Hybrid functional calculations of potential hydrogen storage material: Complex dimagnesium iron hydride

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Hybrid functional calculations of potentialhydrogen storage material: Complex dimagnesiumiron hydride

Bakhtiar Ul Haq a, Mohammed Benali Kanoun b, Rashid Ahmed a,Mohamed Bououdina c,d, Souraya Goumri-Said b,*aDepartment of Physics, Faculty of Science, Universiti Teknologi Malaysia, UTM Skudai, 81310 Johor, Malaysiab Physical Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal

23955-6900, Saudi ArabiacNanotechnology Centre, College of Science, University of Bahrain, PO Box 32038, Kingdom of BahraindDepartment of Physics, College of Science, University of Bahrain, PO Box 32038, Kingdom of Bahrain

a r t i c l e i n f o

Article history:

Received 2 December 2013

Received in revised form

27 March 2014

Accepted 2 April 2014

Available online xxx

Keywords:

Hydrides

DFT

Electronic structure

Optical properties

Storage capacity

* Corresponding author.E-mail addresses: mohammed.kanoun@k

edu.sa (S. Goumri-Said).

Please cite this article in press as: Ul HComplex dimagnesium iron hydridej.ijhydene.2014.04.014

http://dx.doi.org/10.1016/j.ijhydene.2014.04.00360-3199/Copyright ª 2014, Hydrogen Ener

a b s t r a c t

By employing the state of art first principles approaches, comprehensive investigations of a

very promising hydrogen storage material, Mg2FeH6 hydride, is presented. To expose its

hydrogen storage capabilities, detailed structural, elastic, electronic, optical and dielectric

aspects have been deeply analysed. The electronic band structure calculations demon-

strate that Mg2FeH6 is semiconducting material. The obtained results of the optical

bandgap (4.19 eV) also indicate that it is a transparent material for ultraviolet light, thus

demonstrating its potential for optoelectronics application. The calculated elastic proper-

ties reveal that Mg2FeH6 is highly stiff and stable hydride. Finally, the calculated hydrogen

(H2) storage capacity (5.47 wt.%) within a reasonable formation energy of �78 kJmol�1, at

room temperature, can be easily achievable, thus making Mg2FeH6 as potential material for

practical H2 storage applications.

Copyright ª 2014, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

Introduction

Rapid lessening of limited conventional energy resources and

their noxious impacts on nature in the form of environmental

pollution has stimulated remarkable research interests to-

wards the search of alternative energy resources. Further-

more, the underlined subject of the ongoing research is that,

aust.edu.sa (M.B. Kanoun

aq B, et al., Hybrid fun, International Journa

14gy Publications, LLC. Publ

the novel energy resources must be sustainable, efficient,

cleaner and economical, as well as should be abundantly

available in nature. Hydrogen, being an efficient energy carrier

is of high importance for energy production as it accomplishes

all the mentioned required nuts and bolts of future energy

demand. However, the major challenge for its practical

application, especially exploitation of this unlimited energy

source for transportation, still unresolved because of its

), [email protected] (R. Ahmed), souraya.goumri-said@kaust.

ctional calculations of potential hydrogen storage material:l of Hydrogen Energy (2014), http://dx.doi.org/10.1016/

ished by Elsevier Ltd. All rights reserved.

mailto:[email protected]




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www.elsevier.com/locate/he

http://dx.doi.org/10.1016/j.ijhydene.2014.04.014



i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e92

limited storage capacity and reversibility issue under specific

conditions. Though several methods have been proposed,

such as storing H2 as pressurised gas, liquid H2 under low

temperatures, metal (H2 atoms occupy interstices sites avail-

able within the lattice of the compounds) and complex hy-

drides (ionic hydrides) known as solid storage [1], etc. Among

these abundant available metal and complex hydrides

together with superior thermodynamic properties and high

reversible storage characteristics compared to both gas and

liquid storage, are considered themost appropriate in terms of

its cyclic ability and safety issues for their practical applica-

tions [1e7].

