PHYSICAL REVIEW B 72, 073201 共2005兲
Density-functional band-structure calculations of magnesium alanate Mg„AlH4…2
O. M. Løvvik and P. N. Molin
Center for Materials Science and Nanotechnology, University of Oslo, P. O. Box 1126 Blindern, N-0318 Oslo, Norway
共Received 24 November 2004; revised manuscript received 26 April 2005; published 3 August 2005兲
Magnesium alanate 共Mg共AlH4兲2兲 has been proposed as a candidate material for high-density reversible
solid-state hydrogen storage, but so far has not been shown to exhibit reversible hydrogenation. This study
presents the calculated crystal structure and electronic structure of Mg共AlH4兲2 from density-functional bandstructure calculations within the generalized gradient approximation. The calculated structure shows a prolonged c axis compared to the experimental structure; otherwise the agreement is excellent. The electronic
density of states shows that magnesium alanate is nonmetallic with a band gap of around 4 eV. The electronic
structure analysis implies polar covalent bonds both between Mg and H and between Al and H, with the lowest
degree of polarity between Mg and H. The calculated enthalpy of formation suggests that magnesium alanate
is metastable at room temperature, and thus not suitable for reversible hydrogen storage.
DOI: 10.1103/PhysRevB.72.073201
PACS number共s兲: 71.20.⫺b, 61.18.⫺j, 61.12.⫺q, 63.20.⫺e
Since the discovery that hydrogenation of NaAlH4 becomes reversible after the addition of small amounts of Ti,1
there has been an intensive search for new complex hydrides
with attractive hydrogen storage properties.2,3 Magnesium
alanate 共Mg共AlH4兲2兲 is one of the most promising candidates
when only regarding the hydrogen content, which is
9.3 wt %. Of this, 7.0 wt % may be extracted at relatively
low temperature 共135– 163 ° C兲.4–6 However, reversible hydrogenation of Mg共AlH4兲2 at moderate temperature and pressure has not yet been reported. It is not known whether this is
because of thermodynamic or kinetic barriers. Atomistic
modeling may aid in this understanding, but so far there is
only one published modeling study for this material, where
cluster calculations were used as a help in the crystal structure determination.6 Density-functional band-structure calculations have been performed on the lithium alanates,7–13 the
sodium alanates,10,11,13–21 the potassium alanates,10,11,13,22
and calcium alanate.23
The present study calculates the crystal structure of magnesium alanate using band-structure calculations employing
density-functional theory 共DFT兲 at the generalized gradient
approximation 共GGA兲 level. Calculated details on the electronic structure are also presented: the local and total density
of states 共DOS兲, the crystal orbital overlap population
共COOP兲, and the Hirshfeld charges.
The structural relaxations have been performed by using
the Vienna ab initio simulation package 共VASP兲.24,25 The electron density is represented by plane-wave basis sets, and the
projector augmented wave method has been employed—this
is an all-electron method with accuracy comparable to the
most precise DFT methods.26,27 The PW91 functional has
been used for gradient corrections.28 The numerical parameters have been chosen to give an overall numerical error in
the order of 1 meV per unit cell: The plane-wave cutoff energy was 700 eV, the k-grid spacing was 0.05 Å−1, and the
tetrahedron method with Blöchl corrections was used to
smear out the single-particle wave functions. The criterion
for self-consistency was that two consecutive total energies
differed by less than 10−5 eV. The augmentation region,
which is a generalization of the muffin-tin sphere of the lin1098-0121/2005/72共7兲/073201共4兲/$23.00
ear augmented plane-wave method or the core region of the
pseudopotential method, has been chosen to be the smallest
available for all the atoms. The structural minimization was
performed by the residual minimization method direct inversion in iterative subspace implementation of the quasiNewton algorithm. The relaxation was finished when all the
forces were less than 0.03 eV/ Å.
