in b (Cs(2)) and c (Cs(1)) corresponding to the optimized parameters for νr ) 1255 Hz (Table 3). A Gaussian line shape and line width of 80 Hz have been employed in the simulations. Isotropic peaks are marked by asterisks.
of these values, five-parameter fits of spectra for νr ) 3.0-1.2 kHz show that minimum rms deviations are obtained for ψ ) 0° and ξ ) 90° for Cs(1) and ψ ) ξ ) 90° for Cs(2). The optimized parameters (CQ, ηQ, δσ, ησ, and χ) from the fiveparameter fits of the individual spectra using these values as fixed parameters are listed in Table 3. Simulations of the individual manifolds of ssb’s are shown in Figure 5, parts d
Figure 6. 133Cs MAS NMR spectra of Cs2CrO4 (9.4 T) illustrating the clean separation of the overlap for the two manifolds of ssb’s achieved at νr ) 1525 Hz. (a) Experimental spectrum referenced to solid CsCl. (b) Simulation of the spectrum in a employing the mean set of parameters in Table 3 for the two tensorial interactions, the isotropic chemical shifts in Table 5, and a combination of 45 Hz Gaussian and 40 Hz Lorentzian line broadening for all ssb's. The region for the isotropic peaks is shown in the insets. The isotropic peaks are indicated by asterisks.
and e, for Cs(2) and Cs(1), respectively, while Figure 6b illustrates a simulation of the overlapping manifolds for the two sites employing the mean parameters in Table 3. The optimized Cs(1) and Cs(2) data at the different spinning speeds (Table 3) show excellent consistency and high accuracy for each parameter. Decreasing νr into the range 3.0-1.2 kHz merely gives a slight improvement of the error limits and reflects the larger tensorial interactions for the two sites compared to CsVO3 and CsClO4, which reduce the requirements for lowspeed spinning. The weak dependency of the two manifolds of ssb’s to variations of the Euler angles ψ and ξ is justified by the small values of ηQ and ησ for Cs(2) (Vide supra) and for
14878 J. Phys. Chem., Vol. 100, No. 36, 1996 TABLE 3: Optimized Parameters for the from 133Cs MAS NMR at 9.4 Ta method MAS NMR Cs(1)
133Cs
Skibsted et al. Quadrupole Coupling and Chemical Shielding Anisotropy Tensors for Cs2CrO4
νr (Hz)
no. of ssb’sb
rmsmin
CQ (kHz)
ηQ
δσ (ppm)
ησ
χ (deg)
3000 1992 1255
50 66 101
0.0055 0.0048 0.0069
362 ( 2 367 ( 2 369 ( 3 365 ( 2 376 ( 10
0.58 ( 0.02 0.56 ( 0.02 0.55 ( 0.01 0.56 ( 0.01 0.52 ( 0.02
-159 ( 2 -162 ( 1 -162 ( 1 -162 ( 1 -163 ( 2
0.33 ( 0.04 0.31 ( 0.02 0.30 ( 0.02 0.31 ( 0.02 0.26 ( 0.02
17 ( 3 10 ( 2 11 ( 2 12 ( 2 7(2
3000 1992 1255
24 32 52
0.0022 0.0047 0.0035
142 ( 1 140 ( 2 142 ( 1 142 ( 1 138 ( 6
0.13 ( 0.02 0.11 ( 0.02 0.11 ( 0.01 0.11 ( 0.01 0.15 ( 0.02
221 ( 2 222 ( 2 220 ( 1 221 ( 1 222 ( 3
0.11 ( 0.03 0.06 ( 0.02 0.05 ( 0.02 0.06 ( 0.02 0.04 ( 0.02
50 ( 1 52 ( 1 52 ( 1 51 ( 1 52 ( 2
mean data from MAS NMRc single-crystal NMRd MAS NMR Cs(2) mean data from MAS NMRc single-crystal NMRd
a Optimized data from five-parameter fits to the experimental MAS spectra employing the fixed values of the Euler angles ψ ) 0° and ξ ) 90° for Cs(1) and ψ ) ξ ) 90° for Cs(2). The error estimates are 95% confindence limits (see text). b Number of spinning sidebands (ssb’s) used in the optimization. c The mean values are obtained as weighted averages of the optimized data for the different spinning speeds. d Reported data from single-crystal NMR at 4.7 T.7 The error limits for δσ and ησ are calculated from those for the principal elements (δii) using the law of error propagation.
