15018
J. Phys. Chem. C 2009, 113, 15018–15023
19
F Chemical Shift of Crystalline Metal Fluorides: Theoretical Predictions Based on
Periodic Structure Models
Anmin Zheng,† Shang-Bin Liu,*,‡ and Feng Deng*,†
State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Center for Magnetic
Resonance, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China,
and Institute of Atomic and Molecular Sciences, Academia Sinica, P.O. Box 23-166, Taipei 10617, Taiwan
ReceiVed: May 13, 2009; ReVised Manuscript ReceiVed: June 19, 2009
Precise theoretical predictions of 19F NMR parameters are helpful for the spectroscopic identification of
crystalline metal fluorides, especially for metal fluorides that possess multiple crystallographic fluorine sites.
Taking advantage of recent advancements in theoretical methods, 19F NMR chemical shifts of various crystalline
metal fluorides have been theoretically calculated on the basis of the periodic structure models. The theoretical
results reported herein are not only superior to the those predicted by conventional DFT calculation methods
but also render possible refinement of crystallographic data and explicit chemical shift assignments, as
exemplified by various metal fluorides containing multiple crystallographic fluorine sites, such as β-BaAlF5
and Ba3Al2F12.
1. Introduction
Nuclear magnetic resonance (NMR) spectroscopy is known
to be one of the most powerful techniques for exploring the
structures and dynamics of organic, inorganic, and biological
systems. In particular, through the incorporation of spin decoupling, cross-polarization (CP), magic-angle-spinning (MAS),
multiple-quantum (MQ), and two-dimensional (2D) techniques,
recent advances in high-resolution solid-state NMR have been
widely used for studying condensed matters.1-4 Similar to proton
(1H), fluorine-19 is a spin 1/2 nucleus with 100% natural
abundance but with a much wider chemical shift range (ca. 250
ppm vs 20 ppm for 1H),5 making 19F NMR spectroscopy a
sensitive and prominent technique for probing the local environments of various fluorine sites in crystalline and disordered
compounds.6-8 For systems with multiple crystallographic sites,
however, additional constraints imposed by the relative intensities of the resonances make the complete 19F chemical shift (CS)
assignments a challenging task.9 Compared with the more
sophisticated experimental NMR methods mentioned above,
theoretical calculation provides a relatively fast and direct
approach for NMR spectral assignments and identification of
multiple crystalline sites.10-12 Theoretical calculations based on
the density functional theory (DFT) approach have been
successfully applied to predict the 1H/13C/15N/31P NMR parameters, e.g., the isotropic chemical shift, shielding tensors,
quadrupolar coupling constants (QCCs), and electric field
gradient (EFG) constants, for various organic, inorganic, and
biological systems.12-16 As for fluorinated systems, while the
DFT method has been shown useful in predicting accurate 19F
CSs of organic fluorides,8,17-19 few studies have been devoted
to systems with complex structures, particularly those with
multiple crystalline sites, such as metal fluorides.20-22 To mimic
the crystalline structures of various (nonbarium-containing)
metal fluoride compounds, Body et al.22 adopted cluters centered
* To whom correspondence should be addressed. E-mail: dengf@
wipm.ac.cn (F.D.); [email protected] (S.-B.L.).
†
Chinese Academy of Sciences.
‡
Academia Sinica.
on studied fluorine atoms for the DFT calculations at the
B3LYP-GIAO level and obtained a root-mean-square (rms)
deviation of ca. 22 ppm, which is satisfactory considering the
span over the wide 19F CS range (>200 ppm) observed
experimentally. On the other hand, for barium-containing
compounds, maximum calculation errors as large as 90 and 85
ppm were observed for BaZnF4 and β-BaAlF5, respectively,
while a rms deviation of 51 ppm was observed for the cluster
model.22 Such large calculation errors have been attributed to
the simplified cluster models, which failed to represent the
complex crystalline structures, and the poor quality of the
barrium basis sets due to the inavailability of the polarization
functions.
