Cesium-133 NMR study of CsCd(SCN)3: Relative orientation of the chemical shift and electric field gradient tensors

Article abstract of DOI:10.1021/jp970043a

Single-crystal NMR was used to characterize the cesium-133 chemical shift and electric field gradient (EFG) tensors in CsCd(SCN)₃. The principal axes of the two interaction tensors are not coincident, a reflection of the general positioning of cesium nuclei within the unit cell. Relative orientations of the chemical shift and EFG tensors have been determined, but assignment of the two magnetically distinct sites remains elusive. The span of the chemical shift, 94.4 ppm, is moderate in comparison with other cesium salts, and the magnitude of the nuclear quadrupole coupling constant, 148 kHz, is in the midrange of those reported for cesium compounds. Excellent agreement is observed between experimental ¹³³Cs NMR spectra of a stationary powder sample and spectra calculated using NMR parameters from the single-crystal analysis. Moreover, simulations indicate that the static line shape is very sensitive to the relative orientation of the chemical shift and EFG tensors. Experimental ¹³³Cs NMR spectra obtained with magic-angle and variable-angle spinning are well reproduced by calculations utilizing single-crystal NMR data.

Full text of DOI:10.1021/jp970043a

J. Phys. Chem. B 1997, 101, 3727-3733
3727
Cesium-133 NMR Study of CsCd(SCN)3: Relative Orientation of the Chemical Shift and
Electric Field Gradient Tensors
†
†
†,
‡
Scott Kroeker, Klaus Eichele, Roderick E. Wasylishen, * and James F. Britten
Department of Chemistry, Dalhousie UniVersity, Halifax, NoVa Scotia, Canada B3H 4J3, and
Department of Chemistry, McMaster UniVersity, Hamilton, Ontario, Canada L8S 4M1
X
ReceiVed: December 19, 1996
Single-crystal NMR was used to characterize the cesium-133 chemical shift and electric field gradient (EFG)
tensors in CsCd(SCN) . The principal axes of the two interaction tensors are not coincident, a reflection of
3
the general positioning of cesium nuclei within the unit cell. Relative orientations of the chemical shift and
EFG tensors have been determined, but assignment of the two magnetically distinct sites remains elusive.
The span of the chemical shift, 94.4 ppm, is moderate in comparison with other cesium salts, and the magnitude
of the nuclear quadrupole coupling constant, 148 kHz, is in the midrange of those reported for cesium
133
compounds. Excellent agreement is observed between experimental Cs NMR spectra of a stationary powder
sample and spectra calculated using NMR parameters from the single-crystal analysis. Moreover, simulations
indicate that the static line shape is very sensitive to the relative orientation of the chemical shift and EFG
tensors. Experimental 1 Cs NMR spectra obtained with magic-angle and variable-angle spinning are well
reproduced by calculations utilizing single-crystal NMR data.
33
Introduction
Of the quadrupolar nuclei, cesium-133 is unusually favorable
Alderman et al.17 Taken together, computations that were
essentially intractable in the 1970s became trivial in the 1990s.
Second, the growing number of examples of tensor noncoin-
cidence has begun to demonstrate that coincidence of the
chemical shielding and electric field gradient tensors, when not
required by symmetry, is merely a coincidence. From a
theoretical perspective, this assertion comes as no surprise, since
the physical origin of these interactions is completely differ-
ent: the electric field gradient is a first-order property, whereas
for study by NMR. Its 100% natural abundance combines with
a relatively large magnetic moment to produce a receptivity 270
times that of 13C at a constant field. A spin /2 nucleus, Cs
has a moderate chemical shift range of about 600 ppmsthe
largest of the alkali-metal nuclei. Moreover, in the applied
magnetic fields of typical NMR experiments, the nuclear
quadrupole interaction is sufficiently small that first-order
perturbation theory is usually adequate to describe the resulting
line shape.
1,2
7
133
1
8
chemical shielding is a second-order property.
A variety of methods has been employed in determining the
Cesium is found in many important materials, and solid-state
cesium-133 NMR has played a crucial role in their study.
relative orientation of these nuclear interactions. Single-crystal
14,15,19-22
NMR has played a crucial role in this regard,
primarily
1
33
Applications of Cs NMR to such a variety of materials as
because of the straightforward, if somewhat tedious, analysis
of the data to yield unambiguous tensor orientations with respect
3
,4
5-8
9
clay minerals, zeolites,
semiconductors, alkalides and
1
0
11-13
electrides, and doped fullerene superconductors
have
23
51
to the crystal frame. Gornostansky and Stager’s 1967
V
provoked interest in a more complete understanding of the
fundamental interactions underlying the observed spectra.
