Calcium Borohydride for Hydrogen Storage: A Computational Study of

J. Phys. Chem. C 2010, 114, 9503–9509

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Calcium Borohydride for Hydrogen Storage: A Computational Study of Ca(BH4)2 Crystal Structures and the CaB2Hx Intermediate Terry J. Frankcombe* Research School of Chemistry, Australian National UniVersity, ACT 0200 Australia ReceiVed: February 15, 2010; ReVised Manuscript ReceiVed: April 9, 2010

Plane wave density functional theory calculations have been performed to study the potential hydrogen storage material Ca(BH4)2 and the proposed CaB2Hx dehydrogenation intermediate. It is shown that three different published structures of R-Ca(BH4)2 are essentially identical. Likewise, four proposed structures of β-Ca(BH4)2 are the same. The previously proposed CaB2H2 structure of space group Pnma is both structurally unstable and too high in energy to be a Ca(BH4)2 dehydrogenation intermediate. A direct computational search failed to find a viable CaB2Hx candidate structure. 1. Introduction Using hydrogen as an energy carrier is a widely anticipated alternative to the current global dependence on hydrocarbonbased fuels, particularly for vehicular transport. However, physical storage of pure hydrogen on board passenger cars is challenging from an engineering point of view, primarily due to the low density of hydrogen gas and the effort required to compress it to a reasonable density or liquefy it for cryogenic storage at 20 K.1-3 As a result there is a strong worldwide push to develop high hydrogen density materials suitable for use in convenient hydrogen storage systems.3-5 Hydrogen storage systems based on physisorption or inclusion compounds have been explored, from adsorption onto carbons6 and metal-organic frameworks7 to incorporation into clathrate hydrates.8,9 However, it has proved difficult to attain the desired hydrogen densities using these physical storage techniques. A promising alternative to physical storage of molecular hydrogen is storing hydrogen as a hydride, to be decomposed to release H2 at the point of use. Research into hydride-based storage systems, particularly those based on complex metal hydrides, was dramatically boosted by the pioneering work of Bogdanovic´ and Schwickardi10 demonstrating cyclable hydrogen storage in doped NaAlH4. Despite modest recoverable hydrogen densities, problematic heat management, and kinetics issues, NaAlH4 remains a leading contender as a practical hydrogen storage material. The search for the optimum complex metal hydride for use in a hydrogen storage system has continued through the work of many experimental and computational research groups. The focus remains largely on alanates, borohydrides, and amide-like systems of early first and second group metals, as these offer high hydrogen mass densities.11-22 As yet, no material has been identified with high hydrogen densities and favorable kinetics and thermodynamics for use in a hydrogen storage system. A complex metal hydride that has recently received a considerable amount of attention23-38 is calcium borohydride, Ca(BH4)2. This material contains 11.6 wt % hydrogen in total and exists in a number of room temperature polymorphs. Simple stoichiometric arguments suggest a number of potential accessible decomposition reactions. Some of the possibilities are listed below with their effective theoretical hydrogen storage capacities. * E-mail: [email protected].

Ca(BH4)2 f Ca + 2B + 4H2 11.6 wt % (1) 2 10 1 CaB6 + CaH2 + H2 9.6 wt % (2) f 3 3 3 + 2B + 3H CaH f 8.7 wt % (3) 2 2 8.7 wt % (4) f CaB2H2 + 3H2 5 13 1 CaB12H12 + CaH2 + H2 6.3 wt % (5) f 6 6 6 2 1 CaB6H14 + CaH2 + 2H2 f 5.8 wt % (6) 3 3 f CaB2H4 + 2H2 5.8 wt % (7)

