J . Phys. Chem. 1994,98,1544-1551
1544
23Na NMR Spectroscopy of Solids: Interpretation of Quadrupole Interaction Parameters and Chemical Shifts Hubert Koller and Giinter Engelhardt’ Institute of Chemical Technology I , University of Stuttgart, D-70550 Stuttgart, Germany
Amo P. M. Kentgens N S R Center for Molecular Structure, Design and Synthesis, SON/NWO HF- NMR Facilities, Toernmiveld, NL-6525 ED Nijmegen, The Netherlands
Joachim Sauer Quantum Chemistry Group at the Humboldt- University, Max PIanck Society, 0-10117 Berlin, Germany Received: August 4, 1993;In Final Form: October 26, 1993’
Quadrupole coupling constants (QCC), asymmetry parameters of the electric field gradients ( q ) , and isotropic chemical shifts (6,) of sodium-23 were determined by computer simulation of the central transition line shapes of the 23Na M A S N M R spectra of a series of crystalline sodium compounds in which sodium has exclusively oxygen atoms as nearest neighbors. The relations between the crystal structure and the above parameters were discussed qualitatively for typical examples. The bond-valence method is applied to derive empirical models for the calculation of a “shift parameter” ( A ) and of oxygen atomic charges (model I) from which Q C C and 7 were calculated by a simple point charge model. A linear correlation between A and 6, is obtained, indicating that 6, can be characterized by the total valence and the N a - O distances of all oxygen atoms located in a sphere of 3.4 A around the sodiumcation. The correlation obtained between calculated and experimental QCC’s shows that Q C C can be estimated by point charges a t the crystallographic oxygen sites determined from the total covalences of the respective oxygen atoms present in the 3 . 4 4 sphere. Q C C and q were further calculated using oxygen atomic charges obtained from the electronegativity difference of oxygen and the cations (model 11) or from quantum chemical a b inito calculations (model 111). Q C C calculated using charges from models I1 and I11 correlate, in general, less well with the experimental data than those of model I. However, the best correlation for q is observed for model I11 while models 11 and I yield considerable scatter.
Introduction The quadrupole coupling constant, QCC, and asymmetry parameter of the electric field gradient, 7.of quadrupolar nuclei in solids have been studied extensively by NQR, NMR, and other analysis techniques, e.g., electron spin resonance and MGssbauer spectroscopy. This is not surprising as these parameters give information about the local electronic environment of the nucleus and are therefore valuable for the exploration of molecular structure and dynamics. In solid-state NMR, the study of halfinteger quadrupole nuclei in powder samples has become very popular in the past few years. This is due to the fact that these nuclei have become very accessible for NMR investigations thanks to the availability of high-field NMR spectrometers in combination with averaging techniques such as magic angle spinning (MAS)’ and, more recently, double rotation (DOR)*and dynamic angle spinning (DAS).3 Moreover, over two-thirds of the elements in the periodic table have nuclei with half-integer quadrupole spin. Especially the extensively studied molecular sieves and zeolites but also a variety of other inorganic materials of high practical and scientific interest contain half-integer quadrupolar nuclei such as IlB, I7O, 23Na, 27Al, etc. Opposed to this increase of the experimental exploration of quadrupole parameters in various systems, the assessment of these parameters by theoretical means has declined. This can be imputed to the great difficulties encountered by their calculation. Electric field gradients can be calculated using electrostatic or quantum mechanical models. In an electrostatic model, the electric field gradient at the site of a nucleus is calculated due
* To whom correspondence should be addressed. a
Abstract published in Aduonce ACS Absrracts. January 1 , 1994.