Until recently, the assumption that the chemical shielding and
electric field gradient (EFG) tensors are coincident was prevalent
in the analysis of NMR spectra of quadrupolar nuclei. In fact,
prior to 1990, there were only two reports of noncoincidence
14
NMR study of a single crystal of vanadium pentoxide
represents the first example in which the EFG and chemical
shielding tensors were found to be noncoincident. Other
investigations of these tensors by single-crystal NMR have
59
15 17
focused on Co in K3Co(CN)6 and Co(acetylacetonate)3,
O
19 133
20
24
in benzophenone,
Cs in Cs2HgBr4, Cs2SO4, and Cs2-
14,15c
of these tensors.
This assumption may have stemmed from
CrO4, and 87Rb in Rb2CrO4,25 RbClO4, and Rb2SO4.
2
1
22
the practical difficulties associated with theoretical treatments
of spin systems involving both interactions in a general
orientation with respect to one another. In particular, analytical
Considerable effort has been devoted to the development of
techniques for extracting chemical shift and EFG tensors from
2
6-36
NMR spectra of powder samples.
spinning (MAS)
Several magic-angle
expressions can be developed if the tensor orientations are
3
2,33
35,36
assumed coincident;16 otherwise, numerical simulations are
and variable-angle spinning (VAS)
experiments, for example, have been used. In some cases, these
methods yield reliable EFG and chemical shift parameters;
however, it is more difficult to obtain information about the
relative orientation of these tensors. Regardless of the confi-
dence one places in the relatiVe tensor orientations, powder
NMR methods can offer no insight about the absolute orienta-
tions of the tensors with respect to the crystal axes, in the
absence of special symmetry.
required. Moreover, many of the early investigations were
performed using electromagnets where low fields rendered the
chemical shielding interaction negligible, thus tacitly sustaining
the assumption.
Two factors can be identified in the dismantling of this
assumption. First, from a pragmatic perspective, the develop-
ment of faster computers has facilitated the calculation of spectra
using numerical simulations. Efficiency was further improved
with the introduction of the powder-averaging algorithm by
In this paper, we report a cesium-133 single-crystal NMR
study of CsCd(SCN)3. The crystal structure indicates that
cesium nuclei lie in general positions and no symmetry
restrictions are incumbent upon the tensor orientations. Also
*
Author to whom correspondence should be addressed. Phone: 902-
4
94-2564. Fax: 902-494-1310. E-mail: rodw@is.dal.ca.
†
Dalhousie University.
McMaster University.
Abstract published in AdVance ACS Abstracts, April 15, 1997.
1
33
‡
presented are Cs NMR spectra of spinning and stationary
powder samples of CsCd(SCN)3. Successful simulations of
X
S1089-5647(97)00043-6 CCC: $14.00 © 1997 American Chemical Society

3728 J. Phys. Chem. B, Vol. 101, No. 19, 1997
Kroeker et al.
spectra using data obtained from the single-crystal analysis
confirm the single-crystal results.
Experimental Section
Materials. Cesium trithiocyanatocadmate, CsCd(SCN)3, was
prepared by dissolving stoichiometric amounts of Cd(SCN)2 and
CsSCN in a 1:2 ethanol-water mixture.37 Slow evaporation
of the solvent yielded large crystals of the title compound.
Cadmium thiocyanate was prepared by metathesis of cadmium
sulfate and barium thiocyanate.38 Cesium thiocyanate was
synthesized in a similar fashion, from cesium carbonate and
ammonium thiocyanate in water. Starting materials were
obtained from commercial sources and used without further
purification.