the Cs(1) site by the small value for the angle χ. In the latter case this results in a strong correlation between ψ and ξ as observed, e.g., from six-parameter fits of the Cs(1) spectrum at νr ) 1255 Hz, employing a fixed value for only one of the Euler angles ψ () 0°) or ξ () 90°). This leads to a determination for the other angle with a good accuracy, i.e., ( 4° for ξ and ( 6° for ψ. Comparison of the mean data from MAS NMR with those from single-crystal NMR7 (Table 3) demonstrates an excellent consistency. Minor discrepancies are observed only for ησ and χ in case of Cs(1) and for ηQ of the Cs(2) site. Furthermore, the two methods give approximately the same error limits for the parameters, although it appears that the MAS method gives a more accurate value for CQ. 133Cs static-powder NMR spectra of the central and satellite transitions at various field strengths (4.7-11.7 T) have also been reported by the Halifax group11 and used to illustrate the sensitivity of the powder line shape to the relative oriention of the two tensors in addition to their magnitudes. However, the parameters for the interactions were not determined directly from the powder spectra because of the high complexity of unraveling 12-16 parameters from two overlapping powder patterns. On the other hand, the spectra appeared to be fully consistent with simulations based on the single-crystal NMR data. A 133Cs MAS spectrum reported along with the static-powder study11 illustrated the resolution for the two 133Cs sites by this method, although analysis of the distinct envelopes of ssb’s were not attempted. Cs2SO4. The 133Cs MAS NMR spectrum (νr ) 2 kHz, 9.4 T) of Cs2SO4 (Figure 7a) indicates two overlapping manifolds of ssb’s from two Cs sites with quite different quadrupole couplings. An asymmetric envelope of ssb’s extends over ca. 110 kHz for the Cs(1) site (the largest of the two quadrupole couplings), while the other site (Cs(2)) displays a symmetric pattern of ssb’s only up to third-order. Stick plots of the integrated Cs(2) intensities for νr ) 2.0-0.95 kHz at 9.4 T and for νr ) 845 Hz at 7.1 T are shown in Figure 7b-e. Although the envelopes for the few ssb’s in these plots display some asymmetric features, we expect that the small CSA and quadrupole coupling parameters, that possibly result for this site, are associated with large errors. For the Cs(2) site spectra at νr e 1.5 kHz we find that the lowest rms deviation, consistent with the crystal symmetry33 (orthorhombic, Pnam, and with both Cs+ ions in a mirror plane), is obtained for ψ ) 90° and ξ ) 0°. Using these values for ψ and ξ, five-parameter (CQ, ηQ, δσ, ησ, and χ) fitting to the experimental ssb intensities gives the final parameters summarized in Table 4 and the corresponding simulations illustrated in Figure 7f-i. As expected, the error analysis (Table 4) shows that the low number of ssb’s results in an incomplete and
Figure 7. (a) Experimental 133Cs MAS NMR spectrum of Cs2SO4 (9.4 T, νr ) 2.0 kHz) illustrating the overlap of two manifolds of ssb's for two distinct 133Cs sites. The frequency scale is referenced to the isotropic peak for Cs(2), which is cut off at 1/8 of its total height. The inset shows the region for the isotropic peaks (normalized intensity scale), which are marked by a square and an asterisk for Cs(1) and Cs(2), respectively. (b-e) Stick plots of integrated ssb intensities for the Cs(2) site obtained from 9.4 T MAS spectra recorded with spinning speeds of 2.0 kHz (b), 1345 Hz (c), and 950 Hz (d) and from a 7.1 T spectrum at νr ) 845 Hz (e). Simulated ssb manifolds for Cs(2), corresponding to these spinning frequencies and the individual sets of optimized parameters (Table 4), are shown in f-i. All simulations (f-i) include the effect from the two tensorial interactions and employ a combination of 40 Hz Gaussian and 20 Hz Lorentzian line broadening for the ssb’s. The isotropic peak is cut off at half height in b-i.
