Zinc substituted MgH2 - a potential material for hydrogen storage …folk.uio.no/ravi/cutn/totpub/varunaa19.pdf · 2019-05-27 · Zinc hydride has been known for many years as a meta-stable

ww.sciencedirect.com

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6

Available online at w

ScienceDirect

journal homepage: www.elsevier .com/locate/he

Zinc substituted MgH2 - a potential material forhydrogen storage applications

R. Varunaa a,b, H. Fjellvag c, P. Ravindran a,b,c,*

a Department of Physics, Central University of Tamil Nadu, Thiruvarur, Tamil Nadu, 610101, Indiab Simulation Center for Atomic and Nanoscale MATerials, Central University of Tamil Nadu, Thiruvarur, Tamil

Nadu, 610101, Indiac Center for Materials Science and Nanotechnology and Department of Chemistry, University of Oslo, Box 1033

Blindern, N-0315 Oslo, Norway

a r t i c l e i n f o

Article history:

Received 14 February 2019

Received in revised form

29 March 2019

Accepted 1 April 2019

Available online 28 April 2019

Keywords:

Hydrogen storage

Magnesium hydride

Zinc hydride

Density functional theory

Zn substituted MgH2

* Corresponding author.E-mail address: [email protected] (P. Ra

https://doi.org/10.1016/j.ijhydene.2019.04.0160360-3199/© 2019 Published by Elsevier Ltd o

a b s t r a c t

The search for efficient materials for onboard hydrogen storage applications is an emerging

research field. Using density functional calculations, we demonstrate Zn substituted MgH2

as a potential material for hydrogen storage. We predicted the ground state crystal

structure of ZnH2 which is found to be Pna21 (orthorhombic) structure with meta-stable

behavior. The structural phase stability and phase transition of Mg1�xZnxH2 systems

have been analyzed. The H site energy of Mg1�xZnxH2 systems is calculated to understand

the hydrogen desorption process. Our calculations suggest that Zn substitution reduces the

stability of MgH2, thereby it may reduce the decomposition temperature of MgH2. The band

structure and density of states calculations reveal that the Mg1�xZnxH2 systems are

insulators. The chemical bonding behavior of Mg1�xZnxH2 systems is established as iono-

covalent in nature. Moreover, Zn substitution in MgH2 induces disproportionate MgeH

bonds which could also contribute the reduction in the decomposition temperature as well

as H sorption kinetics.

© 2019 Published by Elsevier Ltd on behalf of Hydrogen Energy Publications LLC.

Introduction

The worldwide energy demand coupled with shrinking fossil

fuel resources and environmental pollution are continuously

rising every year which have lead us to an increasing curiosity

to find alternative energy resources. Hydrogen is an ideal

chemical energy carrier that exhibits a high calorific value per

unit mass and is environmentally friendly [1e7]. However, the

main challenge is to store hydrogen safely and efficiently for

mobile and stationary applications. Based on this, many

researchers considered light weight magnesium hydride

vindran).

n behalf of Hydrogen En

(MgH2) for onboard hydrogen storage applications owing to its

high hydrogen storage capacity, low cost, and abundance. But

the practical use of MgH2 for hydrogen storage is hampered by

its high decomposition temperature and quite slow hydrogen

sorption kinetics [8e29]. The high decomposition temperature

in MgH2 is associated with strong ionic bonding. One of the

key solutions for this issue is by adding catalysts or

substituting other elements to make MgeH bond weaker. It is

demonstrated that by increasing the covalency in the hy-

drides, one can reduce their decomposition temperature [30].

Recently, it was reported that additive catalysts added MgH2

improve the hydrogen sorption kinetics and reduce the

ergy Publications LLC.

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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6 13633

sorption temperature of MgH2 [31e38]. Based on these, we

have currently explored how solid solutions involving

meta-stable hydrides such as zinc hydride (ZnH2) with MgH2

can reduce the bond strength and enthalpy of formation and

hence, the decomposition temperature of MgH2.

Zinc hydride has been known for many years as a meta-

stable compound with a white color that will decompose

easily. So, its crystal structure is not yet identified experi-

mentally. Zinc hydride was first synthesized by Schlesinger

et al. in 1947 [39] via the reaction between dimethyl zinc and

lithium aluminium hydride. In 1951, Barbaras et al. [40] syn-

thesized zinc hydride using metal alkyls and lithium

aluminium hydride in ethyl ether solutions. Watkins and

Ashby [41] prepared ZnH2 using zinc halides and alkali metal

hydrides. Few theoretical studies have also been made on

electronic structure, equilibrium geometry, and harmonic

vibrational frequencies of molecular ZnH2 [42e45]. A linear

ZneH molecular structure has been predicted and the equi-

librium ZneH bond distances (range of 1.492e1.662 �A) are also

estimated by the above theoretical studies. From density

functional calculations, Koning et al. [46] reported that, as like

beryllium hydride andmagnesium hydride, molecular ZnH2 is

also possess highly associated hydrogen-bridged coordination

polymer behavior.

Later, Breckenridge et al. [47e49] studied the reaction of

ZnH2 by laser ablation of Zn under hydrogen atmosphere. The

infrared spectra of ZnH2 trapped in low-temperature matrices

have been studied by Greene et al. [50] and later byWang et al.

[51] Shayesteh et al. [52e54] synthesized gaseous ZnH2 mole-

cule by electrical discharge inside a high temperature furnace.

Huang et al. [55] studied the potential energy surface and

vibrational energy levels of molecular ZnH2 using ab-initio

calculations. A few years back, Panagopoulos et al. [56]

investigated the effect of cathodic hydrogen charging on the

structural and mechanical characteristics of zinc. Using X-ray

diffraction, the formation ofmetastable ZnH2 was detected on

the surface layers of zinc after cathodic hydrogen charging.

They have also observed that due to dislocation pinning

mechanisms, the ductility of zinc decreases with the increase

of cathodic hydrogen charging.

MgH2 is strongly ionicwith high thermal stability, whereas,

ZnH2 has noticeable covalency with poor stability and hence

there are practical problems with their use in hydrogen stor-

age applications. The possible ways to destabilize MgH2 is

substituting various elements at the cation or at the anion

sites [57,58]. In our recent studies [59], we attempted to

destabilize MgH2 by substituting fluorine at the anion site.

However, though one can substitute fluorine at H sites in

MgH2, the systembehaves highly stable and its decomposition

temperature increased. So in the present study, we attempted

to substitute Zn at the Mg site to destabilize MgH2. The reason

is that ZnH2 is meta-stable in nature and hence Zn substitu-

tion at Mg site in MgH2 is expected to improve the hydrogen

sorption properties and induce changes in the formation

enthalpy, H site energy, chemical bonding, and electronic

structure of MgH2. From theoretical and experimental studies,

it is reported that Zn substitution in MgH2 improve kinetics

and thermodynamic properties of MgH2 as follows. Chen et al.

[60] reported that stability of MgH2 cluster can be reduced by

substituting transition metals such as Sc, Ti, V, Cr, Mn, Fe, Co,

Ni, Cu, and Zn at a central atom in MgH2 cluster. So, they

concluded that the substitution of the above said transition

metals in MgH2 may improve the hydrogen sorption kinetics.

From experimental studies, Liang et al. [61] noted that

substituting Mg with Zn, Al, Ag, Ga, In or Cd reduces the

stability of MgH2.

Vegge et al. [62] calculated hydride formation energies of

magnesium-3d transitionmetal alloys and reported that there

is a gradual increase in the stability of the hydrides (from

MgSc to MgFe), which is followed by a rapid decrease in the

stability (from MgCo to MgZn). Zhou et al. [63] reported that

the heat of formation decreases when MgH2 is chemically

modified with 3d transition metals. They found that the

reduction of formation enthalpy increases in an order of Fe, Ti,

Co, Zn, Ni, V, Mn, Cu, and Cr. Tsuda et al. [64] presented the

catalytic activities of 3d transition metals M on MgeH disso-

ciation by attachingM on the top of Mg in aMgH2 cluster. They

reported that the catalytic activity of transition metal is

considerably low (except Sc and Ni) due to fully occupied or-

bitals of Zn which does not receive any electrons from MgH2.

Milanese et al. [65] studied the hydrogen sorption kinetics and

storage efficiencies of mechanically activated binarymixtures

ofMg (MgH2) with nine differentmetals (Al, Cu, Fe, Mn,Mo, Sn,

Ti, Zn, and Zr). They concluded that MgeZn mixture has good

reversibility with cyclic effect for hydrogen and also has high

storage efficiency with poor sorption kinetics.

Polanski et al. [66] described the influence of nano-sized

metal oxides such as Cr2O3, TiO2, Fe3O4, Fe2O3, In2O3, and

ZnO on MgH2 powder and found that these metal oxides

(except In2O3) improve the dehydrogenation properties. The

effect of partial substitution of Mg with 3d transition metals

on the formation enthalpy and electronic structure of MgH2

have been studied by Zeng et al. [67] Their results show that

Zn substitution lowers the formation enthalpy. Further, they

showed that the bonding nature of MgH2-3d systems are

governed by ionic as well as covalent bonding. Bhihi et al. [68]

reported that 6.25% of Zn substitution in MgH2 (Mg15ZnH32)

reduce the gravimetric density of hydrogen (6.97 wt%) and on

the other hand, it decreases the formation enthalpy

(�53.04 kJ/mol.H2) which is the advantageous properties for

hydrogen storage applications. They also reported that

increasing the % of Zn substitution affects the gravimetric

density and this can be overcome through a double substitu-

tion (transition metal and either Li or Al) on MgH2. It is inter-

esting to note that the crystal structure of ZnH2 is not yet

explored in any of the theoretical and experimental studies

so far.