to all the surrounding (ionic) charges in the lattice. This is done by expanding the potential function due to the surrounding ions in a series of multipoles and subsequently summing over the lattice. The most severe problems encountered in these calculations is to find the correct polarizabilities which give rise to dipole, quadrupole, and even the octupole moment of the surrounding charge distributions, and the question of overlap effects between different orbitals has to be taken into account.k7 For example, in order to calculate the electric field gradient at the 27Alnucleus in various oxygen surroundings, very different polarizabilities of the oxygens have to be used to get correct predictions in very similar structures.5~6Problems are also encountered in the lattice summations. Depending on the system, different summation procedures have to be used in order to reach convergence.839 Quantum mechanical calculations of electric field gradients have predominantly been performed by ab initio methods. All these studies have concentrated, however, on small molecules or small substructures. Obviously, these calculations are very elaborate, and the choice of the correct basis sets of the atomic orbitals is difficult. For lattices, one generally resorts to semiempirical methods which can be used in a qualitative way. Nagello was able to get good results for a-AlzO,. It may be concluded that at the moment there is not yet a satisfactory method to calculate the electric field gradient from structure data. One would like, however, to interpret experimentally determined quadrupole parameters of a nucleus in terms of the (local) symmetry of the charge distribution surrounding the nucleus. A simple model which correlates local symmetry with the electric field gradient would be helpful with the interpretation of NMR spectra of quadrupolar nuclei. An attempt in this direction was undertaken by Ghose and Tsang” for
0022-3654/94/2098- 1544%04.50/0 0 1994 American Chemical Society
23Na N M R Spectroscopy of Solids aluminum in various oxygen surroundings using the longitudinal strain and shear strain of coordination polyhedra which are a measure of bond length and bond angle variation of the first coordination sphere of a nucleus.12 Ghose and Tsang found that QCC of 27Alin A104tetrahedra in aluminosilicates depends mostly on the shear strain (i.e., bond angle variations ), whereas for A106 octahedra the longitudinal strain and hence bond length variations are more important. The relationship between the shear strain and QCC of A104 tetrahedra has recently also been applied to aluminate and aluminophosphate frameworks.l3J4 However, an attempt to use corresponding parameters on the sodium compounds studied in the present work failed to give a satisfactory correlation. The approach in the present study is to try to correlate the experimental quadrupole coupling parameters of 23Na determined for a number of sodium compounds to those found by a simple electrostatic calculation. In these calculations the atoms (exclusively oxygen) in the first coordination sphere of the 23Na nucleus are considered as simple point charges which, however, are not taken to be the formal charges but are estimated using various empirical relationships as well as a b initio calculations (see below). Quadrupole parameters calculated with the formal charge of -2e a t the oxygen failed completely to give a correlation with the experimental data. Besides the quadrupole parameters, the 23Naisotropic chemical shift, ,6 may provide further information on the structural environment of the sodium atom. However, similar to the situation described above for the field gradients, a rigorous theoretical treatment of the 23Na chemical shift in solids is lacking, and even its empirical interpretation is not well developed. Semiempirical quantum chemical models based on a fixed number of covalent bonds as e.g. applied to 29Sichemical shifts in silicates15 are of limited use owing to the highly ionic sodium4xygen bonds and the variations of the coordination number of sodium cations. It will be shown, however, that the experimental 23Na chemical shifts correlate well with an empirical shift parameter based on the total oxygenxation bond valence and Na-0 distances of all oxygen atoms in the first coordination sphereof the sodiumcation.
Experimental Section Materials. The materials studied were either commercially available or synthesized following procedures published in the literature. The phase identities and purity of the materials were carefully checked by powder X-ray diffraction and/or thermal analysis. The sodium silicates and sodalites were further characterized by 29Si MAS NMR. UNa NMR Measurements. 23Na MAS N M R spectra of the microcrystalline powder samples were measured a t room temperature with a Bruker MSL 400 spectrometer (YO = 105.84 MHz) in ZrO2 rotors of 4-mm 0.d. using a Bruker double-bearing multinuclear C P MAS probe head. Spinning speeds of typically 8 kHz and single-pulse excitation with flip angles below r / 8 (pulse length 1 ps) were used for optimal excitation of the central transition.16 High-power proton decoupling was applied during acquisition where necessary. Up to 500 fid’s were accumulated with a delay of typically 5 s between the excitation pulses to prevent sample heating by high-power decoupling. Relaxation times of 23Na were checked to be short enough with regard to the applied pulse delay. Z3Na N M R spectra of solutions were also measured at 105.84 MHz with a Bruker MSL 400 or a Jeol GX 400 spectrometer. Teflon sample tubes of 10-mm 0.d. were used to prevent background signals from glass tubes. The chemical shifts were referenced to solid NaCl(6, = 0); for the liquids a 0.1 M aqueous NaCl solution was used as a secondary standard (6 = -7.2 ppm against solid NaC117). ComputerSimulations. The quadrupole interaction parameters and isotropic chemical shifts were obtained from computer simulations of the central transition MAS N M R line shapes using
The Journal of Physical Chemistry, Vol. 98, No. 6,1994 1545 a
&PH
b
s C
Figure 1. Sodium coordination in NaH2P04.2H20 (a) and the oxygencentered structure models used in the ab initio calculationsof the charges of the oxygen atoms 0 1 , 0 3 , 0 4 (b), 0 5 (c), and 0 6 (d). Models b and d contain four H2P04- units and nine Na+ cations; model c contains two HzP04-units and seven Na+ cations. As explained in the text, the Na+ cations are replaced by point charges of 4/9e (models band d) and 2/7e (model c) to obtain models which are electrically neutral.