For the calculations of local and total DOS, as well as the
COOP, overlap matrix, and Hirshfeld charges, the ADF-BAND
program was used.29,30 The electron density is here represented by a combination of Slater-type orbitals 共STO’s兲 and
numerical atomic orbitals 共NAO’s兲, which makes the mapping of the local DOS unambiguous. The valence electrons
were described by the sum of one STO and one NAO, and in
addition, two STO’s were used as polarization functions. The
basis sets for Mg and Al both had 2s frozen cores. The VASP
optimized crystal structure was used for these calculations. A
total number of 274 symmetrically unique k points were used
for the numerical integration, and the overall integration accuracy was 10−4. Scalar relativistic effects were included via
the zeroth-order regular approximation.31 This set of parameters suffices to yield an electron density that gives a virtually indistinguishable DOS from calculations with higher accuracy. The DOS calculated from VASP is also very similar
to that from ADF-BAND, which gives confidence that the
results are close to the true DFT values.
The crystal structure of magnesium alanate has previously
been determined by a combined x-ray and DFT cluster calculation study,6 and recently by a combined x-ray and neutron diffraction study.32 The latter was performed at both 8
and 295 K 共at 8 K only using neutron diffraction兲. The lowtemperature data are well suited as a comparison to our calculations at 0 K. The former structure6 was used as input for
our structural relaxations. It is in the space group P3̄m1 with
AlH4− tetrahedra connected to Mg ions in a layered structure
with sheets along the c axis.
The details of the relaxed structure are shown in Table I.
The correspondence is very good, except for the c axis,
which is 2.4% longer than the experimental one.32 The H1 z
coordinate is also slightly off 共2.5%兲 the experimental value
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©2005 The American Physical Society
PHYSICAL REVIEW B 72, 073201 共2005兲
BRIEF REPORTS
TABLE I. The DFT relaxed structure at 0 K compared to the
experimental result at 8 K 共Ref. 32兲. The space group is P3̄m1. Mg
is in the 1a position 共0,0,0兲, Al and H1 are in 2d positions
共1 / 3 , 2 / 3 , z兲, and H2 is in a 6i position 共x , −x , z兲.
a 共pm兲
c 共pm兲
Al z
H1 z
H2 x
H2 z
This study
Expt.
518
598
0.703
0.435
0.167
0.809
520.84共3兲
583.92共5兲
0.6991共12兲
0.4242共12兲
0.1671共8兲
0.8105共11兲
when measured in direct coordinates. In Cartesian coordinates, however, the calculated distance from the H1 ion to
the Mg layer of the same sheet hH1 共see Fig. 1兲 is only
around 0.5% larger than the experimental one. In other
words, the geometry of the sheet is almost perfectly described by DFT, but the distance between the sheets 共e.g.,
measured by ⌬hAl in Fig. 1兲 is around 10 pm too large in the
calculated structure. Most probably the hydrogen-hydrogen
bonds are thus not described appropriately by the GGA. The
error was even larger when using a softer potential 共that is, a
larger augmentation region兲 for the hydrogen atoms, which
means that the correct choice of potentials is crucial. The
same is seen when using a softer Al potential, an effect that
may be due to the harder Al potential allowing a larger part
of the hydrogen orbitals to contribute to the hydrogenhydrogen bond.
The total and local DOS’s were calculated for the relaxed
structure, and are plotted in Fig. 2. Magnesium alanate is
nonmetallic with a calculated band gap of 4.1 eV. Since quasiparticle GW corrections to the calculated band gap in
NaAlH4 increased the estimated band gap by 2 – 3 eV,19 we
expect that it is similarly underestimated in Mg共AlH4兲2. The
valence band consists of two separate bands. The lower band
FIG. 1. 共Color online兲 The calculated crystal structure of
Mg共AlH4兲2 seen along the b axis, from the side of the sheets. Al is
surrounded by four H atoms in slightly distorted tetrahedra, while
Mg is sixfold coordinated in distorted octahedra.
FIG. 2. 共Color online兲 The calculated total and local density of
states 共DOS兲 for the relaxed crystal structure of Mg共AlH4兲2. s, p,
and d orbitals are shown as shaded, solid, and dotted curves. The
energy is measured in eV relative to the Fermi level 共shown as
dashed lines兲.
is dominated by an Al- H ␴ bond, and has only small contributions from Mg. The upper band has three regions. For Mg
these regions are populated by s, p, and d orbitals when
going toward the Fermi level. This is distinctly different
from the situation in NaAlH4, where the cation’s valence
band is practically unfilled.8,18,19,21 The projected DOS of Al
is much more similar to that in NaAlH4, with p orbitals
dominating the upper valence band. H has s orbitals throughout the valence band, also similar to NaAlH4. The conduction band of H has, however, significantly fewer available
states than the valence band, which may imply charge transfer to H.
