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Structure, Vibrational Spectra and 11B‑NMR Chemical Shift of Na8[AlSiO4]6(B(OH)4)2: Comparison of Theory and Experiment Alexander G. Schneider,† Lars Schomborg,‡ Anna C. Ulpe,† Claus H. Rüscher,‡ and Thomas Bredow*,† †

Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich- WilhelmsUniversität Bonn, Beringstraße 4-6, D-53115 Bonn, Germany ‡ Institut für Mineralogie, Leibniz Universität Hannover, Callinstraße 3, D-30167 Hannover, Germany S Supporting Information *

ABSTRACT: Density functional theory (DFT) calculations at generalized gradient approximation (GGA) level were performed to interpret experimental IR and Raman vibrational spectra, to assign 11B-NMR chemical shifts, and to calculate the structure of the tetrahydroxyborate sodalite Na8[AlSiO4]6(B(OH)4)2. Full optimization of the intercalated compound gave the following structural parameters of B(OH)−4 : B−O−B (105.3−115.3°) and B−O−H (111.5−115.4°) angles, B−O (1.476 Å, 1.491 Å) and O−H (0.98 Å) distances. The calculated normal modes were assigned to experimental IR and Raman spectra. In general, close agreement between theory and experiment was obtained. The mean absolute deviation (MAD) is below 11 cm −1. We also calculate the thermodynamical stability of Na8[AlSiO4]6(B(OH)4)2 with respect to Na8[AlSiO4]6(BH4)2 in the context of the tetrahydroborate hydration reaction.

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molecules in solids. For example, Beaird et al.21 calculated (and measured) the dehydration products of NaBO2 ·xH2 O, including NaB(OH)4. They used the Quantum ESPRESSO software package22 and LDA DFT to calculate the structure and Raman spectra. The studies of van den Berg et al.23−25 are still the only theoretical investigations of sodalites with respect to hydrogen storage, to the best of our knowledge. For the investigation of the hydrogen release mechanism and the reversibility of hydration of NaBH426−28 the reactions of the NaBH4−SOD could be a new starting point. In a previous study we developed a theoretical approach to describe the vibrational spectra of NaBH4−SOD.6 In this study we will apply this approach for Na8[AlSiO4]6(B(OH)4)2 (NaB(OH)4-SOD), which is formed during hydrolysis of NaBH4−SOD (cf. eq 1).

INTRODUCTION Sodalites (SODs) belong to the group of zeolites. The framework (or β-cage), which is part of every SOD, is built up by oxygen, trivalent (Al) and tetravalent (Si) cations. Six alkaline cations (M+) per conventional unit cell (CUC) compensate the negative charge of this framework. The cages can be occupied by anions; their charge is counterbalanced by two additional M+ cations per CUC. Starting from the compound Na8[AlSiO4]6Cl2,1 wherein chloride occupies the center of each cage and is tetrahedrally surrounded by four sodium ions, many substitutions are possible. For example, aluminum atoms can be substituted by gallium or silicon atoms by germanium.2,3 Alternatively two sodium ions can be substituted by zinc and two chloride anions by sulfate.4 The formation of Na8[AlSiO4]6(BH4)2 (NaBH4−SOD),5,6 by formally substituting chlorine by BH−4 , is another possibility, which is considered in the present study. There exist a number of previous theoretical studies on SODs in the literature. Fischer and Bell7 calculated the adsorption sites of hydrogen and carbon dioxide in zeolitic imidazolate frameworks at GGA DFT level using the CASTEP software.8 At the same level of theory Huai et al.9 calculated the structure and different properties of an electron-deficient telluride using the VASP software10−14 and the tight-binding linear muffin-tin orbital atomic sphere approximation (TBLMTO-ASA).15 Shannon and Metiu16 investigated isolated water molecules within a sodalite cage at GGA DFT level using VASP.10−14 Mikuła et al.17 investigated vibrational spectra (IR and Raman) of sodalites using the CRYSTAL code18,19 at HF level and the Gaussian0920 program at DFT level, respectively. There are also many theoretical studies of boron-containing © 2016 American Chemical Society

NaBH4‐SOD + 8H 2O → NaB(OH)4 ‐SOD + 8H 2

(1)