the program POWDER of the Bruker Aspect 3000 software package or the Q mas 1/2 model of the WinFit module included in the Bruker WIN-NMR program for PC’s. Calculation of Quadrupole Interaction Parameters. A simple electrostatic model was applied for the calculations of QCC and in which the oxygen ions in the first coordination sphere of the 23Na nucleus are considered as point charges, and their coordinates were taken from crystal structure data. The oxygen charges were derived from empirical relationships which will be considered in detail in a later section and from quantum chemical a b initio calculations (see below). Based on the coordinates and charges (ne)of each oxygen ion in the first coordination sphere, the matrix giving the electric field gradient a t the central sodium nucleus is calculated, i.e., V,, = ne(3x2 - r 2 ) / r 5 ,V, = ne(3xy)/r5,etc. This is done for every oxygen ion, and the final electric field gradient tensor is then diagonalized by orthogonal rotations. The largest principal value V,, = eq found in this way is used to calculate the quadrupole coupling constant QCC = (1 - ym). e2qQ/h,where Q = 0.1 X 10-28mz is the quadrupole moment and ym= -4.1 the Sternheimer antishielding factor of 23Na.1* The asymmetry parameter of the electric field gradient is given by 7 = I( V w - V m ) /Vzd. The calculations are accomplished using a PC program written in Pascal. The program runs on any IBMcompatible PC and can be obtained on request from the authors. Ab Initio Calculation of Oxygen Charges. For the quantum chemical calculations of the oxygen atomic charges finite structure models were derived from the crystal structures which describe the chemical surroundings of the oxygen atoms as good as possible. The design of the models follows the guidelines summarized by Sauer.I9 The oxygen atom coordinated to sodium was arranged in the center of the model, and according to the crystal structure, all nearest-neighbor atoms of that oxygen (including hydrogen bonds) were added and then chemically completed by all further covalently bonded atoms or groups. For reasons given below the sodium cations were added only as point charges. As these point charges do not have a complete coordination sphere, their magnitude was chosen such that neutral models were obtained (see Figure 1). This procedure was applied to all crystallographic oxygen positions coordinated to sodium in the given structure. As an example, Figure 1 shows the corresponding models derived for
1546 The Journal of Physical Chemistry, Vol. 98, No. 6, 1994
Koller et al.
TABLE 1: Experimental UNa Isotropic Chemical Shifts, ti,, Quadrupole Coupling Constants, QCC, and Asymmetry Parameter of the Electric Field Gradient, TJ,of Sodium Compounds and the Calculated Shift Parameter, A, QCC, and TJ Obtained from Models 1-111 (See Text) QCC/MHz calcd compound Na site silicates Na2Si02(0H)r8H20 NazSi02(OH)~7H20Nal NazSi02(OH)~7H20NaZ Na~Si02(OH)~5H20 Nal Na2Si02(0H)r5H20 Nu2 Na2Si02(OH)~4H20Nal Na2SiO2(OH)2*4H20NaZ Na2Si03 ~~-Na2Si205~ P-Na2Si205 Nulb P-Na2Si205 NaZb sodalites Na6[AlSiO4]6 Nag[AlSi04]6(0H)2 Nag[AlSiO&.(OH)r2H20 phosphates NasPsOg Nal NasP3Op Nu2 NaH2P04.2H20 NaH2POqH20 other inorganic compounds Na2S04 NaA102 NaOH NaOHsH20 Na2CrO4 Nu1 Na2Cr04 NaZ NaC104 NaC104.H20 Nul NaCIOqH20 NaZ organic compounds Na2C4H204-H20Nulc Na2C4H20qH20 NaZe NaI.3DMF
9
calcd
I,/ppm (exptl)
A (calcd)
exptl
1
I1
I11
exptl
I
I1
I11
refa
-3.67 -0.94 4.74 -1.50 -7.20 1.80 2.30 15.45 17.40 20.40 8.30
0.790 0.800 0.821 0.843 0.830 0.817 0.752 0.749 0.730 0.684 0.801
1.14 2.56 0.8 1 1.35 2.01 1.80 2.83 1.46 1.82 2.50 2.22
1.14 1.81 1.13 1.03 1.15 1.50 3.06 1.08 2.00 2.02 2.31
0.83 1.31 0.78 0.91 1.08 2.20 2.28 1.91 2.75 2.85 3.32
1.03 1.43 0.85 1.00 1.17 1.38 2.22 1.08
0.50 0.59 0.77 0.45 0.70 0.75 0.17 0.71 1.00 0.00 0.55
0.56 0.65 0.80 0.47 0.84 0.88 0.16 0.80 0.27 0.18 0.71
0.40 0.76 0.74 0.35 0.77 0.64 0.34 0.46 0.16 0.18 0.48
0.45 0.66 0.80 0.37 0.74 0.85 0.13 0.78
31 32
3.00 -4.00 -8.40
0.717
5.90 2.00 1.55
5.19 1.81 1.32
6.60 1.06 1.70
5.67
0.10 0.10 0.16
0.00 0.00 0.00
0.00
0.00
36 48 49
-14.80 -5.60 -4.80 -10.69
0.886 0.876 0.803
2.20 1.57 1.19 1.22
1.94 1.90 1.01
1.91 1.91 0.95 1.18
2.13 2.11 1.01 1.50
0.70 0.55 0.46 0.26
0.18 0.51 0.95
0.25 0.40 0.33 0.67
0.18 0.42 0.59 0.33
50
-8.50 19.00 12.20 5.00 -20.00 -13.90 -25.50 -1 1.70 -12.40
0.853
2.60 2.15 3.50 2.20 2.78 0.5d 0.80 1.71 1.48
1.76
1.55
1.79
0.61
0.07
0.61
2.23 1.19
2.43 2.26
1.67 1.01
0.58 0.60 0.00 0.70 0.57
0.01 0.56
0.00 0.98
0.01 0.61
53 (4 39 54 55
0.87 1.49 1.42
0.94 1.10 1.00
1.18 0.65 0.80
0.35 0.20 0.10
0.98 0.47 0.52