Clearly, Ca(BH4)2 offers considerable potential as a high hydrogen density storage material. There is some uncertainty regarding the structure of the known Ca(BH4)2 polymorphs. While most workers agree with the Fddd structure of R-Ca(BH4)2 presented by Miwa et al.23 in 2006, recently Majzoub and Ro¨nnebro24 and George et al.25 have proposed an alternate structure of F2dd symmetry. Majzoub and Ro¨nnebro also suggest a possible C2/c structure. For β-Ca(BH4)2, Buchter et al.26 proposed three different structures of P42/m and P42 symmetry. George et al.25 and Lee et al.27 agree with the P42/m space group. Majzoub and Ro¨nnebro24 and Filinchuk et al.28 agree on a P4j structure. These latter authors propose that R-Ca(BH4)2 transforms to an R′-Ca(BH4)2 structure of I4j2d symmetry on heating, before transforming completely to the β-Ca(BH4)2 phase. While Majzoub and Ro¨nnebro24 find that the Pbca structure proposed for γ-Ca(BH4)2 is dynamically stable, free energy considerations lead them to suggest that this phase is not the experimentally observed phase. Buchter et al.29 conclude that the Pbca structure is the best fit for the observed phase. Furthermore, there is evidence of a δ phase.30,31 Serious consideration of Ca(BH4)2 as a hydrogen storage material began in earnest in 2006 with Miwa et al.,23 who calculated the dehydrogenation enthalpies of the crystalline material. They found complete dehydrogenation (reaction 1) required 151 kJ/mol H2, while the next-highest hydrogen capacity decomposition to CaB6 and CaH2 (reaction 2) required 32 kJ/mol H2, making the latter of interest for hydrogen storage applications. It is not clear which dehydrogenation path the calcium borohydride system takes. A number of studies have revealed that it is the β and γ forms of Ca(BH4)2 that decompose30,32

10.1021/jp1014109  2010 American Chemical Society Published on Web 05/03/2010

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TABLE 1: Calculated Relative Energies of Proposed Ca(BH4)2 Structures (kJ/mol f.u.)a space group c

Fddd F2dd C2/c I4j2d P4j P42/mc P42/md P42 Pbca

proposed phase

ref

k-space samplingb

as published

relaxed ions

fully relaxed

R R R R′ β β β β γ

23 28 24 28 28 26 26 26 24

2×1×2Γ 2×1×2Γ 4 × 4 × 4 MP 4 × 4 × 4 MP 4 × 4 × 4 MP 4 × 4 × 4 MP 4 × 4 × 4 MP 4 × 4 × 6 MP 2 × 4 × 4 MP

135.87 39.06 169.45 100.73 63.18 307.75 630.60 383.02 13.61

0.03 0.22 26.69 20.15 11.99 11.75 110.59 11.74 13.55

0.00 0.03 0.00 19.64 11.88 11.72 11.72 11.73 13.49

a See text for details. b MP: Monkhorst-Pack grid. Γ: Γ-point centered grid. c The experimental fit of the two presented in the ref. calculated structure of the two presented in the ref.

and that the dehydrogenation is a two-step process.30-34 There is ample evidence that CaH2 is formed in the dehydrogenation reaction.30-35 Solid-gas preparation techniques from possible dehydrogenation products have been demonstrated.36,37 Experimental evidence exists for a number of intermediate and product compounds, including CaB2Hx,31 CaB6,32 CaB12H12,34 and orthorhombic35 and amorphous34 phases. Recently, Ozolins et al.38 and Wang et al.34 have independently calculated the dehydrogenation enthalpy for reactions 2 and 5 (producing CaB6 and CaB12H12, respectively), with Wang et al. also considering reactions 1 and 3 (making Ca metal and CaH2, respectively), adding to the determinations of Miwa et al.23 While all three calculations for reaction 2 broadly agree with values of 32-38 kJ/mol H2, the values for reaction 1 do not agree, with the 83 kJ/mol H2 of Wang et al. substantially different to the 151 kJ/ mol H2 of Miwa et al. The enthalpies for reactions 3 and 5 are calculated to be 56 kJ/mol H2 and 34-36 kJ/mol H2, respectively. This paper looks primarily at the CaB2Hx intermediate proposed by Riktor et al.31 Hence we aim to calculate the reaction energy of reaction 4 and likely variations to make CaB2Hx with x < 6. In the process we shed some light on issues involving the Ca(BH4)2 polymorphs. 2. Methodology The total potential energy of the various crystal structures was calculated using 3D-periodic Kohn-Sham density functional theory.39-41 The Vasp program,42,43 version 4.6, was used to evaluate the potential energy (the sum of the electronic and ion-ion energies) and its derivatives. Projector augmented wave (PAW) potentials44-46 were used to represent the ionic potentials. The H, B, and Ca PAW potentials left 1, 3, and 10 electrons in the valence space; that is, semicore s electrons were not treated as part of the external potential but were allowed to relax fully. The PW91 generalized gradient approximation (GGA) exchangecorrelation functional47 was used throughout. All calculations on solid phases used either Monkhorst-Pack sampling48 or evaluation on a k-space grid centered on the Γ point for the Brillouin zone integration. The linear tetrahedron method49 was used to speed the integral convergence. A plane wave basis set was used, with the k-point grid and plane wave cutoff energy varied to achieve convergence of the total energy to within 1 meV for each cell. Atomic positions and unit cell parameters were relaxed according to the Hellmann-Feynman forces to achieve the minimum total potential energy. For the calculation on H2 the molecule was isolated in a repeating cube with edge length 15 Å and only the H-H bond length allowed to relax, with no reciprocal space integration. 3. Ca(BH4)2 Crystal Structures During convergence testing it was determined that a plane wave cutoff energy of 1000 eV and an augmentation charge