Recently synthesized Mg-based 3d-transition metal hy-

drideMg2FeH6 has attracted considerable attention because of

its appreciable H2 storage capacity (5.47wt.%), high volumetric

H2 density (double than liquid hydrogen) of 150 kgm�3 [8], and

particularly showing exceptional capability of storing thermo-

chemical energy up to 773 K and exhibiting its potential as

catalyst to improve the de/rehydrogenaton properties of other

hydrides [9]. The above characteristics of Mg2FeH6 adding to

that the low cost of its components Mg and Fe metals,

distinguish it from other complex hydrides (for instance

Mg2MHx (M¼Co, Ni)), however, there are still some issues that

need to be raised such as, slow absorption kinetics, high

dissociation temperature and instability, which impend its

practical applications.

To deal with these issues, some experimental and funda-

mental studies have been reported previously at different

levels, for example, crystal structure of Mg2FeH6 was for the

first time determined experimentally by Didisheim et al. [10],

followed by an investigation of its hydrogenation and dehy-

drogenation features by Ivanov et al. [11]. Thereafter, in-

vestigations on the synthesis and characterisation of Mg2FeH6

have been the subject of numerous studies [4,12e25],

including recent report of Retuerto [26], who designed a new

synthesis technique for the fabrication of Mg2FeH6 at rela-

tively high temperature of 750 �C and pressure 2 GPa [26]. More

recently, Danaie et al. [25] have adapted high energy ball

milling technique to synthesize Mg2FeH6 starting from a

mixture of Fe and MgH2 powders. In spite of all these efforts,

compared to MgeMeH (M¼Ni, Co) systems, MgeFeeH equi-

librium ternary alloy phase diagram does not reveal the for-

mation of stable binary alloys. Additionally, none the

conventional synthesis processes is showing potential in the

near future for the possibility of the fabrication of pure

Mg2FeH6 phase. Therefore, comprehensive understanding of

some important aspects regarding H2 storage process in

Mg2FeH6 within available experimental tools is very much

limited.

To overcome upon the above encountered problems,

several research groups have adapted first principles compu-

tational modelling techniques [27e34], to investigate its

properties because of the competence of first principles cal-

culations in determining more precise results within a short

time and much cheaper resources without having prior

knowledge of experimental measurements. Most of these

studies are focused mainly on the electronic structure and

structural properties using density functional density (DFT)

within GGA and LDA approaches. Even then, there exist

several contentious reports regarding the bandgap nature

Please cite this article in press as: Ul Haq B, et al., Hybrid funComplex dimagnesium iron hydride, International Journaj.ijhydene.2014.04.014

(indirect/direct) of Mg2FeH6 as well as about the value of its

bandgap energy, as different reports present different values

in the literature, i.e. 1.74 eV [33], 1.73 eV [28] or 1.91 eV [34]

besides pointing out to its insulating or a semiconducting

nature with direct energy gap of 2.33 eV [35], 1.96 eV [32],

1.87 eV and 2.25 eV [29]. By reviewing more precisely the re-

sults of the above references, it is found that, most of these

first principles DFT studies have been performed at the level of

standard DFT. In fact, it is well known that standard DFT

calculations usually (calculations at the level of standard LDA

and GGA) underestimate the electronic and optical properties

very severely. To deal with such issues especially the calcu-

lations of electronic and other excited state properties of

complex materials, hybrid functionals for exchange correla-

tion energy/corresponding potential are successfully imple-

mented to reproduce appropriate results for the electronic,

structural, elastic and optical properties as well. To the best

knowledge of the authors, no study is reported yet beyond the

standard DFT approaches for the investigation of electronic

along with optical properties of Mg2FeH6 to obtain precise

results.