The present contribution aims to illustrate that reliable
NMR parameters can be readily obtained for various metal
fluorides by using the gauge-including projector augmented
wave (GIPAW) method based on the periodic model to incorporate
the long-range electrostatic effects from the Madelung potential
of the lattices during DFT calculations.23 Accordingly, complete,
unambiguous assignments of 19F NMR chemical shifts can be
achieved even for systems with multiple crystallographic fluoride
sites, such as β-BaAlF5 and Ba3Al2F12 (Figure 1).24,25
2. Computational Method
During the structure optimization and subsequent calculations
of 19F NMR parameters, the electron correlation effects were
modeled using the generalized gradient approximation (GGA)
proposed by Perdew et al. (i.e., the PBE method).26 For structure
optimization, the couplings between the core and valence
electrons were described by ultrasoft pseudopotentials. In
addition, a plane-wave cutoff energy of 300 eV and a default
medium level Monkhorst-Pack k-point grid27 in the CASTEP
package28 were adopted to sample the Brillouin zone. During
the optimization, the unit cell parameters and the coordinates
of the metal atoms were kept fixed, while all fluoride atoms
were allowed to relax to their stable positions. The integrals
over the first Brillouin zone were performed using a MonkhorstPack 4 × 4 × 4 k-point grid to predict the chemical shifts by
the GIPAW method23 based on known crystallographic struc-
10.1021/jp904454t CCC: $40.75  2009 American Chemical Society
Published on Web 07/09/2009
19
F Chemical Shift of Crystalline Metal Fluorides
J. Phys. Chem. C, Vol. 113, No. 33, 2009 15019
Figure 1. Crystalline structures and AlF63- octahedra representation of (a, b) β-BaAlF5 and (c, d) Ba3Al2F12.
tures for Ba2ZnF6, Ba3Al2F12, and β-BaAlF5, whereas the default
fine level Monkhorst-Pack k-point grid in the CASTEP package
was adopted for the other metal fluorides. All wave functions
were expanded in the form of plane waves with a kinetic energy
less than 550 eV during calculations of NMR parameters. The
calculated 19F NMR chemical shifts were referenced to CFCl3
with a known absolute shielding of 143.5 ppm.29,30
3. Results and Discussion
3.1. Validities of Computational Model and Method: Case
of Metal Fluorine Systems with a Single Fluorine Site. The
GIPAW method pioneered by Pickard et al.23a represents a
landmark development in theoretical predictions of NMR
parameters for solid materials. Unlike conventional quantum
chemical approaches such as the GIAO methods available in
Gaussian 03 packages,31 which utilize cluster models based on
atomic orbital bases, the GIPAW method adopts a relatively
simple plane-wave basis set with approximated pseudopotentials
during NMR parameter calculations. Accordingly, all charge
densities and wave functions could be described by the planewave basis set, thus facilitating a full representation of crystalline
solids. Therefore, the GIPAW method, which is applicable for
the infinite periodic systems, allows for accurate DFT calculations of both chemical shifts and related NMR parameters in
solids.11,12,32,33
In order to validate the model and method invoking periodic
structure for CS calculations of solid compounds, we first
predicted 19F CSs of 15 different metal fluorides, viz., MF (M
) Li, Na, K, Rb, and Cs), MF2 (M ) Ca, Sr, Cd, Mg, Zn, and
Ba), MF3 (M ) Al, Ga, and In), and BaLiF3, which possess
only a single crystallographic fluorine site. The results calculated
on the basis of the periodic structure model are summarized in
Table 1 together with those reported in the literature, including
experimental data34,35 and results calculated by the conventional
cluster model.22 Apparently, the theoretical values predicted by
using the periodic structure model in this work were better
coincident with the experimental values. For example, the
maximum error between the calculated and experimental values,
∆δ(cal-exp), observed for the series samples by cluster model
calculations was 45.4 ppm (for LiF, see Table 1).22 This value
markedly decreased to 30.0 ppm when calculated on the basis
of the periodic structure model. Meanwhile, the rms deviation
between the experimental and calculated 19F chemical shift
values was also considerably decreased from ca. 22 ppm for
the cluster model to ca. 7 ppm for the periodic structure model.
These observations suggest that, by taking the shielding
contributions from nearest anions to a central fluorine atom as
well as the long-range electrostatic interactions into account
during NMR calculations, the periodic structure model adopted
herein is more practical in mimicking the structures of inorganic
crystalline materials and hence improving the accuracy of the
predicted 19F CSs.
15020
J. Phys. Chem. C, Vol. 113, No. 33, 2009
Zheng et al.
