A solid-state NMR and computational study of sodium and potassium tetraphenylborates:23Na and39K NMR signatures for systems containing cation-π interactions

Article abstract of DOI:10.1021/jp0468051

Sodium and potassium tetraphenylborates were examined by solid-state ²³Na and ³⁹K NMR spectroscopy. Analyses of solid-state NMR spectra obtained at 4.70, 11.75, and 19.60 T yielded the following ²³Na and ³⁹K NMR parameters: Na[BPh₄], |C _Q| = 1.24 ± 0.05 MHz, η_Q = 0.0 ± 0.1, δ_iso = -45.6 ± 0.5 ppm, and Ω = 14 ± 2 ppm; K[BPh₄], |C_Q| = 1.32 ± 0.05 MHz, η_Q = 0.0 ± 0.1, and δ_iso = -92 ± 1 ppm. In both Na[BPh₄] and K[BPh₄], the electric field gradient and chemical shift tensors at the metal site are axially symmetric, in agreement with the crystallographic symmetry. Extensive quantum mechanical calculations were performed for Na[BPh₄] and K[BPh₄] as well as for a large number of model cation-π systems containing Na⁺ and K ⁺ ions and common aromatic compounds. Experimental and theoretical studies confirm that a highly shielded environment at the metal cation site is a characteristic feature for cation-π interactions, making it useful as a NMR signature for identifying cation-π interactions in proteins and nucleic acids. In this study, powder X-ray diffraction spectra for Na[BPh₄] and K[BPh₄] were also reported.

Full text of DOI:10.1021/jp0468051

J. Phys. Chem. A 2004, 108, 10551-10559
10551
A Solid-State NMR and Computational Study of Sodium and Potassium
39
Tetraphenylborates: 23Na and K NMR Signatures for Systems Containing Cation-π
Interactions
Alan Wong,† Robert D. Whitehead,‡ Zhehong Gan,§ and Gang Wu*,†
Department of Chemistry, Queen’s UniVersity, Kingston, Ontario, Canada K7L 3N6, Department of Chemistry
and Chemical Engineering, Royal Military College of Canada, Kingston, Ontario, Canada K7K 7B4, and
Center of Interdisciplinary Magnetic Resonance, National High Magnetic Field Laboratory,
1800 East Paul Dirac DriVe, Tallahassee, Florida 32310
ReceiVed: July 19, 2004; In Final Form: September 14, 2004
Sodium and potassium tetraphenylborates were examined by solid-state 23Na and 39K NMR spectroscopy.
Analyses of solid-state NMR spectra obtained at 4.70, 11.75, and 19.60 T yielded the following 23Na and 39
K
NMR parameters: Na[BPh4], |CQ| ) 1.24 ( 0.05 MHz, ηQ ) 0.0 ( 0.1, δiso ) -45.6 ( 0.5 ppm, and Ω )
14 ( 2 ppm; K[BPh4], |CQ| ) 1.32 ( 0.05 MHz, ηQ ) 0.0 ( 0.1, and δiso ) -92 ( 1 ppm. In both
Na[BPh4] and K[BPh4], the electric field gradient and chemical shift tensors at the metal site are axially
symmetric, in agreement with the crystallographic symmetry. Extensive quantum mechanical calculations
were performed for Na[BPh4] and K[BPh4] as well as for a large number of model cation-π systems containing
Na+ and K+ ions and common aromatic compounds. Experimental and theoretical studies confirm that a
highly shielded environment at the metal cation site is a characteristic feature for cation-π interactions,
making it useful as a NMR signature for identifying cation-π interactions in proteins and nucleic acids. In
this study, powder X-ray diffraction spectra for Na[BPh4] and K[BPh4] were also reported.
Introduction
techniques that can provide complementary information about
alkali metal cation binding in proteins and nucleic acids.
Noncovalent interactions play an essential role in molecular
recognition and in biomolecular structures. In addition to
conventional noncovalent interactions such as hydrogen bonding,
ion pairing, and hydrophobic interactions, cation-π interactions
have been recognized as an important force in biomolecular
processes.1-3 In proteins, weak cation-π interactions may occur
between charged protein side chains or metal ions and aromatic
amino acid residues such as phenylalanine (Phe), trptophan
(Trp), tyrosine (Tyr), and histidine (His). Similar situations can
also be found in nucleic acids where aromatic bases of adenine
(A), guanine (G), thymine (T), uracil (U), and cytosine (C) may
be involved in cation-π interactions.