Experimentally, NaB(OH)4-SOD has been identified as an intermediate product using 11B-NMR spectroscopy. We compare our calculations to experimental IR, Raman, and 11 B-NMR spectra of directly synthesized NaB(OH)4-SOD.29−31 NaB(OH)4-SOD could be synthesized as a micro crystalline powder as well as larger single crystals. The structure has been solved using X-ray powder diffraction (XRD).29,31 The cubic phase of NaB(OH)4-SOD crystallizes at 295 K in space group (SG) P4̅3n with a lattice constant of a = 9.024 Å and a chemical composition of Na7.6[AlSiO4]6(B(OH)4) 1.7·1.9 H2O (cf. Table Received: June 28, 2016 Revised: September 6, 2016 Published: September 6, 2016 7503

DOI: 10.1021/acs.jpca.6b06508 J. Phys. Chem. A 2016, 120, 7503−7509

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The Journal of Physical Chemistry A S1).29 Since XRD cannot locate the hydrogen positions, vibration spectroscopy can be employed to gain information on the molecular structure of the B(OH)−4 ions. The measured IR vibrational spectrum of NaB(OH)4-SOD can be separated into five significant regions. The first region (3500−3800 cm−1) contains the stretching modes of the OH groups, which are either symmetric, antisymmetric or isolated and thus generally denoted as ν (OH) in the following. In the second region (800−1400 cm−1) are the antisymmetric stretching modes (νas (T-O-T)) of the framework, the third region (600−750 cm−1) contains the symmetric stretching modes (νs (T-O-T)) and the fourth region (400−550 cm−1) contains the deformation modes (δ (O-T-O)) of the framework. Here T stands for aluminum and silicon, respectively. In the low frequency region from 0 to 400 cm−1 δ (O-T-O) and translation (t), torsion (τ) and deformation (δ) modes of the B(OH)−4 units are visible. In the Raman vibrational spectrum the same modes as in the IR spectrum exist but with different intensities due to the corresponding selection rules. The symmetric stretching mode of the B(OH)−4 (νs (B(OH)4)) becomes significant in the Raman spectrum as well as the δ (B(OH)4) modes below 400 cm−1. The main goal of the present study is the theoretical description of the B(OH)−4 unit in the NaB(OH)4-SOD and the reproduction and interpretation of the IR and Raman vibrational spectra (including the isotopic effect with respect to boron) with our tested theoretical setup that has been recently applied to the related compound NaBH4−SOD.6 Of particular interest in the geometry optimization is the determination of the B(OH)−4 hydrogen positions as these cannot be obtained from X-ray diffraction. Additionally the 11B-MAS NMR signals which have been measured for microcrystalline NaB(OH)4SOD will be calculated. A theoretical prediction of the thermodynamical stability is made on the basis of calculated reaction enthalpies and free energies. The crystalline-orbital program CRYSTAL1418,19 was used for optimizations and frequency calculations. The Vienna ab initio simulation package (VASP version 5.3.310−14) was used for chemical shift calculations.

analyzed in the mid-infrared (MIR) range between 370 and 5000 cm−1 with a resolution of 2 cm−1 and 32 scans using the KBr-method. Typically about 1 mg of the sample was diluted in 199 mg of potassium bromide to form a solid pellet. Additionally the samples were analyzed in the far-infrared (FIR) range between 10 and 400 cm−1, using polyethylene (PE) as pellet-matrix. Here about 2 mg of the sample was diluted in 58 mg of PE. FIR and MIR spectra showed an excellent agreement in the overlap range and were therefore merged together. Raman-Analysis. Raman analyses were carried out, using a confocal Bruker Senterra micro-Raman spectrometer equipped with an Olympus BX 51 microscope and an Andor DU420-OE CCD camera. Depolarized spectra were collected at ambient conditions, using the 532 nm laser excitation lime with 20 mW power, under 50× magnification of an Olympus LWD objective for 1 s and 10 acquisition repetitions. The instrumental precision was within ±3 cm−1. NMR. All NMR measurements were carried out using a superconducting Bruker ASX 400 WB FT-NMR spectrometer with a standard Dewar configuration in the absence of proton decoupling at room temperature. The 1H-MAS NMR spectra were obtained at 400.13 MHz using a standard Bruker 4 mm MAS probe with boron nitride stator. Typical conditions were pulse lengths of 4.0 μs and a 10 s recycle delay. 128 scans were accumulated at a MAS rotation frequency of 12.5 kHz. Tetramethylsilane for 1H was used as the reference standard. 11 B-MAS NMR measurements were carried out at 128.38 MHz using a second Bruker standard 4 mm MAS probe which had a ceramic stator which is boron free with sample spinning at 12.5 kHz. Chemical shifts are given relative to BF3·Et2O. For the 11B-MAS NMR experiments, a short single pulse duration of 0.6 μs has been used to ensure homogeneous excitation of the central and all satellite transitions. A recycle delay of 1 s has been used, and 6000 scans have been accumulated. Measuring parameters are given in Table 1. Table 1. Measuring Parameters of Mas-Nmr

