Structure and IR Vibrational Spectra of Na8[AlSiO4]6(BH4)2

Article pubs.acs.org/JPCA

Structure and IR Vibrational Spectra of Na8[AlSiO4]6(BH4)2: Comparison of Theory and Experiment Alexander G. Schneider,† Thomas Bredow,*,† Lars Schomborg,‡ and Claus H. Rüscher‡ †

Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Rheinische Friedrich-Wilhelms Universität Bonn, Beringstrasse 4-6, D-53115 Bonn, Germany ‡ Institut für Mineralogie, Leibniz Universität Hannover, Callinstrasse 3, D-30167 Hannover, Germany ABSTRACT: The structure and IR vibrational spectra of tetrahydroborate sodalite (Na8[AlSiO4]6(BH4)2) were calculated using density functional theory (DFT) methods. The calculations, performed at the GGA hybrid DFT level yield a close agreement with XRD refinements of the structure and allow interpretation of observed bands of the enclosed BH−4 and the framework and, in particular, a verification of hydrogen positions (Buhl, J.-C.; Gesing, T. M.; Rüscher, C. H. Microporous Mesoporous Mater. 2005, 80, 57−63). In a first step, different basis sets and functionals were tested on NaBH4 and Na8[AlSiO4]6Cl2. We show that accurate treatment of B−H stretching modes requires anharmonic corrections, while lattice vibrations are well described within the harmonic approximation.

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INTRODUCTION Sodalites (SODs) form a group of compounds with interesting fundamental aspects in zeolite chemistry. An overview of the SOD framework and symmetry relationships of SOD-type crystal structures has been given by Fischer and Baur.2 The general SOD composition, which crystallizes in space group (SG) P4̅3n, is M8[1T2TO4]X2, where 1T is a trivalent cation (usually Al3+) and 2T is a tetravalent cation (usually Si4+), but others like Ga3+ and Ge4+ can also be part of the structure,3,4 as well as the family of aluminate and silicate SODs, having only Al3+ or Si4+ on T-sites. SOD consists of close-packed truncated octahedral cages formed by, in the case of the alumino-silicate framework, 24 Si/AlO4 tetrahedral units per cage and 6 Si/AlO4 per conventional unit cell (CUC). These units form six- and four-membered rings shared by neighboring cages. Generally, the alumino-silicate SOD framework requires three positive charges per cage for charge compensation and six per CUC. This is achieved by sodium ions as in the mineral SOD, Na8[AlSiO4]6Cl2 (NaCl−SOD). The additional sodium ions compensate for the negative charge of the chloride ions that occupy the centers of the cages. The sodium ions become indistinguishable on the 8e position in P4̅3n close to the sixmembered rings forming a tetrahedron in each cage. Therefore, Na+ can be seen as a shutter of all six-membered rings; therefore, there is no open cage connection in SOD through the six-membered rings. For the general composition, each cage is filled by four Na+ and one monovalent anion, or an anion group, which is BH 4− . In this study, the SOD Na8[AlSiO4]6(BH4)2 (cf. Figure 1) is denoted as NaBH4− SOD in the following. It has been described that both micro- and nanocrystallites of NaBH4−SOD could be obtained easily by soft chemical © 2014 American Chemical Society

Figure 1. CUC of Na8[AlSiO4]6(BH4)2 (without oxygen). Aluminum: dark blue; silicon: red; sodium: green; boron: gray; hydrogen: bright blue.

methods at rather moderate conditions,1,5 at which the capability of the SOD structure for incorporating various ions of different sizes can be explained by the large flexibility through the tilt mechanism and the tetragonal distortion of the Si/AlO4 tetrahedra.6,7 The successful preparation of analogues, Na8[GaSiO4]6(BH4)2 and Na8[AlGeO4]6(BH4)2, was also Received: March 27, 2014 Revised: July 3, 2014 Published: July 25, 2014 7066