TABLE 1: Comparisons of Experimental 19F Chemical
Shifts (in ppm) with Those Obtained by Theoretical
Calculations Based on the Cluster Model and Periodic
Structure Model for Various Fluoride Compounds with a
Single Fluorine Site
compound
LiF
NaF
KF
RbF
CsF
CaF2
SrF2
CdF2
MgF2
ZnF2
BaF2
AlF3
GaF3
InF3
BaLiF3
c
space
group
Fm3jm
Fm3jm
Fm3jm
Fm3jm
Fm3jm
Fm3jm
Fm3jm
Fm3jm
P42/mmm
P42/mmm
Fm3jm
R3jc
R3jcc
R3jc
Pm3jm
cluster modela
periodic structure
modelb
δexpc
δcal
∆δ(cal-exp)
δcal
∆δ(cal-exp)
-201.2
-224
-129.2
-87.2
-6.2
-107
-83.2
-191.2
-196
-201.2
-11.2
-170
-167.2
-206.2
-98.2
-246.6
-253.2
-141.2
-84.9
18.6
-109.0
-93.8
-161.0
-225.3
-191.9
-22.2
-172.7
-153.6
-210.2
-79.3
-45.4
-29.2
-12.0
2.3
24.8
-2.0
-10.6
30.2
-29.3
9.3
-10.0
-2.7
13.6
-4.0
18.9
-220.7
-234.6
-122.7
-95.0
-12.5
-77.0
-73.1
-207.6
-215.4
-219.5
-2.3
-181.5
-170.5
-220.6
-95.3
-19.5
-10.6
6.5
-7.8
-6.3
30.0
10.1
-16.4
-19.4
-18.3
8.9
-11.5
-3.3
-14.4
2.9
a
Theoretical results obtained from ref 22. b This work.
Experimental data ((2 ppm) taken from refs 22, 34, and 35.
3.2. Barium Fluorometalates: Case of Metal Fluorine
Systems with Multiple Fluorine Sites. It has been demonstrated
that NMR calculations by the conventional cluster model failed
to predict 19F CSs accurately for barium fluorometalates with
multiple fluorine sites, such as BaMgF4,36 BaZnF4,37 and
Ba2ZnF6.38 To mimic the crystalline structures of these bariumcontaining compounds, Body et al.22 adopted clusters centered
on the studied fluorine atoms. However, such clusters built up
from the bulk structures were rather awkward due to the low
symmetry of the systems. Moreover, the basis sets in the
Gaussian software, from which no polarization functions for
the barium atom were available, were of poor quality. As a
result, predictions made by the conventional cluster model lead
to sizable computational errors as larger as 90 and 85 ppm for
BaZnF4 and β-BaAlF5, respectively, with a moderate rms
deviation at the level of ca. 51 ppm.22 On the other hand, since
GIPAW calculations invoke reconstructions of all electrons in
the barium atom (Ba: 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 5s2
5p6 6s2) to improve the quality of the barium basis sets,
considerable improvement in calculation accuracy may be
anticipated.
Here, the validities of the GIPAW method based on the
periodic structure model for 19F CS calculations were further
exemplified by a series of barium-containing metal fluoride
compounds. For BaMF4 (M ) Mg or Zn), which belongs to
the orthorhombic (Cmc21) space group, the Ba2+ sites are
coordinated by 11 F- anions, whereas the M2+ cations are
surrounded by 6 F-, in which 4 bridge to the other M2+ and 2
bond with Ba2+. In Ba2ZnF6 which belongs to the space group
I4/mmm, eight next-nearest neighboring (NNN) fluorine atoms
surround a “free” fluorine atom, and free, shared, and unshared
fluorine sites are present. Body et al.22 have defined the isotropic
19
F CS ranges for shared, unshared, and “free” fluorine atoms
encountered in the binary metal fluorine systems. However,
complete, unambiguous 19F CS assignments for most multimetal
fluorine systems, such as R-BaCaAlF7, which contains one
“free” and six unshared fluorine sites,39 are still challenging
tasks.
Table 2 summarizes the experimental and theoretical 19F CSs
for various metal fluorine systems with multiple fluorine sites.