For the most abundant alkali metal ions in biological systems,
Na+ and K+, a large number of experimental and theoretical
studies have been carried out for understanding the structural
feature of cation-π complexes containing small organic mol-
ecules.3 Meanwhile, fewer cases are available in the
literature regarding Na+ and K+ ions in proteins and nucleic
acids.4,5 This is because detecting light alkali metal ions in
proteins and nucleic acids by X-ray crystallography is a
challenging task. Identification of Na+ ions is particularly
difficult, because a Na+ ion has the same number of electrons
as a water molecule, rendering it difficult to distinguish these
two species on an electron density map. Although crystal-
lographic methods for solving (at least partially) this ambiguity
are available,6,7 it is desirable to develop other analytical
Our particular interest in exploring the possibility of solid-
state 23Na and 39K NMR for probing cation-π interactions was
triggered by recent proposals that some of the water molecules
previously reported in protein structures may have actually been
alkali metal cations. For example, Wouters8 reported a new
cation-π binding site in hen egg-white (HEW) lysozyme where
a Na+ ion is located 4 Å above the indole ring of Trp123. A
similar site was identified by Wouters and Maes9 in the crystal
structure of a thermophilic Bacillus stearothermophilus triose-
phosphate isomerase mutant. Gokel and co-workers10 also
proposed that a putative water molecule in tryptophanase is an
alkali metal cation, because it is located 3.7 Å above the
aromatic ring of Tyr429. However, Sarkhel et al.11 recently
reported crystallographic evidence for water-nucleobase “stack-
ing” structures in an RNA pseudokot. This type of structure is
due to lone pair-π (l.p.-π) interactions between water mol-
ecules and nucleobases, for which the water-centroid distance
is typically between 2.93 and 3.78 Å. It is likely that similar
interactions are also operative between water and aromatic
amino acid residues in proteins. Because the water-centroid
distances are very similar to Na+-centroid distances in cat-
ion-π systems, it remains unclear whether Na+-π and
water-π interactions can be unambiguously distinguished by
crystallography. This further emphasizes the need for alternative
techniques that may provide additional information about cation
binding sites in biological macromolecules.
* Address correspondence to this author. E-mail: gangwu@
chem.queensu.ca.
In principle, metal cation NMR is capable of providing direct
information about cation-π interactions. However, until recently
there has been very little NMR data available in this area. Beer
and co-workers12 demonstrated the use of 205Tl (spin 1/2) NMR
† Queen’s University.
‡ Royal Military College of Canada.
§ Center of Interdisciplinary Magnetic Resonance.
10.1021/jp0468051 CCC: $27.50 © 2004 American Chemical Society
Published on Web 10/30/2004

10552 J. Phys. Chem. A, Vol. 108, No. 47, 2004
Wong et al.
TABLE 1: Unit Cell Parameters Determined for K[BPh4]
and Na[BPh4] by X-ray Diffraction Methods
unit cell dimension
compd diffraction method
Z
a ) b (Å)
c (Å)
ref
K[BPh4]
single crystal
single crystal
powder
powder
powder
2
2
2
2
2
11.221(13) 7.894(6) 17
11.211(6) 7.918(7) this work
11.269(3) 7.913(2) this work
Na[BPh4]
11.45
7.41
18
11.524(8) 7.462(7) this work
a Crystals are tetragonal with space group I4h2m.
monochromated Mo KR radiation (λ ) 0.71073 Å), and were
in excellent agreement with the literature values (see Table 1).
Solid-State NMR. Solid-state 23Na and 39K NMR experi-
ments were performed on a Bruker Avance-500 NMR spec-
trometer (11.75 T) operating at 132.285 and 23.335 MHz for
23Na and 39K nuclei, respectively. The radio frequency (rf) field
strength was 90 and 50 kHz at the 23Na and 39K Larmor
frequencies, respectively. Static 39K spectra were recorded by
using both a Hahn-echo sequence19 and a Quadrupole Carr-
Purcell Meiboom-Gill (QCPMG) sequence.20 Solid-state 23Na
experiments were also performed on a Bruker ASX-200 NMR
spectrometer (4.70 T) operating at 52.937 MHz for 23Na. The
rf field strength was 77 kHz at the 23Na frequency. Solid-state
39K MAS NMR spectra at 19.6 T (38.718 MHz for 39K nuclei)
were obtained at the National High Magnetic Field Laboratory
(Tallahassee, Florida), using a Bruker DRX spectrometer and
a 4-mm MAS probe. All 23Na and 39K chemical shifts were
referenced to NaCl(aq) and KCl(aq), respectively. Spectral
simulations were performed with WSOLIDS.21
Figure 1. Unit cell for K[BPh4] viewed along the a-axis (A) and the
c-axis (B). (C) Model used in quantum mechanical calculations.
Hydrogen atoms are omitted for clarity. Color code: K (red), B (green),
and C (gray).
in studying cation-π interactions in solution. For alkali metal
cations, several solid-state 7Li and 23Na NMR studies have been
reported dealing with metallocene compounds.13-16 To establish
solid-state 23Na and 39K NMR as a tool for probing cation-π
interactions, one needs to obtain spectral signatures for such
cation binding sites. Here we report a comprehensive solid-
state NMR study of sodium and potassium tetraphenylborates,
two earliest known compounds containing cation-π interac-
tions. K[BPh4] crystallizes in tetragonal form with space group
I4h2m.17 As shown in Figure 1, in the crystal lattice each K+
ion is surrounded by four phenyl groups. The distance between
the K+ ion and the center of the phenyl ring is 3.343 Å.