dx.doi.org/10.1021/jp503027h | J. Phys. Chem. A 2014, 118, 7066−7073

The Journal of Physical Chemistry A

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reported.8 The enclosure of the BH4 tetrahedron in the SOD cage could be rather interesting in relation with long-lasting investigations on the mechanism of hydrogen release and the nonreloadability of NaBH4, a prominent hydrogen storage material.8−10 The enclosure of BH−4 in the SOD seems also to be a suitable alternative compared to the adsorption of hydrogen in zeolites, as described by Weitcamp et al.11 or suggested by Barrer12 for impregnation of hydrides into zeolites. Therefore, it is interesting to carry out detailed calculations on the structure and properties of NaBH4−SOD, which is the purpose of this study. Among other techniques, vibrational spectroscopy is a tool to identify the chemical nature of the enclosed species. NaBH4− SOD has six modes in the fingerprint region, three symmetric stretching modes (νs(T−O−T)), one asymmetric stretching mode (νas(T−O−T)), and two deformation modes (δ(O−T− O)), where T stands for aluminum (1T) and silicon (2T). Additionally, four modes of the BH4 tetrahedron appear, a bending mode (ν4), an asymmetric stretching mode ν3, a combination mode (ν2 + ν4), and an overtone (2ν4). The aim of the present work is to reproduce the structure and the experimental IR spectrum of NaBH4−SOD with quantum chemical methods in order to develop a theoretical framework for future investigations of reaction intermediates of the hydrogen release of enclosed BH−4 . The calculations were performed with the crystalline-orbital program CRYSTAL09, version 2.0.1.13,14 Preliminary functional and basis set tests were carried out with simpler systems (NaBH4 and Na8[AlSiO4]6Cl2) having similar structural units. Because overtones (2ν4) and combination modes (ν2 + ν4) can not be calculated with the quasiharmonic approach in CRYSTAL09, the wavenumbers of these modes were simply calculated from the fundamental frequencies ν2 and ν4. In the literature, there exists a number of theoretical studies on SODs with different methods. Astala et al.15 calculated the properties of the all-silica SOD ([Si12O24]) at GGA and LDA density functional theory (DFT) levels, respectively, using the VASP (Vienna ab initio simulation package) software.16−19 IR spectra of all-silica SODs were calculated by Nicholas et al.20 using the leapfrog algorithm in a modified version of MOLSIM21 for the molecular dynamics (MD) simulations. The Car−Parrinello (CPMD) method22 was used by Filippone et al.23 for the calculations at the LDA DFT level of the structural and electronic properties and dynamics of NaCl− SOD, resulting in good agreement of the calculated and measured IR spectra. To the best of our knowledge, the only theoretical treatments of SODs with respect to hydrogen storage by van den Berg et al.24−26 examine molecular hydrogen. In these studies, the adsorption and diffusion of molecular hydrogen in different kinds of SODs were calculated with classical pair potentials using DLPOLY27 for MD and MUSIC28 for GCMC (grand canonical Monte Carlo) simulations, respectively. They found that the loading of hydrogen has only a small effect on the framework structure and that the adsorption capacity increases with heavier framework atoms,24 and they predicted that higher capacities can only be reached at low-temperature and high-pressure conditions.26 Therefore, up to now, there exist no theoretical treatments (structural and vibrational spectra) of a BH4 tetrahedron bearing SOD, to the best of our knowledge.

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EXPERIMENTAL DETAILS Synthesis. The syntheses were carried out following Buhl et al.1 Here, 0.6 g of NaBH4 granulate (Merck 806 373), 1 g of Kaolin (Fluka 60609), and 10 mL of a freshly prepared 16 M sodium hydroxide solution were given in a Teflon cup. The Teflon cup was closed and set into a special steel autoclave. These autoclaves were then heated for 24 h at 120 °C. After the reaction, the autoclaves with the inserted Teflon cups were opened, and the excess of sodium hydroxide solution was decanted. The remaining gray-whitish material needed to be washed using a paper filter with distilled water to remove the base. Otherwise, carbonate could have form from atmospheric CO2 in the reaction with the high pH value of the samples. Additionally, remaining NaOH could have crystallize during the following drying process. To remove the base, about 300 mL of distilled water was needed until the pH value of the fresh filtrate was at about 8. After the washing procedure, the samples were dried for 48 h at 80 °C in a drying chamber. The obtained samples were white fine crystalline powders. FTIR Analysis. FTIR analysis was performed on a Bruker Vertex 80v FTIR spectrometer. The measurements were carried out in the mid-IR range from 370 to 5000 cm−1 with a resolution of 2 cm−1. The sample preparation was conducted by the KBr pellet method, with 1 mg of sample diluted in 199 mg of KBr.