0.62 0.48 0.68
0.55 0.49 0.37
56 57
1.81 1.56 1.31
1.91 1.65
0.82 0.77 0.00
0.52 0.35 0.00
0.92 0.88
58
0.678 0.796 0.972 0.879 0.957 0.925 0.904
-9.6 -6.10 -13.74
1.30 0.77 1.18
0.00 0.00
od
33 34 45 46 41
51 52
38
Crystal structure data. Experimentaldata from ref 27. No structure data available. Gaussianline, QCC estimated from the line width according to ref 59. Sodium maleate monohydrate. a
the calculation of the charges of the oxygen atoms in NaH2P 0 ~ 2 H 2 0 .An exception is the anhydrous sodium sodalite where the sodium-centered structure model shown in Figure 3a (completed by hydrogen atoms a t the terminal oxygens) appeared to be more appropriate. Atomic coordinates as deduced from the crystal structures were kept fixed in the calculations. Since relatively large models have to be considered, the a b initio calculations used a minimal basis set. Even then, the largest model computed included 357 Cartesian Gaussian basis functions. The MINI-1 basis set of Huzinaga et a1.20-21with a scaling factor of 1.188 for hydrogen20 was selected. The basis sets for the other atoms were not scaled. It has been shown by Hobza and that MINI-1 basis sets perform well for molecular interactions and yield dipole moments which agree very well with those computed by larger basis sets, e.g., the 6-31G* basis set. Since the basis set superposition errors are relatively the MINI- 1 basis sets are also useful for ionic complexes. To further reduce possible errors on the oxygen charges connected with an artificial transfer of charge from the oxygen atoms to the sodium cations due to basis set superposition effects, we decided to treat the sodium cations as point charges without any basis functions on these sites as already mentioned above. The calculations were made within the SCF approximation and employed the direct TURBOMOLE code.24 The charges were obtained from a Mulliken population analysis. The CPU times on IBM-RISC workstations were in the range between a few minutes and several hours depending on the size of the model.
Results and Discussion Table 1 summarizes the quadrupole parameters QCC and
and the isotropic chemical shifts (corrected for quadrupolar shift contributions),, ,6 obtained from thesimulation of the23NaMAS NMR spectra of a series of sodium compounds in which sodium has only oxygen atoms in its first coordination sphere. Figures 2 and 3 show selected examples of the experimental spectra along with the simulated line shapes. It is obvious that even subtle details of the spectral patterns are well reproduced in the simulations, indicating the reliability of the determined parameters. The estimated error is about 0.05 MHz for QCC, about 0.1 for 9, and less than 0.1 ppm for 6,. The total range of QCC extends from 0.77 MHz (sodium maleate hydrate) to 5.90 MHz (anhydrous sodalite), and the full range between 0 and 1 is observed for 9. 6, varies between 20.4 and -25.5 ppm, i.e., by about 45 ppm. In the following sections, the relations between structural features and chemical shifts and quadrupole parameters will first be discussed from a qualitative point of view and exemplified by selected examples. Subsequently, quantitative correlations between the structure and the experimental NMR data will be considered.
Qualitative Considerations Chemical Shifts. Several authors have suggested a correlation between 6, of 23Na and the coordination number of sodium.25-27 However, these conclusions were based on only few examples and cannot be confirmed by the larger body of data presented in Table 1 . As shown in Figure 4, the shift regions for the 5- and 6-fold coordinations overlap heavily. Figure 5 shows the 23Na MAS NMR spectra of a series of sodium compounds in which the oxygen atoms are bonded to
The Journal of Physical Chemistry, Vol. 98, No. 6, 1994 1547
ZjNa N M R Spectroscopy of Solids Na$iO,(OH),.8H,O
a
C
N~Si0,(OH)~5Hz0
experiment
I
I
,
,
I
I
-20 6/PPm
0
20
I
,
,
-60
-40
A
I
components
-30
-10
-20
10
0 8,s 1 PPm
30
20
Figure 4. Plot of formal coordination numbers versus isotropic Z3Na chemical shifts, 8,, for sodium-oxygen coordinations present in the compounds given in Table 1.
(( V I
Na$iO,(OH),~7H,O
6,. = 19.0 ppm
Jn
NaAIO,
A
t,A simulation
l
I
I
I
,
0
,
-20
I
,
40
I QCC
1.46 MHz
I
\ h=0.71
I
-60
6,. = -14.8 ppm
5,= -5.6 ppm
SlPPm
FigureZ. Experimentaland simulated 23NaMAS NMRspectra of sodium silicate hydrates, Na$3Oz(OH)~nH20 with n = 8, 7, 5 , 4. anhydrous sodium sodalite Na6[%Al6Ozd
1
1
components
components
20
1
Nak3DMF
r4
I QCC = 2.60 MHz I
a
0 6,. = -25.5 ppm I
30
.
,
20
I
I
.
10
,
I
0
,
.
1
u\ 1
-10 -20 6 1 ppm
,
.
-30
,
NaCIO4 .
-40
,
.