Therefore in this present study, the calculations are per-

formed on Mg2FeH6 by employing hybrid functionals (PBE0

and HSE06) and scrutinize their effect on the electronic as well

as optical properties, and in turn their effect on hydrogen

storage capabilities in comparison with standard DFT calcu-

lations. Moreover, in order to explore the real potential of

Mg2FeH6, a comprehensive understanding of its physical

properties, at quantummechanical scale is always in demand

and of great importance. As an example, the knowledge of

elastic properties of Mg2FeH6 is important. Similarly, some

hydride materials have been reported suitable as an alterna-

tive to transparent conducting oxides (TCO) for solar cell

technology. Accordingly, the study of the optical properties of

Mg2FeH6 will help to explore its potential for optoelectronic

applications as well. Taking the benefits of the first principles

approaches, the study was extended to structural, elastic,

electronic, optical and dielectric properties.

Computational details

Calculations in this work were carried out by employing pro-

jector augmented-wave (PAW) scheme of calculation [36,37]

as realized in Vienna ab-initio simulation package (VASP)

[38,39]. The PAWmethod was preferred over the full-potential

plane wave approach (FP-PW) because the former can opti-

mize large super cells in a reasonable time without compro-

mising on the quality of the results. For Mg and Fe, 3s2, 3d7and

4s1 states electrons were treated as valence whereas 1s1 for H

atoms. The exchange and correlations energy were treated

within the PerdeweBurkeeErnzerhof (PBE) GGA approxima-

tion in standard DFT calculations for the sake of comparison

with hybrid functional calculations [40]. For hybrid functional

calculations, the HeydeScuseriaeErnzerhof (HSE06) [41] and

PBE0 [42] hybrid energy functionals were used. PBE0 and

HSE06 approximations are somewhat similar, in a sense, as in

both approaches 25% of the exact screened HartreeeFock

exchange is mixed with the 75% of gradient-corrected PBE

exchange functional, but in both approaches long range




Fig. 1 e (a) The unit cell structure of cubic K2PtCl6-type Mg2FeH6 and (b) polyhedral presentation.

i n t e rn a t i o n a l j o u rn a l o f h y d r o g e n en e r g y x x x ( 2 0 1 4 ) 1e9 3

interaction part of the exact exchange is treated differently. In

HSE functional, short-range part of the exact exchange is only

preserved and long-range part of exact exchange is cut off,

that made this approach more efficient. For both local and

non-local parts, the value of screening parameter (u) used is

0.2 A�1, which is identical to the value reported in reference

[41]. A 500 eV energy cut off was used to carry out the calcu-

lations. Brillouin zonewas sampled using theMonkhorst-Pack

(MP) method [43] with a maximum separation of 0.3 A be-

tween two points in the Brillouin zone. This separation gives

8� 8� 8 mesh for the four-atom unit cell. The SCF cycle was

stopped after the energy difference between two consecutive

iterations was less than 10�5 eV.

Results and discussion

Structure and elastic properties

The simulated unit cell of Mg2FeH6 has been schematically

shown in Fig. 1(a). The structural geometry of Mg2FeH6 is

analogous to that of cubic K2PtCl6 (fluorite-type) structure [10].

Mg2FeH6 has a lattice constant a¼ 6.443 A, space group Fm3m,

and contains 36 atoms per unit cell. Mg and Fe atoms have

fixed atomic coordinates and are, respectively, positioned at

tetrahedral and octahedral coordinates such as Mg (8c) (1/4, 1/

4, 1/4); and Fe (4a) (0, 0, 0). However H has variable position in

(24e) (x, 0, 0) [26,32]. Fig. 1(b) shows the polyhedral geometry of

Mg2FeH6, which is well analogous to the one schematized by

Retuerto et al. [26] in their experimental report. It is evident

that each Fe atom is surrounded by 6 hydrogen atoms that

make orthogonal planes to each Fe atom. Furthermore, the

polyhedral FeH6 complexes are tetrahedrally coordinated to

Mg atoms resulting in an fcc lattice in which the polyhedral

FeH6 resides at the centre. Unit cell structure of Mg2FeH6, with

the above details was fully relaxed. The calculated value for

lattice constant is reported in Table 1 alongwith experimental

data [10] for comparison. It can be noticed that with respect to

the experimental value, the calculated lattice parameter is

slightly underestimated within 0.51%. Using the hybrid


calculations, the calculated equilibrium properties are also

found to be in good agreement with the experimental data [9].