Single-Crystal NMR. A crystal of CsCd(SCN)3 was mounted
3
in a hollow, three-sided, 4-mm alumina cube. The orientation
of the crystal axes with respect to the cube frame was determined
by placing the mounted crystal on an X-ray diffractometer and
indexing a sufficient number of reflections. Cesium-133 NMR
spectra of the crystal were acquired at 52.48 MHz on a Bruker
AMX-400 spectrometer (9.4 T) with a Doty single-crystal probe
(Doty Scientific, Columbia, SC). The sweep width was 200
kHz, and 64 transients were coadded. Each spectrum consisted
of 2 K points zero-filled to 4 K. The “solution π/2” pulse width
was calibrated using a solution of 0.5 M CsCl(aq) to be 2.5 µs
(
νrf ) 100 kHz). For the crystal, a small flip angle correspond-
133
ing to about 30° was used. Due to the long Cs nuclear spin-
lattice relaxation time, a recycle delay of 2 min was required.
Spectra were referenced to the 0.5 M CsCl(aq) peak.
Figure 1. (A) Energy levels of a spin 7/
nucleus for a particular
2
crystallite orientation in an applied magnetic field and (B) the resulting
NMR spectrum.
NMR Spectra of Powders. A static spectrum of CsCd-
SCN)3 at 52.48 MHz was obtained using a 5-mm Bruker probe
(
with a solenoidal coil oriented perpendicular to the applied
magnetic field. A finely ground sample was packed into about
1
cm of a 5-mm-diameter glass NMR tube and plugged. This
tube was placed in the center of the coil. The solution π/2 pulse
width was 2.9 µs (νrf ) 86 kHz). One quarter of this value
was used for the single-pulse excitation. A spectral width of
1
00 kHz was used. Eight hundred eighty scans were collected
with a recycle delay of 2 min. Each transient consisted of 2 K
points zero-filled to 4 K.
MAS and VAS NMR spectra were obtained at 26.24 MHz
using a Bruker MSL-200 spectrometer operating at 4.7 T.
Rotors (7 mm) were packed with a finely ground sample and
spun at 3-4 kHz. A typical experiment utilized a 125-kHz
spectral width, coadding several hundred transients of 8 K data
points. Before Fourier transformation, the data file was zero-
filled to 16 K. A recycle delay of 2 min was used, and νrf
ranged from 40 kHz for the MAS spectrum to 67 kHz for the
VAS spectra. VAS experiments were carried out with a Bruker
MAS probe by changing the angle of rotation from 54.74°.
Calibration of the spinning angle utilized the central transition
of CsSCN (Vide infra).
Figure 2. Typical cesium-133 NMR spectrum of a CsCd(SCN)
3
crystal. All peaks arising from one of the magnetically distinct sites
are indicated by asterisks. Shoulders visible near the outermost sets
of satellites are due to crystal twinning.
Spectral Simulations. NMR spectral simulations of station-
ary and spinning samples were performed using QUADSPIN,
a C program developed in this lab which utilizes the powder-
averaging algorithm of Alderman et al.17 For spinning samples,
QUADSPIN computes the free induction decay of a spin system
subject to both chemical shielding and a first-order quadrupole
perturbation. This program accounts for a general relative
orientation of these tensors and, in spinning powder simulations,
a general axis of rotation with respect to the applied magnetic
field direction. These calculations were carried out with an IBM
Results and Discussion
Single-Crystal NMR Spectra. The energy level diagram
7
of a spin /2 nucleus in a strong magnetic field consists of eight
energy levels and, hence, seven single-quantum transitions
133
(Figure 1). A typical Cs NMR spectrum of the CsCd(SCN)3
single crystal is shown in Figure 2. From this spectrum, it is
evident that two seven-peak patterns are present. In order to
understand this, one must examine the space group symmetry
of the crystal.
8
0486 and a SGI Indy workstation equipped with a R4600
CsCd(SCN)3 crystallizes in a monoclinic lattice, with the
space group P21/c. Four formula units are present in the unit
3
7
processor.

Cesium-133 NMR Study of CsCd(SCN)3
J. Phys. Chem. B, Vol. 101, No. 19, 1997 3729
TABLE 1: Cesium-133 Chemical Shift Parameters, in Hz,a
from a Least-Squares Fit of Central Transition Peak
Positions in CsCd(SCN)
3
at 52.48 MHz. Standard
Deviations Given in Parentheses
parameter
site 1
site 2
σ
1
860(20)
3690(20)
-540(30)
580(30)
2750(10)
1490(20)
-1540(20)
2250(10)
-1120(10)
-1190(20)
A
B
X
σ
X
1660(20)
σ
-
1080(20)
628(8)
2320(10)
C
A
X
σ
2
Y
σ
-
B
Y
σ
-
4
7
-
80(10)
220(8)
20(10)
80(10)
C
Y
σ
A
Z
σ
B
Z
σ
Z
C
a
Referenced to 0.5 M CsCl(aq) at 0.0 Hz.