TABLE 2: Comparisons of Experimental 19F Chemical
Shifts (in ppm) with Those Obtained by Theoretical
Calculations Based on the Cluster Model and Periodic
Structure Model for Various Fluoride Compounds with
Multiple Fluorine Sites
space
compound group F site δexpc
BaZnF4
F1
F2
F3
F4
BaMgF4
Cmc21 F1
F2
F3
F4
R-BaAlF5 P212121 F1
F2
F3
F4
F5
γ-BaAlF5
P21
F1
F2
F3
F4
F5
F6
F7
F8
F9
F10
Ba2ZnF6
I4/mmm F1
F2
F3
R-BaCaAlF7 P12/n1 F1
F2
F3
F4
F5
F6
F7
c
Cmc21
-161.2
-84.2
-99.2
-157.2
-160.2
-87.2
-79.2
-169.2
-113.2
-108.2
-123.2
-132.2
-154.2
-121.2
-118.2
-113.2
-130.2
-121.2
-143.2
-121.2
-127.2
-134.2
-147.2
2.8
-149.2
-134.2
-127.2
-146.2
-143.2
-52.2
-123.2
-120.2
-127.2
cluster modela
periodic structure
modelb
δcal
∆δ(cal-exp)
δcal
∆δ(cal-exp)
-116.4
-46.8
-54.7
-66.9
-80.4
-48.8
-45.7
-141.6
-65.7
-78.1
-91.3
-66.4
-175
-77.3
-69.5
-73.3
-97.5
-39.8
-199
-61.6
-65.7
-78.1
-91.3
22.3
-128.9
-97.6
-66.0
-132.2
-131.3
-52.6
-95.2
-121.4
-99.0
44.8
37.4
44.5
90.3
79.8
38.4
33.5
27.6
47.5
30.1
31.9
65.8
-20.8
43.9
48.7
39.9
32.7
81.4
55.8
59.6
61.5
56.1
55.9
19.5
20.3
36.6
61.2
14.0
11.9
-0.4
28.0
-1.2
28.2
-160.3
-77.7
-108.9
-150.3
-174.5
-91.4
-80.0
-184.3
-127.6
-115.4
-145.2
-131.0
-171.6
-146.3
-121.3
-125.4
-145.6
-136.9
-124.2
-127.7
-127.6
-115.4
-145.2
7.4
-161.2
-125.3
-138.1
-152.0
-149.5
-16.0
-132.9
-129.2
-136.3
0.9
6.5
-9.7
6.9
-14.3
-4.2
-0.8
-15.1
-14.4
-7.2
-22.0
1.2
-17.4
-25.1
-3.1
-12.2
-15.4
-15.7
19.0
-6.5
-0.4
18.8
2.0
8.9
4.6
8.9
-10.9
-5.8
-6.3
36.2
-9.7
-9.0
-9.1
a
Theoretical results obtained from ref 22.
Experimental data taken from ref 34.
b
This work.
In the case of calculations based on the conventional cluster
model at the B3LYP level, in which the 6-311+G(d), LanL2DZ,
and CRENBL basis sets were adopted to describe the central
fluorine atom, the rest of the F atoms, and the metal atoms,
respectively, the 19F CSs so predicted were overestimated by
ca. 90.3, 79.8, and 36.6 ppm for BaZnF4, BaMgF4, and Ba2ZnF6,
respectively (Table 2).21 On the other hand, with the exception
of the F4 site in R-BaCaAlF7, the 19F CSs calculated by the
GIPAW method led to much smaller ∆δ(cal-exp) errors (Table
2). It is obvious that the GIPAW method based on the periodic
structure model adopted herein is capable of improving the
accuracies of the predicted 19F CSs for systems with multiple
fluorine sites.
On the basis of our analyses of 48 fluorine sites from 21
different metal fluorides (Tables 1 and 2), it is indicative
that reliable 19F CSs of metal fluorides may be predicted by
combining the GIPAW method and periodic structural model.
Figure 2 displays the correlations of experimental and
calculated 19F CSs obtained from various metal fluorides. All
data points were drawn from Tables 1 and 2, including
experimental and corresponding theoretical results calculated
on the basis of the simplified cluster model, and those
predicted herein by the GIPAW method based on the periodic
structual model. As can be seen from Figure 2, a good linear
correlation between the experimental chemical shifts and
19
F Chemical Shift of Crystalline Metal Fluorides
J. Phys. Chem. C, Vol. 113, No. 33, 2009 15021
Figure 2. Correlations of experimental and calculated 19F isotropic
chemical shifts for all F sites in various metal fluorides listed in Tables
1 and 2. The solid line represents a linear fit to the results obtained by
the periodic structure model. The dashed line corresponds to δiso,cal )
δiso,exp.
those calculated by the GIPAW method was observed, which
may be expressed as
δexp ) 0.86((0.03)δcal - 14.6((3.9);
R2 ) 0.98
(1)
Since a much smaller rms deviation (7.6 ppm) was observed
for calculated isotropic CSs (Tables 1 and 2) based on the
periodic structural model compared to that by the cluster model
(22.0 ppm), it is conclusive that theoretical calculations of NMR
parameters by the GIPAW method based on the periodic
structure model are indeed far superior to the convential GIAO
method based on the cluster model, particularly for crystalline
solids with multiple crystallographic sites.