d

The

cutoff of 700 eV was sufficient to converge the total energies of Ca(BH4)2 structures to the desired level, so these values were used throughout. For the Brillouin zone integration both Monkhorst-Pack and Γ-point centered grids were trialled, with the grid increased in size until convergence was reached for the energy of the relevant published structure. The most efficient grid type for each structure, in the sense of that requiring the least computational time to calculate the sufficiently converged energy, was selected and subsequently used for all calculations on that structure. The selected k-point sampling grids are listed in Table 1. Generally Monkhorst-Pack sampling was more efficient. In some large unit cells small Monkhorst-Pack grids did not leave enough sampled k-points to allow the linear tetrahedron method to be applied whereas the small Γ-centered grids did, making the Γ-centered grids more efficient. Table 1 lists the calculated energies of the various Ca(BH4)2 crystal structures. The energies are given in kJ/mol per Ca(BH4)2 formula unit (f.u.) and are relative to the lowest value calculated. For each structure three energies are presented. Under the heading “as published” are the energies calculated at the lattice parameters and atomic positions published in the source literature. Energies under “relaxed ions” are the energies from allowing the ion positions within the crystal to relax, keeping the lattice parameters fixed. Finally, the energies listed under “fully relaxed” are those resulting from optimizing all degrees of freedom. The calculated relaxed energies do not allow one to clearly discriminate between the proposed structures. For the R phase, all three proposed structures relaxed to essentially equal energies. For the β phase, three of the four published structures relaxed to equal energy geometries. The P4j structure proposed by Filinchuk et al.28 did relax to a structure with a calculated energy slightly higher than that of the other three proposed β phase structures, but the energy difference (0.16 kJ/mol) was not larger than the convergence limit (of order 0.05 kJ/mol) by a sufficient amount to enable one to say confidently that the potential energy of this structure was indeed higher. Filinchuk et al.28 observed a second order phase transition from the R phase to a phase labeled R′. Despite being observed as a second order transition, there is a large difference in the calculated potential energies of the proposed R and R′ structures, almost 20 kJ/mol. Curiously, this is higher than the calculated γ phase energy. These energetics are consistent with the R and R′ phases exhibiting very different internal dynamics. The γ phase structure proposed by Majzoub and Ro¨nnebro24 stands out as exhibiting very small changes in the energy on relaxation, gaining only 0.1 kJ/mol. This is not particularly surprising, as these authors use a methodology virtually identical to that used here to optimize the coordinates of this structure. In that context, there is no obvious reason for the C2/c structure

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J. Phys. Chem. C, Vol. 114, No. 20, 2010 9505 around 0.009 Å in the a direction in the F2dd structure, and the lattice distorts from β ) 120° to β ) 123.6° in the C2/c structure). The simple symmetry breaking is a reflection of the fact that both F2dd and C2/c are maximal subgroups of Fddd. As stated above, the calculated energy differences are not sufficiently large to declare either of these distortions “real”. Indeed, zero-point phonon motion in the crystals is likely to be of substantially larger magnitude than these small differences. Similar transformations can be made between the descriptions of the proposed β phase structures. P4j and P42 are maximal subgroups of P42/m, each representing breaking a single symmetry. Here the two P42/m structures are presented as one, as the fully relaxed geometries were identical to reasonable precision, despite the different initial structures. The unit cells of the three β phase structures coincide. The coordinates can be approximately transformed from P4j via

xP42/m ≈ yP4j yP42/m ≈ xP4j zP42/m ≈ zP4j - 1/4

Figure 1. R-Ca(BH4)2 structure showing the relationship between the Fddd/F2dd and C2/c unit cells. The view is along the c axis of the Fddd/F2dd unit cell and the b axis of the C2/c unit cell. The Fddd/ F2dd cell is indicated by the rectangle, the C2/c unit cell is indicated by the parallelogram. The a direction is horizontal.