Our main objective in the present study is to destabilize

MgH2 by reducing the strong ionic interaction betweenMg and

H so that it can be used for practical hydrogen storage appli-

cations. So, we focus on predicting the ground state crystal

structure of ZnH2 and analyzed the chemical bonding by

substituting Mg with Zn in MgH2. The important properties

like enthalpy of formation, enthalpy of mixing, and hydrogen

site energy of Mg1�xZnxH2 systems were calculated. The band

structure and density of states (DOS) of Mg1�xZnxH2 systems

were analyzed to understand the electronic ground state

by Zn substitution. The chemical bonding analyses of these

systems have been done through partial DOS, charge density,

electron localization function, Bader effective charge, Born

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 613634

effective charge, and crystal orbital Hamiltonian population

analyses.

It may be noted that zinc is having higher atomic weight

than magnesium and also each zinc atom replace one mag-

nesium atom in MgH2. Hence, the gravimetric density of

hydrogen will decrease with increases of Zn concentration in

MgH2. For example, 12.5% of Zn substituted MgH2, the gravi-

metric density of hydrogen is reduced from 7.66wt% to 6.41wt

%. For 50% Zn substituted MgH2, the gravimetric hydrogen

density is further reduced to 4.3 wt%. For ZnH2, the gravi-

metric density is much lower (2.99 wt %) compared to that of

MgH2. So, one can compromise the gravimetric density in

order to achieve appropriate decomposition temperature and

reaction kinetics.

Computational details

We have utilized the density functional theory (DFT) [69] with

plane-wave basis sets as implemented within the Vienna ab-

initio simulation package (VASP) [70] for all our calculations.

The projector augmented wave (PAW) [71] pseudo-potentials

were used. The generalized gradient approximation pro-

posed by Perdew, Burke, and Ernzrhof (GGA-PBE) [72] were

used to obtain accurate bond lengths and bond energy. The

ground state geometries were designated by minimizing

stresses and Hellmann�Feynman forces using the conjugate-

gradient algorithm until the force acting on all atomic sites

were less than 10�3 eV/�A. The total energy difference between

two consecutive iterations was set to 10�6 eV.

Our previous studies show that the plane wave cutoff of

350 eV is sufficient to accurately describe the structural pa-

rameters of MgH2 and hence we have used the same for all the

present calculations. The substitution of Zn in MgH2 have

been done using a supercell approach. We have used 1 � 1 x 2

supercell in order to achieve 25%, 50%, and 75% Zn substitu-

tion in P42/mnm phase of MgH2. For 12.5%, 37.5%, 62.5%, and

87.5% Zn substitution, we have constructed 2� 2� 1 super cell

of MgH2 in P42/mnm phase whereas 2 � 1 � 1 super cell for

Pna21 phase. Brillouin zone integrations were done using

Monkhorst-Pack k-point meshes [73]. A k-point grid of

11 � 8 � 11 was used for structural optimization of ground

state Pna21 structure of ZnH2 and the same density of k-point

was used for the substituted systems. For DOS calculations,

we have used the tetrahedron method with Bl€ochl correction

with higher k-point density. The band structures were drawn

along the high symmetry directions in the irreducible part of

the first Brillouin zone.

Results and discussions

Structural phase stability and ground state crystal structureof ZnH2

In order to identify the ground state crystal structure of ZnH2,

we have considered thirty seven potential AB2 types of

structural variants and substituted with Zn at the A site and H

at the B site. The involved structure types for our structural

phase study are SnF2 (C12/c1) [74], BaF2 (Fm3m) [75], BeH2

(Ibam) [76], MgH2 (P42/mnm) [77], BeF2 (P43n) [78], SrH2 (P63/

mmc) [79], BeF2 (P3121) [80], BeF2 (P6222) [81], SrH2 (Pnam) [82],

BaH2 (Pnma) [83], CaH2 (Pnma) [84], BeF2 (R3m) [78], ZnCl2 (P42/

nmc) [85], ZnCl2 (P121/n1) [86], ZnF2 (Pbcn) [87], ZnCl2 (Pna21)

[88], MgF2 (Pnnm) [89], TiH2 (I4/mmm) [90], ZnBr2 (I41/acd) [91],

ZnI2 (I41/acd) [92], ZnCl2 (I42d) [86], d-MgH2 (Pbc21) [93], MgH2

(Pbca) [93], BeCl2 (I43m) [78], CdBr2 (P63/mmc) [94], HgBr2(Cmc21) [95], HgBr2 (P3) [96], MgCl2 (P3m1) [97], ZnBr2 (I41/a)

[91], ZnCl2 (P42/n) [85], TiO2-anatase (I41/amd) [9], MgB2

(P6mmm) [98], TeAg2 (P21/c) [9], ε-BeH2 (P213) [99], g-SnF2(P41212) [100], b-SnF2 (P212121) [100], and b-MgH2 (Pa3) [9].

The structure type specifications found above refer to the

symmetry of the initial guess structures. From the chosen

structural starting points, full geometry optimization have

been carried out using force as well as stress minimization.

The calculated total energy per formula unit (f.u) and the cor-

responding equilibrium volume per f.u of all the 37 different

structures considered are tabulated in supporting information

Table S1. Analyzing the total energy values for the above 37

different structural types, we have found that the minimum

energy structure for the compound ZnH2 is Pna21 (ortho-

rhombic). It may be noted that ZnCl2 also possess the same

crystal structure as that of ZnH2 in the ground state. In order to

have a wide view of the competitive lower energy structures,

we have displayed the optimized energy/f.u versus volume/f.u

curve for 10 structural variants with the lowest energy in Fig. 1.

The calculated total energy as a function of volume has been

fitted to so-called the universal equation of state (UEOS) to

calculate the bulkmodulus (Bo) and its pressure derivative (Bo’).

The equilibrium volume for the ground state structure of ZnH2

(Pna21) was obtained as 38.84 Å3. From the UEOS fitting, the

calculated bulk modulus and its pressure derivative for ZnH2

are 7.408 GPa and 5.681, respectively. The lower bulk modulus

of ZnH2 indicates that it is comparatively soft material.

The calculated total energy versus volume relation in Fig. 1

shows that pressure-induced structural transitions occur in

ZnH2 upon increasing pressures as well as expanded volumes.

So, if ZnH2 in Pna21 phase is exposed to external pressures, it

transforms to P41212 (tetragonal) phase at 0.75 GPa. It may be

noted that MgH2 also posses this tetragonal structure at high

pressure. It is interesting to note from Fig. 1(b) that when we

expand the ZnH2 lattice, it transforms to an orthorhombic

structure with space group P212121. In general, when one

applies pressure, the systems usually transform from lower

symmetry structure to a high symmetry structure and the

present observation of orthothombic-to-tetragonal pressure

induced structural transition in ZnH2 is consistent with the

above viewpoint.

The calculated equilibrium volume, bulk modulus, and

pressure derivative of bulk modulus for ZnH2 in high pressure

tetragonal P41212 phase are 36.90 Å3, 7.057 GPa, and 6.726,

respectively. The bulk modulus and its pressure derivative for

the orthorhombic P212121 phase which is stable in the

extended volume are 7.891 GPa and 5.782, respectively. In

order to identify the transition pressure with an associated

volume jumps, we show a pressure-volume curve for ZnH2 in

Fig. 2. From Fig. 2, we found that the pressure induced phase

transition occurs at 0.75 GPa and the associated volume

change is 3.14%. So, this phase transition can be considered as

a first order phase transition. The transition pressure for the

Fig. 1 e (Color online) (a) Normal and (b) Enlarged view of the calculated unit cell volume versus total energy curves for ZnH2

in its ground state and other closer energy structures. The inset shows the energy versus volume range where

pressure-induced structural phase transitions happening.

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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6 13635

Pna21 to P212121 phase transition occurred at �0.22 GPa with

an associated volume jump of 2.41%.

The optimized equilibrium structural parameters for MgH2

in its ground state and that for ZnH2 in its ground state

structure along with high pressure tetragonal as well as

expanded volume orthorhombic phase for ZnH2 were listed in

Fig. 2 e (Color online) The calculated pressure versus

volume curve for ZnH2.

Table 1. The calculated equilibrium structural parameters for

MgH2 are found to be in good agreement with corresponding

experimental data and that from previous DFT calculations.

The predicted ground state crystal structure of ZnH2 is visu-

alized in Fig. 3(a) alongwith stable phases at high pressure and

the expanded volume in Fig. 3(b) and 3(c), respectively. In the

ground state structure of ZnH2, each unit cell contains four Zn

atoms and eight H atoms where each Zn atom is tetrahedrally

coordinated with H atoms and each H atom is coordinated

with two Zn atoms as shown in Fig. 3(a). At the equilibrium

volume, the calculated average ZneH bond length is 1.674 �A

and the shortest HeH separation in ZnH2 is 2.687�A. In the high

pressure phase as well as the orthorhombic phase that

stabilize at an expanded volume of ZnH2 also has similar

coordinations for both H and Zn atoms (see Fig. 3(b) and 3(c)).