3.3. Complete 19F Chemical Shift Assignments of
β-BaAlF5 and Ba3Al2F12. The solid-state 19F MAS NMR spectra
obtained using high spinning speeds are normally capable of
providing information on the environments of fluorine sites for
both crystalline and disordered compounds.7,8 Nevertheless, the
19
F chemical shift assignments for some of the crystalline metal
fluorides that possess multiple fluorine sites remain ambiguous
based on the experimental NMR method. For example,
β-BaAlF5, which is built up by isolated infinite chains of cornersharing (AlF6)3- octahedra (Figure 1a and b) involving 2 Al
and 10 nonequivalent F sites. Among them, the F sites can
further be divided into two groups, namely, shared (F1 and F5)
and unshared (F2-F4 and F6-F10) sites.24 Similarly, the
structure of Ba3Al2F12, which is built up from four connersharing (AlF6)3- octahedra, involves one Al and eight nonequivalent F sites: two shared F (F1 and F2), two free (F3 and
F4), and four unshared (F5-F8) sites (Figure 1c and d).25 It is
well-known that the 19F isotropic CS is very sensitive to the
environments of the fluorine atom. However, a complete,
unambiguous assignment of the 19F MAS NMR spectrum of
complicated fluoride systems, such as β-BaAlF5, which exhibits
10 peaks with similar (ca. (10%) intensities, is a challenging
task even when acquired by sophisticated NMR pulse sequences.
Recently, Martineau et al. reported9 the assignments of crystalline β-BaAlF5 and Ba3Al2F12 based on the poorly resolved 19F
resonance peaks obtained by the combined 2D 19F-27Al CPHETCOR and 19F-19F DQ-SQ MAS NMR correlation spectroscopy techniques. Nevertheless, the authors also pointed out
that precise CS assignments of the F3 and F4 sites in Ba3Al2F12
remained ambiguous even if such sophisticated experimental
techniques were adopted.9
As we have verified above, the GIPAW method in conjunction with the periodic structure model is a reliable technique to
predict accurate 19F CSs for barium-containing fluoride compounds. As such, such a combined method should also afford
complete 19F CS assignments for complex barium fluorometalate
systems, such as β-BaAlF5 and Ba3Al2F12. The 19F CS values
calculated on the basis of the periodic structure model for each
fluorine site of crystalline β-BaAlF5 are listed in Table 3, which
are typically off the experimental CSs by only ca. 2-11 ppm,
revealing a remarkable improvement in accuracy compared to
the conventional calculation based on the cluster model.8,22 It
is well-known that optimization of structure warrants a more
realistic prediction of atomic positions in the unit cell, and hence
TABLE 3: F-Al Bond Lengths and 19F Chemical Shifts for Each Fluorine Site of Crystalline β-BaAlF5 Calculated on the Basis
of Various Modelsa
19
bond length (Å)
b
F site
PM
PM-opt
cluster
F(1)-Al(2)
F(1)-Al(1)
F(2)-Al(2)
F(3)-Al(2)
F(4)-Al(2)
F(5)-Al(1)
F(5)-Al(2)
F(6)-Al(1)
F(7)-Al(1)
F(8)-Al(2)
F(9)-Al(1)
F(10)-Al(1)
1.830
1.912
1.788
1.796
1.784
1.875
1.858
1.811
1.736
1.790
1.756
1.794
1.860
1.888
1.794
1.800
1.790
1.892
1.866
1.817
1.791
1.797
1.772
1.801
-173.8
-173.8
-101.4
-91.9
-57.1
-171.1
-171.1
-80.9
-102.6
-60.6
-51.3
-106.9
superposition
-152.2
-152.2
-139.2
-117.2
-127.2
-150.2
-150.2
-126.2
-127.2
-110.2
-130.2
-137.2
b
F chemical shift (ppm)
PM
PM-opt
fitting (PM-opt)c
Exp.d
-164.1
-164.1
-147.3
-127.2
-117.5
-160.1
-160.1
-130.4
-151.3
-94.2
-128.4
-153.2
-163.9
-163.9
-144.4
-125.0
-111.4
-158.9
-158.9
-134.0
-149.8
-101.9
-128.2
-153.5
-154.7
-154.7
-137.7
-120.8
-109.0
-150.3
-150.3
-128.5
-142.4
-100.7
-123.6
-145.6
-154.6
-154.6
-138.9
-121.3
-109.2
-148.8
-148.8
-127.5
-140.8
-99.0
-124.5
-144.6
a
The conventional cluster model (cluster), superposition model, and periodic structure models deduced from experimental crystallographic
data before (PM) and after (PM-opt) structure optimization. b Theoretical results predicted on the basis of the cluster model and superposition
model referred from refs 22 and 8. c Fitting values derived from eq 1 (see text). d Experimental data referred from ref 9.