proposed by them for the R phase to have relaxed so much in this work, either with fixed lattice parameters or on full relaxation. With the exception of the Pbca γ phase structure, all tested structures showed a substantial decrease in the energy on relaxation of the ion positions. On the other hand, only the C2/c structure mentioned above and the calculated P42/m structure of Buchter et al.26 showed meaningful decreases in energy on also relaxing the lattice parameters. Notably these two structures were two of the three starting structures based on calculation rather than experimental measurement. Closer inspection of the coordinates of the fully relaxed structures, presented in the accompanying Supporting Information, reveals that the relaxations of the three proposed structures for the R phase did indeed relax to essentially the same structure, as did the four published structures for the β phase. For the R phase, the Fddd and F2dd unit cells coincide. The coordinates given in the F2dd space group can be converted to correspond to those given for the Fddd space group by

xFddd ≈ xF2dd - 0.006 yFddd ≈ yF2dd zFddd ≈ zF2dd

(8)

With this transformation the fractional coordinates of the two relaxed structures differed by around 0.001 or less, with H1 and H2 (H3 and H4) of the F2dd structure corresponding to H2 (H1) of the Fddd structure. Clearly the transformation from the C2/c description is slightly more complex, with the latter being monoclinic. The relationship between the Fddd/F2dd and C2/c unit cells is indicated in Figure 1. The final F2dd and C2/c structures have slightly lower symmetry than the Fddd structure (the 32h hydrogen positions split into two groups separated by

(9)

with H1, H2, H3, and H4 of the P4j structure corresponding to H3, H1, H2, and H3 of the P42/m structure, respectively. Similarly, the approximate transformation from P42 is given by

xP42/m ≈ yP42 yP42/m ≈ xP42 zP42/m ≈ zP42 - 0.0226

(10)

with H1, H2, H3, and H4 of the P42 structure corresponding to H1, H3, H3, and H2 of the P42/m structure, respectively. The symmetry breaking among these structures was stronger than for those of the R phase, with fractional coordinate differences of the order of 0.05. Having identified representative structures for each phase, we now turn to specific differences between the published and calculated structures. Selected geometric measures are indicated in Table 2. The “as published”, “relaxed ions”, and “fully relaxed” columns in this Table are as for Table 1. Material densities were reproduced well by the calculations, with the fully relaxed unit cells differing in volume from the published structures by at most 1.5%. The BH4 ions in the calculated structures were larger than in the experimental fits, with B-H distances around 1.22 Å (compared to 1.11-1.17 Å for fits to the diffraction patterns for hydrogen-containing crystals of Fddd and I4j2d symmetry, shorter for the deuteridederived experimental P42/m structure). The shapes of the BH4 ions in all of the calculated structures were similar, with the shape measures τ and δ (see Table 2; smaller is more symmetric) taking the slightly asymmetric values 4.0-5.3% and 0.01-0.2 Å, respectively, in all of the calculated structures. In the I4j2d R′ crystal, the change in ∠BH4 shown in Table 2 reflects a substantial rotation of the BH4 ions around the c axis direction upon relaxation. This is by far the greatest geometric change on optimization observed in this work. The change in the Ca-B distance in the P42/m β structure reflects a wholesale 2° rotation of the BH4 positions and orientations around the [001] screw axis. 4. CaB2Hx Intermediate The total potential energy of the Pnma CaB2H2 structure proposed by Riktor et al.31 was evaluated in a similar manner

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TABLE 2: Lattice Constants and Selected Structural Measures for Published and Calculated Ca(BH4)2 Structuresa space group Fddd

c

I4j2d

P42/mc

Pbca

proposed phase

ref

geometric featureb

as published

R

23

a b c B-H1 B-H2 B-B τ δ a c B-H1 B-H2 τ δ ∠BH4 a c B-H1 B-H3 Ca-B τ δ a b c τ δ

8.791 13.137 7.500 1.124 1.107 3.798 10.4% 0.026 5.8446 13.2279 1.158 1.168 2.4% 0.009 11.22° 6.9468 4.3661 1.022 1.056 2.931 15.5% 0.095 13.35 8.76 7.35 4.4% 0.011