Overall, it is observed that both hybrid functionals give

somewhat lower value of the lattice constant in comparison

with GGA-PBE. This might happen due the enhanced elec-

tronic localization, resulting into tight inter-atomic bonding.

In order to investigate the strengthandmechanical stability

of Mg2FeH6, the three independent elastic constants C11, C12

and C44, were calculated. The obtained values of C11, C12 and

C44 are 249, 88.4 and 65.5 GPa, respectively. As they satisfy the

BorneHuang mechanical stability criterion [44] defined for

cubic structures, i.e. (C11eC12)> 0, (C11þ 2C12)> 0 and C44> 0,

which reveal that Mg2FeH6 is a mechanically stable material.

After obtaining elastic constants, the polycrystalline bulk

modulus (B), shearmodulus (G) and Young’s modulus (Y) were

also calculated by employing the VoigteReusseHill (VRH)

approximation [45]. The calculated polycrystalline elastic

constants are found to be 142, 71, and 182.7 GPa for B, G and Y,

respectively. It is predicted that Mg2FeH6 has a low bulk, Shear

and Young’s moduli, consistently indicating that it is a mate-

rial with low hardness. While comparing to the recent litera-

ture on hydrides [46], the calculated elastic constants and

mechanical properties, such as the bulk modulus, one can see

similar trends compared to some other relatedmetal hydrides

such as ε-ZrH2 [47], where DFT basedmethods have been used

to understand the relationship between structure and elastic

constants. Moreover, according to classical criteria of Pugh’s

modulus ratio B/G (as proposed by Pugh [48]), a material is

brittle (ductile) if the B/G ratio is less than 1.75 [48e51]. In our

case, for our considered compound, B/G value of 2.0 is larger

than 1.75, i.e. this material will behave in a ductile manner.

Electronic structure and related properties

To illustrate the electronic structure ofMg2FeH6, Fig. 2 displays

the total and partial density of states obtained at GGA-PBE,

HSE06 and PBE0 level of approximations. As shown in previ-

ous section, the calculated values of the lattice constant, at

the level of PBE0 and HSE06, are in close agreement with GGA-

PBE results, therefore to save calculations time, as input, GGA-




Table 1 e Results of GGA-PBE, PBE0 and HSE06 calculations of lattice parameter a (A), and band gaps compared withexperimental and other reported theoretical values.

Lattice parameter Band gap

GGA-PBE HSE06 PBE0 Previous work Exp. GGA-PBE HSE06 PBE0 Previous work

Mg2FeH6 6.361 6.328 6.316 6.3736a, 6.414b, 6.4436c 6.443g 1.96 4.19 4.97 1.74c, 1.73e, 1.91a, 2.33d, 1.96b, 2.25f

a Orgaz et al [34].b Zhou et al [32].c Orgaz et al [33].e Halilov et al [28].d Zhang et al [33].f Zareii and Sarhaddi [35].g Dornheim et al [2].


PBE relaxed structures have been used to proceed to the study

of the electronic properties. In these figures, zero represents

the Fermi level (EF). In general qualitative nature of DOS pro-

files with GGA-PBE, PBE0 and HSE06 are nearly analogous and

show the semiconductor nature of Mg2FeH6, whereas DOS

profiles of PBE0 and HSE06 display an energy bandgap wider

than GGA-PBE [4]. Moreover, PDOS shows several interesting

features. At the bottom of the valence band, i.e. between �10

and �5 eV, the first valence band is composed of low-lying

energy bands, reflecting the Fe-(s,d) and H-s bonding in-

teractions. The states between �5 and �2 eV are involved

essentially from H-s states with a small contribution from Fe-

Fig. 2 e Calculated total and partial densities of states (DOS) for

calculations. The line at zero is the Fermi level.


p and Mg-p states. The upper region of the valence-band

complex is mostly due to the Fe d-states compared with H(s)

andMg(s, p). The lowest conduction band derivesmainly from

the corresponding anti-bonding fromMg states, whereas their

contribution is small in the occupied state.

