19F Chemical Shift of Crystalline Metal Fluorides: Theoretical

Jul 9, 2009 - 127I NMR calculations in binary metal iodides by PBE-GGA, YS-PBE0 and mBJ exchange correlation potentials. M. Bashi , H.A. Rahnamaye ...
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J. Phys. Chem. C 2009, 113, 15018–15023

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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

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F Chemical Shift of Crystalline Metal Fluorides

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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.

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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

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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.

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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).

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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.

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