inaccurate set of values for the parameters. The error limits for CQ are similar to those obtained for the other cesium salts, whereas ησ is undetermined and the values for ηQ, δσ, and χ
133Cs
Quadrupole Coupling and Chemical Shielding Tensors
TABLE 4: Optimized Parameters for the from 133Cs MAS NMR at 9.4 and 7.1 Ta site
νL (MHz)
Cs(1)
52.45
Cs(2)
39.34 mean datac 52.45 39.34 mean datac
133Cs
J. Phys. Chem., Vol. 100, No. 36, 1996 14879
Quadrupole Coupling and Chemical Shielding Anisotropy Tensors for Cs2SO4
νr (Hz)
no. of ssb’sb
rmsmin
CQ (kHz)
ηQ
δσ (ppm)
ησ
χ (deg)
2000 1345 950 845
55 58 84 96
0.0038 0.0032 0.0083 0.0042
2000 1345 950 845
7 9 11 11
0.0012 0.0013 0.0038 0.0039
262 ( 2 261 ( 1 261 ( 2 260 ( 1 261 ( 1 18 ( 10 19 ( 2 20 ( 1 19 ( 2 20 ( 1
0.01 ( 0.03 0.01 ( 0.01 0.00 ( 0.02 0.01 ( 0.02 0.01 ( 0.01 (0.07)d 0.19 ( 0.20 0.34 ( 0.11 0.16 ( 0.16 0.27 ( 0.11
38 ( 8 32 ( 4 30 ( 2 31 ( 2 31 ( 2 18 ( 16 17 ( 7 14 ( 4 15 ( 5 15 ( 4
0.35 ( 0.26 0.41 ( 0.20 0.54 ( 0.15 0.52 ( 0.14 0.49 ( 0.14 (0.63)d (0.72)d 0.14 ( 0.71 (0.73)d 0.14 ( 0.71
62 ( 4 63 ( 4 58 ( 5 59 ( 5 61 ( 4 (65)d 81 ( 70 77 ( 21 90 ( 32 81 ( 21
Optimized data from five-parameter fits to the experimental MAS spectra employing fixed values for two of the Euler angles, e.g., ψ ) ξ ) 0° for Cs(1) and ψ ) 90° and ξ ) 0° for Cs(2). The error estimates are 95% confindence limits (see text). b Number of spinning sidebands (ssb’s) used in the optimization. c The mean values are obtained as weighted averages of the optimized data for the different spinning speeds at 7.1 and 9.4 T. d The error analysis shows that this parameter is statistically undefined. The listed value corresponds to that from the optimization. a
must be considered estimates only. From the parameters it appears that σzz and Vzz are located in the crystallographic mirror plane without coinciding. Anyway, the mean values for the optimized parameters show that, even in this case of very small tensorial interactions, the effects from the CSA and quadrupole interactions may be distinguished. Stick plots of the corresponding integrated Cs(1) intensities from the 133Cs MAS spectra used for Figure 7 are shown in Figure 8a-d. The envelopes of the ssb’s for this site bear a clear resemblance to those observed for CsClO4 (Figure 4), demonstrating that the quadrupole coupling is the dominant of the two anisotropic interactions. Preliminary seven-parameters fits to the experimental ssb’s in Figure 8a-d show that the quadrupole coupling tensor is axially symmetric within the error limits. This implies that the Euler angle ξ becomes undefined.16 Of the possible combinations of values for the two other angles (ψ, χ ) 0° or 90°), consistent with the crystal structure, fiveparameter fits give the lowest rms deviations for ψ ) 0° and χ * 0°, 90°. The optimized parameters for the magnitudes of the tensors and the angle χ are listed in Table 4, and the corresponding simulations are shown in Figure 8e-h. An excellent agreement between experimental and simulated spectra are observed for all spinning speeds. Especially, the clear reflection in the simulations of the rather small but distinct asymmetries for the ssb intensities from the singularities (“horns”) of the satellite transitions emphasizes the high quality and reliablility of the 133Cs MAS NMR spectra (Figure 8a-d). 133Cs Isotropic Chemical Shifts. 