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parameter

EXPERIMENTAL DETAILS Synthesis. For FTIR-, Raman- and NMR-analysis powder samples were synthesized following Pietsch et al.31 Four grams of boric acid (H3BO3, Riedel-de Haën 31146), 1 g of the matrix reactant kaolinite (Fluka 60609), and 10 mL of a freshly prepared 16 M sodium hydroxide (NaOH, Merck 10646790) solution were used as reactants to yield NaB(OH)4-SOD and were added into a Teflon liner. The Teflon liner was closed and set into a 50 mL Teflon coated Berghof DAE-2 steel autoclave. These autoclaves were then heated for 48 h at 200 °C. After the reaction the autoclaves with the inserted Teflon cups were opened and the excess of sodium hydroxide solution was decanted. The remaining greyish materials needs to be washed with distilled water to remove the base, otherwise carbonate could form due to atmospherically absorbed CO2 in the reaction with the high pH-value of the samples. Additionally remaining NaOH could crystallize during the following drying process. To remove the base about 500 mL of distilled water is needed until the pH-value of the fresh filtrate is at about 8. After the washing procedure, the samples were dried for 48 h at 80 °C in a drying chamber. FTIR-Analysis. The FTIR-measurements were carried out using the Bruker Vertex 80v spectrometer. The samples were

rotor speed (vrot) no. of scans accumulated (NS) recycle delay (D1) pulse duration (P1)

1

H-MAS NMR 12.5 kHz 128 10 S 4.0 Μs

11

B-MAS NMR 12.5 kHz 6000 1S 0.6 Μs

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COMPUTATIONAL DETAILS Basic Details. The same parameters, functionals, and basis sets were used as in our previous study of NaBH4-SOD,6 only the overlap and penetration threshold for Coulomb-integrals, overlap threshold for HF-exchange-integrals and pseudooverlap were set to stricter values, 10−9 and 10−18, respectively. We used the PWGGA32 functional and CRYSTAL standard basis sets (cf. Table 2). Geometry Optimization. Due to the broken stoichiometry of the structure at 295 K, the experimental high-temperature phase at 350 K, in P4̅3n with a = 9.0534 Å, was taken as the starting structure of the geometry optimization.30 Since in this high-symmetry phase the eight oxygen atoms of the B(OH)−4 units are distributed over three equivalent sites of the three 24i Wyckoff positions and one 12f Wyckoff positions (cf. Table 3), the positions were manually set in the unit cell. 7504


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The Journal of Physical Chemistry A Table 2. CRYSTAL Standard Basis Sets Used for the Calculations atom

basis set

Na B O H Al Si

8-511G33 6-21G*34 6-31d135 5-11G*36 85-11G*37 86-311G**38

ΔR HT° =

∑ vAHT° A

ΔR GT° =

∑ vAGT° (2)

A

in which H°T is the standard enthalpy at temperature T, G°T the free standard energy at temperature T and vA are the stoichiometric coefficients, with negative signs for reactants and positive signs for products. The enthalpy and free energy in eq 2 are given by

Table 3. Experimental Atomic Positions of NaB(OH)4-SOD at 350 K in Fractional Units30 atom

Wyckoff pos.

x/a

y/a

z/a

occ.