R′

β

γ

28

26

24

relaxed ions

1.220 1.230 3.825 4.0% 0.008 1.222 1.219 4.5% 0.018 40.44° 1.220 1.224 2.897 5.2% 0.017

4.4% 0.011

fully relaxed 8.7648 13.1287 7.4910 1.220 1.230 3.821 4.1% 0.008 5.9201 13.0861 1.223 1.220 4.2% 0.020 38.98° 6.9342 4.3555 1.219 1.224 2.890 5.3% 0.017 13.3825 8.7627 7.3712 4.4% 0.011L

a Distances in Å. b τ is (maxidi - minidi)/dj, where di are the six H-H edge lengths of the BH4 tetrahedra and dj is the average edge length, expressed as a percentage. δ is the distance between the B atom position and the mean of the four H atom positions in the BH4 tetrahedra. ∠BH4 is a measurement of the rotation of the BH4 tetrahedra around [001]. c The experimental fit of the two presented in the ref.

Figure 2. Pnma CaB2H2 structures. The structure proposed by Riktor et al.31 on the left, and after relaxation of the ionic positions on the right.

to the Ca(BH4)2 phases above. A 4 × 10 × 10 MonkhorstPack grid was used for the k-space sampling. On relaxation of the ion positions, Riktor’s Pnma CaB2H2 crystal underwent significant rearrangement. The crystal resulting from this relaxation is shown in Figure 2, alongside the published structure.31 Relaxation from the structure on the left of Figure 2 to that on the right reduced the calculated energy of the crystal by more than 500 kJ/mol f.u. For this relaxed structure a reaction energy can be calculated for decomposition of Ca(BH4)2 to CaB2H2, according to reaction 4. Using the

energy of relaxed β-Ca(BH4)2 and H2 yields a reaction energy of 529 kJ/mol as written, or 176 kJ/mol H2. The Pnma structure was found to not be stable upon symmetry-breaking perturbations. Relaxing the positions of the atoms within the cell when starting from a structure with random ion displacements of less than 0.05 Å resulted in even larger structural changes. The relaxed structure bore no resemblance to the Pnma structure, with the unit cell containing linear (BH)-B-B-(BH3) and diamond-shaped (BH2)(BH2) units. The large reaction energy for reaction 4 compared to the 32-38 kJ/mol H2 calculated23,34,38 for decomposition to CaH2 and CaB6 via reaction 2, and the very large structural changes on relaxation, suggest that the published Pnma CaB2H2 phase is not the intermediate phase observed on dehydriding Ca(BH4)2. If these calculations do not support the Pnma structure that has been proposed as the observed intermediate CaB2Hx phase, an obvious question is: What is the structure of the observed intermediate phase? It should be noted that the X-ray diffraction patterns observed by Riktor et al. were not very sensitive to the hydrogen atom positions, being dominated by the Ca and B scattering. Furthermore, the space group of the proposed structure was not determined analytically from systematic absences, but rather from other considerations. Accordingly, in this work alternative structures were sought by assuming that the positions of the Ca and B atoms within the orthorhombic cell are approximately those proposed for the Pnma structure. Into that framework hydrogen atoms were inserted without regard for any symmetry within the cell. The positions of the hydrogen atoms were then relaxed in the fixed environment of the Ca and B lattice. It was assumed that the hydrogen atoms would be bound to the B atoms, following the well-established structural motif of the lightweight complex metal hydrides generally, and complex borohydrides specifically. As the eight B atoms in the unit cell

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TABLE 3: Calculated Reaction Energies for Reaction 11 for Various Relaxed Hydrogen Structures, along with the Number of Hydrogen Atoms Per Formula Unit, x, and the Number of Moles of H2 Released, 4 - x/2a compositionb

x

H2 released

relaxed H

1,0

1

7/2

1,1

2

3

2,0

2

3

0,2

2

3

1,2

3

5/2

2,1

3

5/2

2,2

4

2

825 (236) 763 (254) 778 (259) 786 (262) 697 (279) 709 (284) 655 (327)

2,3e

5

3/2

3,1

4

2

3,2f

5

3/2

symmetrisedc Pnma Pnma Pnma P21/c P21/c Pnma Pm P21/c

660 (330) 618 (412)