133Cs isotropic chemical shifts (δiso) have been determined from the 133Cs MAS NMR spectra at 9.4 T and are listed in Table 5 along with the CSA principal tensor elements (δii), calculated from δiso and the corresponding data for δσ and ησ (Tables 1-4). For each compound δiso is obtained from the isotropic peak, observed in the spectrum recorded at highest spinning speed, by correction for the second-order quadrupolar-induced shift of the central QS ) (-5/1960) CQ2(1 transition. However, this shift (∆ν1/2,-1/2 7 34 2 + ηQ )/νL for I ) /2) is rather small for the salts considered here at 9.4 T, giving the largest shift of 7.2 Hz for Cs(1) in Cs2CrO4. The isotropic shifts for CsClO4 and Cs2SO4 agree well with those reported earlier (Table 5) from 133Cs MAS NMR.20 Similarly, comparison of the MAS NMR (this work) and single-crystal NMR7 data for the isotropic shifts and the individual shielding tensor elements for Cs2CrO4 shows excellent agreement. In addition, the level of accuracy obtained by MAS at 9.4 T is at least as good as that obtained from singlecrystal NMR at 4.7 T. Assignment of 133Cs Quadrupole Coupling Constants. To investigate possible correlations between CQ and the geometry of the 133Cs coordination polyhedra and thereby assign the observed NMR parameters to the individual crystallographic
Figure 8. (a-d) Stick plots of experimental ssb intensities for the Cs(1) site in Cs2SO4 obtained from 133Cs MAS spectra (9.4 T) of the central and satellite transitions for spinning speeds of 2.0 kHz (a), 1345 Hz (b), and 950 Hz (c) and from a 7.1 T spectrum with νr ) 845 Hz (d). The simulations shown in e-h employ the individual sets of optimized parameters for Cs(1) listed in Table 4 as determined from the corresponding stick plots in a-d. A combination of 40 Hz Lorentzian and 40 Hz Gaussian line broadening has been used for all simulations. The isotropic peak is cut off at half height in all stickplots and simulations.
Cs sites for Cs2SO4 and Cs2CrO4, an estimate (V′) for the EFG tensor is calculated employing the point-monopole model and considering only charges of oxygens within the first coordination sphere of the Cs+ ion. Using formal oxygen charges (qi ) -2e) this approach has recently been employed for the assignment of 27Al quadrupole coupling parameters for tetrahedrally coordinated Al sites in calcium aluminates.35 Recently, Koller et al.36 showed that reasonable estimates of 23Na quadrupole constants for a series of sodium compounds can be obtained
14880 J. Phys. Chem., Vol. 100, No. 36, 1996 TABLE 5:
133Cs
Isotropic Chemical Shifts and CSA Principal Tensor Elements for the Cesium Salts studied by MAS NMRa
compd CsVO3 CsClO4 Cs2CrO4
Cs(1) Cs(2)
Cs2SO4
Skibsted et al.
Cs(1) Cs(2)
δisob (ppm)
δxx (ppm)
δyy (ppm)
δzz (ppm)
ref
-255.2 ( 0.3 -220.5 ( 0.3 -223.2 -321.5 ( 0.3 -323.2 ( 1.2 -195.0 ( 0.3 -196.2 ( 1.6 -154.6 ( 0.3 -155.2 -122.9 ( 0.3 -123.2
-320.0 ( 1.7 -205.4 ( 1.0
-280.4 ( 1.4 -212.7 ( 1.0
-165.2 ( 1.3 -243.4 ( 0.7
-427.6 ( 1.8 -426.2 ( 2.0 -77.9 ( 2.3 -81.2 ( 3.0 -131.5 ( 2.7
-377.4 ( 1.7 -383.2 ( 2.0 -91.1 ( 2.3 -89.2 ( 3.0 -146.7 ( 2.3
-159.5 ( 1.0 -160.2 ( 2.0 -416.0 ( 1.0 -418.2 ( 2.0 -185.6 ( 2.0
-114.4 ( 5.8
-116.5 ( 5.6
-137.9 ( 4.0
this work this work 20 this work 7 this work 7 this work 20 this work 20
a The principal tensor elements and δ b iso are relative to solid CsCl. Obtained from the isotropic peak in MAS NMR spectra at 9.4 T by correction for the second-order quadrupolar shift of the central transition.