-50
/
-60
Figure 5. 23Na MAS NMR spectra of sodium salts containing oxyanions of elements of the third row of the periodic table. ,6 is indicated by arrows.
components 200
-200
0
-400
6lppm
Figure 3. Structural environment of sodium (a, c) and experimental and simulated 23Na MAS NMR spectra (b, d) of anhydrous sodium sodalite, Na6[Si6A1&4] (a, b) and NaJ.3DMF (c, d). The asterisk in spectrum b denotes spinning sidebands; the lines at -14 ppm in spectrum b and at 8-10 ppm in spectrum d originate from impurities.
various elements of the third row of the periodic table. The positions of 6, are indicated by arrows and show a systematic
shift to high field with increasing atomic number of the third-row elements (see also Table 1). As a consequence, it may be concluded that 6, is related to the particular chemical environment of the oxygen atoms coordinated to sodium. To get further insights into these relations, we have measured the concentration dependence of the 23Na chemical shifts of selected sodium salts in water. In Figure 6 the experimental shifts are plotted against the salt concentrations of the solutions. At infinite dilution, all curves move toward a unique shift value of -7.2 ppm, which correspond to the chemical shift of fully hydrated Na+ measured for a 0 . 1 M aqueous NaCl solution with reference to solid NaCl. However, the slopes of the curves are very different. With increasing salt concentration the shifts increase for NazSiO3 and to a lesser extent also for NaOH but decrease weakly for Na2H2P04 and strongly for NaC104. Extrapolation to high concentrations, i.e., approaching the composition of the pure salts, yields shift values which parallel a t least qualitatively those measured for the four solid compounds (NazSi03, 15.45 ppm; NaOH, 12.20 ppm; NazHzPOcHzO, -10.69 ppm; NaC104, -25.50 ppm; see Table 1). The concen-
Koller et al.
1548 The Journal of Physical Chemistry, Vol. 98, No. 6, 1994 -4
a
C
b
d
0 Na,Si03
NaOH
-5
-6
V
NaH,PO, NaCIO,
0
io. . 1
0 0
e e
.
v.
-8 -9
1
.
V
vvv
v v v
*
*
V
-10 0
1
2
3
4
5
6
concentration I mole.1-1
Figure 8. Structural environments of sodium in sodiumsilicate hydrates Na2SiOz(OH)ynH20 with n = 8 (a), 7 (b), 5 (c), and 4 (d) according to the crystal structures given in refs 31-34.
Figure6. Plotof23Nachemicalshifts,S,,versusconcentrationsofaqueous
solutions of Na2SiO3, NaOH, NaH2P04, and NaC104.
6-
g
7-
2 6E P
8 54-
I
I
I
0
1
I
2
I
3
I
4 5 accWI,i MHZ
,
6
8
I
7
8
1
Figure 7. Calculated quadrupolecouplingconstants, QCC,rc, of selected
sodium-oxygencoordinationswith different symmetriesand coordination numbers (see text). tration dependence of the 23Na chemical shift in aqueous solutions of various sodium salts has already been reported by several authors2fQ9 and was explained by the formation of transient contact ion pairs of the sodium cation and the anion. With increasing salt concentration the number of ion pairs willalso increase; i.e., the average sodium chemical shift observed in the solutions is more and more affected by the short-range interaction between the Na+ cation and the adjacent anion in the ion pair. This interaction is, of course, at maximum for the solid compounds formed by stable complexes between sodium and the anions. For the oxyanions considered here, it is highly probable that the interaction proceeds via a charge transfer from the oxygen atoms of the anions to the sodium atom, which, however, is characteristically modified by the particular structure and the central atom of the anion. The conclusion is that the distinct chemical shift effects observed for 23Na in different compounds in the solution as well as in the solid state have the same origin, the particular bonding situation of the oxygen atoms in the anions. It will be shown below that this property can be described by the valence, i.e., the total bond valence, of the oxygen atoms. Of course, 6, of the solids is further affected by the Na-0 distances and the coordination number of the sodium. Quadrupole Parameters. As a first guideline for a qualitative interpretation of the quadrupole interaction in structural terms, Figure 7 gives a schematic representation of the quadrupole coupling constants calculated by the point charge model for different sodium-xygen polyhedra assuming oxygen charges of
-le and Na-0 distances resulting in unity valence for sodium with the different coordination numbers (2.31,2.40,2.46,2.52, and 2.57 A for coordination numbers 4-8, re~pectively).