First-principles determination of the ground-state structure of Mg(BH₄)₂

Abstract

The ground-state structure of magnesium tetrahydroborate, Mg(BH₄)₂, is still under debate. The experimentally and theoretically proposed structures mismatch, and even among the computationally determined structures a disagreement still exists. The main debated question is related to the lattice stability of the proposed structures. We combined several computational methods to build and compute the lowest energy structure. We found that the building motif of the crystalline structure of alkali and earth-alkaline metal tetrahydroborates is dictated by the coordination of metal atom. We report here the case of Mg(BH₄)₂.

Introduction

Magnesium tetrahydroborate has been proposed as a promising material for solid-state hydrogen storage due to its high hydrogen content, 14.9 wt% of atomic hydrogen. Even if the compound has attracted interest since 1950, in particular as to the synthesis [1] and later as regarding the structure determination [2], still today it is unclear which structure is exactly the ground-state. In [2], it is reported the existence of two crystalline modifications: α-tetragonal lattice (a = 13.57 Å, c = 15.5 Å) and β-cubic face-centred lattice (a = 15.5 Å). The polymorphic transition occurs at temperature T = 186°. Searching for the structural information on the ICSD returns with just the recent structure reported by Vajeeston et al. in 2006 [3]. Their results were published one month after another paper on similar calculations [4]. They reported [3] the symmetry group Pmc2₁ (IT 26) as the lowest total energy structure that is found among 28 potential structures. In [4], two phases were suggested: trigonal and monoclinic phases, of which the trigonal $P\overline{3}{m}_1$ (IT 164) was found to be the most stable structure. One year later some experimental structure determination studies were reported [5], [6], [7], [8]. In [5], the polymorphic transition α-Mg(BH₄)₂ → β-Mg(BH₄)₂ in the temperature range (180, 190) °C is confirmed and at low temperature only the α-Mg(BH₄)₂ is present. In [7], the low temperature phase is identified with the hexagonal symmetry group P6₁ (IT 169) and the high temperature phase is identified with orthorhombic symmetry group Fddd (IT 70). A confirmation that the experimental structure at low temperature has hexagonal symmetry with a group P6₁ come from another work [8] in which they clearly stated that the structure of Mg(BH₄)₂ is quite complex and that the previous [4], [3] theoretically predicted structures did not fit with the experimental crystal structure refinements. Although that, another DFT study [9] published last year reported about the systematic searching for the ground-state, and they showed that the structure Pmc2₁ proposed two years before [3], in fact, is slightly unstable due to the presence of imaginary frequencies after phonon analysis. Furthermore, they proposed, as the ground-state structure, the crystalline phase with a symmetry group $I\overline{4}m2$ (IT 119). Another recent paper [10] argued that the ground-state structure reported by Ozolins [9] is thermodynamically unstable because of imaginary modes in the acoustic phonon branch. They found the structure with symmetry group F222 (IT 22) as the true ground-state structure. Finally, another recent paper [11] reported the P6₁22 (IT 178) structure as the lowest energy structure, in agreement with the experimental structure reported by Cerny [8] in some respects. Actually, the P6₁22 symmetry is a super-group of the experimentally observed P6₁ symmetry. How to explain and solve the discrepancies between theoretically proposed structures and experimentally resolved structures? Actually, since the first synthesis of Mg(BH₄)₂ reported by Wiberg and Bauer [1] several attempts and a lot of efforts have been directed towards new synthesis route and structure determination. At that time huge interest was going on to develop in metal tetrahydroborates, M(BH₄)₂, where M = Li, Na, K, Be, Mg, Ca thanks in particular to the work of Schlesinger and Brown started already a decade earlier [13], [12]. Since then they have been widely exploited as versatile nucleophilic reducing agents capable of attacking centre of low electron density. Their large-scale industrial production was introduced in the early 1960s with the Bayer process [14], which proves that such class of materials is not completely unknown and that their chemical properties are already well recognized and used for reducing organic functional groups. Nowadays, many different new approaches have been developed to synthesize Mg(BH₄)₂. Surprisingly, it has been observed that the structure of metal tetrahydroborates depends on the synthesis route [14]. That means that the same compound could show different structures depending on whether it has been synthesized using a solvent (wet chemistry synthesis) or by the solid state synthesis methods, because the presence of the solvent, even at very low concentration, could promote different crystallization processes that can end up with different crystal structures. Therefore, the polymorphism of such a kind of compound is a direct consequence of the synthesis route, as also recently pointed out [15]. However, the chemical and physical reasons why the metal tetrahydroborates can undergo to a wide range of polymorphic phases are not yet clear. One reason could be that the (BH4)⁻ anion, despite it is iso-electronic with methane, it acts as a versatile ligand capable of forming many coordination compounds by 3-centre (B–H) → M bonds to less electropositive metals, as reported for transition and lanthanide metals [16], [17]. Moreover, most of the discrepancies between theoretical and experimental structures could be attributed to the fact that the total energy calculations deal with perfect crystal lattice at temperature T = 0 K while the experimental structure determination has to cope with the practical difficulty to obtain pure and crystalline compounds as possible. In both the cases, anyway a scrupulous internal consistency should be achieved to enable comparison between different structures, independently on the specific method and refinement tool that have been used.