by this model, employing effective charges for the oxygen anions. This approach has been adopted here, and by following Koller et al.,36 the effective oxygen charges are obtained as qi ) (-2 + ∑fij)e, where fij is the covalence of the oxygen (i)cation (j) bond, calculated from the equations of Brown and Shannon37 and from the chemical bond data of Brown and Altermatt.38 For the cesium salts considered here, this gives effective oxygen charges between q ) -0.60e (O(2) for CsClO4) and q ) -1.14e (O(3) for Cs2CO3). To expand the range of experimental values for the quadrupole couplings, the present analysis also includes preliminary parameters for Cs2CO3 obtained from a high-speed (νr ) 6.0 kHz) 133Cs MAS NMR spectrum at 9.4 T. This spectrum (not shown) displays two well-separated manifolds of ssb’s in agreement with the monoclinic crystal structure of Cs2CO3 (space group P21/c),39 which includes two crystallographic Cs sites. The envelopes of ssb’s are symmetric about the isotropic peak for both sites at νr ) 6.0 kHz, and asumming the presence of only the quadrupole coupling, two-parameter fits and error analyses of the ssb manifolds give the quadrupole coupling parameters CQ ) 695 ( 14 kHz and ηQ ) 0.34 ( 0.05 for Cs(1) and CQ ) 479 ( 23 kHz and ηQ ) 0.58 ( 0.07 for Cs(2). The corresponding isotropic chemical shifts are δiso ) -44.7 ( 0.3 ppm and δiso ) -121.6 ( 0.3 ppm for Cs(1) and Cs(2), respectively. It is noted that the calculations of the effective oxygen charges and the geometrical estimate of the EFG tensor for Cs2CO3 employed the unit cell parameters for Cs2CO339 but the atomic coordinates for the isostructural compound Rb2CO3,39 since the atomic coordinates reported for Cs2CO3 give an unusually short Cs-O bond length (dCs(1)-O(1) ) 2.31 Å), resulting in a very low effective charge for O(1), i.e., qO(1) ) -0.22e. From reported XRD data and estimated oxygen effective charges, the point-monopole calculations give the values listed in Table 6 for the quadrupole coupling constants CQest ) (1 γ∞)eQVzz′/h and the asymmetry parameters ηQest ) (Vyy′ - Vxx′)/ Vzz′ for the studied cesium salts. The values for CQest assume the 133Cs quadrupole moment Q ) -3 × 10-31 m2 and the Sternheimer antishielding factor γ∞) -102.5 for 133Cs, where the latter has been taken from an old theoretical calculation.40 A tentative assignment of the observed NMR parameters to the crystallographic Cs sites 1 and 2 for Cs2SO4, Cs2CrO4, and Cs2CO3, employing observed and estimated quadrupole coupling constants, is given in Table 6. For both Cs2SO4 and Cs2CrO4 the crystallographic Cs(1) and Cs(2) sites are assigned to the largest and smallest quadrupole couplings, respectively, which may reflect the fact that the environments of the Cs sites in the orthorhombic crystal structures for Cs2CrO4 (Pnma)31,32 and Cs2SO4 (Pnam)33 are very similar. However, this assignment is opposite to that suggested for Cs2CrO4 by Power et al.,7 who employed the symmetry and orientation of the EFG tensor elements, calculated using the same approach as here but with
TABLE 6: Assignment of 133Cs Quadrupole Coupling Parameters from a Calculated Estimate of the Electric Field Gradient Tensor for the Cesium Salts Studied in this Work compd
Cs sitea
CQb (kHz)
ηQb
CQest c (kHz)
ηQest c
1 2 1 2 1 2
225 133.6 365 142 261 20 695 479
0.47 0.11 0.56 0.15 0.01 0.27 0.34 0.58
215 122 459 211 427 67 1,096 984
0.73 0.20 0.48 0.37 0.88 0.11 0.37 0.54
CsVO3 CsClO4 Cs2CrO4 Cs2SO4 Cs2CO3
a The nonequivalent Cs sites are indexed according to the structure references.31-33,39 b Experimental quadrupole coupling parameters. c Estimated parameters from a point-monopole calculation of the EFG tensor using effective charges for the oxygens surrounding the Cs+ ion (see text).