TABLE 2: Averaged Cesium-133 Chemical Shift Tensor
a
Principal Components in ppm (Top Row) and Direction
Figure 3. Rotation plots illustrating variations in the cesium-133 central
transition peak position as a function of the rotation angle. Solid lines
represent fits to eq 1.
Cosines Relative to the Orthogonalized Crystal Frame
b
(Bottom Rows) in CsCd(SCN)
3
δ
11
δ
22
δ
33
93.8c
72.6c
-0.367
-0.283
-0.886
-0.6c
-0.435
-0.790
+0.433
cell, but all cesium nuclei are crystallographically equivalent.
Crystallographic equivalence arises from nuclei which are
related by any symmetry operation and demands only that the
principal components of the interaction tensors be identical.
-0.822
+
+
0.544
0.167
1
33
a
Referenced to 0.5 M CsCl(aq) at 0.0 ppm. b Direction cosines of
site 2 can be generated from those of site 1 by ( xj , y, jz ). Errors in the
principal components estimated to be (0.5 ppm.
Thus, in a powder sample, a single site is observed in the Cs
NMR spectrum (Vide infra). However, in order to predict how
many signals will be observed in the single-crystal NMR
spectrum, it is necessary to consider the distinction between
crystallographic and magnetic equivalence. Magnetic equiva-
lence emerges when nuclei are related by symmetry elements
that retain an equivalent orientation with respect to the applied
magnetic field. Sites related by a center of inversion, for
instance, are magnetically equivalent, whereas rotation axes or
mirror planes imply magnetic nonequivalence. Clearly, it is
possible for multiple signals to be observed from a crystal with
a single crystallographic site if they are symmetry-related in
such a way that their principal components are not oriented
identically. In the case of CsCd(SCN)3, a given cesium nucleus
in the unit cell is related to another in the cell by an inversion
center (magnetically equivalent) and the remaining two by a
screw axis (magnetically nonequivalent). Consequently, the
resulting spectrum consists of two seven-peak patterns reflecting
this symmetry arrangement. Due to the crystallographic
equivalence, the principal components of the chemical shielding
and nuclear quadrupole interaction tensors obtained from
analysis of each magnetically distinct site will be identical, but
their orientations will be related by rotation about the crystal b
axis.
c
σ
1
2
σ
σ
Y
σ
σ
ν
ν
ν
XX ) (A
- B
+ A
+ B
)
(2)
(3)
(4)
Y
Z
Z
σ
YY
1
2
σ
Z
σ
Z
σ
X
σ
X
) (A - B + A + B )
σ
ZZ
1
2
σ
X
σ
X
σ
Y
σ
Y
) (A - B + A + B )
σ
σ
σ
ν
ν
ν
) ν ) -CZ
(5)
(6)
(7)
XY
YX
σ
XZ
σ
σ
) ν ) -CY
ZX
σ
YZ
σ
σ
X
) ν ) -C
ZY
Upon diagonalization of the chemical shift tensor, one obtains
σ
σ
σ
the principal values, ν11 , ν22 , ν33 and the direction cosines
relating the principal axis system (PAS) of the chemical shift
tensor to the cube frame. The chemical shift tensor averaged
from the two sites has a span of 94.4(5) ppm and an isotropic
value of 55.3(5) ppm; the asymmetry in the chemical shift
tensor, ηCS, is 0.38(5). The Euler angles rotating the cube frame
into the orthogonalized crystal frame, (a*, b, c), are R′ ) 98.7°,
â′ ) 98.4°, and γ′ ) 240.3°. By rotation according to these
angles, the orientation of each chemical shift PAS in the crystal
frame was determined (Table 2).
Cesium-133 NMR spectra were acquired as a function of
crystal orientation in the magnetic field. Rotations were
performed about the orthogonal X, Y, and Z axes of the cube
frame, with 21 spectra acquired for each rotation; these
corresponding to 9° increments of the rotation angle, ψ. Each
peak was assigned to the appropriate transition and site.