15022
J. Phys. Chem. C, Vol. 113, No. 33, 2009
Zheng et al.
mental data (δexp)9 and theoretical CS (δcal) values obtained from
the PM-opt model. Note that the errors of the fitting results are
within ca. (3.0 ppm and the rms is only at ca. 1.1 ppm level,
affording unambiguous assignments for the 10 19F resonance
peaks obtained from crystalline β-BaAlF5. Our 19F chemical shift
assignments based on the PM and PM-opt models were in good
agreement with the results based on the sophisticated 2D
19
F-27Al CP-HETCOR and 19F-19F DQ-SQ MAS NMR
correlation spectroscopy techniques by Martineau et al.9 It
should be noted that the cluster model calculations failed to
provide accurate 19F CS predictions which were comparable to
the experimental results (see Table 3), leading to ambiguous
19
F CS assignments for each fluorine site.22 Although some
improvements have been made to predict 19F CSs based on the
so-called “superposition model”, the calculated results can only
provide assignments for the F1 and F5 sites based on the change
trend of 19F chemical shift (see Table 3).8,9 Thus, it is evident
that 19F isotropic chemical shifts calculated on the basis of the
PM model are far superior to those predicted on the basis of
the cluster or superposition models, facilitating unambiguous
spectral assignments for each fluorine site in the system.
Similar CS calculations based on the PM and PM-opt models
were also performed to identify various fluorine sites of
crystalline Ba3Al2F12. Although a recent experimental study
using 19F-27Al and 19F-19F dipolar-based 2D NMR experiments9 showed improved resolution of the 19F MAS spectrum,
some limitations remain in assigning the CSs for the two shared
fluorine sites (F3 and F4) of Ba3Al2F12 (Figure 1c), exhibiting
similar connectivity. In this context, theoretical 19F CSs predicted
herein based on the optimized structure (PM-opt) model, again,
offer an avenue for complete, unambiguous CS assignments.
For example, the theoretically predicted 19F chemical shifts of
the F1, F2, and F5-F8 sites (see Table 4) were found to be
much closer to the experimental data,9 whereas the 19F CS of
the F3 site was found to be ca. 20-30 ppm downfield from the
F4 site regardless of the structure (PM or PM-opt) models used.
Moreover, the fitting values (with a rms value of ca. 2.0 ppm)
for the F3 and F4 sites were confirmed to be -33.0 and -51.5
ppm, respectively. The theoretical approaches adopted herein
therefore enable us to afford complementary supports for the
complete spectral assignments of Ba3Al2F12 fluoroaluminate.
Figure 3. Correlations of calculated and experimental 19F chemical
shifts for each fluorine site of crystalline β-BaAlF5 (see Table 2). The
results were obtained on the basis of periodic models deduced from
crystallographic data before (PM; 0) and after (PM-opt; O) structure
optimization at the GGA/PBE level, and those derived from eq 1 (fitting;
2) are depicted. The dashed line corresponds to δiso,cal ) δiso,exp.
affords a more reliable prediction of NMR parameters.9 By
optimizing the structure at the GGA/PBE level (hereafter
denoted as the “PM-opt model”), all fluorine atoms in each unit
cell should be relaxed to constitute a stable periodic structure,
leading to a slight increase (typically ca. 0-0.085 Å, see Table
3) in Al-F bond lengths for the β-BaAlF5 system when
compared with those predictions made without structure optimization.24 The latter which made use of only crystallographic
data but not structure optimization is hereafter referred to the
“PM model”.
It is noted that the 19F CSs predicted on the basis of the PM
and PM-opt models represent considerable improvements in
accuracies compared to a previous theoretical study based on
the conventional cluster model for crystalline β-BaAlF5 (see
Table 3). Compared to the experimental results, while the 19F
CSs calculated for each fluoroine site are similar when the PM
and PM-opt models were used, those predicted by the PM-opt
model are obviously better than those predicted by the PM
model, as shown in Figure 3. Similar trends were also found in
NMR parameter predictions of biological systems,12 suggesting
that structure optimization undoubtedly leads to much better
calculation results. Also shown in Figure 3 and Table 3 are the
fitted results using eq 1, which was derived from the experi-
4. Conclusions
In summary, we have demonstrated that reliable predictions
of NMR parameters may be obtained for complicated crystalline
metal fluoride systems by theoretical calculations based on
periodic structure models. Accordingly, excellent agreements
on the calculated 19F chemical shifts for various fluorine sites
compared to the existing experimental results were achieved.
That the slope of experimental vs calculated CSs in eq 1 deviated
from unity and that an average calculated error of ca. 10 ppm
TABLE 4: 19F Chemical Shift (in ppm) for Each Fluorine Site of Crystalline Ba3Al2F12 Calculated on the Basis of the PM and
PM-opt Models
F site
F1
F2
F3
F4
F5
F6
F7
F8
Exp.a
clusterb
PMc
PM-optc
fittingd
-153.3
-161.9
-168.5
-167.4
-158.4
-151.6
-170.2
-165.1
-164.7
-156.1
-50.8 (?)