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COMPUTATIONAL DETAILS Parameters and Functionals. In all calculations, the truncation criteria for bielectronic integrals were set to 10−7 (overlap and penetration threshold for Coulomb integrals, overlap threshold for HF exchange integrals, pseudo-overlap) and 10−14 (pseudo-overlap). The SCF (self-consistent field) convergence threshold on the total energy was set to 10−7 au for geometry optimizations and to 10−10 au for frequency calculations. A maximum trust radius of 0.3 Bohr was used, and a Monkhorst−Pack net of 8 × 8 × 8 was employed. A weighting factor (α) for the Kohn−Sham matrix mixing of 0.5 was used. The Anderson method was used for accelerating convergence.29 Geometry Optimization. The experimental structures were used as the starting point of each geometry optimization. The quality of the resulting structure was checked by comparing calculated and measured lattice constants as well as atomic positions. The mean absolute deviation (MAD) of the fractional coordinates (Δq) with respect to the experimental values was calculated as Δq =

1 3n

N

3

∑ Aiξi ∑ (qij − Q ij)2 i

j=1

(1)

In eq 1, N stands for the number of nonequivalent atoms in the primitive unit cell (PUC), n stands for the number of atoms in the CUC, ξi is the Wyckoff position of atom i, Ai is the occupation number of the Wyckoff position ξi, qij are the calculated fractional coordinates of atom i, and Qij are the experimental fractional coordinates of atom i. Calculation of IR Spectra. The IR spectra were calculated with fully optimized structural parameters. The intensities were calculated by a Berry phase approach.30 The calculated modes were visualized with the program Jmol31 and could thereby be assigned to the different mode types. Here, modes with intensities less than 50 km/mol were neglected. 7067



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The results of the basis set and functional tests of NaBH4 are shown in Table 2. Three different experimental references for the vibrational frequencies were considered, denoted by their year of publication. One can see that the CRYSTAL standard basis sets with arrangement 1 provide the best agreement with the experimental values. The functional evaluation is not as straightforward as finding the best basis set. PBESOL and SOGGAXC are the functionals with the smallest deviation of the calculated enthalpy but with the highest deviation of the lattice constant and highest Δq value. The least deviation with respect to the lattice constant is provided by PBE and PWGGA. PBE as well as PBE0 show the highest deviation to the enthalpy. PBE, PWGGA, PW1PW, and PBE0 give the lowest Δq values. The deviations of the calculated enthalpy with PWGGA and PW1PW are located between SOGGAXC and PBE0. The lowest Δf values were obtained with PWGGA and PBE. In summary, PWGGA has been selected as the best compromise with regard to enthalpy, structure, and frequencies and has been used for all subsequent calculations. One can observe (cf. Table 3) that the MAD of the frequencies of 44− 52 cm−1 is mainly due to the deviation of the asymmetric stretching mode ν3. The deviation of the calculated asymmetric stretching mode from the experimental reference is larger than 80 cm−1. This difference is not due to technical parameters such as SCF convergence and integral truncation thresholds as this has been carefully checked. Also, the numerical procedure to calculate the second derivatives has almost no effect on ν3. The deviation of ν3 was substantially decreased by an anharmonic correction, according to

As for the atomic positions, the MAD of the calculated spectra is calculated Δf =

n

1 n

∑ (νi − Ni)2 (2)

i

In eq 2, n stands for the number of modes, νi is the calculated wavenumber of mode i, and Ni is the measured value of mode i. The standard atomization enthalpies (H°AE,T) were calculated ° T= HAE,

∑ vAHT°(A(g)) − HT°(solid state) A

(3)

in which H°T(solid state) is the standard enthalpy of the solid state at temperature T, H°T(A(g)) is the standard enthalpy of the gaseous atoms at temperature T, calculated with converged basis sets, and vA are the stoichiometric coefficients. The enthalpy in eq 3 is given by H(T ) = E L + E0 + E T + pV

(4)

Here, EL is the electronic energy, E0 the zero-point energy (ZPE), ET the vibrational energy, p is the pressure, and V is the volume. In all IR spectra, the highest calculated intensity was normalized to the experimental mode with the highest relative absorption (rel. abs.). The intensities of overtones and combination modes 2ν4 and ν2 + ν4, respectively, were arbitrarily set to the intensity of ν3.