formal oxygen charges. The correlation between the experimental CQ values and CQest is illustrated in Figure 9a, where a linear regression analysis gives
CQexp ) 0.532CQest + 52 kHz
(3)
with a correlation coefficient R ) 0.96. The estimated quadrupole couplings are generally larger than those determined experimentally, which may reflect the crude approximations used in the calculations of the EFG tensors and a less accurate value for the Sternheimer antishielding factor. For example, we note that a 1:1 correlation for CQexp and CQest is obtained for the present data employing γ∞ ) -54.1. Calculation of the two smaller elements of the quadrupole tensor (Vxx and Vyy) from the data in Table 6 leads to the correlation between experimental and estimated quadrupole tensor elements shown in Figure 9b, where linear regression gives Viiexp ) 0.59Vest ii and R ) 0.97. Although the quality of this correlation is similar to that observed for the largest principal elements only (Figure 9a, eq 3), the relative variations of the individual tensor elements result in only a fair agreement between the asymmetry parameters ηQexp and ηQest (Table 6). This observation is in accord with similar results reported for ηQ(23Na) by Koller et al.36 and is ascribed to the simplicity of the model. Conclusions By employing highly stabilized low-speed MAS NMR, the magnitudes and relative orientation of the tensors for small CSA and quadrupole coupling interactions for half-integer quadrupolar nuclei can be accurately determined, as illustrated by detailed analysis of 133Cs MAS NMR spectra of four cesium salts. Comparison of our data for Cs2CrO4, with those recently determined from 133Cs single-crystal NMR,7 shows that about the same level of accuracy can be obtained by the two methods.
133Cs
Quadrupole Coupling and Chemical Shielding Tensors
J. Phys. Chem., Vol. 100, No. 36, 1996 14881 thank the Aarhus University Research Foundation for equipment grants and the Danish Technical Research Council for financial support of this research (J. No. 15-5329-1). References and Notes
Figure 9. Linear correlations between experimental and estimated (a) 133Cs quadrupole coupling constants (Cexp versus Cest) and (b) quadQ Q rupole tensor elements (Viiexp versus Viiest) for the studied cesium salts. The values for CQest (Table 6) and Viiest are calculated estimates of the 133Cs EFG tensor obtained using XRD structural data and including effects from the first coordination sphere of cesium only (see text). In a, open circles represent values for CsVO3 and CsClO4, while the data for the two Cs sites in Cs2CrO4, Cs2SO4, and Cs2CO3 are indicated by filled circles, open squares, and filled squares, respectively.
Furthermore, the Cs2CrO4 results also illustrate the power of the MAS method in that high resolution can be achieved for multiple sites in powder samples. The Euler angles (ψ, χ, and ξ) from MAS NMR and the orthorhombic crystal structures (with the Cs+ ions located in a mirror plane) for all studied cesium salts reveal that the unique elements of the CSA and EFG tensor (i.e., σzz and Vzz) do not coincide and that these two principal elements are situated within the mirror plane of the Cs+ ion. In some cases the crystallographic symmetry of the Cs site may be utilized to constrain two of the Euler angles at fixed values (i.e., 0° or 90°) in the optimizations to the MAS NMR spectra. Finally, correlations between the experimental 133Cs quadrupole tensor elements and calculated approximate values for these tensor elements can be used to assign the parameters for Cs2CrO4, Cs2SO4, and Cs2CO3 to the distinct Cs sites in the crystal structures. Acknowledgment. The use of the facilities at the University of Aarhus NMR Laboratory, sponsored by Teknologistyrelsen, the Danish Research Councils (SNF and STVF), Carlsbergfondet, and Direktør Ib Henriksens Fond, is acknowledged. We