The obtained results of the energy bandgap (Eg) value for

Mg2FeH6 at the level of GGA-PBE, HSE06 and PBE0 are sum-

marized in Table 1. The analysis of GGA-PBE DOS plot and

band structure (not shown here) for Mg2FeH6 with the band

structure reported in other Refs. [28,29,33,34], suggests that

Mg2FeH6 is a direct bandgap semiconductor. Therefore, in

Table 1, previous LDA and GGA-PBE bandgap results reported

Mg2FeH6 using (a) GGA-PBE, (b) PBE0, and (c) HSE06





by other theoretical calculations are listed. However, at this

stage, we did not find any experimental data in literature for

comparison. The calculated GGA-PBE band gap value is about

1.96 eV. Though the results obtained in this study, at the level

of GGA-PBE, are in agreement with other calculations,

whereas standard LDA and GGA-PBE methods sufficiently

underestimate the bandgap energy value for semiconductors

and insulators in addition to the erroneous prediction of

ground states properties of strongly correlated materials. As

PBE0 and HSE06 functionals have been reported to be suitable

to reproduce better values of the band gap energy [52],

therefore in addition to GGA-PBE, PBE0 and HSE06 functionals

have been implemented for band structure calculations to

improve the bandgap value of Mg2FeH6. The calculated

bandgap energy value with PBE0 is found to be slightly higher

than the bandgap value obtained with HSE06.Since there is no

experimental data available in literature on energy bandgap

related to Mg2FeH6, calculations based on GGA-PBE for pure a-

MgH2 as reported by Ahuja and co-workers [53], can be

considered as reference, i.e. Eg¼ 3.47 eV, which strongly un-

derestimates the value of Eg relative to the expected experi-

mental value (5.6 eV) [54]. However, it was found that PBE0 and

HSE06 functionals improve the value of the band gap of pure

a-MgH2; 4.58 and 5.31 eV, respectively, which are in better

agreement with the experimental value of 5.6 eV. Accordingly

and by analyzing other studies performed with PBE0 and

HSE06 on some other semiconductors available in literature, it

can be concluded that for electronic properties, hybrid func-

tionals are more appropriate for Mg2FeH6.

More importantly and for H2-storage, from PDOS, it can be

noticed that the s-state electrons of H atoms contribute more

near the Fermi level, thus, it is easier to release H atoms. A

particular emphasiswasdevoted to theenthalpyof energy (DH)

for the hydride system by considering the following reaction:

2Mgþ Feþ 3 H2/Mg2FeH6

The corresponding value of the enthalpy of energy can be

calculated using the following expression:

DH ¼ 13

�E�Mg2FeH6 � 2EðMgÞ � EðFeÞ � 3ðH2Þ

��

where the total energies (E) of Mg2FeH6, Fe and Mg were ob-

tained by geometry relaxations. To estimate the properties of

H2 molecule, a simple cubic unit cell was used by taking large

value of lattice constant. The enthalpy of energy of H2 for

Mg2FeH6 is found about �84.34 kJ (mol H2)�1 which is in good

agreement with the experimental value of �98 kJmol�1 of H2

[2]. The capacity of H2-storage in Mg2FeH6 was also estimated,

which is about 5.47 wt.%. These findings are very competitive

compared to the characteristics of MgH2, which is another

potential H2-storage material, with a formation energy of

�78 kJmol�1 and H-storage capacity 7.65 wt.% [2,7].