Pnma

825 (236) 753 (251) 769 (256) 786 (262) 697 (279) 709 (284) 655 (327) 595 (396) 660 (330)

relaxed ionsd 713 § (204) 492 (164) 641 § (214) 481 (160) 377 (151) 410 (164) 476 (238) 455 § (304) 562 § (281) 377 (251)

a Energies in kJ/mol (kJ/mol H2 in parentheses). b For example, 1,2 means 1 H per B1, 2 H per B2, etc., in the starting structure. c Highest symmetry nearby structure space group and energy. d Those marked with § did not change the structure substantially. e Derived from 2,2. f No nearby higher symmetry found.

can be divided into two sets of four equivalent atoms, referred to as B1 and B2, H atoms were added in sets of four per unit cell, at a random distance 1.0-1.3 Å from the boron atoms. This yields a compositional search space with an integer number of H atoms bound to each B atom (typically 0-3) of two different types. We use the B1 and B2 labels consistent with Riktor et al. For each hydrogen composition (with a certain number of hydrogen atoms bound to each of the B1 boron atoms and a certain number bound to each of the B2 boron atoms) hydrogen atoms were added with the B-H bonds oriented in random directions within the unit cell. A number of initial random structures were generated for each, which were then allowed to relax to minimize the total electronic energy. This procedure can be considered to be similar to a restricted form of a methodology referred to as Kick.50 A number of relaxations were run for each composition, with the heaver ion positions fixed and initially random B-H bond orientations. Generally new random initial structures were tested until a number converged to the same BHn morphology and orientations, and that corresponded to the lowest energy structure found for that composition. The results are presented in Table 3, under the “relaxed H” heading, as calculated reaction energies for the decomposition of β-Ca(BH4)2 to the newly determined structure and H2, reaction 11:

Ca(BH4)2 f CaB2Hx + (4 - x/2)H2

(11)

For composition a, b (denoting a hydrogens on each B1 and b hydrogens on each B2), x in reaction 11 equals a + b. Note that substantially reduced geometric convergence thresholds were used in these relaxations in the interest of computational efficiency.

For more than half of the compositions considered, in the lowest energy structures the relaxed hydrogen atoms returned to the (010) planes of the heavy atom structure, giving infinite Ca-B-H sheets. These structures were very close to structures of Pnma symmetry (though, of course, different to the CaB2 H2 structure proposed by Riktor et al.). The lowest energy structures with two hydrogens per B2 (0,2, 1,2, 2,2 and 3,2) did not relax to sheeted structures, as described below. The 0,2 and 1,2 compositions relaxed to structures close to P21/c structures, while the nominally-2,2 composition (see below) relaxed to a structure near Pm special positions. No space group matching the 3,2 crystal could be found beyond P1. The 0,2 and 1,2 structures simply had one of the hydrogen atoms bonded to B2 out of the Ca-B-H plane, with bonds rotated roughly 60° out of the (010) plane to approximately the [310] direction. On the other hand, the structures starting from the 2,2 and 3,2 compositions completely rearranged the B-H configuration. These structures contained one Ca-B-H plane containing BH, BH2 and (in the 3,2 case) BH3 units. In the other plane of Ca and B ions the hydrogens bonded to B1 remained in the (010) plane. The B2 atoms had three hydrogens each in a trigonal planar structure with only one B-H bond in the (010) plane of the heavier atoms. Nonetheless, the 2,2 and 3,2 designations are retained here as enumerations of the searched parameter space. For all the lowest-energy structures found, the ionic positions were shifted to the nearby higher-symmetry geometries mentioned above and the hydrogen positions relaxed further. The resulting energies are given in Table 3 under “symmetrised”, with the relevant space group. In all cases the energies of the idealized structures were equal to or lower than those calculated without regard to symmetry. The 2,3 composition listed in Table 3 was not investigated starting from random hydrogen orientations like the others described above. Rather, this was a structure devised by replicating the out of (010) plane BH3 units in the Pm structure of the nominally-2,2 composition in the other (010) plane of calcium and boron, according to the P21/c space group. Initial testing with a lone hydrogen atom added per crystallographic unit cell had indicated that the B1-H bond was more stable than the B2-H bond by almost 20 kJ/mol. This lowhydrogen-loading B1 preference was not evident in the hydrogenloaded structures whose energies are shown in Table 3. The higher symmetry structures were allowed to relax with respect to the positions of all ions, giving the energies under the ‘Relaxed ions’ heading in Table 3. All of the structures underwent a substantial reduction in the total electronic energy and substantial changes to the positions of the ions. Only four structures did not undergo a substantial change in the internal structure on unrestricted relaxation. These four are marked with a § symbol in Table 3. The Pm structure from the 2,2 composition relaxation maintained the approximate calcium and boron structure at that fit to diffraction measurements of Riktor et al., but once more underwent substantial hydrogen rearrangement on complete ionic position relaxation. A 1D hydrogen bridged BH2 chain structure appeared in the unit cell of this structure, similar to the chains in the Pnma structure proposed by Riktor et al.31 As a final test, the four “stable” structures marked with a § symbol in Table 3, as well as the Pm structure from the 2,2 composition, were reoptimized, including lattice constant relaxation. These relaxations did not maintain the lattice constants suggested by the experiments of Riktor et al. The a lattice constant increased in all cases, by between 24% and 34%, while