The calculated average ZneH bond length is 1.671 �A and the

shortest HeH bond length is 2.632 �A for the high pressure

phase at the phase transition point i.e at 0.75 GPa. The

calculated average ZneH bond length is 1.675 �A and the

shortest HeH bond length is 2.696 �A for the orthorhombic

phase in the phase transition point.

The ground state crystal structure of MgH2 along with

12.5% (Mg0.875Zn0.125H2), and 62.5% (Mg0.375Zn0.625H2) Zn

substituted MgH2 are plotted in supporting information Figs.

S1(a), S1(b), and S1(c), respectively. Fig. S1(a) represents the

ground state crystal structure of a-MgH2 in P42/mnm (tetrag-

onal) phase and each unit cell contains two Mg and four H

atoms. Each Mg atom is octahedrally coordinated to six H

atoms, whereas each H atom is coordinated to threeMg atoms

as shown in Fig. S1(a). At the equilibrium volume, the calcu-

lated average bond length between Mg and H is 1.942 �A and

minimumHeH bond length is 2.487�A. In 12.5% Zn substituted

Table 1 e The optimized equilibrium structural parameters at the ground state for MgH2 and ZnH2 and the structuralparameters for the high pressure tetragonal P41212 and the expanded volume orthorhombic P212121 phases in theircorresponding structural phase transition point.

Structure type Space group Unit cell(�A) Wyckoff position Volume of unit cell (�A3)

a b c

MgH2 P42/mnm 4.4928 4.4928 3.0037 Mg(2a): 0,0,0 60.63

(4.4982) (4.4982) (3.0075) H(4f):0.304,0.304,0 (0.304,0.304,0) (60.85) [77]

ZnH2 Pna21 4.8692 6.3559 4.7211 Zn(4a):0.059,0.125,0.377 146.11

H(4a): 0.046,0.099,0.024

H(4a): 0.111,0.658,0.972

ZnH2 (at 0.75 GPa) P41212 4.7624 4.7624 6.1654 Zn(4a):0.184,0.184,0 139.83

H(8b): 0.277,0.334,0.232

ZnH2 (at �0.22 GPa) P212121 4.8271 4.8258 7.3368 Zn(4a):0.499,0.248,0.125 170.91

H(4a): 0.749,0.102,0.998

H(4a): 0.648,0.493,0.254

Fig. 3 e (Color online) The crystal structures of ZnH2 in (a) Pna21 (ground state), (b) P41212 (high pressure), and (c) P212121(expanded lattice) phase.

Table 2 e The calculated enthalpy of formation (DHf) performula unit obtained as a function of Zn concentration inMgH2 for the ground state structure and estimatedbandgap (Eg) values of Mg1¡xZnxH2 in P42/mnm andPna21 phases.

Compound Calculated DHf (kJ/mol) Calculated Eg(eV)

P42/mnm Pna2

MgH2 �52.775 3.714 4.992

Mg0.875Zn0.125H2 �36.819 2.720 4.612

Mg0.75Zn0.25H2 �21.656 2.283 4.394

Mg0.625Zn0.375H2 �5.458 1.514 4.078

Mg0.5Zn0.5H2 2.639 0.711 4.060

Mg0.375Zn0.625H2 9.338 1.161 3.881

Mg0.25Zn0.75H2 14.167 0.822 3.810

Mg0.125Zn0.875H2 21.897 1.255 3.720

ZnH2 29.348 1.006 3.557

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 613636

MgH2, each cation is octahedrally surrounded by 6 H atoms

(see Fig. S1(b)) and for 62.5% Zn substituted MgH2, each cation

is surrounded by 4 H atoms as depicted in Fig. S1(c).

Phase stability, phase transition, and phase mixing by Znsubstitution in MgH2

In order to understand the structural phase stability of

Mg1�xZnxH2 systems, we have calculated the enthalpy of for-

mation (DHf) of these systems using the following equation,

DHf

�Mg1�xZnxH2

� ¼ E�Mg1�xZnxH2

�� ð1� xÞEðMgÞ � xEðZnÞ� EðH2Þ

(1)

where E(Mg1�xZnxH2), E(Mg), E(Zn), and E(H2) are the total

energy obtained for the optimized geometry of Mg1�xZnxH2,

hexagonal Mg, hexagonal Zn, and molecular H2, respectively.

The calculated DHf for all these systems in their ground state

structure are listed in Table 2. Fig. 4 represents the calculated

DHf of Mg1�xZnxH2 systems in both P42/mnm and Pna21structures as a function of Zn concentration. This figure

illustrates that one can reduce the stability of MgH2 by

substituting Zn at Mg site since the calculated absolute value

of DHf decrease with increase of Zn concentration in MgH2.

Hence the Zn substituted MgH2 systems are less stable

compared with pure MgH2.

The decreasing trend in stability with Zn substitution in

MgH2 can be understood as follows. In pure MgH2, the pres-

ence of strong ionic bonding betweenMg and Hmake it highly

stable. On the other hand, our bonding analyses discussed

Fig. 5 e The difference in the enthalpy of formation

between P42/mnm and Pna21 structure of Mg1¡xZnxH2 as a

function of Zn concentration.

Fig. 6 e The calculated enthalpy of mixing as a function of

Zn concentration in MgH2.

Fig. 4 e The calculated enthalpy of formation as a function

of Zn concentration in MgH2.

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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6 13637

later (subsection Analysis of chemical bonding in MgH2 by Zn

substitution) show that Zn substitution reduces the ionicity by

introducing covalency into the systemand hence the enthalpy

of formation decrease with the increase of Zn concentration.

From the decreasing trend in structural stability with Zn

substitution in MgH2, one may expect that the dehydrogena-

tion enthalpy of Mg1�xZnxH2 also decreases with increasing

Zn concentration. As a result, one can reduce the decompo-

sition temperature which is one of the desirable properties for

MgH2 to use in hydrogen storage applications. The linear

variation between the enthalpy of formation and Zn concen-

tration implies that these systems obey Vegard's law.We have

calculated the difference between the enthalpy of formation

of P42/mnm and Pna21 structures of Mg1�xZnxH2 as a function

of Zn concentration to understand the phase stability and

phase transition point and found that the structural phase

transition from P42/mnm to Pna21 occurs at 40% Zn substitu-

tion in MgH2 (see Fig. 5).

The enthalpy of mixing (DHm) of Mg1�xZnxH2 has been

estimated using the following equation,

DHm

�Mg1�xZnxH2

� ¼ E�Mg1�xZnxH2

�� ½ð1� xÞEðMgH2Þþ ðxÞEðZnH2Þ� (2)

where E(Mg1�xZnxH2), E(MgH2), and E(ZnH2) are the total en-

ergies for Mg1�xZnxH2, MgH2, and ZnH2 in their optimized

ground state geometry. The DHm of Mg1�xZnxH2 systems as a

function of Zn concentration are shown in Fig 6. The calcu-

latedDHm of endmaterials (MgH2 and ZnH2) is zero since these

are ideal compounds. For the intermediate systems in

P42/mnm phase, the estimated DHm values are positive and

low, which gives hint that single phase of Mg1�xZnxH2 may

form at a reasonable temperature and other thermodynamic

conditions. On the other hand, for the intermediate systems in

Pna21 phase, the calculated DHm are negative. This implies

that these systems are stable and it is experimentally possible

to synthesize them. In our previous study [59], we have re-

ported that the enthalpy of mixing of fluorinated MgH2 is less

positive (below 4 kJ/mol) and hence the single phase of Mg2-H2�xFx may be synthesized experimentally [101]. The present

calculations are valid only at 0 K. In order to account for

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 613638

temperature effects to analyze phase mixing one should

go beyond first principle calculations as done by Pinatel

et al. [102].

The binary phase diagram of MgeZn system show that no

binary intermetallic compounds will form up to 50 atomic

percentage of Zn in Mg for the temperature up to 340 +C [103].

Our calculated enthalpy of formation as a function of Zn

substitution show that the optimum MgeZn composition

useful for H storage application with desirable H desorption

temperature lye within the composition range (i.e.

Mg0.5Zn0.5H2) and hence, onemay expect a robust reversible H

storage system from Zn substitutedMgH2 with desirable other

hydrogen storage properties.

Hydrogen site energy in Zn substituted MgH2

In order to interpret the influences of Zn substitution on the

stability of MgH2, we have calculated the H site energy

(H desorption enthalpy) [104e106]. The H site energy is the

energy needed to remove anH atom from its host lattice and is

calculated [107] by the following relation,

EdðHÞ ¼ EðAnH2n�1Þ þ�12

�EðH2Þ � EðAnH2nÞ (3)

The calculated H site energy versus composition for

Mg1�xZnxH2 in their corresponding ground state structure is

plotted in Fig. 7 where H desorption enthalpy is reduced from

115.69 kJ/mol (1.20 eV) to 87.29 kJ/mol (0.91 eV) when we

completely replace Mg with Zn in MgH2. The calculated H site

energy of MgH2 is relatively high which point out that the H

atoms are strongly bound to theMg. This is the reason for high

H desorption temperature since the desorption temperature

mainly involves the breaking of MgeH bonds. Besides, one can

expect poor reaction kinetics because the diffusion of

hydrogen atom through this highly stable hydride is expected

to be slow. Our calculated [59] H site energy forMgH2 is in good

agreement with corresponding value reported by Vajeeston

et al. [108] The calculated H site energy as a function of Zn

substitution in MgH2 varies in zig-zag manner as shown in

Fig. 7. The overall observation is that the H site energy de-

creases with respect to that of MgH2 by Zn substitution except

for the compositions Mg0.375Zn0.625H2 and Mg0.125Zn0.875H2.