-6.7
-10.8
-21.6
-33.0
-30.5 (?)
-32.7
-44.3
-43.1
-51.5
-115.7
-84.2
-122.7
-124.1
-121.2
-113.0
82.9
-126.5
-121.9
-119.3
-127.9
-92.5
-141.6
-136.3
-131.7
-146.4
-112.2
-161.6
-158.8
-151.0
a
Experimental data referred from ref 9. b Theoretical results predicted on the basis of the cluster model referred from ref 22. c Theoretical
results calculated on the basis of periodic structure models deduced from experimental crystallographic data before (PM) and after (PM-opt)
structure optimization. d Fitting values derived from eq 1 (see text).
19
F Chemical Shift of Crystalline Metal Fluorides
was observed for the barium-containing compounds may be
attributed to the complexity of the crystalline metal fluoride
systems. The theoretical results obtained by such calculation
methods were found to be far superior to the conventional DFT
calculations based on the cluster model, thus rendering confirmation of spectral assignments and refinement of crystallographic data obtained from experimental studies. It is anticipated that the calculated results may be further improved at the
expanse of calculation time by adopting a denser k-point grid
and a larger energy cutoff during periodic models calculations.
Acknowledgment. This work was supported by the National
Natural Science Foundation of China (20703058, 20773159, and
20673139), the National Basic Research Program of China
(2009CB918600), and the National Science Council (NSC952113-M-001-040-MY3), Taiwan. The authors are grateful to
the National Center for High-performance Computing (NCHC,
Taiwan) and Shanghai Supercomputer Center (SSC, China) for
their support in computing facilities.
References and Notes
(1) Laws, D. D.; Bitter, H.; Jerschow, A. Angew. Chem., Int. Ed. 2002,
41, 3096.
(2) Klinowski, J., Ed. New Techniques in Solid-State NMR. Topics in
Current Chemistry; Springer: Berlin, Heidelberg, New York, 2004.
(3) Caravatti, P.; Braunschweiler, L.; Ernst, R. R. Chem. Phys. Lett.
1983, 100, 305.
(4) Geen, H.; Titman, J.; Gottwald, J.; Spiess, H. W. Chem. Phys. Lett.
1994, 227, 79.
(5) Berger, S., Braun, S., Kalinowski, H.-O., Eds. NMR-Spektroskopie
Von Nichtmetalle, Bd. 4: 19F-NMR-Spektroskopie; Georg Thieme Verlag:
Stuttgart, Germany, 1994.
(6) (a) Miller, J. M. Prog. Nucl. Magn. Reson. Spectrosc. 1996, 28,
255. (b) Stebbins, J. F.; Zeng, Q. J. Non-Cryst. Solids 2000, 262, 1. (c)
Bureau, B.; Silly, G.; Buzare, J.-Y.; Emery, J.; Legein, C.; Jacoboni, C. J.
Phys.: Condens. Matter 1997, 9, 6719.
(7) Martineau, C.; Body, M.; Legein, C.; Silly, G.; Buzare, J. Y.; Fayon,
F. Inorg. Chem. 2006, 45, 10215.
(8) Body, M.; Silly, G.; Legein, C.; Buzare, J.-Y. Inorg. Chem. 2004,
43, 2474.
(9) Martineau, C.; Legein, C.; Buzare, J. Y.; Fayon, F. Phys. Chem.
Chem. Phys. 2009, 11, 950.
(10) Moon, S.; Case, D. A. J. Comput. Chem. 2006, 27, 825.
(11) Yates, J. R.; Pickard, C. J.; Payne, M. C.; Dupree, R.; Profeta, M.;
Mauri, F. J. Phys. Chem. A 2004, 108, 6032.
(12) Zheng, A.; Liu, S. B.; Deng, F. J. Comput. Chem. 2009, 30, 222.
(13) Xu, X. P.; Au-Yeung, S. C. F. J. Phys. Chem. B 2000, 104, 5641.
(14) (a) Zheng, A.; Yang, M.; Yue, Y.; Ye, C.; Deng, F. Chem. Phys.
Lett. 2004, 399, 172. (b) Su, Y. C.; Zheng, A.; Li, S. H.; Chen, L.; Deng,
F. Chin. J. Magn. Reson. 2006, 23, 293. (c) Wu, Z.; Zheng, A.; Yang, J.;
Deng, F. Chin. J. Magn. Reson. 2007, 24, 501.
(15) Mirzaei, M.; Hadipour, N. L. J. Phys. Chem. A 2006, 110, 4833.