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RESULTS AND DISCUSSION Reference Systems. Reference systems with simpler crystal structures were used for basis set and functional testing in order to reduce the computational effort. Therefore, NaBH4 was used to describe the modes of the BH 4 tetrahedron, and Na8[AlSiO4]6Cl2 was used to describe the modes of the SOD cage. For both systems, triple-zeta POB basis sets (Peintinger− Oliveira−Bredow)32 and CRYSTAL standard basis sets (cf. Table 1) were tested by using PBE33 as the exchange and

ν3anharm = ν3 − 2ν3xe

in which νanharm is the corrected wavenumber, ν3 is the quasi3 harmonic calculated wavenumber, and xe is the anharmonic constant. Because anharmonic constants of asymmetric stretching modes cannot be calculated with CRYSTAL09 (only the anharmonic constant of one X−H bond and anharmonic constants of symmetric stretching modes), the anharmonic constant of the symmetric stretching mode of the BH4 tetrahedron was used to correct the asymmetric stretching mode ν3, similar to a previous study of Pascale et al.49 The deviation of ν3, calculated with PWGGA and the CRYSTAL standard basis sets, can be reduced to 14−29 cm−1. After correction, the MAD Δf is 11−19 cm−1, which is in the accuracy range of standard DFT calculations. NaCl−SOD crystallizes in SG P4̅3n with a lattice constant of 8.88 Å.50 The results of the basis set tests and functional tests of NaCl−SOD are shown in Table 4. One can see that for NaCl−SOD, the CRYSTAL standard basis sets provide the best agreement with the experimental values of the structural parameters and the vibrational frequencies. PBE and PWGGA give quite similar results, as expected. Surprisingly, the corresponding hybrid methods PBE0 and PW1PW give larger deviations both for enthalpy and structural parameters. PBESOL is the least suitable functional for the present test case. SOGGAXC gives a good account of the thermodynamics, but it shows deviations of structural and vibrational properties as large as PBESOL. Therefore, PWGGA has been regarded as the best compromise for the calculation of enthalpy, structure, and vibrational frequencies.

Table 1. CRYSTAL Standard Basis Sets Tested for Calculations atom

basis set

H Na B O Al Si Cl

5-11G*37 8-511G38 6-21G*39 6-31d140 85-11G*41 86-311G**42 86-311G43

(5)

correlation functional. Additional combinations of exchange and correlation functionals were tested with the results of the basis set test, PBE/PBE,33 PWGGA/PWGGA34 (PWGGA), PBESOL/PBESOL35 (PBESOL), SOGGA36/PBE33 (SOGGAXC), PWGGA/PWGGA34 with 20% Hartree−Fock exchange (PW1PW), and PBE/PBE33 with 25% Hartree−Fock exchange (PBE0). NaBH4 crystallizes in SG Fm3̅m with a lattice constant of 6.15 Å.44 The hydrogen atoms are on a half-occupied 32f position, resulting in two possible arrangements of the BH4 tetrahedron, arrangement 1 (Figure 2 left) and arrangement 2 (Figure 2 right). 7068



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Figure 2. CUC of NaBH4 with arrangement 1 (left) and arrangement 2 (right). Sodium: green; boron: gray; hydrogen: blue.

Table 2. Results of the Basis Set and Functional Tests of NaBH4a Basis Set Test with PBE basis set arrangement

H°AE,theo,298 K [kJ/mol45]

POB-1 POB-2 CRYSTAL-1 CRYSTAL-2

1662 (−68) 1664 (−66) 1657 (−73) 1660 (−70) Functional

functionals

H°AE,theo,298 K [kJ/mol]45

PBE PWGGA PW1PW PBESOL PBE0 SOGGAXC

1657 (−73) 1671(−59) 1672 (−58) 1726 (−4) 1660 (−70) 1709 (−22)

Δq

a [Å]44

Δf (2004) [cm−1]47

6.02 (−2.1) 1.2 68 74 5.99 (−2.5) 1.3 73 79 6.13 (−0.3) 1.0 45 52 6.11 (−0.6) 1.1 52 58 Test with the CRYSTAL Standard Basis Sets for Arrangement 1

a [Å]44 6.13 6.10 6.08 5.99 6.08 5.98

Δf (1971) [cm−1]46

(−0.3) (−0.8) (−1.2) (−2.6) (−1.2) (−2.8)

Δf (2008) [cm−1]48

CPU [s]

76 81 51 58

2166.9 2051.1 2049.5 1834.5

Δq

Δf (1971) [cm−1]46

Δf (2004) [cm−1]47

Δf (2008) [cm−1]48

CPU [s]