Fig. 7 e The calculated H site energy as a function of Zn

concentration in MgH2.

Hence, one can expect that the Zn substitution reduces the

hydrogen desorption temperature of MgH2, thereby hydrogen

sorption reaction could be improved for Zn substituted MgH2.

For pristine ZnH2, the H site energy is very low (87.29 kJ/mol or

0.91 eV) as compared to that of MgH2 due to the meta-stable

nature of ZnH2 and hence, one could expect lower decompo-

sition temperature in ZnH2 over MgH2.

Electronic structure of Mg1�xZnxH2

The computed band structures for MgH2, 50% Zn substituted

MgH2, and ZnH2 are shown in Fig. 8(a)e8(c), respectively. The

band structure shows that MgH2 is an indirect bandgap ma-

terial since the valence band maxima (VBM) and the conduc-

tion band minima (CBM) does not meet at the same k-point in

the Brillouin zone. The calculated bandgap of MgH2 is 3.69 eV

and this is consistent with previous studies [59,109]. However,

this value is deviated from experimental optical measure-

ments [110] for MgH2 (5.6 ± 0.1 eV) since the bandgap calcu-

lated from GGA/LDA is usually underestimate. To predict the

accurate bandgap one should use either hybrid functional or

GW calculations but this is out of the scope of the present

study.

For 50% Zn substituted MgH2 (see Fig. 8(b)), the calculated

bandgap value is 4.06 eV. In this system, the VBM and CBM are

located at the same G-point and hence, it is a direct bandgap

material. Moreover, Zn substitution brings additional states to

the valence band (VB). For ZnH2, the calculated band structure

(see Fig. 8(c)), demonstrates a direct bandgap (3.56 eV) feature

with both VBM and CBM located at G-point. Our calculations

suggest that the Mg1�xZnxH2 systems can be classified as an

insulator. Moreover, Zn substitution inMgH2 brings indirect to

direct transition and hence this may improve the optical ab-

sorption coefficient of MgH2 by Zn substitution.

The total DOS for Mg1�xZnxH2 systems in their ground state

crystal structures are shown in Fig. 9. The calculated bandgap

values of Mg1�xZnxH2 listed in Table 2. The non-linear varia-

tion of the bandgap of MgH2 as a function of Zn concentration

in P42/mnm phase is mainly due to the change in unit cell

volume aswell as competition between ionicity and covalency

by Zn substitution in MgH2. It is evident from Fig. 9 that the

bandgap of pure ZnH2 is smaller compared with that of pure

MgH2. The smaller bandgap value of ZnH2 is associated with

weaker bond strength (as evident from H site energy calcula-

tions). Moreover, there is a gradual decrease in the band gap

value as a function of Zn concentration until 37.5% Zn sub-

stitution. Consistent with our results, previous theoretical

studies reported that 6% Zn substituted MgH2 (Mg15ZnH32)

[67,111] and 20% Zn substituted MgH2 (Mg8Zn2H20) [63] have

the band gap value of around 3.1 eV and 2.5 eV, respectively.

Analysis of chemical bonding in MgH2 by Zn substitution

Partial density of states, charge density, and electronlocalization function analysesTo characterize the bonding interaction between the constit-

uents of Mg1�xZnxH2 systems, we have plotted partial DOS,

charge density, and electron localization function (ELF)

[112e114]. In the partial DOS ofMgH2 (refer Fig. 10(a)), it is to be

noted that the VB is mainly originated from H-s state with a

Fig. 8 e (Color online) The calculated band structures of (a) MgH2, (b) Mg0.5Zn0.5H2, and (c) ZnH2. The Fermi level is set to zero.

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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6 13639

small contribution from Mg-s and Mg-p states since there is a

charge transfer from the Mg sites to H sites. The small Mg-s,p

electronic states present in the valence band are energetically

degenerate with the H-s states in the entire valence band

indicating that there is noticeable covalent interaction present

in-betweenMg and H. Hence, one can conclude that MgH2 has

a strong ionic bonding with small covalent character.

For Mg0.5Zn0.5H2 system, the partial DOS is plotted in

Fig. 10(b). From the VB, one can notice that the Mg-s states are

smaller than that of neutral Mg and at the same time H-s

states at the VB have higher value indicating that Mg donated

Fig. 9 e (Color online) The calculated total DOS of MgH2 as a f

its valence electrons to H. On the other hand, the Zn-s states in

the VB is higher than Mg-s states indicating that Mg donated

most of its s electrons to H. From the partial DOS of

Mg0.5Zn0.5H2 and ZnH2 shown in Fig. 10(b) and 10(c), respec-

tively, one can notice that the Zn(s)�H(s) bonding hybrids are

formed around �3.5 and �4.5 eV and also Zn-s and H-s states

are energetically degenerate in the entire valence band

reflecting the presence of substantial covalent type of inter-

action between Zn andH. The charge transfer fromMg/Zn-s to

H states along with charge sharing between Zn-s states and H

are the dominant bonding interaction in Zn substituted MgH2

unction of Zn substitution. The Fermi level is set to zero.

Fig. 10 e (Color online) The calculated partial DOS of (a)

MgH2, (b) Mg0.5Zn0.5H2, and (c) ZnH2. The Fermi level is set

to zero.

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 613640

systems. The overall observation is that Mg1�xZnxH2 systems

are governed by mixed iono-covalent bond and the covalent

contribution increases with the increase of Zn concentration.

The charge density and ELF of MgH2 are plotted in Fig. 11(a)

and 11(d), respectively. Due to charge transfer from Mg to H

site in MgH2, the highest charge density resides in the im-

mediate vicinity of the nuclei at the H site. Almost spherical

charge distribution at the H site reconfirms that the interac-

tion between Mg and H is dominantly ionic. However, the

finite non-spherical charges present in-between Mg and H as

well as in-between H atoms indicate the presence of notice-

able covalent bonding between the constituents. It is known

that the region with an ELF value of 1.00, 0.50, and 0.00 rep-

resents fully localized electrons, fully delocalized electrons,

and very low charge density, respectively. The calculated ELF

plot for MgH2 (see Fig. 11(d)) shows that the electrons have a

paired character with predominant maximum ELF of about

0.9 at theH sites and non-spherical ELF distribution betweenH

atoms indicate that there is finite covalent bonding between

the H atoms. Moreover, there is a non-spherical ELF distrib-

uted between Mg and H indicating partial covalency. The

overall conclusions from charge density and ELF analyses for

MgH2 is that there is predominantly ionic bonding present

between Mg and H with small directional character present

between Mg and H as well as between H atoms.

In order to understand the role of Zn substitution on vari-

ation in the bonding behavior of MgH2, we have plotted charge

density and ELF plot for Mg0.5Zn0.5H2 in Fig. 11(b) and 11(e),

respectively. The nature of charge distribution seen in

Fig. 11(b) appears to be typical for compounds with iono-

covalent bonding. The charge density analysis shows that

the H closer to Mg has more spherically distributed charge

than that closer to Zn. Further, there is negligible charge

density present between Mg and H and in contrast, there is

substantial charge accumulated in between Zn and H. The

important observation is that the Zn substitution introduces

covalency which weakens the strong ionic bonding present

between Mg and H in the undoped MgH2. ELF of Mg0.5Zn0.5H2

system is shown in Fig. 11(e) also clearly indicate that there is

negligible amount of paired electron present in-between Mg

and H and there is a large amount of paired electrons present

in-between Zn and H. Further, the non-spherical distribution

of ELF in-between H atoms and in-between H and Zn along

with higher non-spherical character of ELF than that in MgH2

substantiate that Zn substitution enhances the covalency.

From the partial DOS, charge density, and ELF plot of

Mg0.5Zn0.5H2 system, it was indeed confirmed that the Zn

substitution reduced the ionic bonding interaction between

Mg and H and enhance the covalency in the system.

In contrast to MgH2, in the case of ZnH2, the calculated

charge density and ELF showed in Fig. 11(c) and 11(f) clearly

indicate that Zn is bondedwith H in a directionalmanner. The

non-spherical distribution of charge density and ELF along

with the large value of charge and ELF value in-between Zn

and H as well as in-between H indicates that there is a strong

covalent interaction between these atoms. So, when we

compared the bonding interaction of MgH2 with that of ZnH2,

we conclude that ZnH2 has more covalency.

Bader topological analysisTo quantify the amount of electrons present at the constitu-

ents of the compounds, we have made Bader topological

analysis. In the Bader charge analysis, each atom in a com-

pound is surrounded by a surface (called Bader regions) that

run throughminima of the charge density and the total charge

of an atom is determined by integration within the Bader re-

gion [115e117]. The calculated Bader effective charge (BC) for

the constituents in Mg1�xZnxH2 are listed in Table 3. The

positive value of BC represents electron depletion while the

negative value represents electron accumulation. The esti-

mated BC of the constituents in MgH2 shows that Mg donates

around 1.59 electrons to the H sites which reflects ionic

character. But the smaller value of the BC at the H sites (�0.79)

over the pure ionic value (�1) clearly indicates that MgH2 do

not reach a purely ionic bond with H in �1 state. Our calcu-

lated BC values for the constituents in MgH2 is in good

agreement with the corresponding value calculated by

Vajeeston et al. [118].