According to powder X-ray diffraction data given in the
International Centre for Diffraction Data (ICDD) database,18 Na-
[BPh4] is isostructural to K[BPh4] with a slightly shorter cation-
centroid distance. To supplement our experimental solid-state
NMR data, we also perform quantum mechanical calculations
on both electric field gradient (EFG) and magnetic shielding
properties at the metal nuclear site for K[BPh4] and Na[BPh4].
Finally, we perform extensive quantum mechanical calculations
for a number of Na+-π and K+-π systems containing common
aromatic ligands.
Powder X-ray Diffraction. The powder X-ray diffraction
data were collected on a Thermo ARL Scintag ×1 Advanced
Diffraction System, using Cu KR 1 radiation (λ ) 1.50562 Å),
with fixed slit widths of 4, 2, 0.5, and 0.2 mm. The data were
collected from 5° to 90° 2θ in continuous mode at a rate of 2°
per minute with a step increment of 0.02° and preset time of
0.5 s. A high-purity solid-state (liquid nitrogen cooled) germa-
nium detector was used. Data were processed on a Pentium PC,
using Thermo ARL Diffraction Management System Software
for the Window NT (version 1.39-1B). Background subtraction
and smoothing of the raw data were carried out with a boxcar
curve fit (filter width of 1.5°) and FFT smoothing (resolution
0.01°). PE Werner’s TREOR90 autoindexing program from the
Thermo ARL Crystallography (version 1.2) suite was used to
determine the unit cell parameters utilizing these Miller indices.
Quantum Mechanical Calculations. All quantum mechan-
ical calculations were performed on a SunFire 6800 symmetric
multiprocessor system (24 × 900 MHz processors and 24 GB
of memory) with the Gaussian98 suite of programs.22 Calcula-
tions of the 23Na and 39K electric field gradients (EFG) and
chemical shielding (σ) parameters for these models were
performed at the Hartree-Fock (HF) SCF and density functional
theory (DFT) levels with standard basis sets. The principal
components of the EFG tensor, qii, were computed in atomic
units (1 au ) 9.717365 × 1021 V m-2), with |qzz| > |qyy| >
|qxx| and qzz + qyy + qxx ) 0. The principal magnetic shielding
tensor components (σii) were computed with σiso ) (σ11 + σ22
+ σ33)/3 and σ33 > σ22 > σ11. In MAS NMR experiments for
quadrupolar nuclei, the measurable quantities are the quadrupolar
coupling constant (CQ), the asymmetry parameter (ηQ), and the
isotropic chemical shift (δiso). To make direct comparison
between the calculated 23Na and 39K NMR parameters and the
experimental results, the following equations were used:
Experimental Section
Sample Preparation. Sodium tetraphenylborate, Na[BPh4],
was obtained from Sigma-Aldrich (Ontario, Canada) and used
without further purification. Powder X-ray diffraction measure-
ments suggested that the Na[BPh4] sample was pure and in the
same crystal form as that reported in the literature(see Table
1). Potassium tetraphenylborate, K[BPh4], was prepared by
adding KCl(aq) into an aqueous solution of Na[BPh4]. White
fine precipitates were filtered and washed with deionized water.
Crystals of K[BPh4] were grown from acetone/water. The unit
cell parameters for K[BPh4] crystals were determined on a
Bruker SMART CCD 1000 X-ray diffractometer with graphite-

Solid-State NMR of Cation-π Systems
J. Phys. Chem. A, Vol. 108, No. 47, 2004 10553
CQ [MHz] ) e2qzzQ/h ) -243.96Q [barn]‚qzz [au] (1)
ηQ ) (qxx - qyy)/qzz
δiso ) σref - σiso
(2)
(3)
where Q is the nuclear quadrupole moment, e is the elementary
charge, h is the Planck constant, and σref is the magnetic
shielding constant for the primary chemical shift reference
sample. Standard values of Q were used in this study, Q(23Na)
) 0.104 barn and Q(39K) ) 0.055 barn (1 barn ) 10-28 m2).23
The primary chemical shift reference is computed for fully
hydrated Na+ and K+ ions, [Na(H2O)6]+ and [K(H2O)6]+. The
fully optimized MP2/6-311G(d,p) geometries of [Na(H2O)6]+
and [K(H2O)6]+ were found to have an Oh symmetry with Na-
Ow ) 2.433 Å and K-Ow ) 2.712 Å, respectively. To minimize
the systematic basis-set variations, we used these MP2/6-311G-
(d,p) geometries to calculate σref for individual basis sets
separately. It should be noted that the computed value of σref
depends also on the exact geometry used for the hydrated metal
ion cluster. For example, σref(23Na) is 583.70 ppm for [Na-
(H2O)6]+ when the cluster is optimized at the MP2/6-311G-
(d,p) level. This value is 5.02 ppm smaller than that reported
for [Na(H2O)6]+ optimized at the HF/6-31G(d) level.24
Figure 2. Experimental (trace) and standard (stick) powder X-ray
diffraction spectra for (A) Na[BPh4] and (B) K[BPh4].