Na Al Si O(cage) B O(molecule) O(molecule) O(molecule) O(molecule)

8e 6d 6c 24i 2a 24i 24i 24i 12f

0.196 0.25 0.25 0.151 0 0 0.073 0.073 0.832

0.196 0 0.5 0.450 0 0.141 0.859 0.897 0

0.196 0.5 0 0.141 0 0.927 0 0.103 0

1 1 1 1 1 0.0833 0.0833 0.0833 0.167

HT° = Eel + E0 + E T + pV GT° = HT° − T ·ST°

(3)

Here, the electronic energy is given by Eel, the zero-pointenergy (ZPE) by E0, the vibrational energy by ET, the pressure by p, the volume by V, the temperature by T and the entropy by ST. ET in eq 3 is given by N

ET =

∑ ν

3NLℏων eℏων / kBT − 1

(4)

and ST by n

ST = −kB ∑ Wν ln(Wν) ν=1

The positions of the hydrogen atoms are not given in the experimental reference (cf. Tables S1 and 3).29,30 Therefore, standard values were assumed for initial O−H distances and B− O−H angles. A B−O distance of 1.48 Å, an O−H distance of 0.95 Å, and an O−B−O angle of 109.47° were set. The optimization of the atomic positions and the lattice constants was performed under symmetry restrictions, so a cubic lattice was maintained. The quality of the optimized structure was checked by the mean absolute deviation (MAD, Δq6) of the atomic positions of the cage forming atoms (cf. Table S1) and by the deviation of the calculated lattice constant from the experimental value at 295 K.29 Since motions of the B(OH)−4 unit in the sodalite are present, which lead to an averaged structure with cubic symmetry,39 and it is only possible to calculate unit cells with predefined fixed configurations, we used different starting structures and orientations in the geometry optimizations to yield the most stable one. Frequency Calculations. The frequency calculations were only performed for the fully relaxed structures, including lattice parameter, except where noted otherwise. The intensities of the IR and Raman vibrational spectra of the optimized structure were calculated with a coupled-perturbed Hartree−Fock/ Kohn−Sham approach (CPHF/KS).40−42 Through visualization of the calculated modes with the program Jmol,43 the modes could be related to different mode types. In the IR and Raman vibrational spectra shown below all modes are plotted, but they are only labeled when the intensity is larger than 50 km/mol for IR and 2.5% relative intensity for Raman spectra. In all spectra the highest calculated intensity was normalized to the experimental mode with the highest relative absorbance and relative intensity, respectively. The standard enthalpy of reaction (ΔRHT° ) and the free standard energy of reaction (ΔRGT° ) with respect to the NaBH4SOD were calculated as

(5)

with Wν = =

Nν N e−hων / kBT ∑ν e−hων / kBT

(6) 11

Chemical Shift. The B chemical shifts of the CRYSTAL14-optimized structures were calculated with VASP using the PAW (projector augmented-wave) method.44,45 A well converged cutoff energy of 700 eV and a Monkhorst−Pack grid of 2 × 2 × 2 were used. The number of bands were set to 160 for the cells and 40 for molecules, respectively. For the element boron, a harder PAW pseudopotential (B_h) was used while standard PAW pseudopotentials were employed for all other elements.44,45 The chemical shifts of the NaB(OH)4-SOD were referenced to gaseous BF3O(Et)2 (box size 10 Å3), which was also optimized with CRYSTAL14.

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RESULTS AND DISCUSSION Structure, Chemical Shift, and Thermodynamics. The resulting lattice constant, standard enthalpy of reaction, free standard energy of reaction and MAD of atomic positions for NaB(OH)4-SOD are given in Table 4. One can see (cf. Table 4) that the formation of NaB(OH)4SOD from NaBH4−SOD and H2O (cf. eq 1) is highly exothermic and exergonic. Therefore, NaB(OH)4-SOD is a possible intermediate product of hydration of NaBH4−SOD. One can see that the lattice constant agrees very well with the experiment and deviation of the atomic positions is only 1.6%. O−Si−O angles of 105.5−116.2° and O−Al−O angles of 106.3−113.5° are obtained (cf. Table 5). Four angles are smaller and two are larger than 109.5° for all SiO4 and for three AlO4 tetrahedra. In the three other AlO4 tetrahedra three angles are larger and three are smaller than 109.5°. The calculated 7505