In the case of Mg0.5Zn0.5H2, Mg and Zn donate 1.56 and

0.69 electrons to the H sites respectively which is much

smaller than the value obtained from the pure ionic picture.

Moreover, H atom neighboring to Mg and Zn receives 0.54

electrons whereas that neighboring to Mg atoms alone re-

ceives 0.78 electrons (see Table 3). This is mainly due to

disproportionate bond induced by Zn substitution in MgH2.

Our analyses show that for 50% Zn substituted MgH2, the H

atoms receives an average of around 0.23 electrons less than

that in pure MgH2. These results reflect that the Zn substi-

tution weakens the ionic bond between the Mg and H. In

contrast to the MgH2 system, the calculated BC for Zn and H

Fig. 11 e (Color online) The charge density and ELF plot for (a) and (d) MgH2, (b) and (e) Mg0.5Zn0.5H2, (c) and (f) ZnH2. (Note:

Planes are chosen such a way that the MgeH, HeH, and ZneH bonds are clearly seen).

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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6 13641

atoms in ZnH2 indicate that the ionicity is drastically

reduced in ZnH2 over MgH2. The conclusions arrived from

the BC analysis are consistent with the charge density, ELF,

and partial DOS analyses.

Born effective charge analysisBorn effective charge (BEC) analysis is another tool to quantify

charges in each atomic sites to evaluate the bonding charac-

teristics and were calculated using the Berry-phase approach

based on the modern theory of polarization which is imple-

mented in the VASP code. We have used the King-Smith and

Vanderbilt [119,120] method to calculate the polarizations of

perturbed cells. The Born effective charge tensors Z* of the

ions of Mg1�xZnxH2 systems have been calculated and listed in

Table 4. The diagonal components of the BEC tensors will

carry information about howmuch charge is transferred from

one site to other sites. For an ionic compound, the off-diagonal

components of the BEC tensorwill be zero or very small. In the

case of MgH2, the diagonal components are almost equal

Table 3 e Calculated Bader effective charges (BC) for theconstituents of Mg1¡xZnxH2 systems.

Compound atom BC (e)

MgH2 Mg 1.5869

H �0.7934

Mg0.5Zn0.5H2 Mg 1.5613

Zn 0.6955

H3 (neighboring to Mg) �0.7749

H8 (neighboring to Mg and Zn) �0.5382

ZnH2 Zn 0.7585

H �0.3792

(Zxx ¼ Zyy z Zzz) at the Mg as well as H sites. For both atoms,

most of the off-diagonal components are turn out to be zero

except Zyx components indicating strong ionic bonding. The

overall conclusion is that the MgeH bond has a large ionic

character with a small woof of covalency.

For Mg0.5Zn0.5H2, the diagonal components of the effective

charges at the Zn, Mg, and H sites are not equal (Zxx s Zyy s

Zzz) and the off-diagonal components have finite values. This

clearly reflects that the Zn atom brings covalency when it is

substituted in the MgH2 system. Further, the H neighbored by

Mg has the BEC value of �0.82 and that neighboring to Mg and

Zn has a value of �0.57 clearly showing that the introduction

of Zn brings a disproportionate bond. As like Mg0.5Zn0.5H2, the

pure ZnH2 has a covalent bond since the diagonal components

of the effective charges at Zn and H sites are not equal and the

off-diagonal components have noticeably large values. More-

over, the diagonal components of BC at H site is more than

nominal ionic value due to the fact that the dynamic charges

arising from covalency also added to the static charge. These

results are consistent with the other chemical bonding anal-

ysis done above.

Crystal orbital Hamiltonian population analysisIn order to get more insight into the chemical bonding, we

have also calculated the crystal orbital Hamiltonian popula-

tion (COHP). COHP [121e123] is the DOS weighted by the cor-

responding Hamiltonian matrix elements and this identifies

the location of bonding, antibonding, and nonbonding states

of the bonding pair and alsomeasures the strength of bonding

(magnitude of bonding) interaction between the constituents.

The negative COHP designates the bonding character whereas

the positive COHP denote the antibonding character. The

Table 4 e The calculated diagonal and off-diagonal components of Born-effective-charge-tensor elements (Z*) for theconstituents of Mg1¡xZnxH2 systems.

Compound atom Zxx Zyy Zzz Zxy Zyz Zzx Zxz Zzy Zyx

MgH2 Mg 1.851 1.851 1.942 0.120 0 0 0 0 0.120

H �0.902 �0.902 �0.948 �0.201 0 0 0 0 �0.201

Mg0.5Zn0.5H2 Zn 1.052 1.462 1.138 �0.216 0.106 �0.130 0.083 �0.050 0.213

Mg 1.705 1.692 1.835 0.112 0.066 0.138 �0.177 0.033 �0.069

H1 �0.577 �1.018 �0.415 �0.229 �0.114 �0.075 �0.122 �0.098 �0.239

H3 �0.854 �1.045 �0.658 �0.134 0.032 �0.005 0.107 0.027 �0.125

H5 �0.787 �0.556 �0.839 0.059 �0.039 0.251 0.302 0.004 0.025

H8 �0.563 �0.521 �1.061 �0.036 �0.040 �0.188 �0.189 �0.019 0.005

ZnH2 Zn 1.503 1.335 1.483 �0.281 0.304 �0.130 0.010 �0.263 0.166

H1 �0.466 �0.679 �1.009 ..0.030 �0.302 �0.090 �0.077 �0.270 �0.149

H2 �1.042 �0.649 �0.479 �0.301 �0.002 �0.013 �0.016 �0.000 �0.325

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 613642

calculated bond strength of the bonding pairs obtained from

integrated COHP (iCOHP) up to Fermi level for Mg1�xZnxH2

systems are listed in Table 5. Fig. 12(a) shows the calculated

COHP of bonding pairs in MgH2. If we analyze the COHP of

MgeH bonding pair, all the bonding states are filled and the

antibonding states are empty (see Fig. 12(a)) so one could

expect high stability. Apart from our enthalpy of formation

analysis, the high stability of MgH2 was already found through

experimental [21] as well as other theoretical studies [26]. Due

to the filling of maximum bonding states in MgeH pair, one

can expect strong bond between Mg and H. Consistent with

this viewpoint, the calculated iCOHP value for MgeH bonding

pair is relatively high. So if one wants to reduce the decom-

position temperature of MgH2, one should weaken the MgeH

bond. Moreover, the bonding interaction between H atoms are

considerably weak since both of the bonding and antibonding

states are present within the VB region of COHP and hence the

iCOHP value is very small.

From the analyses of the calculated COHP for Mg0.5Zn0.5H2

(see Fig. 12(b)), we found that the MgeH bonding pair has

bonding states located in the whole valence band range and

the calculated average iCOHP value for MgeH pair is �0.63 eV.

As the substitution of Zn introduces disproportionate bonds,

the detailed analysis of bond strength for MgeH bonds from

the calculated iCOHP values in Table 5 vary between �0.49 to

Table 5 e The calculated bond strength between thebonding pairs in Mg1¡xZnxH2 systems from integratedcrystal orbital Hamiltonian population.

Compound Interaction Bond strength (eV)

MgH2 MgeH �0.63

HeH �0.07

Mg0.5Zn0.5H2 MgeH �0.63 (average)

MgeH4 �0.69

MgeH5 �0.49

MgeH8 �0.71

ZneH �0.52 (average)

ZneH2 �0.36

ZneH5 �0.66

ZneH8 �0.56

HeH �0.09

ZnH2 ZneH �0.40

HeH �0.02

�0.71 eV. Because of this disproportionate bond formation,

the H site energy calculated for H neighboring to Mg atoms

alone has a value of 108.85 kJ/mol and that neighboring to Zn

and Mg has a value varying from 91.14 to 98.07 kJ/mol. The

hydrogen closer to Zn is weakly bonded with neighboring Mg

and that neighboring to Mg atoms alone is strongly bonded to

Mg as evident from calculated iCOHP values. So, the present

study suggests that the Zn substitution weaken some of the

MgeH bonds in Mg0.5Zn0.5H2 and hence one can expect that H

will be removed in relatively lower temperature than that in

Fig. 12 e (Color online) The calculated COHP between

constituents in (a) MgH2, (b) Mg0.5Zn0.5H2, and (c) ZnH2.

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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6 13643

pure MgH2 system. If we analyze the COHP of ZneH pair in

Mg0.5Zn0.5H2, we found that both bonding and antibonding

states are present within the valence band and hence the

calculated average iCOHP value for ZneHpair is only�0.56 eV.

It is well known that the filling of antibonding states lowers

the stability of the system. The observation of filling of anti-

bonding states in ZneHpair could explainwhy the enthalpy of

formation for Mg0.5Zn0.5H2 is lower than that of MgH2.

In the case of ZnH2, the COHP for the ZneH pair is shown

in Fig. 12(c). It may be noted that for the ZneH bonding pairs,

the antibonding states are dominated in the top of the

valence band. The band filling of the bonding analysis shows

that in order to achieve the maximum stability, all the

bonding states should be filled and the antibonding states

should be empty. However, the filling of antibonding states in

the COHP of ZneHpair could explainwhy ZnH2 ismeta-stable

in nature.