(16) Sanz, D.; Claramunt, R. M.; Saini, A.; Kumar, V.; Aggarwal, R.;
Singh, S. P.; Alkorta, I.; Elguero, J. Magn. Reson. Chem. 2007, 45, 513.
(17) Wiberg, K. B.; Zilm, K. W. J. Org. Chem. 2001, 66, 2809.
(18) Harding, M. E.; Lenhart, M.; Auer, A. A.; Gauss, J. J. Chem. Phys.
2008, 128, 244111.
J. Phys. Chem. C, Vol. 113, No. 33, 2009 15023
(19) Jameson, C. J.; Jameson, A. K.; Honarbakhsh, J. J. Chem. Phys.
1984, 81, 5266.
(20) Cai, S. H.; Chen, Z.; Hu, X.; Wan, H. L. Chem. Phys. Lett. 1999,
302, 73.
(21) Cai, S. H.; Chen, Z.; Wan, H. L. J. Phys. Chem. A 2002, 106,
1060.
(22) Body, M.; Silly, G.; Legein, C.; Buzare, J.-Y. J. Phys. Chem. B
2005, 109, 10270.
(23) (a) Pickard, C. J.; Mauri, F. Phys. ReV. B 2001, 63, 245101. (b)
Umari, P.; Gonze, X.; Pasquarello, A. Phys. ReV. B 2004, 69, 235102. (c)
Pickard, C. J.; Mauri, F. Phys. ReV. Lett. 2003, 91, 196401.
(24) Le Bail, A.; Ferey, G.; Mercier, A. M.; de Kozak, A.; Samouel,
M. J. Solid State Chem. 1990, 89, 282.
(25) Kaiser, V.; Babel, D. Z. Anorg. Allg. Chem. 2004, 630, 794.
(26) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77,
3865.
(27) Monkhorst, H.; Pack, J. D. Phys. ReV. B 1976, 13, 5188.
(28) Segall, M. D.; Lindan, P. J. D.; Probert, M. J.; Pickard, C. J.; Hasnip,
P. J.; Clark, S. J.; Payne, M. C. J. Phys.: Condens. Matter 2002, 14, 2717.
(29) Yates, J. R.; Dobbins, S. E.; Pickard, C. J.; Mauri, F.; Ghi, P. Y.;
Harris, R. K. Phys. Chem. Chem. Phys. 2005, 7, 1402.
(30) All calculated 19F NMR chemical shifts were referenced to CFCl3
in this work. For experimental and theoretical 19F CS values cited from the
literature (cf. refs 22 and 35) that were originally referred to C6F6, their
CSs were recalibrated to CFCl3 by taking a difference between δC6F6 and
δCFCl3 of -164.2 ppm.
(31) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,
M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.;
Burant, J. C.; Millam, J. M.; Lyengar, S. S.; Tomasi, J.; Barone, V.;
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,
X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.;
Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Camml, R.;
Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.;
Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels,
A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;
Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,
P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.;
Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,
B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03,
revision B.05; Gaussian, Inc.: Pittsburgh, PA, 2003.
(32) Profeta, M.; Mauri, F.; Pickcard, C. J. J. Am. Chem. Soc. 2003,
125, 541.
(33) Harris, R. K.; Joyce, S. A.; Pickard, C. J.; Cadars, S.; Emsley, L.
Phys. Chem. Chem. Phys. 2006, 8, 137.
(34) Bureau, B.; Silly, G.; Emery, J.; Buzare, J.-Y. Chem. Phys. 1999,
249, 89.
(35) (a) Scholz, G.; Kemnitz, E. Solid State Sci. 2009, 11, 676. (b)
Wuttke, S.; Coman, S. M.; Scholz, G.; Kirmse, H.; Vimont, A.; Daturi,
M.; Schroeder, S. L. M.; Kemnitz, E. Chem.sEur. J. 2008, 14, 11488. (c)
Scholz, G.; Korup, O. Solid State Sci. 2006, 8, 678. (d) Scholz, G.; Dörfel,
I.; Heidemann, D.; Feist, M.; Stösser, R. J. Solid State Chem. 2006, 179,
1119.
(36) Gingl, F. Z. Anorg. Allg. Chem. 1997, 623, 705.
(37) Lapasset, J.; Bordallo, H. N.; Almairac, R.; Nouet, J. Z. Kristallogr.
1996, 211, 934.
(38) von Schnering, H. G. Z. Anorg. Allg. Chem. 1967, 353, 13.
(39) Werner, F.; Weil, M. Acta Crystallogr., Sect. E 2003, 59, 17.
JP904454T