For the first- and second-row elements, we used standard basis
sets such as 6-31G(d), 6-311G(d,p), 6-311++G(2d,2p), cc-
pVDZ, cc-pVQZ, and Ahlrichs VTZ. For the third-row K atom,
we used two different all-electron basis sets. The first one is a
medium-size split valence basis set, 6-31G(d), recently reported
by Rassolov et al.25 This basis set has a contraction scheme of
(22s, 16p, 1d) f [5s, 4p, 1d]. The second all-electron basis set
is a 6-311G type valence triple-ú basis set reported by Blaudeau
et al.26 This basis set uses a general contraction scheme of (14s,
12p, 3d) f [8s, 7p, 1d]. In addition, various diffuse and
polarization functions were also added to the 6-311G type basis
set.
Results and Discussion
Powder X-ray Diffraction. In solid-state NMR experiments,
one generally uses polycrystalline (or powdered) samples. It is
also a common practice among solid-state NMR spectroscopists
to rationalize the observed NMR parameters (tensors) in relation
to molecular structural features observed in the crystal structure
of the compound in question. Because crystal structures are very
often determined with X-ray or neutron diffraction experiments
on single-crystal samples, it is not always clear whether a
particular powder sample used in the NMR experiment should
exhibit the same crystal form as that reported in the single-
crystal X-ray or neutron diffraction study. One convenient way
to check the crystallographic characteristics of the NMR sample
is to carry out X-ray powder diffraction measurements. Experi-
mental powder X-ray diffraction spectra for Na[BPh4] and
K[BPh4] are shown in Figure 2, together with the standard
spectra from the ICDD database.18 On the basis of these X-ray
diffraction data, we can conclude that both samples used in our
NMR experiments are in the same crystal forms as those used
in the previous crystallographic studies. For K[BPh4], we also
performed an independent single-crystal X-ray diffraction
experiment, to further confirm that our synthesis had produced
the correct compound. Unit cell parameters for Na[BPh4] and
K[BPh4] are summarized in Table 1. These results firmly
established the validity of our interpretation of solid-state NMR
data on the basis of crystallographic results.
Figure 3. Experimental and calculated 23Na MAS spectra for Na[BPh4].
Experimental parameters are as follows: for 4.70 T, spinning frequency
) 15 kHz, 64 transients, recycle delay ) 10 s; and for 11.75 T, spinning
frequency ) 10 kHz, 64 transients, recycle delay ) 5 s.
Solid-State NMR. Figure 3 shows the 23Na MAS spectra
for Na[BPh4] at 4.70 and 11.75 T. Each of the spectra exhibits
a typical line shape arising from the second-order quadrupole
interaction. Simulations of the observed MAS spectra yielded
the following 23Na NMR parameters for Na[BPh4]: |CQ| ) 1.24
( 0.05 MHz, ηQ ) 0.0 ( 0.1, and δiso ) -45.6 ( 0.5 ppm.
Because the chemical shielding anisotropy (CSA) information
is unavailable from MAS spectra, we recorded static spectra
for Na[BPh4] at 4.70 and 11.75 T (see Figure 4). By simulta-
neously fitting the static spectra recorded at these two fields,
we obtained an axially symmetric 23Na chemical shift tensor
with a span (Ω ) σ33 - σ11) of 14 ( 2 ppm for Na[BPh4]. The
unique axis of the 23Na chemical shift tensor is the most

10554 J. Phys. Chem. A, Vol. 108, No. 47, 2004
Wong et al.
Figure 4. Experimental and calculated 23Na static spectra for Na[BPh4].
Experimental details are as follows: for 4.70 T, 202 transients, recycle
delay ) 10 s; and for 11.75 T, 139 transients, recycle delay ) 2 s.
shielded. The 23Na NMR tensors found for Na[BPh4] are quite
similar to those reported for sodium metallocenes.16
Figure 5. Experimental and calculated 39K NMR spectra for K[BPh4].
(A) The 39K MAS spectrum was obtained at 19.6 T. Experimental
parameters are the following: spinning frequency ) 10 kHz, recycle
delay ) 1 s, 5624 transients. (B) The static 39K spectrum was obtained
at 11.75 T, using a Hahn echo sequence. Experimental parameters are
the following: recycle delay ) 2 s, 83149 transients, total experimental
time ) 46 h.
Figure 5 shows the 39K MAS and static spectra for K[BPh4]
obtained at 19.60 and 11.75 T, respectively. Spectral analyses
produced the following 39K NMR parameters for K[BPh4]:
|CQ |) 1.32 ( 0.05 MHz, ηQ ) 0.0 ( 0.1, and δiso ) -92 (
1 ppm. The 39K CSA for K[BPh4] is too small to be reliably
measured. In principle, the 39K CSA for K[BPh4] should be
slightly larger than the 23Na CSA for Na[BPh4]. However,
γ(39K) is much smaller than γ(23Na), making it difficult to
observe small 39K CSA contributions. At 11.75 T, a span of 20
ppm for 39K CSA would contribute only 360 Hz to the total
line width of approximately 8 kHz observed for K[BPh4]. For
this reason, it is not possible to accurately determine the 39K
CSA for K[BPh4]. Because of the low 39K NMR frequency, it
is generally difficult to obtain high-quality 39K NMR spectra.