Conclusions

Though ZnH2 is synthesized experimentally long back, due

to the meta-stable nature of this compound its ground state

crystal structure is unknown till date. Using the state-of-

the art density functional calculations we have predicted

the ground state structure and the unit cell parameters of

ZnH2 by considering 37 potential trial structures. Also, in

order to reduce the strong ionic bonding between Mg and H,

we have substituted Zn at the Mg sites in MgH2 and

executed a systematic study of the phase stability, phase

transition, phase mixing, electronic structure, and chemical

bonding of Mg1�xZnxH2 systems and made the following

conclusions.

� Using the total energy minimization, we have predicted

that the ground state crystal structures of ZnH2 is ortho-

rhombic with space group Pna21 and the calculated equi-

librium structural parameters are listed. The calculated

enthalpy of formation for ZnH2 is a small positive value

and this could explain why this material is meta-stable.

� The calculated enthalpy of formation and H site energy of

Mg1�xZnxH2 systems affirm that MgH2 is highly stable, and

Zn substituted MgH2 systems are less stable than MgH2.

� From the calculated total energy as a function of Zn

substitution in MgH2, we have predicted a composition

induced structural phase transition from tetragonal P42/

mnm to orthorhombic Pna21 structure occurred at 40% Zn

substitution in MgH2.

� From the calculated enthalpy of mixing, we concluded that

Mg1�xZnxH2 systems can form single phase and they can be

experimentally synthesized using appropriate thermody-

namical conditions.

� The calculated H site energy of Mg1�xZnxH2 systems in-

dicates that the H neighboring to Zn can be removed more

easily than that neighboring to Mg atoms alone.

� The electronic structure studies reveal that Mg1�xZnxH2

systems are insulators. The non-linear variation in the

bandgap values as a function of Zn substitution is mainly

due to the competition between ionic and covalent bond in

these systems.

� The chemical bonding analyses from partial DOS, charge

density, ELF, BC, BEC, and COHP concludes that Mg1�xZnx-

H2 systems have iono-covalent interaction between the

constituents.

� From the detailed chemical bonding analysis, we have

found that Zn substitution induced disproportionate bonds

and this could reduce the decomposition temperature.

Overall, the present results suggest that one can reduce the

stability ofMgH2 by Zn substitution. From the calculatedH site

energy and the identification of the formation of dispropor-

tionate bonds by Zn substitution in MgH2, we have indicated

that H can be removed easily in Zn substituted MgH2. Hence,

the Mg1�xZnxH2 systems can be considered as a promising H

storage materials.

Acknowledgement

We gratefully acknowledge the Department of Science and

Technology, Ministry of Science and Technology, India for the

financial support via grant no. SR/NM/NS-1123/2013 to carry out

this research and Research council of Norway for computing

time on the Norwegian supercomputer facilities (Project No:

NN2875K). R.Varunaa wishes to thank Dr. A. Krishnamoorthy

andMr.M. R. AshwinKishore for their valuable discussions and

critical reading of the manuscript.

Appendix A. Supplementary data

Supplementary data to this article can be found online at

https://doi.org/10.1016/j.ijhydene.2019.04.016.

r e f e r e n c e s

[1] Schlapbach L, Zuttel A. Hydrogen-storage materials formobile applications. Nature 2001;414(6861):353e8.

[2] Veziro�glu TN, S‚ ahi S. 21st century's energy: hydrogenenergy system. Energy Convers Manag 2008;49(7):1820e31.

[3] Balat M. Potential importance of hydrogen as a futuresolution to environmental and transportation problems. IntJ Hydrogen Energy 2008;33(15):4013e29.

[4] Doll C, Wietschel M. Externalities of the transport sectorand the role of hydrogen in a sustainable transport vision.Energy Policy 2008;36(11):4069e78.

[5] Kler AM, Tyurina EA, Potanina YM, Mednikov AS.Estimation of efficiency of using hydrogen and aluminumas environmentally-friendly energy carriers. Int J HydrogenEnergy 2015;40(43):14775e83.

[6] Gielen D, Boshell F, Saygin D. Climate and energy challengesfor materials science. Nat Mater 2016;15(2):117e20.

[7] Nowotny J, Hoshino T, Dodson J, Atanacio AJ, Ionescu M,Peterson V, Prince KE, Yamawaki M, Bak T, SigmundW, et al.Towards sustainable energy. generation of hydrogen fuelusing nuclear energy. Int J Hydrogen Energy 2016;41:12812.

[8] Yu R, Lam PK. Electronic and structural properties of MgH2.Phys Rev B 1988;37(15):8730.

[9] Vajeeston P, Ravindran P, Kjekshus A, Fjellvag H. Pressure-induced structural transitions in MgH2. Phys Rev Lett2002;89(17):175506.

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 613644

[10] Isidorsson J, Giebels I, Arwin H, Griessen R. Opticalproperties of MgH2 measured in situ by ellipsometry andspectrophotometry. Phys Rev B 2003;68(11):115112.

[11] Ohba N, Miwa K, Noritake T, Fukumoto A. First-principlesstudy on thermal vibration effects of MgH2. Phys Rev B2004;70(3). 035102.

[12] Vajeeston P, Ravindran P, Vidya R, Fjellvag H, Kjekshus A.Design of potential hydrogen-storage materials using first-principle density-functional calculations. Cryst Growth Des2004;4(3):471e7.

[13] Lasave J, Dominguez F, Koval S, Stachiotti M, Migoni R.Shell-model description of lattice dynamical properties ofMgH2. J Phys: Condens Matter 2005;17(44):7133.

[14] Vajeeston P, Ravindran P, Kjekshus A, Fjellvag H.Theoretical modeling of hydrogen storage materials:prediction of structure, chemical bond character, andhigh-pressure behavior. J Alloy Comp 2005;404:377e83.

[15] Vajeeston P, Ravindran P, Hauback B, Fjellvag H,Kjekshus A, Furuseth S, Hanfland M. Structural stability andpressure-induced phase transitions in MgH2. Phys Rev B2006;73(22):224102.

[16] Bouhadda Y, Rabehi A, Bezzari-Tahar-Chaouche S. First-principle calculation of MgH2 and LiH for hydrogen storage.Revue des Energies Renouvelables 2007;10(4):545e50.

[17] Pozzo M, Alfe D. Structural properties and enthalpy offormation of magnesium hydride from quantum MonteCarlo calculations. Phys Rev B 2008;77(10):104103.

[18] Park MS, Janotti A, Van de Walle CG. Formation andmigration of charged native point defects in MgH2: first-principles calculations. Phys Rev B 2009;80(6). 064102.

[19] Grau-Crespo R, Smith K, Fisher T, De Leeuw N,Waghmare U. Thermodynamics of hydrogen vacancies inMgH2 from first-principles calculations and grand-canonical statistical mechanics. Phys Rev B2009;80(17):174117.

[20] Vajeeston P, Ravindran P, Fjellvag H. The search for novelhydrogen storage materials: a theoretical approach. Int JNucl Hydrog Prod Appl 2009;2(2):137e47.

[21] Beattie SD, Setthanan U, McGrady GS. Thermal desorptionof hydrogen from magnesium hydride (MgH2): an in situmicroscopy study by environmental sem and tem. Int JHydrogen Energy 2011;36(10):6014e21.

[22] Paik B, Walton A, Mann V, Book D, Jones I, Harris I. Electronenergy-loss spectroscopy study of MgH2 in the plasmonenergy range. Appl Phys Lett 2012;100(19):193902.

[23] Vajeeston P, Sartori S, Ravindran P, Knudsen K, Hauback B,Fjellvag H. MgH2 in carbon scaffolds: a combinedexperimental and theoretical investigation. J Phys Chem C2012;116(40):21139e47.

[24] Kuzovnikov M, Efimchenko V, Filatov E, Maksimov A,Tartakovskii I, Ramirez-Cuesta A. Raman scattering studyof a-MgH2 and g-MgH2. Solid State Commun2013;154:77e80.

[25] Zhang J, Zhou Y, Ma Z, Sun L, Peng P. Strain effect onstructural and dehydrogenation properties of MgH2 hydridefrom first-principles calculations. Int J Hydrogen Energy2013;38(9):3661e9.

[26] Reshak A. MgH2 and LiH metal hydrides crystals as novelhydrogen storage material: electronic structure and opticalproperties. Int J Hydrogen Energy 2013;38(27):11946e54.

[27] Abdellatief M, Campostrini R, Leoni M, Scardi P. Effects ofSnO2 on hydrogen desorption of MgH2. Int J HydrogenEnergy 2013;38(11):4664e9.

[28] Lakhal M, Bhihi M, Labrim H, Benyoussef A, Naji S, Belhaj A,Khalil B, Abdellaoui M, Mounkachi O, Loulidi M, et al.Kinetic Monte Carlo and density functional study ofhydrogen diffusion in magnesium hydride MgH2. Int JHydrogen Energy 2013;38(20):8350e6.

[29] Kurko S, Milanovi�c I, Novakovi�c JG, Ivanovi�c N,Novakovi�c N. Investigation of surface and near-surfaceeffects on hydrogen desorption kinetics of Mg. Int JHydrogen Energy 2014;39(2):862e7.

[30] Grochala W, Edwards PP. Thermal decomposition of thenon-interstitial hydrides for the storage and production ofhydrogen. Chem Rev 2004;104(3):1283e316.

[31] Lakhal M, Bhihi M, Benyoussef A, El Kenz A, Loulidi M,Naji S. The hydrogen ab/desorption kinetic properties ofdoped magnesium hydride MgH2 systems by first principlescalculations and kinetic Monte Carlo simulations. Int JHydrogen Energy 2015;40(18):6137e44.