1.0 1.0 1.1 1.5 1.1 1.6

45 44 77 56 83 64

52 52 83 62 89 69

51 52 85 61 91 68

2049.5 2054.6 3327.5 2533.4 2992.2 987.4

Variables: Atomization enthalpy (HAE,theo,T ° ) in kJ/mol, deviation in parentheses45 [kJ/mol]; lattice constant (a) in Å, deviation in parentheses44 [%]; deviation of atomic positions (Δq) in %; deviation of the wave numbers (Δf) in cm−1; calculation time (CPU on a single Quad-Core AMD 2378 Opteron 2.4 GHz processor) [s]. The results with the smallest deviation and with the lowest calculation time are highlighted in bold. a

and H are in good agreement with the calculated positions. The calculations of NaBH4−SOD and NaBH4 show that bond length (1.23 Å) and H−B−H angle (109.5°) of the BH−4 tetrahedra are virtually identical in both compounds, in accordance with the experimental crystallographic values and refinements, respectively1,44 (1.17 Å, 109.5°). It was checked that removal of symmetry restrictions in the optimization did not lead to significant changes. All frequencies are well reproduced except for ν3 (cf. Tables 5 and 7). It differs by 75 cm−1 from the experimental value (2287 cm−1). With the anharmonic correction, applied as for NaBH4 (see above), of the asymmetric stretching mode (Δfanharm), the MAD of the frequencies is reduced to 18 cm−1. Now, the difference between the calculated and experimental value of ν3 is only 7 cm−1 (cf. Figure 3 and Table 7). A close agreement of calculated and experimental peak positions of the framework vibrations is also seen in Figure 3. In the CUC, there are 36 framework atoms and, therefore, 108 zero-wavevector framework modes. As pointed out by Creighton et al.,53 this leads to 105 optical modes with irreducible representations 3A1 + 5A2 + 8E + 13T1 + 14T2 in the factor group, 14T2 belonging to the infraredactive symmetry species. Creighton et al.53 obtained the peak positions based on the Wilson GF method using some

Table 3. Calculated Asymmetric Stretching Mode (ν3) of the BH4 Tetrahedron in NaBH4 Obtained with the Tested Functionals and Deviations from Experiment (Δν3) in kJ/ mol Δν3 functional

ν3

197146

200447

200848


2377 2384 2427 2383 2436 2386

80 87 130 86 139 89

93 100 143 99 152 102

95 102 145 101 154 104

Na8[AlSiO4]6(BH4)2. Na8[AlSiO4]6(BH4)2 was calculated with the basis sets and functional resulting from the evaluations of the reference systems. The resulting lattice constant, standard atomization enthalpy, MAD of calculated atomic positions, and vibrational frequencies for NaBH4−SOD are given in Table 5, and the atomic positions are shown in detail in Table 6. One can see that the lattice constant and the atomic positions of the framework atoms (Si, O, and Al) are well reproduced and that the experimentally refined positions of B 7069



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Table 4. Results of the Basis Set and Functional Tests of Na8[AlSiO4]6Cl2a Basis Set Test with PBE basis set


POB CRYSTAL

24036 (−1179) 23515 (−1701)

Δf [cm−1]52

CPU [s]

30 17

56063.7 21152.8

Δq

Δf [cm−1]52

CPU [s]

0.3 0.3 0.2 0.3 0.2 0.3

17 16 30 22 33 20

21152.8 22550.7 22578.7 29032.7 25096.3 24350.7

Δq

a [Å]50

8.97 (0.9) 0.2 8.86 (−0.2) 0.3 Functional Test with the CRYSTAL Standard Basis Sets

functionals



23515 (−1701) 23753 (−1462) 23464 (−1752) 20254 (−4961) 23207 (−2009) 24781 (−435)

a [Å]50 8.86 8.86 8.82 8.80 8.82 8.80

(−0.2) (−0.3) (−0.7) (−0.9) (−0.7) (−0.9)

Variables: Atomization enthalpy (H°AE,theo,T) in kJ/mol, deviation in parentheses51 [kJ/mol]; lattice constant (a) in Å, deviation in parentheses50 [%]; deviation of atomic positions (Δq) in %; deviation of the wave numbers (Δf) in cm−1; calculation time (CPU on a single Quad-Core AMD 2378 Opteron 2.4 GHz processor) [s]. The results with the smallest deviation and with the lowest calculation time are highlighted in bold. a