~OIt follows from these calculations that QCC is zero for regular tetrahedral or octahedral coordinations, increases for trigonal bipyramidal or quadratic pyramidal symmetry, and is largest for planar coordinations of four or six oxygen ions around sodium. Any deviation from these regular coordination symmetries and differences in the charges of the oxygen atoms will further affect the size of QCC. In line with these general conclusions, it is not surprising that no direct relation between thechemical composition of the samples and QCC is observed in Table 1; e.g., sodium silicates and sodium phosphates cover similar ranges for QCC and 1. Nevertheless, Table 1 shows that the quadrupole interaction depends sensitively on the structural environment of the sodium atom which will be demonstrated below by a few selected examples. Figure 2 displays the 23Na MAS N M R spectra of the four sodium silicate hydrates of composition Na2SiO2(OH)ynH20 with n = 8, 7, 5, 4. Despite the fact that these materials differ only in the water content, their spectra are very different and indicate the presence of distinct sodium coordinations. The structures of these compounds are formed from monomer [Si02(OH)2I2- silicate anions, water molecules, and sodium cati0ns.3~-3~The silicate anions and water molecules are linked via hydrogen bonds. The crystal structures illustrated in Figure 8 show that the sodium cations of the four compositions are differently coordinated by oxygen atoms of water molecules or silicate anions. In Na2Si02(0H)2*8H20a single sodium site is surrounded by six water molecules forming a distorted octahedral NaOa coordination31 (Figure 8a) which give rise to the single quadrupolar powder pattern observed in the spectrum (see Figure 2a). In contrast, the crystal structures of the compositions with n = 7, 5 , and 4 reveal two distinct sodium environments in each of these compounds, and two resonance lines appear in the corresponding spectra (see Figure 2b-d). In NazSiOz(OH)2*7H20,N a 1 is coordinated by by five water molecules and one oxygen atom of the Si02(0H)z2- anion and Na2 by six water molecules32 (Figure 8b). The two sodium ions in NazSiO2(OH)2*5H20 are also 6-fold coordinated. N a l has six water molecules and Na2 three water molecules and three oxygen atoms of silicate anions as nearest neighbors33 (Figure 8c). The two sodium sites in NazSiO2(OH)~4H20 are both 5-fold coordinated. Here, N a 1 is surrounded by three water molecules and two oxygen atoms of a single silicate anion, while Na2 is surrounded by four water molecules and one oxygen atom of a silicate anion34 (Figure
23Na N M R Spectroscopy of Solids 8d). The different sodium coordinations are clearly reflected in the corresponding quadrupole interactions (see Table 1) which are for example generally smaller for the sodium ions surrounded by six HzO molecules than for those having oxygen atoms of water and silicate anions in the first coordination sphere. However, an unambiguous assignment of the lines to the distinct sodium sites in the structures is not feasible from these qualitative considerations but can be derived from the quantitative correlations given below. The anhydrous sodium aluminosilicate sodalite Na,j[AlSiO& shows, besides a weak, narrow line at -14 ppm of a rehydrated impurity, a very broad line with a typical quadrupolar line shape (Figure 3b), indicating a large local electric field gradient with nearly axial symmetry at the sodium site.35 The sodalite framework is built up by a space filling array of 4668polyhedra (sodalite or 8-cages) consisting of alternating A104/2and Si0412 tetrahedra. The sodium cations are located close to the centers of the six-membered rings, thus forming a nearly planar coordination to six oxygen atoms of the same ring36(Figure 3a). As shown in Figure 7, this rather unusual geometry results in a large field gradient at the sodium site. The simulation of the quadrupolar MAS powder pattern yields QCC = 5.90 MHz, which, to the best of our knowledge, is the largest QCC value observed for sodium so far. A similar QCC of 5.8 MHz has been reported for dehydrated zeolite NaA3’ where the sodium cations are also located within the 6-ring windows of sodalite cages, the latter being, however, connected by four-membered rings forming double 4-rings and larger a-cages. Considerably smaller quadrupole interactions are observed for sodium in sodalites containing besides the sodium cations further guest species, e.g., OH-, C104-, NOz-, or H2O.35 In those structures, Na moves from the 6-ring windows into the sodalite cages and shows a more or less distorted nonplanar coordination to three oxygen atoms of the framework 6-rings at one side and to one or more oxygen atoms of the guest anions or HzO on the opposite side. The 23Na MAS N M R spectrum of the compound NaJ.3DMF (DMF = dimethylformamide) is shown in figure 3d. The simulation yields QCC = 1.18 MHz and q = 0, indicating a comparatively small and axially symmetric field gradient. In this structure,j* sodium is coordinated by oxygen atoms of six D M F molecules (Figure 3c) with equal Na-O distances of 2.41 1 A. The much longer Na-J distance of 6.98 A suggests that the local electric field gradient a t the sodium arises mainly from the D M F molecules. The coordination polyhedron formed by the six DMFoxygen atoms around sodium may be described by an -30° twisting of two opposite triangles of an octahedron (Figure 3c). The oxygen atoms are equivalent by the crystallographic D3 symmetry. According to Figure 7, an intermediate QCC between the octahedral and regular trigonal prismatic symmetry is to be expected for this coordination which is in agreement with the experimental finding. A considerably large QCC of 3.50 MHz is found for anhydrous sodium hydroxide, as already reported by Dec et al.25 The crystal structure of NaOH39 reveals that sodium is surrounded by five hydroxide ions in a quadratic pyramidal arrangement which according to Figure 7 is characterized by a strong quadrupole coupling.