[32] El Khatabi M, Bhihi M, Naji S, Labrim H, Benyoussef A, ElKenz A, Loulidi M. Study of doping effects with 3d and 4d-transition metals on the hydrogen storage properties ofMgH2. Int J Hydrogen Energy 2016;41(8):4712e8.

[33] Kumar S, Jain A, Miyaoka H, Ichikawa T, Kojima Y. Catalyticeffect of bis (cyclopentadienyl) nickel II on the improvementof the hydrogenation-dehydrogenation of Mg-MgH2 system.Int J Hydrogen Energy 2017;42(27):17178e83.

[34] Kumar S, Tiwari GP. Thermodynamics and kinetics ofMgH2-nfTa2O5 composite for reversible hydrogen storageapplication. J Mater Sci 2017;52(12):6962e8.

[35] Kumar S, Kojima Y, Kain V. Nano-engineered Mg-MgH2

system for solar thermal energy storage. Sol Energy2017;150:532e7.

[36] Kumar S, Singh A, Tiwari GP, Kojima Y, Kain V.Thermodynamics and kinetics of nano-engineered Mg-MgH2 system for reversible hydrogen storage application.Thermochim Acta 2017;652:103e8.

[37] Kumar S, Singh A, Kojima Y, Dey GK. Tailoring thethermodynamics and kinetics of Mg-Li alloy for a MgH2-based anode for lithium-ion batteries. Energy Technol2017;5(9):1546e51.

[38] M. Abdellaoui, M. Lakhal, H. Benzidi, O. Mounkachi, A.Benyoussef, A. El Kenz, M. Loulidi, The hydrogen storageproperties of Mg-intermetallic-hydrides by ab initiocalculations and kinetic Monte Carlo simulations, Int JHydrogen Energy

[39] Finholt A, Bond Jr A, Schlesinger H. Lithium aluminumhydride, aluminum hydride and lithium gallium hydride,and some of their applications in organic and inorganicchemistry. J Am Chem Soc 1947;69(5):1199e203.

[40] Barbaras GD, Dillard C, Finholt A, Wartik T, Wilzbach K,Schlesinger H. The preparation of the hydrides of zinc,cadmium, beryllium, magnesium and lithium by the use oflithium aluminum hydride. J Am Chem Soc1951;73(10):4585e90.

[41] Watkins JJ, Ashby E. Reaction of alkali metal hydrides withzinc halides in tetrahydrofuran. A convenient andeconomical preparation of zinc hydride. Inorg Chem1974;13(10):2350e4.

[42] Simons G, Talaty ER. Fsgo model for core d electrons:optimized structures for third row hydrides. J Chem Phys1977;66(6):2457e61.

[43] Pyykk€o P. Diracefock one-centre calculations. Part7.divalent systems MHþ and MH2 (M¼ Be, Mg, Ca, Sr, Ba, Ra,Zn, Cd, Hg, Yb and No). J Chem Soc, Faraday Trans 1979;275:1256e76.

[44] Tyrrell J, Youakim A. Equilibrium geometries and electronicstructures of transition metal dihydrides. A comparison ofthe ab initio effective core potential and all-electronmethods. J Phys Chem 1980;84(26):3568e72.

[45] Platts JA. Theoretical electron densities in transition metaldihydrides. J Mol Struct: THEOCHEM 2001;545(1e3):111e8.

[46] De Koning A, Boersma J, Van der Kerk G. Reactions of zinchydride and magnesium hydride with pyridine; synthesisand characterization of 1, 4-dihydro-1-pyridylzinc and-

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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 6 13645

magnesium complexes. J Organomet Chem1980;186(2):159e72.

[47] Breckenridge W, Wang J-H. Initial internal energydistributions of ZnH (ZnD) produced in the reaction of Zn(4s4p3P1) with H2, D2, and HD. Chem Phys Lett1986;123(1e2):17e22.

[48] Breckenridge W, Wang J-H. Dynamics of the reactions of Zn(4s4p3P1) with H2, HD, and D2: rotational and vibrationalquantum-state distributions of ZnH (ZnD) products. J ChemPhys 1987;87(5):2630e7.

[49] Breckenridge W. , Activation of H-H, Si-H, and C-H bonds bynsnp excited states of metal atoms. J Phys Chem1996;100(36):14840e55.

[50] Greene TM, Brown W, Andrews L, Downs AJ, Chertihin GV,Runeberg N, Pyykko P. Matrix infrared spectroscopic and abinitio studies of ZnH2, CdH2, and related metal hydridespecies. J Phys Chem 1995;99(20):7925e34.

[51] Wang X, Andrews L. Infrared spectra of Zn and Cd hydridemolecules and solids. J Phys Chem A 2004;108(50):11006e13.

[52] Shayesteh A, Appadoo DR, Gordon IE, Bernath PF. Vibration-rotation emission spectra of gaseous ZnH2 and ZnD2. J AmChem Soc 2004;126(44):14356e7.

[53] Shayesteh A, Gordon IE, Appadoo DR, Bernath PF. Infraredemission spectra and equilibrium bond lengths of gaseousZnH2 and ZnD2. Phys Chem Chem Phys 2005;7(17):3132e42.

[54] Shayesteh A, Yu S, Bernath PF. Gaseous HgH2, CdH2, andZnH2,. Chem Eur J 2005;11(16):4709e12.

[55] Huang ZG, Yu L, Dai YM. An ab initio potential energysurface and vibrational energy levels of ZnH2. J ComputChem 2010;31(5):986e93.

[56] Panagopoulos C, Georgiou E, Chaliampalias D. Cathodichydrogen charging of zinc. Corros Sci 2014;79:16e20.

[57] Shelyapina M, Fruchart D, Wolfers P. Electronic structureand stability of new FCC magnesium hydrides Mg7MH16 andMg6MH6 (M¼ Ti, V, Nb): an ab initio study. Int J HydrogenEnergy 2010;35(5):2025e32.

[58] Abdellaoui M, Lakhal M, Bhihi M, El Khatabi M,Benyoussef A, El Kenz A, Loulidi M. First principle study ofhydrogen storage in doubly substituted Mg based hydridesMg5MH12 (M¼ B, Li) and Mg4BLiH12. Int J Hydrogen Energy2016;41(45):20908e13.

[59] Varunaa R, Ravindran P. Phase stability, phase mixing, andphase separation in fluorinated alkaline earth hydrides. JPhys Chem C 2017;121(40):21806e20.

[60] Chen D, Wang Y, Chen L, Liu S, Ma C, Wang L. Alloyingeffects of transition metals on chemical bonding inmagnesium hydride MgH2. Acta Mater 2004;52(2):521e8.

[61] Liang G. Synthesis and hydrogen storage properties of Mg-based alloys. J Alloy Comp 2004;370(1e2):123e8.

[62] Vegge T, Hedegaard-Jensen LS, Bonde J, Munter TR,Nørskov JK. Trends in hydride formation energies formagnesium-3d transition metal alloys. J Alloy Comp2005;386(1e2):1e7.

[63] Zhou D-W, Ping P, Liu J-S, Lu C, Hu Y-J. First-principles studyon structural stability of 3d transition metal alloyingmagnesium hydride. Trans Nonferrous Metals Soc China2006;16(1):23e32.

[64] Tsuda M, Dino WA, Kasai H, Nakanishi H, Aikawa H.MgeH dissociation of magnesium hydride MgH2 catalyzedby 3d transition metals. Thin Solid Films2006;509(1e2):157e9.

[65] Milanese C, Girella A, Bruni G, Berbenni V, Cofrancesco P,Marini A, Villa M, Matteazzi P. Hydrogen storage inmagnesiumemetal mixtures: reversibility, kinetic aspectsand phase analysis. J Alloy Comp 2008;465(1e2):396e405.

[66] Polanski M, Bystrzycki J. Comparative studies of theinfluence of different nano-sized metal oxides on the

hydrogen sorption properties of magnesium hydride. J AlloyComp 2009;486(1e2):697e701.

[67] Zeng X, Cheng L, Zou J, Ding W, Tian H, Buckley C. Influenceof 3d transition metals on the stability and electronicstructure of MgH2. J Appl Phys 2012;111(9). 093720.

[68] Bhihi M, El Khatabi M, Lakhal M, Naji S, Labrim H,Benyoussef A, El Kenz A, Loulidi M. First principle study ofhydrogen storage in doubly substituted Mg based hydrides.Int J Hydrogen Energy 2015;40(26):8356e61.

[69] Hohenberg P, Kohn W. Inhomogeneous electron gas. PhysRev 1964;136(3B):B864.

[70] Kresse G, Furthmuller J. Efficiency of ab-initio total energycalculations for metals and semiconductors using a plane-wave basis set. Comput Mater Sci 1996;6(1):15e50.

[71] Bl€ochl PE. Projector augmented-wave method. Phys Rev B1994;50(24):17953.

[72] Perdew JP, Burke K, Ernzerhof M. Generalized gradientapproximation made simple. Phys Rev Lett 1996;77(18):3865.

[73] Monkhorst HJ, Pack JD. Special points for Brillouin-zoneintegrations. Phys Rev B 1976;13(12):5188.

[74] McDonald RC, Hau HH, Eriks K. Crystallographic studies oftin (II) compounds. I. crystal structure of tin (II) fluoride,SnF2. Inorg Chem 1976;15(4):762e5.