Observed central transition positions were fit to sinusoidal curves
to obtain parameters related to the chemical shift tensor (Figure
A similar procedure was followed in the analysis of the
quadrupole-induced splittings. Since the observed splittings,
νm ) νmTm-1 - ν1-mT-m, between symmetrical satellite peaks
∆
23
3
):
are related to the nuclear quadrupole interaction in the laboratory
frame by a constant, one approach is to average the satellite
σ
i
σ
i
σ
i
σ
i
2
1
ν (ψ) ) A + B cos 2ψ + C sin 2ψ (i ) X, Y, Z) (1)
splittings:
since the central transition is unaffected to first order by the
quadrupole interaction. A set of coefficients, A , B , and C ,
was generated for each rotation, yielding nine for each site
eQVzz
7
18
)
[6∆ν3/2 + 3∆ν5/2 + 2∆ν7/2]
(8)
σ
σ
σ
h
(
Table 1). These are related to the chemical shift tensor in the
where z is the direction of the applied magnetic field and Vzz
represents the z component of the electric field gradient, eqzz.
cube frame according to the following expressions:

3730 J. Phys. Chem. B, Vol. 101, No. 19, 1997
Kroeker et al.
TABLE 4: Averaged 133Cs Nuclear Quadrupole Interaction
Tensor Principal Components, in kHz (Top Row), and
Direction Cosines Relative to the Orthogonalized Crystal
a
Frame (Bottom Rows) of CsCd(SCN)
3
eQV11/h
.17b
eQV22/h
147.2b
-0.490
-0.871
-0.022
eQV33/h
1
-148.4b
-0.727
+0.423
-0.540
+0.480
-0.249
-0.841
a
Direction cosines of site 2 can be generated from those of site 1
b
by ( xj , y, jz ). Errors in the principal components estimated to be (3
kHz.
into the crystal frame, as for the chemical shift tensor (Table
4
). The magnitude of the quadrupole coupling constant is the
largest component, eQV33/h ) 148(3) kHz. Utilizing the
following convention for the EFG tensor principal components,
Figure 4. Rotation plots illustrating variations in the cesium-133
quadrupolar interaction in the laboratory frame (eq 8) as a function of
the rotation angle. Solid lines represent fits to eq 9.
|V | g |V | g |V |
(16)
3
3
22
11
one can also obtain the asymmetry in the quadrupole interaction
tensor,
TABLE 3: Cesium-133 Quadrupole Splitting Parameters
3
for CsCd(SCN) , in kHz, from a Least-Squares Fit to
Equation 9. Standard Deviations Given in Parentheses
V - V
22
1
1
parameter
site 1
site 2
ηQ )
) 0.98(3)
(17)
Q
X
V33
A
45.0(5)
-96.6(5)
-48.5(2)
-23.8(5)
68.8(5)
33.4(7)
-71.4(9)
88.4(9)
12.1(5)
88.4(5)
23.1(5)
Q
B
X
Q
C
-
26.8(5)
32.0(5)
From the direction cosines, it is clear that the chemical shift
and EFG tensors are not coincident. The Euler angles relating
the chemical shift PAS to the EFG have been derived according
to the convention that R represents a positive rotation about
the z axis of the EFG tensor in its PAS, â represents a positive
rotation about the new y axis, and γ is a positive rotation about
the new z axis. Thus, R ) 113°, â ) 105°, and γ ) 140°.
One can make use of the symmetry relationship between the
two magnetically distinct sites to arrive at an estimate of the
errors to which these results are subject. First, since the nuclei
are crystallographically equivalent, the principal components
for the two sites should be equal. Hence, the difference in these
is indicative of the minimum error associated with the magni-
tudes. Second, according to the crystal symmetry, rotation of
one experimentally determined tensor by 180° about the
crystallographic b axis should align the principal axes. To the
extent that these axes differ, one has a measure of the error
associated with the absolute orientations. On this premise, we
find the absolute orientations to be accurate to about 3°.
Assignment of Tensor Orientations. The presence of two
magnetically inequivalent cesium sites raises the question of
assignment: which set of tensor orientations corresponds to
which cesium site in the unit cell? A variety of approaches
has been considered to distinguish between the two possible
assignments.