Larsen et al.20 demonstrated the use of a QCPMG sequence to
improve on the overall sensitivity for 39K NMR experiments.
The basic idea of QCPMG is to collect as many echoes as
possible during a single excitation. This method is particularly
beneficial for samples with relatively long transverse relaxation
times. Here we decided to test this approach with K[BPh4]. The
results of the 39K QCPMG experiment for K[BPh4] are shown
in Figure 6. For K[BPh4], we observed a total of 5 echoes, which
corresponds to a transverse relaxation time of approximately 5
ms. As shown in Figure 6B, a direct Fourier transformation of
the observed echoes results in a powder pattern composed of
spikelets. Another way of processing the QCPMG data is to
add all whole echoes together and then to perform Fourier
transformation. This data processing method generates a con-
ventional static spectrum as shown in Figure 6C, which can be
compared directly with the Hahn-echo spectrum shown in Figure
5B. For K[BPh4], the sensitivity improvement of the QCPMG
experiment is not as large as that demonstrated by Larsen et
al.20 It is likely that the very short T2 observed for K[BPh4], 5
ms, diminishes the benefit of the QCPMG experiment in this
particular case.
Calculations for Na[BPh4] and K[BPh4]. To supplement
our experimental solid-state NMR data, we performed quantum
mechanical calculations of EFG and chemical shielding tensors
at the metal site for both Na[BPh4] and K[BPh4]. The molecular
cluster used in the calculations is depicted in Figure 1C. This
molecular cluster has a net charge of -1. We have also tried to
use a cluster model containing two more cations along the c-axis.
The results were essentially the same as those with the cluster
model shown in Figure 1C. For K[BPh4], the crystal structure
was used directly in the calculation without geometry optimiza-
tion.17 For Na[BPh4], only unit cell dimensions are known from
powder X-ray diffraction studies.18 Attempts to obtain single
crystals for Na[BPh4] in this laboratory were unsuccessful.
Therefore, we decided to construct a cluster model using a
combination of powder diffraction data and geometry optimiza-
tion. In particular, because the Na and B atoms appear at special
positions along the c-axis of the crystal lattice, the distance
between these two atoms is equal to c/2 (3.731 Å), which is
determined from our powder diffraction experiments (see Table
1). Using this Na-B distance as a constraint, we then fully
optimized the cluster structure at the HF/6-31G(d) level. The
optimized cluster structure has C2V symmetry. Some structural
details for cluster models for Na[BPh4] and for K[BPh4] are
given in Table 2. Overall, the molecular cluster for Na[BPh4]
is very similar to that for K[BPh4], except that the distance

Solid-State NMR of Cation-π Systems
J. Phys. Chem. A, Vol. 108, No. 47, 2004 10555
Figure 6. (A) Multiple echos observed in the 39K QCPMG experiment
for K[BPh4] at 11.75 T. The experimental parameters are as follows:
A delay of 50 µs after each pulse was used to minimize the effects of
acoustic ringing and pulse breakthrough. The acquisition period for
each echo was set to 1000 µs, which gives a separation of 1000 Hz
between spikelets. Other experimental parameters are the following:
dwell time ) 10 µs, recycle delay ) 2 s, 39325 transients, total
experimental time ) 22 h. (B) The spikelet QCPMG spectrum produced
by direct Fourier transformation of the multiple echos. (C) The static
spectrum produced by summing up five QCPMG echos. (D) Calculated
static spectrum.
Figure 7. Aromatic molecules used in the quantum mechanical
calculations.
Calculations for Model Cation-π Systems. To date there
has been very little experimental NMR data for Na+-π and
K+-π complexes. To establish the general trend in these
systems, we employ a computational approach to examine 23Na
and 39K NMR parameters for a series of cation-π complexes
containing Na+ and K+ ions and common aromatic molecules.
Figure 7 shows the aromatic compounds used in this study. All
molecular geometries used in the computations were optimized
at the MP2/6-311G(d,p) level. Optimizations were also per-
formed at HF and B3LYP levels and the computed NMR
parameters (data not shown) are similar to those computed with
the MP2 structure. The distances between the Na+ ion and the
centroid position of the aromatic plane are found to be in a
range between 2.3 and 2.6 Å. The computed 23Na and 39K NMR
results for these model complexes are given in Tables 4 and 5,
respectively. The values of CQ(23Na) and CQ(39K) are in line
with those of most of Na+ and K+ compounds. One common
feature of the computed NMR parameters shown in Tables 4
and 5 is that the metal nucleus is highly shielded in cation-π
systems compared with the situations found in most Na+ and
K+ complexes where the cation is generally coordinated to
oxygen and nitrogen ligands. For example, the chemical shifts
for the Na-π complexes lie in a narrow range between -33
and -46 ppm. These values are well outside the chemical shift
range for most Na compounds, from 20 to -20 ppm. It is also
interesting to note that the 23Na chemical shifts for these model
between the Na+ ion and the center of the phenyl ring is slightly
shorter than the corresponding distance in K[BPh4]. This is in
agreement with the expectation that a Na+ ion interacts with a
π system more strongly than does a K+ ion. This discrepancy
between Na+ and K+ is also reflected in the unit cell dimensions
for the two compounds, c ) 7.462 Å for Na[BPh4] and c )
7.918 Å for K[BPh4]. The computed 23Na and 39K NMR tensors
for Na[BPh4] and K[BPh4] are summarized in Table 3. In
general, the computed NMR tensors are in reasonable agreement
with the experimental values, provided that the basis set used
for the metal atom is at a triple-ú level. For 23Na NMR
parameters, it appears that HF/6-31G(d) calculations can also
yield reliable results. The accuracy of the computed 23Na NMR
parameters for Na[BPh4] is comparable to that reported in our
earlier studies.28,29 Calculations of 23Na NMR parameters at
similar levels of theory have also been reported by Tossell30
for Na+ complexes with crown ethers and by Willans and
Schurko16 for sodium metallocenes. For 39K NMR parameters,
very little computational data are available in the literature. The
calculated results for K[BPh4] are quite encouraging. As solid-
state 39K NMR is becoming feasible,31 it would be useful to
systematically examine the accuracy of the current computation
methods in determining 39K NMR properties.