Table 5. Results of the Calculation of Na8[AlSiO4]6(BH4)2 (PWGGA, CRYSTAL basis sets)a H°AE,theo,298 K [kJ/mol]

a [Å]1

Δq

Δf [cm−1]

Δfanharm [cm−1]

CPU [s]

25981

8.85 (−0.7)

0.4

28

18

42002.1

Table 7. Results of the Calculation of the Modes of Na8[AlSiO4]6(BH4)2a

Variables: Atomization enthalpy (HAE,theo,T ° ) in kJ/mol; lattice constant (a) in Å, deviation in parentheses1 [%]; deviation of the atomic positions (Δq) in %; deviation of the wave numbers (Δf) in cm−1; calculation time (CPU on a single Quad-Core AMD 2378 Opteron 2.4 GHz processor) [s]. a

mode

wavenumber (calculated)

wavenumber (measured)

δ(T−O−T)

417 437 469 690 735 756 960 970 985 1109 2362 2280 2219 2401

436

δ(T−O−T) νs(T−O−T) νs(T−O−T) νs(T−O−T) νas(T−O−T) νas(T−O−T) νas(T−O−T) ν4 ν3 νanharm 3 2ν4 ν2 + ν4

generalized Si−O, Al−O bond stretching and Si−O−Al, O− Si−O, and O−Al−O bending force constants. Moreover, these authors could give relations between the tilt angle and Al−O− Si angles and peak positions and intensity in the spectra. Our results describe well the six peaks observed in the spectra by the nine strongest peaks obtained by calculation. Because the used basis sets and functionals reproduced the experimental structure and energetics well, the motion of sodium through the six-membered ring was also investigated at this level.54 The position of one sodium atom within the cage was varied along the space diagonal in order to calculate the potential curve. For each point of the trajectory, a restricted geometry optimization was performed. Every atom was allowed to relax except for the varied sodium and the boron atoms on corners of the CUC. The potential curve is shown in Figure 4, where the distance and energy are given with respect to the original position of the sodium atom. In addition, the position of the center of the six-membered ring is given. One can see that no additional energetic minimum exists. Due to the high barrier, we conclude that there is no free motion of the sodium atoms in the perfect structure. In future studies, MD techniques will be applied to study the Na motion in more detail.

a

467 666 709 733 984

1134 2287 2239 2387

Frequencies in cm−1.

Additionally, possible rotation of BH−4 was investigated. The maximal rotation corresponds to the inversion of the tetrahedra. Because there are two BH−4 per CUC, the two possible structures were calculated, an inversion of the tetrahedron within the cage (middle) and the inversion of both tetrahedra (both). The results are shown in Table 8. The MAD of the frequencies is very large. The corresponding structures are 109 (middle) and 153 kJ/mol (both) (cf. Tables 5 and 8) less stable, respectively, compared to the minimum structure. Additionally, the first three frequencies are imaginary, with significant absolute values; therefore, these structures are higher-order saddle points. Because of the large MAD of the frequencies and the large relative energy, the free rotation of

Table 6. Atomic Positions (Experimental1 and Calculated) of NaBH4−SOD in Fractional Units x/a

y/a

z/a

atom

Wyckoff pos.

experimental

calculated

experimental

calculated

experimental

calculated

Na Al Si O B H

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

0.1834 0.25 0.25 0.1391 0.0 0.4240

0.1760 0.25 0.25 0.1392 0.0 0.4195

0.1834 0.0 0.5 0.1487 0.0 0.4240

0.1760 0.0 0.5 0.1485 0.0 0.4195

0.1834 0.5 0.0 0.4390 0.0 0.4240

0.1760 0.5 0.0 0.4315 0.0 0.4195

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released and ions like OH−, H−, or H+ or even the zeolitic property of de- and rehydration occur in the NaBH4−SOD.