Optical properties

Comprehensive data about the optical properties of a material

can be derived using dielectric function ε(u)¼ ε1(u)þ iε2(u) over

the entire photon energies. For inter-band transitions, the


dielectric function is computed using momentum representa-

tion. The dispersive (Real) part (ε1(u)) of the dielectric function

describes the propagation properties whereas the absorptive

(Imaginary) part(ε2(u)) is associated to the optical absorption in a

medium and is directly linked with the electronic structure.

The imaginary part (ε2(u)) can be derived from [3]:

ε2 ¼ 2e2pUε0

Xk;V;C

��jCKjbu$rjjV

K

��2d�ECk � EV

k � E�

where jCK and jk

C are the wave functions corresponding to

energies ECk and EV

k , respectively, ε0 represents the permittivity

of free space, the unit cell volume is defined by U, u de-

termines the polarization of the incident electric field, r and k

represent the vectors in the real and reciprocal lattice,

respectively. The knowledge of both real and imaginary parts

of the dielectric tensor will allow the calculation of other

important linear optical properties such as the reflectivity (R),

the refractive index (n) and the absorption coefficient (A).

Hereafter, only the calculations of the optical properties of

Mg2FeH6 using GGA-PBE and HSE06 functionals are reported,

because PBE0 is leading to the same results as HSE06. The

calculated macroscopic dielectric functions are plotted in

Fig. 3. It is clearly shown in Fig. 3(a) that GGA-PBE curve un-

derestimates the band edge because of its severe underesti-

mation of the electronic bandgap energy. However the nature

of the calculated band edge by HSE06 ismore or less analogous

with GGA-PBE. It means that the inclusion of the hybrid

functionals description does not affect the nature/character of

band edge though it reasonably improves the bandgap value

as compared to the standard GGA. The absorption peak ob-

tained via HSE06 is moved to higher energies compared to

GGA-PBE. As shown in Fig. 3(a), depiction of the direct and

indirect transitions is appropriately performed with all

methods. There is a pronounced sharp peak at about 5.33 eV

in the calculated ε2(u) spectrum close to the absorption edge.

Without taking into account light polarization effect, in the

imaginary part of the dielectric function, it is noted (above the

excitonic peak) the presence of three key spectral features

related to the peaks in the spectrum obtained using HSE06

functionals [3]. The second peak at around 6.38 eV mainly

corresponds to the transitions occurring from the uppermost

band of the valence bands to conduction band states.Whereas

the complicated third peak between 7 eV and 10 eV is pri-

marily originated by the transitions taking place from Fe3d

valence bands to conduction bands [3]. Furthermore, the peak

located at 10.8 eV is largely arising from Mg 2p orbitals of

Mg2FeH6. The real part of the dielectric function is obtained by

Kramer-Kronig transformation. The calculated real part of the

dielectric function for Mg2FeH6 with GGA-PBE and HSE06 are

shown in Fig. 3(b). In the case of HSE06, the real part Re(u)

shows again a sharp peak at about 5.33 eV, which is obviously

linked to the peak of the dielectric function’s imaginary

component. And then, the curves decrease to values close to

zero at 9.81 eV. For GGA-PBE, the curve of the real part of ε(u) is

incredibly analogous to the HSE06 hybrid functional. The

value of HSE06 dielectric constant is predicted to be ε(0)¼5.70 eV. Thus, it can be concluded that the calculated macro-

scopic static electronic dielectric constants by hybrid method

ameliorates the values of ε(0) than GGA-PBE (4.4 eV).




Fig. 3 e Calculated optical properties of Mg2FeH6. (a) Imaginary part of the dielectric function (b) real part of the dielectric

function; (c) reflectivity (d) refractive index; and (e) absorption coefficient.


The refractive index n(u) that determines the propagation

of light photons in a medium is also investigated. The calcu-

lated refractive index dispersion curve of energy is plotted in

Fig. 3(c). As can be seen, the dispersion curve of HSE06 is

similar to the result of GGA-PBE. The calculated refractive

index value of 2.1 is found to be smaller than previous results

(2.39) with GGA-PBE. The calculated static refractive index n(0)

is 2.1, which indicates that the light photons can pass through

Mg2FeH6 with a speed 2.1 times more than that of vacuum.