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The distances and angles (except for the dihedral angles) of both B(OH)4 units in the CUC are almost identical (cf. Table 5). Three B−O distances of each unit are 1.476 Å and the fourth distance is 1.491 Å, which differ at most only 0.02 Å from the distances of the refined experimental structure at 295 K,29 while all O−H distances are close to 0.98 Å. In addition to the different B−O distances the BO4 tetrahedra are slightly distorted with angles between 105.3° and 115.3°, which deviate from the perfect tetrahedra angle assumed for the refinements of the structure of the NaB(OH)4-SOD at 295 K.29 Four angles are smaller and two angles are larger than 109.5°. The B−O−H angles in both units are between 111.5° and 115.4°. Therefore, we suggest that the individual B(OH)−4 units form slightly distorted tetrahedra, wherein all B−O and O−H distances are similar. The average over all unit cells of the crystal gives a perfect tetrahedral structure and cubic symmetry. Since the experimental lattice constant and the atomic positions are reproduced well, the optimized structure can be used for further calculations (frequencies, chemical shift). The experimental NMR chemical shift of the 11B atoms in NaB(OH)4-SOD is 1.9 ppm (cf. Figure S1 in the Supporting Information), which differs only by 3.1 ppm from our calculated shift (cf. Table 4). This deviation is within the typical deviations between calculated and measured chemical shifts for solids.46,47 Since only the nearest neighbors have a significant influence on the chemical shift of an atom, the result of our calculation is a validation of our optimized bond length of the B(OH)−4 units. IR and Raman Vibrational Spectra. The measured and calculated IR vibrational spectra are in close agreement (cf. Figure 2 and Figure S3 in Supporting Information). The deviations of the main peaks situated at 480, 650, 950, and 3650 cm−1 are less than 20 cm−1.

Table 4. Results of the Calculation of Na8[AlSiO4]6(B(OH)4)2 (PWGGA,32 CRYSTAL Basis Sets): Standard Enthalpy of Reaction (ΔRH°T) and Free Standard Energy of Reaction (ΔRGT° ) in kJ/mol, Lattice Constant (a) in Å, Deviation in Parentheses29 [%], Deviation of the Atomic Positions (Δq) in %, NMR Chemical Shift (δ) with Respect to BF3O(Et)2 in ppm, Deviation in Parentheses [ppm] ΔRHT° [kJ/mol]

ΔRGT° [kJ/mol]

a [Å]29

Δq [%]

δ(11B) [ppm]

−776

−691

8.94 (−0.9)

1.6

− 1.2 (3.1)

Table 5. Calculated Bond Angles and Distances of Na8[AlSiO4]6(B(OH)4)2 (PWGGA,32 CRYSTAL Basis Sets)a

a

kind of angle/distance

angle/distance

∠(OSiO) ∠(OAlO) ∠(B(1)OH) ∠(B(2)OH) ∠(OB(1,2)O) d (B(1,2)−O) d (O−H)

105.5−116.2 106.3−113.5 111.5, 112.4, 114.6, 115.4 111.6, 112.4, 114.5, 115.4 105.3, 107.2, 107.6, 108.1, 113.0, 115.3 1.476 (three times), 1.491 0.98 (eight times)

Distances (d) in Å, angles in °.

angles differ less than 1.7° from the angles of the refined experimental structure.29 This indicates that the experimental structure is reproduced reasonably well with the used method (cf. Figure 1).

Figure 2. Measured (red) and calculated IR vibrational spectrum (relative absorbance) of Na8[AlSiO4]6(11B(OH)4)2 (black) and Na8[AlSiO4]6(10B(OH)4)2 (green).

Figure 1. Optimized CUC of Na8[AlSiO4]6(B(OH)4)2 (without framework oxygen). Aluminum: gray; silicon: brown; sodium: blue; boron: green; hydrogen: white, oxygen: red.

The observed shoulders at 880, 1111, and 1203 cm−1 are assigned to deformation modes of the B(OH)−4 units (δ (B(OH)4). This is confirmed by TIR spectra.39 In the region below 400 cm−1 the first intense signals belong to translation modes of sodium (t(Na)), torsion and translation modes of the B(OH)−4 units (t,τ(B(OH)4) and deformation modes of the cage (δ(O-T-O)). Deformation and symmetric stretching (νs(B(OH)4) modes of the B(OH)−4 units are hidden by the cage modes in the experimental spectrum. One can see in Figure 3 and Figure S4 in Supporting Informaton, that the theoretical models reproduce the Raman spectrum with a

Now it is possible to make predictions of the positions of the OH groups of the B(OH)−4 units, in particular the positions of the hydrogen atoms, which are not located by XRD. Two B(OH) 4− units in the optimized CUC are symmetry inequivalent, which results in eight different oxygen and hydrogen positions, respectively (see Table S2 in the Supporting Information). 7506


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have not been determined experimentally and therefore we need a full optimization.