X
Q
A
Y
Q
Y
B
118.1(7)
2.1(3)
-70.2(2)
-3.0(5)
78.2(5)
Q
C
A
Y
Q
Z
Q
B
Z
Q
CZ
This averaged value was plotted as a function of ψ for each
rotation (Figure 4) and fit to
eQV (ψ)
zz
i
Q
Q
Q
)
A + B cos 2ψ + C sin 2ψ (i ) X, Y, Z) (9)
i i i
h
thereby yielding a set of nine coefficients for each site (Table
). These are related to the nuclear quadrupole interaction
tensor, eQVij/h, in the cube frame according to the following
3
3
9
expressions:
eQVXX
1
3
Q
X
Q
Y
Q
Y
Q
Z
Q
Z
)
)
)
(-2A + A - B + A + B )
(10)
(11)
(12)
(13)
(14)
(15)
h
eQVYY
1
3
Q
Y
Q
Z
Q
Z
Q
X
Q
X
(-2A + A - B + A + B )
h
eQVZZ
1
3
Q
Z
Q
X
Q
X
Q
Y
Q
Y
To assign the orientation of the chemical shift tensors, one
might attempt to calculate the chemical shielding of a cesium
nucleus in the unit cell. Although ab initio calculations of
chemical shieldings are becoming increasingly reliable for first-
and second-row elements, trustworthy computations of heavier
(-2A + A - B + A + B )
h
eQVXY
eQVYX
Q
)
) -CZ
h
h
4
0,41
elements such as cesium are not yet feasible.
Moreover,
eQVXZ
eQVZX
the covalent nature of the bonding in many of the well-studied
elements permits calculations to be performed on a single
molecule. For an ionic system like the one at hand, it would
be necessary to include some reasonably sized volume sur-
rounding the atoms of interest. While this may be possible for
systems with fewer, or lighter, ions, the constituent components
of the unit cell of interest would require prohibitively lengthy
computational times to obtain meaningful results at the present
time.
Q
)
) -CY
h
h
eQVYZ eQVZY
Q
)
) -CX
h
h
Diagonalization of the eQVij/h tensor yields principal compo-
nents eQV11/h, eQV22/h, and eQV33/h. The direction cosines
orienting these components in the cube frame can be rotated

Cesium-133 NMR Study of CsCd(SCN)3
J. Phys. Chem. B, Vol. 101, No. 19, 1997 3731
Chemical shift tensor assignments may be based on qualitative
considerations of the local cesium environments. In some cases,
for example, the nuclei of interest occupy special positions in
the cell which place symmetry constraints on the orientations.
This is not so in CsCd(SCN)3scesium placements are com-
pletely general. For some nuclei, empirical guidelines have been
offered for understanding their orientations. From a close
examination of the local environment at the two magnetically
nonequivalent sites, it is impossible to assign the sites based
on their chemical shifts. Cesium nuclei are relatively isolated
-
with respect to the [Cd(SCN)3] network. It is necessary to
conclude that any relationship between the local structure and
the orientation of the 1 Cs chemical shielding tensor is governed
by subtle and complicated effects which are not apparent upon
inspection.
33
A similar approach can, in principle, be employed to
adjudicate between the orientations of the EFG tensors. In this
case, however, qualitative arguments based on local symmetry
and structural characteristics are even less trustworthy, since
the EFG tensor is known to be sensitive to longer range effects
than the chemical shielding tensor. More promising is the point
charge model described by Slichter.42 This model has been used
extensively over the years and has proven itself to be a reliable
2
1,32d
tool when care is taken in interpreting the results.
In
essence, this model simply considers each atom in the lattice
as a point charge and computes the electric field gradient at a
particular position. In its application to this system, the
computed EFG tensor for a given cesium nucleus reproduces
the relative magnitudes of the principal components adequately.
The result of greatest interest, however, is the orientation of
these components, and this is found to compare equally well to
either experimental orientation. For example, the largest
component determined by the point charge model essentially
bisects the angle formed between the largest components of the
two sites.
Figure 5. Calculated (A) and experimental (B) cesium-133 NMR
powder patterns of CsCd(SCN) acquired at 52.48 MHz. Calculated
3
spectrum is based on parameters obtained from single-crystal NMR
data: δ11 ) 93.8 ppm; δ22 ) 72.6 ppm; δ33 ) -0.6 ppm; eQV33/h )
148 kHz; ηQ ) 0.98; R ) 113°; â ) 105°; γ ) 140°.