10556 J. Phys. Chem. A, Vol. 108, No. 47, 2004
Wong et al.
TABLE 2: Selected Distances (Å) and Bond Angles (deg) for Cluster Models of Na[BPh4] and K[BPh4]
Na[BPh4]a
K[BPh4]b
bond
angle
bond
angle
Na-C(1)
Na-C(2)
Na-C(3)
Na-C(4)
3.017
3.147
3.472
3.640
B-Na-B′
180.0
104.8
103.7
112.2
112.2
K-C(1)
K-C(2)
K-C(3)
K-C(4)
3.191
3.238
3.343
3.403
B-K-B′
C(1)-B-C(1)
C(1)-B-C(1′)
180.0
102.8
112.9
C(1)-B-C(1′)
C(5)-B-C(5′)
C(1)-B-C(5)
C(1′)-B-C(5′)
Na-B
3.731
7.462
1.672
1.668
K-B
3.947
7.894
1.643
B-B′
B-B′
B-C(1)
B-C(5)
B-C(1)
a Fully optimized at the HF/6-31G(d) level. See text for details. b From ref 17.
TABLE 3: Experimental and Calculated NMR Parameters for Sodium and Potassium Tetraphenylborates
method/basis set
σ
iso (ppm)
σrefa (ppm)
δisob (ppm)
Ωc (ppm)
CQ (MHz)
Na[BPh4]
HF/6-31G(d)
625.2
622.9
622.9
623.0
628.2
621.4
621.6
621.0
617.3
583.7
584.9
583.9
584.1
588.7
584.7
587.6
563.8
571.8
576.6d
-41.6
-38.0
8.9
8.8
-1.31
HF/6-311G(d,p)
-1.31
HF/6-31G(d)/6-311G(d,p)
HF/6-31G(d)/6-311++G(2d,2p)
HF/6-31G(d)/cc-pVDZ
HF/6-31G(d)/Ahlrichs VTZ
HF/6-31G(d)/cc-pVQZ
B3LYP/6-31G(d)
-39.0
9.2
-1.34
-38.9
8.9
8.0
10.5
8.1
9.1
8.3
14 ( 2
-1.32
-39.5
-1.08
-36.8
-1.35
-34.0
-1.24
-57.2
-0.82
B3LYP/6-311G(d,p)
exptl
-45.6
-1.24
-45.6 ( 0.5
-1.24 ( 0.05e
K[BPh4]
HF/6-31G(d)
1349.0
1344.5
1346.2
1346.7
1332.2
1320.7
1323.0
1259.1
1238.4
1238.2
1237.7
1242.7
1212.1
1211.5
1271d
-89.8
-106.2
-108.0
-109.0
-89.5
-108.6
-111.5
-92 ( 1
16.0
23.4
25.4
25.1
13.9
22.4
25.0
-0.69
HF/6-311G(d,p)
-1.47
HF/6-31G(d)/6-311G(d,p)
HF/6-31G(d)/6-311++G(2d,2p)
B3LYP/6-31G(d)
B3LYP/6-311G(d,p)
B3LYP/6-31G(d)/6-311G(d,p)
exptl
-1.41
-1.42
-0.22
-1.27
-1.20
-1.32 ( 0.05e
b
a Calculated for [M(H2O)6]+ (M ) Na and K) fully optimized at the MP2/6-311G(d,p) level. δiso ) σref - σiso
.
c Ω ) σ33 - σ11. d From ref 27.
e The sign of CQ was assumed on the basis of quantum mechanical calculations.