The calculated static refractive index efficiently satisfies the

condition n2(0)¼ ε1(0), indicating the authenticity and accu-

racy of the calculations for optical properties. Moreover, n(u)

exhibits some structures that have the same origin as that of

structures appearing in ε2(u).


To investigate the ratio of incident and reflected light beam

from Mg2FeH6 hydride, the reflectivity R(u) spectra against

photon energy, is plotted in Fig. 3(d), where the calculated

curves related to both approaches (PBE-GGA and HSE06) are

shown. The prominent peak due to the excitonic absorption is

found to be positioned around 5.3 eV [3]. The peaks at 6.33 and

9.63 eV in the reflectivity curve plot are linked to the peaks in

the dielectric function (Fig. 3(b)). These peaks are the inter-

band transitions modified by excitonic effects. Furthermore,

R(u) curve as shown in Fig. 3(d) reveals a reflectivity index less

than 20% in the energy regime 0e2.5 eV, showing it as a

transparentmaterial for the light photons that carry an energy

less than 2.5 eV. This may show the potentiality of Mg2FeH6 to

be considered as alternative to transparent conducting oxides




Table 3 e Mulliken Bond population of Mg2FeH6

Bond Mulliken population Length (A)

HeFe 0.74 1.560

HeH �0.08 2.204

HeMg �0.30 2.250

MgeFe �0.56 2.754


(TCOs) for solar window. However, with a broad structure in

the energy regime 4.30e20 eV, it behaves as an opaque ma-

terial with maximum reflectivity at 13.90 eV.

The knowledge of optical absorption coefficient and ab-

sorption edge is important for understanding the electronic

structure and optically induces transitions. To understand the

absorption of light in Mg2FeH6, absorption spectra were

calculated as a function of photon energy (Fig. 3(e)). The op-

tical bandgap calculated from the absorption spectra is

equivalent to 2.30 eV with GGA-PBE and to 4.19 from HSE06

calculations. The absorption spectra exhibits a broad struc-

ture in the energy regime 2.91 to 24.37 eV with a maximum

value of A(u)¼ 2.15709� 106 cm�1 at photon energy 7.74 eV.

This reveals that Mg2FeH6 strongly absorbs UV light within the

mentioned energy range.

Dielectric properties, born effective and Mulliken charges

Dielectric response isof great importance inorder to identify the

contribution of electronic, lattice vibrations andmore generally

the electrostatic resonance. In the present first principles cal-

culations, the dielectric response is calculatedby combining the

contribution of electric and lattice vibrations to the dielectric

response. In the calculations, scissor correction has not been

incorporated, since the attained tensor is diagonal with one

component, ε11¼ ε22¼ ε33¼ εN¼ 5.465 due to the particular

crystal symmetry of Mg2FeH6. Unluckily, being Mg2FeH6 a new

compound, no experimental data as well as theoretical studies

related to the dielectric properties are available in literature for

comparison. However, εN value is found to be following the

tendencyofsomeresults related tootherhydridesas reported in

the literature, such as LiH and AlH3 [55].

The knowledge of Born effective charge (Z*) performs a key

role in the understanding of dynamics of a crystal lattice. In

polar crystals origin, because of the splitting of longitudinal

optical (LO) and transverse optical (TO) phonon modes, long

range Coulomb interaction between their nuclei arises.

Moreover, coupling between the electric fields and optical

phononmodes is well understood and quantified [56]. In Table

2, the calculated Z* related to the atoms con-

stitutingMg2FeH6in asymmetric unit, together with their

Mulliken charges, are reported. It is well known that the form

of Z* results directly from the site symmetry of the atoms.

Thus, Z*(Mg) and Z*(Fe) are diagonal with one component,

whereas Z*(H) has two components that remain diagonal.