However, since the variation occurs simultaneously in both sites,
this approach is also inconclusive.
In summary, the orientational assignment of the experimen-
tally determined interaction tensors remains elusive. However,
the insight provided by these failed attempts proves valuable:
each of the two chemical shielding tensor orientations and each
of the electric field gradient orientations appears to be sur-
rounded by similar environments when assigned to the same
cesium nucleus, bearing no obvious relation to neighboring
nuclei or anionic fragments. The fact that the relative orienta-
tions are yet very different emphasises that the orientational
behavior of these interaction tensors is exceedingly sensitive
to the surrounding environment.
The failure of the point charge model to aid in the assignment
of the two orientations merits a few comments. At first, the
special utility of this method for ionic systems appears to be an
advantage for the case of CsCd(SCN)3. A problem is encoun-
tered, however, in assigning charges to the thiocyanate anion.
Clearly, it cannot be treated as a point charge, but the distribution
of charge among the three constituent atoms is not obvious.
Based on the natural bond orbital charges from a high-level ab
initio calculation of the SCN anion,43 it appears that the terminal
atoms can be reasonably assigned charges of -0.5 each, while
the central carbon is not appreciably charged. The recognition
that charge assignment schemes are ultimately arbitrary must
be accepted as a limitation in the model. Any scheme designed
to circumvent this problem by accounting for the electron
distribution in the surrounding lattice necessitates the invocation
of quantum mechanical computations.
In every example of noncoincidence presented by single-
crystal NMR, at least one of the axes is determined by
14,15c,20-22
symmetry.
By contrast, the crystal structure of CsCd-
(SCN)3 indicates that no local symmetry effects are present to
impose constraints on the cesium-133 tensors. Correspondingly,
the orientations of the chemical shielding and electric field
gradient tensors are also free of symmetry constraints. This
appears to be the first report of a single-crystal NMR study in
which these tensor orientations are completely free of symmetry
limitations.
Another potential source of information about the tensor
orientations is the line widths.23 Intermolecular dipolar interac-
tions contribute to the line widths observed in solid-state NMR
experiments. Since the largest component of the dipolar
coupling tensor is always along the internuclear vector, a
comparison of the relative line widths between sites may permit
a qualitative assessment of the orientation sufficient to make
assignments. The remote positioning of the cesium atoms in
the crystal lattice suggests that such dipole couplingsshetero-
and homonuclearswill be small, but they may be large enough
to influence the line widths. In the present case, the line width
of the central transition does indeed appear to be affected by
dipolar interactions and ranges from 180 to 360 Hz for different
orientations of the crystal in the applied magnetic field.
133Cs NMR Spectrum of a Stationary Sample. In order to
compare the parameters determined from the single-crystal NMR
study, a static spectrum of finely ground CsCd(SCN) was
3
obtained at 9.4 T (Figure 5). The calculation of this spectrum
required as input the three principal components of the chemical
shift tensor, the nuclear quadrupole coupling constant, the
asymmetry in the EFG, and three Euler angles to specify the
relative orientation of the two tensors. The computed spectrum
agrees well with the experiment.
In many cases, when single-crystal NMR data are unavailable,
the analysis of static powder patterns can be a challenge. It is

3732 J. Phys. Chem. B, Vol. 101, No. 19, 1997
Kroeker et al.
Figure 7. Calculated (A) and experimental (B) cesium-133 VAS
spectra of CsCd(SCN) acquired in an applied magnetic field of 4.7 T
3
at a spinning angle of 52.25°. The calculated spectrum is based on
parameters obtained from single-crystal NMR data (see Figure 5).
Figure 6. Simulated static cesium-133 NMR spectra depicting
variations in the line shape due to systematic modifications of the angle,
â, between the largest components of the chemical shift and electric
field gradient tensors. Dotted lines highlight the movement of the steps.
All other parameters as in Figure 5.
There has been a great deal of interest in the development of
iterative fitting schemes for powder NMR spectra of quadrupolar
nuclei. The motivation is provided, in large part, by the
difficulties sometimes encountered in growing sufficiently large
single crystal. This limitation often necessitates acquiring NMR
spectra of powder samples and attempting to disentangle the
respective interactions by simulations of the experimental
spectra. However, many pitfalls are associated with this
enterprise, and so far, the success of such iterative algorithms
has been limited to special cases.