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CONCLUSION AND OUTLOOK In the present work, Na8[AlSiO4]6(BH4)2 was studied with periodic DFT methods. The aim was to find adequate theoretical methods to describe the experimental results of Na8[AlSiO4]6(BH4)2 in terms of structural, energetic, and spectroscopic properties. For this purpose, various basis sets and functionals were tested for two reference systems (NaBH4 and Na8[AlSiO4]6Cl2). It was observed that the PWGGA functional in combination with CRYSTAL standard basis sets closely reproduces the experimental values for NaCl−SOD and NaBH4, except for ν3 of the BH4 tetrahedron. An anharmonic correction of this mode leads to significantly improved results. With these resulting basis sets, functionals, and the anharmonic correction, Na8[AlSiO4]6(BH4)2 was calculated, and the experimental IR spectrum was reproduced with mean errors of 18 cm−1. This is accurate enough to allow for characterization of various possible enclosed species that might occur as intermediates in the oxidation reaction of BH−4 . Additionally, it could be shown that the motion of Na+ through the sixmembered rings and the rotation of the BH−4 tetrahedra is rather unlikely in the ideal rigid structure. Dynamic effects, defects, and structural relaxation may thus become important to describe diffusion and reaction leading to intermediates during reaction with water. Further investigations to better understand this will be performed in forthcoming studies.

Figure 3. Measured (red) IR spectrum of Na8[AlSiO4]6(BH4)2 and calculated values (black) of the frequencies with the anharmonic correction of ν3.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +49 (0)228 733839. Fax: +49 (0)228 739064. Notes

Figure 4. Potential curve for sodium migration through the sixmembered ring.

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). All plots were made with gnuplot,57 and all structure pictures were obtained with Diamond.58

Table 8. Results of the Calculation of Na8[AlSiO4]6(BH4)2 with Inverted Tetrahedra (see text; PWGGA, CRYSTAL basis sets)a tetrahedra

H°AE,theo,298 K [kJ/mol]

a [Å]

Δq

Δf [cm−1]

CPU [s]

middle both

25880 25835

8.85 (−0.7) 8.85 (−0.7)

0.2 1.1

153 140

76579.5 40767.9

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Variables: Atomization enthalpy (HAE,theo,T ° ) in kJ/mol; lattice constant (a) in Å, deviation in parentheses1 [%]; deviation of the atomic positions (Δq) in %; deviation of the wave numbers (Δf) in cm−1; calculation time (CPU on a single Quad-Core AMD 2378 Opteron 2.4 GHz processor) [s]. a

REFERENCES

(1) Buhl, J.-C.; Gesing, T. M.; Rüscher, C. H. Synthesis, Crystal Structure and Thermal Stability of Tetrahydroborate Sodalite Na8[AlSiO4]6(BH4)2. Microporous Mesoporous Mater. 2005, 80, 57−63. (2) Fischer, R. X.; Baur, W. H. Symmetry Relationships of Sodalite (SOD)-Type Crystal Structures. Z. Kristallogr. 2009, 224, 185−197. (3) Wiebcke, M.; Sieger, P.; Felsche, J.; Engelhardt, G.; Behrens, P.; Schefer, J. Sodium Aluminogermanate Hydroxosodalite Hydrate Na6+x[Al6Ge6O24](OH)x · nH2O (x ≈ 1.6, n ≈ 3.0): Synthesis, Phase Transitions and Dynamical Disorder of the Hydrogen Dihydroxide Anion, H3O−2 , in the Cubic High-Temperature Form. Z. Anorg. Allg. Chem. 1993, 619, 1321−1329. (4) Murshed, M. M.; Gesing, T. M. Isomorphous Gallium Substitution in the Alumosilicate Sodalite Framework: Synthesis and Structural Studies of Chloride and Bromide Containing Phases. Z. Kristallogr. 2007, 222, 341−349. (5) Buhl, J.-C.; Schomborg, L.; Rüscher, C. H. Tetrahydroborate Sodalite Nanocrystals: Low Temperature Synthesis and Thermally Controlled Intra-Cage Reactions for Hydrogen Release of Nano- and Micro Crystals. Microporous Mesoporous Mater. 2010, 132, 210−218.

the tetrahedra is very unlikely. This is different in NaBH4, where high dynamics of boron and hydrogen has been observed in the experiment.55 It may be noted that Na+/K+ exchange was observed in NaBH4−SOD and in NaCl−SOD above about 523 K.8 Na+ self-diffusion coefficients of 10−13−10−14 cm2/s between 773 and 1173 K were reported.56 These effects have not been further investigated here. However, such considerations may be important for future work to better understand the reaction intermediates during hydrogen release, that is, how hydrogen is 7071



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Structure and IR Vibrational Spectra of Na8[AlSiO4]6(BH4)2

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