TABLE 4: Calculated 23Na NMR Parameters for Na+-π Complexesa,b
ligand
Na-X distancec (Å)
Na-centroid (Å)
δ
iso (ppm)
W (ppm)
CQ (MHz)
ηQ
five-member ring
1, furan
2.750-2.845
2.640-2.918
2.533
2.492
-40.268
-37.188
17.183
24.397
-1.435
-2.004
0.756
0.660
2, pyrrole
six-member ring
3, benzene
4, fluorobenzene
5, phenol
6, nitrobenzene
7, aniline
8, pyridine
9, C5H4(O)NH
10, C5H3(O)NHNH2
20, (benzene)2
aromatic amino acid
11, histidine
12, phenylalanine
13, tyrosine
14, tryptophan (5 ring)
14, tryptophan (6 ring)
nucleic acid base
15, thymine
2.803
2.432
2.511
2.378
2.493
2.389
2.411
2.425
2.346
2.421
-40.757
-41.106
-40.117
-42.723
-39.934
-41.421
-36.592
-33.586
-45.479
18.543
16.714
17.559
14.053
17.810
16.127
13.919
11.933
31.429
-1.080
-1.097
-1.140
-1.078
-1.124
-1.144
-1.239
-1.533
-2.185
0.000
0.037
0.088
0.120
0.016
0.090
0.425
0.603
0.000
2.772-2.874
2.755-2.878
2.849-2.866
2.771-2.826
2.744-2.926
2.798-2.922
2.735-2.951
2.800
2.833-2.966
2.774-2.821
2.750-2.838
2.673-2.747
2.700-2.824
2.651
2.411
2.412
2.434
2.328
-46.030
-40.074
-39.859
-40.878
-39.403
12.164
19.305
18.450
14.396
24.900
-1.255
-1.150
-1.183
-1.713
-1.253
0.324
0.011
0.051
0.505
0.056
2.925-3.001
2.972-3.054
2.779-2.865
2.750-2.818
2.741-2.879
2.706-2.779
2.764-2.901
2.638
2.693
2.435
2.516
2.449
2.473
2.475
-37.472
-37.405
-36.107
-43.414
-42.164
-44.372
-39.475
7.746
7.062
9.720
6.819
14.590
8.657
8.154
-1.021
-0.888
-1.329
-1.151
-1.227
-1.252
-1.192
0.198
0.214
0.663
0.390
0.340
0.460
0.193
16, uracil
17, cytosine
18, adenine (5 ring)
18, adenine (6 ring)
19, guanine (5 ring)
19, guanine (6 ring)
a All structures were optimized at the MP2/6-311G(d,p) level. b Both magnetic shielding and EFG calculations were performed at the HF/6-
31G(d) level. c X refers to CAr, NAr, or OAr atoms.
(gas-phase) Na+-π complexes are quite close to the value for
a free Na+ ion, -39 ppm.27 This suggests that the weak Na+-π
interaction does not cause large perturbations to the electronic
structure of the Na+ ion. Similar trends are also observed for
the 39K chemical shifts listed in Table 5.
To further study the 23Na and 39K NMR parameters in
cation-π systems, we performed a series of computations for
Na+-benzene and K+-benzene complexes as a function of
cation-π separation. The calculated results are summarized in
Table 6. In general, 23Na and 39K NMR parameters are quite

Solid-State NMR of Cation-π Systems
J. Phys. Chem. A, Vol. 108, No. 47, 2004 10557
TABLE 5: Calculated 39K NMR Parameters for K+-π Complexesa,b
ligand
K-X distancec(Å)
K-centroid (Å)
δ
iso (ppm)
W (ppm)
CQ (MHz)
ηQ
five-member ring
1, furan
2, pyrrole
six-member ring
3, benzene
4, fluorobenzene
5, phenol
6, nitrobenzene
7, aniline
8, pyridine
9, C5H4(O)NH
10, C5H3(O)NHNH2
20, (benzene)2
aromatic amino acid
11, histidine
12, phenylalanine
13, tyrosine
14, tryptophan (5 ring)
14, tryptophan (6 ring)
nucleic acid base
15, thymine
16, uracil
17, cytosine
18, adenine (5 ring)
18, adenine (6 ring)
19, guanine (5 ring)
19, guanine (6 ring)
2.962-3.213
2.995-3.145
2.837
2.828
-70.485
-67.614
38.980
33.836
-0.745
-1.214
0.799
0.603
3.201
2.882
2.865
2.831
2.881
2.752
2.844
2.891
2.861
-71.715
-70.776
-69.409
-71.267
-70.560
-69.306
-66.580
-61.900
-84.195
4.995
7.073
9.700
6.034
9.175
10.719
15.086
13.792
0.160
-0.742
-0.821
-0.893
-0.738
-0.972
-0.776
-0.705
-1.109
-1.730
0.000
0.101
0.108
0.168
0.105
0.119
0.564
0.507
0.000
3.149-3.187
3.103-3.162
3.171-3.230
3.055-3.113
3.084-3.265
3.172-3.210
3.066-3.270
3.161, 3.153
2.850-3.581
3.109-3.145
3.083-3.139
2.975-3.041
3.029-3.128
2.832
2.812
2.797
2.763
2.783
-57.687
-69.688
-69.348
-68.057
-68.029
21.104
9.215
10.712
15.418
15.372
-1.366
-0.913
-0.926
1.180
0.347
0.07
0.184
0.397
0.070
1.024
3.240-3.316
3.291-3.372
3.098-3.204
3.050-3.114
3.062-3.186
3.003-3.068
3.061-3.185
2.990
3.048
2.793
2.845
2.804
2.794
2.802
-65.165
-64.543
-64.532
-70.034
-69.519
-72.763
-67.591
7.493
6.953
10.346
15.567
10.165
20.579
7.064
-0.526
-0.468
-0.783
-0.772
-0.719
-0.771
-0.664
0.070
0.088
0.562
0.306
0.340
0.306
0.089
a All structures were optimized at the MP2/6-311G(d,p) level. b Both magnetic shielding and EFG calculations were performed at the HF/6-
31G(d) level. c X refers to CAr, NAr, or OAr atoms.