Table 2 e Born effective charge tensors ðZ�abÞ, average

oftheir eigenvalues (l)[ 1/3 Tr(Z*), and Mulliken charges(QM) of the different atoms constituting the Mg2FeH6Unit(in jej)Atom Z* tensor l QM

Mg0@�3:05 0 0

0 �3:05 00 0 �3:05

1A �3.05 1.55

Fe0@2:081 0 0

0 2:08 00 0 2:08

1A 2.08 �1.28

H0@�0:747 0 0

0 0:09834 00 0 0:099

1A �0.18322 �0.3


It is observed that Fe ion contains “elements of effective

charge tensors” closer to so called (þ2) ionic charge. Accord-

ingly, it can be concluded that the bonding between Fe ions

and H ions surrounding it, is mainly of ionic nature. However,

Mg shows maximum effective charge value of �3.05 that is

50% lower than that of its static charge þ2. Similarly the

hydrogen ion also shows a substantial decrease in its effective

charge (þ1). Interestingly, for Mg2FeH6, H and Mg are showing

a pronounced variation in their static charges compared to Fe.

Similar behavior is also observed from the Mulliken effective

charges. Indeed, according to their Mulliken charges, posi-

tively charged (Mg) ions aremoderately electron donorswhere

negatively charged (Fe and H) ions are electron acceptors.

Similarly, the ionic value of Fe(þ2) is very obviouswhereas the

values of H and Mg are not very clear. However, strong

changes in Z*(Mg) and Z*(H) on lower side, from their reference

ionic values (by considering closed shell model configuration),

substantiates to covalent bonding character. Indeed, it is

known that a high value of the bond population indicates a

covalent bonding whereas a low value indicates an ionic na-

ture. Positive and negative values indicate bonding and anti-

bonding states, respectively. In this case, the Mulliken distri-

bution has been calculated using CASTEP package [57,58]. This

plane wave pseudo-potential DFT computational code was

conjointly used to investigate also the bonding character of

Mg2FeH6 by computing Mulliken bond population. To obtain

these results, self-consistent cycles were converged within a

tolerance of 10�14 Ha on the potential residual. The electronic

wave functions were expanded in plane waves up to kinetic

energy cutoffs of 400 eV. Mulliken bond population and bond

length between different constituents, as reported in Table 3,

indicate that Mg atoms show inclination towards falling in the

bond population and even that show trend to become nega-

tively charged when they are coupled to Fe or H atoms. On the

other hand, whenMg atoms are substituted byMg or H atoms,

Mulliken bond population become more covalent. Hence,

these results suggest a mixed covalent-ionic character of

bonding inMg2FeH6 hydride, i.e. the bondingwithMg atoms is

of ionic nature as in the case between H atoms whereas

bonding between Fe and His significantly of covalent nature.

Conclusion

In the present research work, structural, electronic, optical,

dielectric, dynamic and elastic properties of Mg2FeH6 have

been investigated at the level of standard DFT and beyond by

implementing hybrid exchange correlation functionals within

DFT. The obtained results show thatMg2FeH6 is physically less

hard, and that H atoms can be easily released from it. In

addition, Mg2FeH6 exhibits noteworthy optical properties





thereby showing its potential as an alternative to TCOs for

solar window, therefore it can be exploited as base materials

for optoelectronic devices. Overall, first principles in-

vestigations reveal that Mg2FeH6 hydride, is one of the most

promising material among H-storage complex 3d-transition

metal hydrides. Further investigations at all levels with novel

experimental researchwork aswell as theoretical calculations

for establishing its structure-to-property relation in order to

expose its practical potential for hydrogen energy as well as in

optoelectronics, are of great importance and need to be

accomplished.

Acknowledgements

Authors from Universiti Teknologi Malaysia would like to

thank the financial support from the Ministry of Higher Edu-

cation (MOHE) Malaysia/Universiti Teknologi Malaysia

(UTM) of this research work through grant number

Q.J13000.7126.00J33. Moreover great thanks to the research

computing service at KAUST for the access to computational

resources.

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