[75] Davey WP. The absolute sizes of certain monovalent andbivalent ions. Phys Rev 1922;19(3):248.

[76] van Setten MJ, de Wijs GA, Brocks G. First-principlescalculations of the crystal structure, electronic structure,and thermodynamic stability of Be(BH4)2. Phys Rev B2008;77(16):165115.

[77] Moser D, Bull DJ, Sato T, Nor�eus D, Kyoi D, Sakai T,Kitamura N, Yusa H, Taniguchi T, Kalisvaart WP, et al.Structure and stability of high pressure synthesized MgeTMhydrides (TM¼ Ti, Zr, Hf, V, Nb and Ta) as possible newhydrogen rich hydrides for hydrogen storage. J Mater Chem2009;19(43):8150e61.

[78] Zwijnenburg MA, Cora F, Bell RG. Isomorphism ofanhydrous tetrahedral halides and silicon chalcogenides:energy landscape of crystalline BeF2, BeCl2, SiO2, and SiS2. JAm Chem Soc 2008;130(33):11082e7.

[79] Smith JS, Desgreniers S, Klug DD, John ST. High-densitystrontium hydride: an experimental and theoretical study.Solid State Commun 2009;149(21e22):830e4.

[80] Lacks DJ, Gordon RG. Crystal-structure calculations withdistorted ions. Phys Rev B 1993;48(5):2889.

[81] Narten A. Diffraction pattern and structure ofnoncrystalline BeF2 and SiO2 at 25 C. J Chem Phys1972;56(5):1905e9.

[82] Zintl E, Harder A. Konstitution der erdalkalihydride. BerBunsenges Phys Chem 1935;41(1):33e52.

[83] Snyder G, Borrmann H, Simon A. Crystal structure ofbarium dihydride, BaH2. Z Kristallogr 1994;209(5). 458e458.

[84] Bergsma J, Loopstra BO. The crystal structure of calciumhydride. Acta Crystallogr 1962;15(1):92e3.

[85] Brehler B. Kristallstrukturuntersuchungen an ZnCl2. ZKristallogr 1961;115(1e6):373e402.

[86] Brehler B. , Uber das a-und b-ZnCl2. Naturwissenschaften1959;46(19). 554e554.

[87] Kabalkina S, Popova S. Phase transition in zinc andmanganese fluorides at high pressures and hightemperatures. Dokl Akad Nauk SSSR 1963;153(6):1310.

[88] Yakel H, Brynestad J. Refinement of the crystal structure oforthorhombic zinc chloride. Inorg Chem 1978;17(11):3294e6.

[89] Bach A, Fischer D, Mu X, Sigle W, van Aken PA, Jansen M.Structural evolution of magnesium difluoride: from anamorphous deposit to a new polymorph. Inorg Chem2011;50(4):1563e9.

[90] Yakel H. Thermocrystallography of higher hydrides oftitanium and zirconium. Acta Crystallogr 1958;11(1):46e51.

i n t e rn 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 4 4 ( 2 0 1 9 ) 1 3 6 3 2e1 3 6 4 613646

[91] Chieh C, White MA. Crystal structure of anhydrous zincbromide. Z Kristallogr 1984;166(1e4):189e98.

[92] Fourcroy P, Carre D, Rivet J. Structure cristalinae de l'Iodurede zinc ZnI2. Acta Crystallogr, Sect B: Struct CrystallogrCryst Chem 1978;34(11):3160e2.

[93] Moriwaki T, Akahama Y, Kawamura H, Nakano S,Takemura K. Structural phase transition of rutile-type MgH2

at high pressures. J Phys Soc Jpn 2006;75(7). 074603e074603.[94] Mitchell RS. Single crystal x-ray study of structural

polytypism in cadmium bromide. Z Kristallogr1962;117(1e6):309e18.

[95] Braekken H. Zur kristallstruktur des quecksilberbromidsHgBr2. Z Kristallogr 1932;81(1e6):152e4.

[96] Hostettler M, Schwarzenbach D, Helbing J, Dmitriev V,Weber H-P. Structure and SHG of the high pressure phase IVof HgBr2. Solid State Commun 2004;129(6):359e63.

[97] Bassi I, Polato F, Calcaterra M, Bart J. A new layer structureof MgCl2 with hexagonal close packing of the chlorineatoms. Z Kristallogr 1982;159(1e4):297e302.

[98] Jones ME, Marsh RE. The preparation and structure ofmagnesium boride, MgB2. J Am Chem Soc 1954;76(5):1434e6.

[99] Vajeeston P, Ravindran P, Kjekshus A, Fjellvag H. Structuralstability of BeH2 at high pressures. Appl Phys Lett2004;84(1):34e6.

[100] Denes G, Pannetier J, Lucas J. About SnF2 stannous fluoride.II. crystal structure of b-and g-SnF2. J Solid State Chem1980;33(1):1e11.

[101] Pighin S, Urretavizcaya G, Castro F. Reversible hydrogenstorage in Mg(HxF1�x)2 solid solutions. J Alloy Comp2017;708:108e14.

[102] Pinatel E, Corno M, Ugliengo P, Baricco M. Effects ofmetastability on hydrogen sorption in fluorine substitutedhydrides. J Alloy Comp 2014;615:S706e10.

[103] Peng J, Zhong L, Wang Y, Lu Y, Pan F. Effect of extrusiontemperature on the microstructure and thermalconductivity of Mge2.0Zne1.0Mne0.2Ce alloys. Mater Des2015;87:914e9.

[104] Dai J, Song Y, Yang R. First principles study on hydrogendesorption from a metal (¼ Al, Ti, Mn, Ni) doped MgH2 (110)surface. J Phys Chem C 2010;114(25):11328e34.

[105] Zhang J, Zhou Y, Ma Z, Sun L, Peng P. Strain effect onstructural and dehydrogenation properties of MgH2 hydridefrom first-principles calculations. Int J Hydrogen Energy2013;38(9):3661e9.

[106] Kurko S, Milanovi�c I, Novakovi�c JG, Ivanovi�c N,Novakovi�c N. Investigation of surface and near-surfaceeffects on hydrogen desorption kinetics of Mg. Int JHydrogen Energy 2014;39(2):862e7.

[107] Li S, Jena P, Ahuja R. Dehydrogenation mechanism incatalyst-activated MgH2. Phys Rev B 2006;74(13):132106.

[108] Vajeeston P, Ravindran P, Fichtner M, Fjellvag H.Influence of crystal structure of bulk phase on the

stability of nanoscale phases: investigation on MgH2

derived nanostructures. J Phys Chem C2012;116(35):18965e72.

[109] Van Setten M, Popa V, De Wijs G, Brocks G. Electronicstructure and optical properties of lightweight metalhydrides. Phys Rev B 2007;75(3):035204.

[110] Isidorsson J, Giebels I, Arwin H, Griessen R. Opticalproperties of MgH2 measured in situ by ellipsometry andspectrophotometry. Phys Rev B 2003;68(11):115112.

[111] Mamula BP, Novakovi�c JG, Radisavljevi�c I, Ivanovi�c N,Novakovi�c N. Electronic structure and charge distributiontopology of MgH2 doped with 3d transition metals. Int JHydrogen Energy 2014;39(11):5874e87.

[112] Becke AD, Edgecombe KE. A simple measure of electronlocalization in atomic and molecular systems. J Chem Phys1990;92(9):5397e403.

[113] Silvi B, Savin A. Classification of chemical bonds based ontopological analysis of electron localization functions.Nature 1994;371(6499):683.

[114] Savin A, Nesper R, Wengert S, F€assler TF, ELF. The electronlocalization function. Angew Chem, Int Ed1997;36(17):1808e32.

[115] Bader R. Atoms in molecules: a quantum theory. Oxforduniv. press; 1990.

[116] Fonseca Guerra C, Handgraaf J-W, Baerends EJ,Bickelhaupt FM. Voronoi deformation density (VDD)charges: assessment of the Mulliken, Bader, Hirshfeld,Weinhold, and VDD methods for charge analysis. J ComputChem 2004;25(2):189e210.

[117] Henkelman G, Arnaldsson A, J�onsson H. A fast and robustalgorithm for Bader decomposition of charge density.Comput Mater Sci 2006;36(3):354e60.

[118] Vajeeston P, Ravindran P, Fjellvag H. Theoreticalinvestigations on low energy surfaces and nanowires ofMgH2. Nanotechnology 2008;19(27). 275704.

[119] King-Smith R, Vanderbilt D. Theory of polarization ofcrystalline solids. Phys Rev B 1993;47(3):1651.

[120] Vanderbilt D, King-Smith R. Electric polarization as a bulkquantity and its relation to surface charge. Phys Rev B1993;48(7):4442.

[121] Dronskowski R, Bloechl PE. Crystal orbital Hamiltonpopulations (COHP): energy-resolved visualization ofchemical bonding in solids based on density-functionalcalculations. J Phys Chem 1993;97(33):8617e24.

[122] Deringer VL, Tchougr�eeff AL, Dronskowski R. Crystalorbital Hamilton population (COHP) analysis as projectedfrom plane-wave basis sets. J Phys Chem A2011;115(21):5461e6.

[123] Maintz S, Deringer VL, Tchougr�eeff AL, Dronskowski R.Analytic projection from plane-wave and PAWwavefunctions and application to chemical-bondinganalysis in solids. J Comput Chem 2013;34(29):2557e67.