Crucial to the development of any such program are reliable
data with which to compare results. Single-crystal NMR is an
indispensable tool for this purpose, since results from powder
samples must have an independent reference. Therefore, the
current study provides a fully characterized model compound
for use in testing simulation programs. Moreover, CsCd(SCN)3
provides a rigorous test for iterative fitting methods. Its lack
of symmetry for the cesium sites requires that all eight
parameters be considered variable. The high asymmetry in the
electric field gradient tensor concentrates the satellite peak
maxima about the isotropic chemical shift, causing pairs of
satellite subspectra to be identical and removing these telltale
instructive to consider how one might proceed in the case of
CsCd(SCN)3 without single-crystal data. Assuming negligible
second-order quadrupole effects, the central transition can be
analyzed to obtain the principal components of the chemical
shift tensor. The analysis can become complicated if satellite
peak maxima overlap with the shoulders of the central transition,
but for CsCd(SCN)3, it appears that these discontinuities are
obscured by the span of the chemical shift. Observing no such
satellite peak maxima, one surmises that the asymmetry in the
electric field gradient is close to 1. If the far outer shoulders
are resolved, the total span of the spectrum can be used to
compute the magnitude of the quadrupole coupling constant.
These five parameters can usually be estimated with relative
ease. The remaining challenge is to determine the three Euler
angles describing the relative orientation. In the absence of
symmetry restrictions, these parameters can be very difficult to
identify and will invariably involve extensive “trial and error”.
The importance of knowing the relative tensor orientations
“
horns” from observation.
133Cs NMR Spectra of Spinning Samples. The magic-angle
in simulations of powder patterns, both spinning and stationary,
has been amply evidenced.2
6-33
In fact, simulations of first-
spinning spectrum of CsCd(SCN)3 was acquired in an applied
magnetic field of 4.7 T and simulated using the parameters
obtained from the single-crystal NMR study. Good agreement
is observed between the calculated and experimental spectra.
Variable-angle spinning spectra were also collected at various
angles, θ, with respect to the applied magnetic field. The
example displayed in Figure 7 shows a spectrum obtained with
θ ) 52.25°. Agreement between calculated and experimental
spectra is good in all cases. The rotation angles were calibrated
order quadrupolar patterns can be misleading if incorrect
assumptions about the Euler angles are used to simplify the
computation. The sensitivity of a static spectrum to a given
angle is illustrated by fixing seven parameters in the simulation
and varying the angle between the largest components of the
two tensors (Figure 6). The positions of the shoulders shift by
more than 5 kHz at 9.4 T as the angle, â, is increased from 0
to 90°. It is important to note, however, that the sensitivity of
the static line shape to a given Euler angle does not necessarily
imply that there is a single, well-defined solution in the fitting
of a calculated spectrum to the experimental spectrum.
1
33
using VAS
Cs NMR spectra of cesium thiocyanate in a
4
4
manner previously described. A static spectrum of finely
ground CsSCNacquired at 52.48 MHz exhibited a central

Cesium-133 NMR Study of CsCd(SCN)3
J. Phys. Chem. B, Vol. 101, No. 19, 1997 3733
transition broadened only by anisotropic chemical shielding and
clearly separated from peak maxima associated with the
satellites. This central transition powder pattern was analyzed
to yield the principal components of the chemical shift tensor
in ppm: δ11 ) 139(2), δ22 ) 129(2), and δ33 ) 30(2). Rotation
angles calibrated by this technique are estimated to be accurate
to within 0.05°. The utility of VAS in the determination of
relative tensor orientations is under investigation in our labora-
tory.
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133
demonstrated by the characterization of all relevant Cs NMR
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Acknowledgment. We are grateful to the Natural Sciences
and Engineering Research Council (NSERC) of Canada for
supporting this work through research and equipment grants.
Ms. Katherine Robertson is acknowledged for her assistance
with some crystallographic aspects of this study. S. K. thanks
NSERC, the Walter C. Sumner Foundation, and the Izaak
Walton Killam Trust for postgraduate scholarships. R.E.W. is
grateful to the Canada Council for a Killam Research Fellow-
ship. All spectra were obtained at the Atlantic Region Magnetic
Resonance Centre, supported by NSERC of Canada.
(
9
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