TABLE 6: Calculated 23Na and 39K NMR Parameters for Cation-Benzene Complexesa
M-centroid
system
M-CAr (Å)
((0.05 Å)
δ
iso (ppm)
δ (ppm)
δ| (ppm)
W (ppm)
CQ (MHz)
Na+-benzene
1.997
2.460
2.803
3.150
3.697
1.42
2.02
2.42
2.82
3.42
59.36
107.020
-9.939
-34.575
-42.224
-42.348
-35.864
-55.511
-53.119
-49.699
-46.004
142.884
45.572
18.544
7.475
5.493
-0.724
-1.080
-0.750
-0.250
-25.146
-40.757
-44.732
-43.576
-39.542
4.351
free Na+ ion
K+-benzene
1.997
2.460
3.150
3.697
4.070
4.733
1.42
2.02
2.82
3.42
3.82
4.52
349.916
23.500
525.739
71.454
-67.915
-72.298
-70.817
-68.255
-1.117
-72.266
-75.331
-74.131
-71.785
-69.123
526.856
143.720
7.416
3.614
-2.737
-0.830
-0.227
-0.129
-0.078
-70.427
-73.500
-71.449
-68.551
-66.013
1.833
0.968
0.868
free K+ ion
a Both magnetic shielding and EFG calculations were performed at the HF/6-31G(d) level.
sensitive to the cation-benzene distance. As shown in Figure
8, the value of CQ shows an interesting dependence on the
cation-benzene separation. When the metal ion is far away from
the benzene ring (>3.5 Å), the EFG at the metal nucleus is
essentially zero, just as the case for a free ion. As the cation-
benzene distance gets shorter, negative values of CQ are
observed. When the cation-benzene separation reaches a critical
distance (approximately 1.9 and 1.8 Å for Na+-benzene and
for K+-benzene, respectively), the EFG at the metal nucleus
vanishes. For distances below this critical distance, CQ becomes
positive and increases drastically with a decrease of the cation-
benzene separation. This observation immediately suggests that,
when Na+ and benzene are sufficiently close, the spherically
distributed orbitals of Na+ are “polarized” by the benzene
molecule to induce an opposite EFG that partially cancels the
EFG generated by the benzene molecule itself. However, one
should exercise caution in interpreting these data, because the
very short cation-benzene distances may not be realistic.
The magnetic shielding at the metal nucleus also shows an
interesting dependence on the cation-benzene separation. More
specifically, the metal nucleus becomes significantly less
shielded (with positive chemical shifts) when the cation is moved
close to the benzene ring. This clearly suggests that the
diamagnetic ring current does not play any significant role in
this case, because it would cause an increase in magnetic
shielding at the metal nucleus. Further examination of the
chemical shift tensor components reveals that only the magnetic
shielding along the directions perpendicular to the C6 axis (σ )
changes as the cation approaches the benzene, whereas the
magnetic shielding along the C6 axis (σ|) remains at a value
very similar to that for a free ion. For a free ion, the origin of
magnetic shielding is purely diamagnetic according to the
Ramsey formalism. For cation-benzene complexes, the calcula-
tions show that the paramagnetic shielding contribution becomes
important as the cation is moved toward the benzene. This is
similar to the case of decamethylaluminocenium cation reported
by Schurko et al.32 A detailed analysis of the paramagnetic
contributions from individual molecular orbitals for Na[BPh4]
and K[BPh4] is beyond the scope of this paper.

10558 J. Phys. Chem. A, Vol. 108, No. 47, 2004
Wong et al.
Figure 8. Computed NMR parameters for Na+- and K+-benzene complexes as a function of cation-centroid distance. The chemical shift tensor
components, δ and δ|, correspond to directions perpendicular and parallel to the C6 axis of the complex, respectively.
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We have obtained solid-state 23Na and 39K NMR spectra for
Na[BPh4] and K[BPh4] at 4.70, 11.75, and 19.60 T. The 23Na
and 39K chemical shifts found for Na[BPh4] and K[BPh4] are
among the most shielded values compared with other sodium
and potassium compounds. Extensive quantum mechanical
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Acknowledgment. This research was supported by the
Natural Sciences and Engineering Research Council (NSERC)
of Canada. All quantum mechanical calculations were performed
at the High Performance Computing Virtual Laboratory (HPCVL)
at Queen’s University. G.W. thanks Queen’s University for a
Chancellor’s Research Award and the Province of Ontario for
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