Quantitative Correlations It follows from the qualitative considerations presented above that an adequate description of the chemical environment of the oxygen atoms surrounding the sodium atom is necessary for a quantitative interpretation of the quadrupole parameters and chemical shifts of 23Na in structural terms. A suitable concept for that purpose is the empirical bond-valence approach in which the valence, i.e., the strength of the distinct bonds formed by an atom, can be determined from the corresponding bond length.@ Since the valence can be thought of as the number of electrons taking part in chemical bonding, it seems reasonable to derive
The Journal of Physical Chemistry, Vol. 98, No. 6, 1994 1549
SCHEME 1
u parameter
specific quantities from the bond valences of the oxygen-cation bondswhich describe thechargedistribution in the sodium-xygen coordinations and are, therefore, related to the electric field gradient and chemical shift of the sodium atom. According to the bond-valence sij of a bond between an oxygen atom i and a cation j can be calculated by eq 1
where ri, (in angstroms) is the oxygen-cation bond length as determined by crystal structure analysis, ro is the empirically derived length of a oxygen-cation bond of unit valence and is tabulated for most cations in ref 30, and B = 0.37 is a constant. If an oxygen atom is involved in hydrogen bonds, si, of those bonds can be determined from Figure 1 of ref 30. Following the procedures discussed below and outlined in Scheme 1, specific expressions have been derived from the bond valence sij to determine both the oxygen charges for the calculations of the quadrupole parameters and an empirical shift parameter for the correlation with the isotropic chemical shifts of sodium. si, of oxygen-cation bonds in the structures of Table 1 were calculated from the corresponding oxygen-cation bond lengths taken from the literature (see references in the last column ofTable l), except thosestructures for which reliable bond lengths are not available. Only oxygen atoms located in a sphere of 3.4-%r.radius around the sodium position were included in the calculations since it turned out that effects of further distant oxygen atoms can be neglected. Chemical Shifts. The specific contribution of a certain oxygen atom to the chemical shift of the sodium cation to which it is coordinated is assumed to be related to its total atomic valence Wiand the sodium-oxygen distance ri. Wiof the distinct oxygen atoms i present in the structures studied here were obtained from the sum of the oxygen-cation bond valences si, of all cations j bonded to the oxygen which also includes the sodium cation (eq 2).
y.=
&, f
Wi covers the range between 1.82 (for the oxygen of a H20
molecule in Na2Si02(OH)2.8H20) and 2.16 (for the oxygen in the perchlorate anion of NaC104.H20). The Na-O distances ri vary between 2.25 %r. (in Na3P309) and 3.38 A (in Na2SiOz(OH)2*4Hzo), and since the chemical shift contribution of the distinct oxygens around sodium is expected to decrease with increasing Na-0 distance, the effect of the latter is described by
Koller et al.
1550 The Journal of Physical Chemistry, Vol. 98, No. 6, 1994
1
30 I
t
0
6 5
0.6
4
3
I;.
..
2 1
0 -
\..\
4
-20
-308 0.5
f
'
'
0.6
I
0.7
'
'
I
0.8
I
I
'
0.9
1.0
I
6
1.1
' '
I
lo
tt
1
5 1
1
li " .
1
1.o
0.8
I.
0.4
0.2 0.0 1 .o 0.8
0.4 o.6
8=
t :::
'
A
Figure 9. Plot of isotropic 23Na chemical shifts,, ,a parameter A (see text).
0.8
versus the shift
0.6 0.4
an l/rf dependence. Assuming that the chemical shift of the sodium cation is the sum of the shift contributions of all oxygen atoms located in a sphere of 3.4-A radius around sodium (see above), a shift parameter A is defined according to eq 3
The best correlation between A and the experimental isotropic shifts 6,, occurred for n = 2.87, which is close to n = 3. Thus, a distance dependence of l/ri3 has been assumed in eq 3. The shift parameters A calculated by eq 3 are given in Table 1, and the correlation between A and the experimental 23Na chemical shifts 6,, is illustrated in Figure 9. Linear regression analysis results in the correlation equation
6,, = -133.6A
+ 107.6
(4)
with a correlation coefficient of 0.91 and a standard deviation of 4.1 ppm. It should benoted that similar correlations between the total bondvalenceof the four oxygen atomsofthe SiO, tetrahedron and the 29Si chemical shifts in silicates were reported by Sheriff and Grundy4' and Smith et al.42 Quadrupole Parameters. Three different models were applied to determine the charges of the oxygen necessary for the point charge calculations of QCC and 7. Since different approximations were used in the distinct models, they will, of course, result in different values of the oxygen charges, and the question arises which model will be most appropriate to reproduce the experimental QCC and 7 values by the point charge calculations. The first model (model I in Scheme 1) is based on the oxygen-cation bond valence sij from which the covalenceJj of each bond is calculated by the empirical equation of Brown and Shannon.43 f j
= asijM
In this equation a and M a r e empirical parameters depending on the number of core electrons of the cations in the oxygen+ation bonds,43 and sij is the oxygen-cation bond valence as obtained from eq 1. The charge qi of the oxygen atom is calculated from the sum of all covalences minus two (eq 6).