(1) Samoson, A.; Kundla, E.; Lippmaa, E. J. Magn. Reson. 1982, 49, 350. (2) Skibsted, J.; Bildsøe, H.; Jakobsen, H. J. J. Magn. Reson. 1991, 92, 669. (3) Jakobsen, H. J.; Skibsted, J.; Bildsøe, H.; Nielsen, N. C. J. Magn. Reson. 1989, 85, 173. (4) Skibsted, J.; Nielsen, N. C.; Bildsøe, H; Jakobsen, H. J. J. Magn. Reson. 1991, 95, 88. (5) Gornostansky, S. D.; Stager, C. V. J. Chem. Phys. 1967, 46, 4959. (6) Spiess, H. W.; Haas, H.; Hartmann, H. J. Chem. Phys. 1969, 50, 3057. (7) Power, W. P.; Mooibroek, S.; Wasylishen, R. E.; Cameron, T. S. J. Phys. Chem. 1994, 98, 1552. (8) Vosegaard, T.; Skibsted, J.; Bildsøe, H.; Jakobsen, H. J. J. Magn. Reson. (in press). (9) Baugher, J. F.; Taylor, P. C.; Oja, T.; Bray, J. P. J. Chem. Phys. 1969, 50, 4914. (10) Cheng, J. T.; Edwards, J. C.; Ellis, P. D. J. Phys. Chem. 1990, 94, 553. (11) Power, W. P.; Wasylishen, R. E.; Mooibroek, S.; Pettitt, B. A.; Danchura, W. J. Phys. Chem. 1990, 94, 591. (12) Edwards, J. C.; Adams, R. D.; Ellis, P. D. J. Am. Chem. Soc. 1990, 112, 8349. (13) France, P. W. J. Magn. Reson. 1991, 92, 30. (14) Hirshinger, J.; Granger, P.; Rose´, J. J. Phys. Chem. 1992, 96, 4815. (15) Koons, J. M.; Hughes, E.; Cho, H. M.; Ellis, P. D. J. Magn. Reson. Ser. A. 1995, 114, 12. (16) Skibsted, J.; Nielsen, N. C.; Bildsøe, H.; Jakobsen, H. J. Chem. Phys. Lett. 1992, 188, 405. (17) Skibsted, J.; Nielsen, N. C.; Bildsøe, H.; Jakobsen, H. J. J. Am. Chem. Soc. 1993, 115, 7351. (18) Vosegaard, T.; Skibsted, J.; Bildsøe, H.; Jakobsen, H. J. J. Phys. Chem. 1995, 99, 10731. (19) See Reference 7 and references cited there in. (20) Mooibroek, S.; Wasylishen, R. E.; Dickson, R.; Facey, G. J. Magn. Reson. 1986, 66, 542. (21) Feigelson, R. S.; Martin, G. W.; Johnson, B. C. J. Cryst. Growth 1972, 13/14, 686. (22) Jakobsen, H. J.; Daugaard, P.; Langer, V. J. Magn. Reson. 1988, 76, 162; U. S. Patent Number 4, 739, 270, April 19, 1988. (23) Maier, T. D.; Huang, T. H. J. Magn. Reson. 1991, 91, 165. (24) Chu, P. J.; Gerstein, B. C.; Nunan, J.; Klier, K. J. Phys. Chem. 1987, 91, 3588. (25) Spiess, H. W. in: NMR Basic Principles and Progress, Eds. Diehl, P., Fluck, E., Kosfeld, E.; Springer: Berlin, 1978; Vol. 15. (26) Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; Vetterling, W. T. Numerical Recipes, The Art of Scientific Computing, Cambridge University Press, 1987, Chapter 14. (27) Koons, J. M.; Hughes, E.; Ellis, P. D. Anal. Chimica Acta 1993, 283, 1045. (28) Hawthorne, F. C.; Calvo, C. J. Solid State Chem. 1977, 22, 157. (29) Granzin, J. Z. Kristallogr. 1988, 184, 157. (30) Fernandez, C.; Amoureux, J. P.; Bodart, P., Maijanen, A. J. Magn. Reson. Ser. A 1995, 113, 205. (31) Miller, J. J. Z. Kristallogr. 1938, 99A, 32. (32) Morris, A. J.; Kennard, C. H. L.; Moore, F. H.; Smith, G.; Montgomery, H. Cryst. Struct. Comm. 1981, 10, 529. (33) Nord, A. G. Acta Chem. Scand. 1976, A30, 198. (34) Samoson, A. Chem. Phys. Lett. 1985, 119, 29. (35) Skibsted, J.; Henderson, E.; Jakobsen, H. J. Inorg. Chem. 1993, 32, 1013. (36) Koller, H.; Engelhardt, G.; Kentgens, A. P. M.; Sauer, J. J. Phys. Chem. 1994, 98, 1544. (37) Brown I. D.; Shannon, R. D. Acta Crystallogr. A 1973, 29, 266. (38) Brown I. D.; Altermatt, D. Acta Crystallogr. B 1985, 41, 244. (39) Ehrhardt, H.; Schweer, H.; Seidel, H. Z. anorg. allg. Chem. 1980, 462, 185. (40) Sternheimer, R. M. Phys. ReV. 1966, 146, 140.
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