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the b lattice constant decreased by up to 22%. Relaxed unit cell volumes differed from the experimentally derived cell by up to 29%. Despite these large relaxations, the calculated reaction energies for reaction 11 were in the 149-234 kJ/mol H2 range. While a substantial improvement on the fixed-lattice reaction energies shown in Table 3, these energetics cannot compete with the 32-38 kJ/mol H2 calculated for reactions 2 and 5, or the 56 kJ/mol H2 calculated for reaction 3.23,34,38

Frankcombe National Facility at the Australian National University and the theoretical chemistry group of the Leiden Institute of Chemistry. Supporting Information Available: Parameters of the optimized Ca(BH4)2 structures and selected CaB2Hx structures accompany this manuscript. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes

5. Conclusion In this work a range of the structures for the various polymorphs of Ca(BH4)2 that have been proposed in the literature have been studied using periodic DFT calculations. Three proposed structures for the R phase and four for the β phase were considered, along with the proposed R′ and γ structures. Although starting with different geometries and different symmetries, all the proposed R phase structures relaxed to essentially the same structure, as did all the proposed β phase structures. Relevant coordinate transformations and relations between the unit cells are given in section 3. As indicated in Table 1, the differences in the calculated potential energies of these crystals are not sufficiently different to claim that one space group is favored over the other. It is possible that the inclusion of finite temperature effects11 may separate the orthorhombic/ monoclinic description, though this seems unlikely. Given the similarities of the structures and in the absence of further information on symmetry breaking, it seems reasonable to describe these crystals using the highest symmetry space group of those proposed; namely Fddd and P42/m for the R and β phases, respectively. Note that the PAW-DFT calculations performed in this work reproduced the experimentally determined lattice constants for the Ca(BH4)2 crystals. As an illustration, the calculated cell volumes differed from the source experimentally determined values by -0.5%, +1.5%, -0.6%, and +0.6% for the Fddd (R), I4j2d (R′), P42/m (β), and Pbca (γ) structures, respectively. However, it is likely that the correct, anisotropic application of the quasiharmonic approximation11 would reduce this agreement. It is worth pointing out that in this work only single crystallographic unit cells were used in the calculations, with periodic boundary conditions. This approach can only find nearby structures with the same length or smaller spacial periodicities. Specifically, deformations of the type investigated by Lee et al.27 [in which deformations within a
2 ×
2 × 1 supercell of the P42/m structure β-Ca(BH4)2 were shown to lead to a slightly lower energy structure] cannot be found using the current approach. This applies equally to the calculations on the Ca(BH4)2 and CaB2Hx crystals. The calculations performed in this work do not support the CaB2H2 structure proposed by Riktor et al.31 as an intermediate in the decomposition of Ca(BH4)2. The calculated reaction energy for reaction 4 was much larger than for competing reactions—though, once more, vibrational effects which reduce the reaction energy by up to 20 kJ/mol H2 in similar reactions51 were not considered—and the proposed structure was not a stationary point on the CaB2H2 potential energy surface. Furthermore, a search for CaB2Hx structures using the Pnma calcium and boron lattice of Riktor et al. did not reveal any serious candidate structures for reaction 11 to produce a CaB2Hx intermediate in the dehydrogenation of Ca(BH4)2. Acknowledgment. This work was supported with computational resources from the National Computing Infrastructure

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