0.2 0.0 0 0
1
2
3
4
5
6
0.0 0.2 0.4 0.6 0.8 1.0
accCaI, M H ~ 'Icaic Figure 10. Plots of experimental values of QCC and 7 versus the correspondingdata calculated by models I, 11,and I11 (see text and Table 1).
of Pauling@ (model I1 in Scheme 1)
zij = 1 - exp[-(xi
- xj)'/4]
(7) where xi and xj are the electronegativities of the oxygen atoms i and the cationsj in the bond. The oxygen charge qi is then given by the sum of the ionic characters of all bonds of the oxygen atom:
Since electronegativities are available for all elements?, model I1 is universally applicable but yields a less reliable description of the charge distribution. This is particularly true for the transition metals, and therefore, NazCr04 was not included in the calculations. Oxygen atomic charges between -0.44e and -1.5 l e have been obtained by this model. Finally, for selected structures the charges of the oxygen atoms were determined by quantum chemical ab initio calculations (model 111) as described in the Experimental Section. The oxygen charges determined are in the range -0.70e to -1.18e. The results obtained for QCC and 7 from the point charge model calculations (see Experimental Section) using the oxygen charges of models I, 11, and I11 are collected in Table 1 and plotted against the experimental data in Figure 10. The best fit between the calculated and experimental QCC values is clearly observed for model I (Figure loa). Linear regression analysis results in the correlation equation
QCC,,, = 1.06QCC,,,,,,,
+ 0.19
(9)
with a correlation coefficient of 0.91 and a standard deviation of 0.44 MHz. Though the QCC values calculated from the charges of models I1 and I11 also describe the gross trends of the Since chromium in NazCrO4 shows large deviations from the experimental data, they show, in general, larger deviations (see empirical relation of eq 5,43 and no reliable neutron diffraction data are available for the hydrogen atoms in N ~ z C ~ H ~ O V H Z O ,Table 1 and Figure 10c,e). NaJ-3DMF, and NaH2P04.H20, model I has not been applied Different from QCC, the best correlation between the calculated to these structures. The oxygen charges determined by this and experimental values of 7 is observed for model I11 (Figure procedure cover the range of -0.56e to -1.27e. 100, while the correlations of models I and I1 are very poor (Figure 10b,d). Omitting 7 of N a l in NasP309, which shows an A second set of oxygen atomic charges was calculated from exceptionally large deviation, linear regression analysis of the the ionic character Zij of the oxygen bonds given by the formula
23Na N M R Spectroscopy of Solids data of model I11 yields
with a correlation coefficient of 0.90 and a standard deviation of 0.11,
Conclusions Although rather crude approximations were introduced in the empirical models developed in this study for the calculation of the quadrupole interaction parameters (QCC and q ) and chemical shifts (6,) of 23Na in sodium-oxygen coordinations, reasonable correlations have been obtained between the calculated and experimental data. The general conclusion may be drawn that the bond-valence approach is a suitable concept to establish empirical relations between the crystal structure and 6, as well as QCC as calculated by the simple point charge model. Within this concept it follows that 6, is related to the total valence and the Na-0 distances of all oxygen atoms located in a sphere of 3.4-A diameter around the sodium cation, while the electric field gradient a t theZ3Nanucleus and, therefore, QCC may be described by point charges at the crystallographic oxygen sites determined from the total covalences of the respective oxygen atoms present in the 3.4-A sphere (model I). QCC calculated from oxygen atomic charges which were obtained from the electronegativities of oxygen and the cations (model 11) or quantum chemical a b initio calculations (model 111) correlate, in general, less well with the experimental data. Surprisingly, the best correlation for 7 is observed if the charges from the a b initio calculations were used while the bond-valence and electronegativity model yield considerable scatter. Since q is the ratio of the principal values of the field gradient tensor, this probably means that the ab initio calculations do predict the relative sizes of the charges within one structure fairly well. The ab initio model is, however, less reliable in predicting the absolute values of the charges correctly as the calculated and experimental QCC values do not correlate so well. In fact, the range of charges found by the a b initio calculations is the smallest which explains that the calculated QCC values in Figure 10e all bunch together. On the other hand, the bond-valence model is probably quite good at estimating the effective charges of most oxygens. As 7) deviates substantially in certain cases, it may well be that this model only fails for certain specific oxygen atoms. Owing to their relatively large standard deviations, even the best correlations obtained are obviously of limited use for the direct calculation of accurate values of, ,6 QCC, or q from crystal structures. The correlations can be applied, however, to predict approximate values of these parameters which may be useful for the correct attribution of distinct lines in the Z3NaN M R spectra to the specific crystallographic sodium sites. In fact, the assignment as given in Table 1 of the spectra showing two lines has been accomplished this way. Furthermore, comparison of the experimentally determined values of 6, and QCC with those estimated from structure data opens a new possibility to prove the correctness of a proposed crystal structure and/or to aid the structure refinement. Comparison with model structures may be of special use in glassy materials where no crystal structure data exist. Then N M R can give an indication of the local environment of the nucleus under study. Acknowledgment. Support of this work by the Deutsche Forschungsgemeinschaft and the Alfried Krupp von Bohlen und Halbach-Stiftung is gratefully acknowledged. References and Notes (1) Andrew, E. R. Philos Trans. R . SOC.London, A 1981, 299, 505.
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