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CONCLUSION AND OUTLOOK Na8[AlSiO4]6(B(OH)4)2 was studied with periodic DFT methods. The aim was to identify the geometry of the enclosed B(OH)−4 ion including the positions of the hydrogen atoms, the theoretical analyses of the vibrational spectra and the conformation of this compound as a possible intermediate product of the hydration reaction of Na8[AlSiO4]6(BH4)2. As in a previous study of the compound NaBH4-SOD,6 we used CRYSTAL standard basis sets and the PWGGA functional. In the optimized geometry BO4 group forms a slightly distorted tetrahedron with B−O distances of about 1.5 Å. The OH groups are tilted with B−O−H angles of 111.5− 115.4°. The experimental chemical shift, the IR and Raman vibrational spectra were reproduced well, which validate the optimized structure. Additionally it was shown that the isotopic effect in the spectra is not negligible but is not seen in measured spectra due to the width of the signals at room temperature. The formation of Na8[AlSiO4]6(B(OH)4)2 starting from Na8[AlSiO4]6(BH4)2 is highly exothermic. Therefore, this compound is a stable intermediate product of the hydration reaction. Further studies are needed to clarify the reaction mechanism. Since we reproduced all experimental results well, we are confident that the used method is applicable for other enclosed oxygen containing molecules, such as OB(OH)−2 , BO−2 , etc.

Figure 3. Measured (red) and calculated Raman vibrational spectrum (relative intensities) of Na8[AlSiO4]6(11B(OH)4)2 (black) and Na8[AlSiO4]6(10B(OH)4)2 (green).

similar quality as the IR spectrum, except for some intensities. The relative intensities, however, remain approximately the same as in the measured spectra and we can assign every signal. As expected the B(OH)−4 Raman modes become more intense, when compared to the IR spectrum, in particular for the symmetric stretching mode. Since the previous calculations were done for 11B atoms and the 10B isotope occurs naturally by 20%, we also considered the isotopic effect of boron (cf. Figures 2 and 3). The deformation modes are shifted around 30 cm−1 to larger wavenumbers in both spectra, as expected due to the mass effect. These shifts should lead to additional B(OH)−4 modes in the experimental spectra. However, due to the width of the experimental signals, the isotopic effect cannot be identified in the measured spectra at room temperature. We have performed additional calculations with fixed parameter. We found that this leads to moderate changes in the calculated IR frequencies by up to 15 cm−1, which is within our error range. We provide selected frequencies of both optimization methods in Table 6. One can see that the calculations with fixed parameter lead to a slight deterioration for most modes. We will not use this approach in future studies, since we are going to calculate compounds which structures

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b06508. Table of optimized atomic positions of NaB(OH)4-SOD in fractional units, IR and Raman vibrational spectra of NaB(OH)4-SOD, 11B- and 1H NMR spectra of NaB(OH)4-SOD (PDF)

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*E-mail: [email protected]; phone: +49 (0)228 733839; fax: +49 (0)228 739064.

Table 6. Selected Experimental IR Frequencies (ν ) and Deviations of Calculations (Δν) of Na8[AlSiO4]6(B(OH)4)2 (PWGGA,32 CRYSTAL Basis Sets) with Full Optimization (FO) and Fixed Lattice Parameter (FLP) in cm−1 ν

3654 3621 1204 1105 998 875 723 698 656 457 426 286 200 114

Δν

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the Deutsche Forschungsgemeinschaft (DFG) within the project “Transport and reaction properties of new Boron-hydride-hydrate-oxide sodalites”(BR1768/8-1 and RU764/6-1). We thank M. Fechtelkord for the NMR measurements at the Institut für Geologie, Mineralogie und Geophysik of the Ruhr-Universität Bochum. All plots were made with gnuplot48 and all calculated structure drawings were obtained with Jmol.43

Δν

FO

FLP

25 34 −16 −15 −14 1 25 22 13 4 1 10 5 4

AUTHOR INFORMATION

Corresponding Author

exp

exp

ASSOCIATED CONTENT

S Supporting Information *

36 39 −2 19 −23 11 26 12 5 −10 −5 6 20 5

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REFERENCES

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