The calculated Hirshfeld charges support that there
is transfer of electrons to H. Both Mg and Al are found
to lose electrons; Mg 0.4e and Al 0.3e 共this is similar to what
was found for Al in Li3AlH6兲.11 This is taken up in similar amounts by the H1 ions, which are only bonded to Al
共electron gain of 0.11e兲, and by the H2 ions, which are
bonded to both Al and Mg 共electron gain of 0.13e兲. The
electron density taken from Mg is thus redistributed within
the AlH4 tetrahedron.
On the other hand, when turning to the COOP of magnesium alanate shown in Fig. 3, we see that there is also a
significant positive overlap between both Al- H and Mg- H.
All the orbitals contribute to this overlap, which suggests
that there is a covalent type bonding both between Al- H and
between Mg- H. The integrated COOP is only indicative of
the strength of the covalence, and a somewhat more reliable
quantitative measure is the calculated overlap population matrix. This shows that the overlap population between Mg and
the H2 ions is around 0.37, while that between Al and H2 is
around 0.54. The overlap between Al and H1, which has no
nearest Mg neighbor, is 0.80, which designates a quite strong
covalent bond. The overlap between Al and H is similar to
that seen in the alkali-metal alanates, while that between Mg
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PHYSICAL REVIEW B 72, 073201 共2005兲
BRIEF REPORTS
FIG. 3. The calculated crystal orbital overlap population
共COOP兲 between the metal atoms and H in the relaxed structure of
Mg共AlH4兲2. A positive COOP means positive overlap, that is, bonding. Negative overlap corresponds to antibonding. The integrated
COOP is shown as dotted lines up to the Fermi level, where the
total integrated COOP is shown as a number. The energy is measured in eV relative to the Fermi level 共shown as dashed lines兲.
and H is almost three times that between Na and H in
NaAlH4.33 We may thus conclude that there is a much higher
degree of covalency between Mg and H in Mg共AlH4兲2 than
between Na and H in NaAlH4. Since the ionicity at the same
time is weaker in Mg共AlH4兲2, the conclusion is that
Mg共AlH4兲2 has primarily covalent bonding character. Similar
to what was found in sodium alanate,19,33 the bonds between
Al and H are of polar covalent character. There is also some
polarity between Mg and H, but to a lesser extent than between Al and H. This is distinctly different from the bonding
between Na and H in NaAlH4, which is almost purely ionic.
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Another feature of Mg共AlH4兲2 that is different from NaAlH4
is the weak bonding between the sheets, which most probably is of van der Waals type.
The calculated uncorrected total energy 共with respect
to the non-spin-polarized energy of the isolated atoms兲
of Mg共AlH4兲2 was compared to that of the constituting
elements. This gives the formation enthalpy Hform, which
was found to be Hform = −21.0 kJ/ mol H2. Magnesium alanate is thus stable at 0 K, but much less stable than NaAlH4,
which has Hform = −54.9 kJ/ mol H2.33 The criterion for a hydride to be stable at room temperature is that Hform ⬍
−39 kJ/ mol H2,34 which means that the synthesized Mg
alanate most probably is metastable at room temperature.
This also explains why rehydrogenation of MgH2 to Mg
alanate has not been achieved at reasonable pressure.
Mg共AlH4兲2 is thus probably not suitable as a reversible hydrogen storage material.
The crystal structure and detailed electronic structure of
magnesium alanate have been determined by densityfunctional band-structure calculations. The calculated crystal
structure almost perfectly reproduces the experimental structure at 8 K,32 except that the distance between the AlH4 tetrahedra in the c direction is too large, resulting in a too large
c axis. The calculated DOS shows that magnesium alanate is
nonmetallic with a band gap of 4.1 eV. Calculated projected
DOS’s, COOP, overlap populations, and Hirshfeld charges
show a covalent type of bonding between Mg and H, with a
weak degree of polarity. The Alu H bonds are also polar
covalent, with somewhat stronger ionicity. The calculated
formation enthalpy implies that magnesium alanate is not
useful for reversible hydrogen storage.
O.M.L. acknowledges discussions with Anita Fossdal.
Economic support from the Norwegian Research Council
through the Nanomat program and generous grants of computational resources via the NOTUR project are also acknowledged.
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