Metallization of Magnesium Polyhydrides Under Pressure

4.5 MB·English

by  David C. Lonie

MetallizationofMagnesiumPolyhydridesUnderPressure
David C. Lonie,1 James Hooper,1 Bahadir Altintas,1,2 and Eva Zurek1,∗
1DepartmentofChemistry, StateUniversityofNewYorkatBuffalo, Buffalo, NY14260-3000, USA
2Department of Computer Education and Instructional Technologies,
Abant Izzet Baysal University, 14280, Golkoy, Bolu-Turkey
Evolutionarystructuresearchesareusedtopredictstablephaseswithuniquestoichiometriesinthehydrogen–
richregionofthemagnesium/hydrogenphasediagramunderpressure. MgH ,MgH andMgH arefound
4 12 16
tobethermodynamicallystablewithrespecttodecompositionintoMgH andH near100GPa,andalllieon
2 2
theconvexhullby200GPa. MgH containstwoH− anionsandoneH moleculeperMg2+ cation,whereas
4 2
thehydrogenicsublatticesofMgH andMgH arecomposedsolelyofHδ− molecules. Thehigh–hydrogen
12 16 2
contentstoichiometrieshavealargedensityofstatesattheFermilevel, andtheT ofMgH at140GPais
3 c 12
1 calculatedtobenearlythreetimesgreaterthanthatoftheclassichydride,MgH2,at180GPa.
0
2 PACSnumbers:71.20.Dg,74.62.Fj,62.50.-p,63.20.dk

n
a
I. INTRODUCTION Herein, evolutionary structure searches are used to seek
J
outthestoichiometriesandstructuresofmagnesiumpolyhy-
1
drides, MgH with n > 2, under pressure. MgH is pre-
2 In 1935, Wigner and Huntington predicted that hydrogen, n 4
dicted to become stable with respect to decomposition into

] which exists in the paired molecular state at ambient pres- MgH2 and H2 near 100 GPa, and it remains the most stable
i sures and temperatures, would become an alkali–metal–like stoichiometryuntilatleast200GPa. Cmcm–MgH contains
c 4
s monoatomic solid when compressed to pressures exceeding twohydridichydrogensandonehydrogenmoleculeperMg2+
- 25 GPa [1]. This turned out to be a bit of an underes- cation,anditbecomesmetallicasaresultofpressure–induced
l
r timate. Structure searches based upon density functional band overlap. However, due to the low density of states at
t
m theory calculations have identified a number of molecular the Fermi level, the estimated T at 100 GPa is only ∼10 K
c
. (P ≤ 400 GPa) [2] and quasi–molecular or atomic (P = higherthanthatofP63/mmc–MgH2 at180GPa. Twoother
t 0.5−5TPa)[3,4]structuresinthecoldphasediagram,and
a stoichiometries, MgH12 and MgH16, are calculated as being
m experiments in diamond anvil cells show that the insulating thermodynamicallystableathigherpressures. Becausethese
phase III with paired hydrogens is stable over a broad tem- hydrogen rich phases exhibit an “Hδ− belt” surrounding the
- 2
d perature range and up to at least 360 GPa [5]. Recent ex- Mg2+ cations, and do not contain any hydridic hydrogens,
n perimentalworkatroomtemperatureabove220GPa, which theyhaveahighdensityofstatesattheFermilevel. Assum-
o showed a pronounced softening of one of the Raman active ingtypicalvaluesoftheCoulombpseudopotential, theT of
c molecular vibrons upon compression [6], and potential con- c
MgH is calculated as being between 47-60 K at 140 GPa.
[ 12
ductivity [7] has generated much excitement [8]. The newly Phases with a greater ratio of Hδ−:H− tend to have a larger
2
1 discovered phase IV of hydrogen is thought to be a mixed densityofstatesattheFermilevel,andahigherT .
c
v structure composed of layers of molecular units, as well as
0 weaklybondedgraphene–likesheets[9,10].Superconductiv-
5
ityatpressuresof450GPaandtemperaturesupto242Khas II. COMPUTATIONALMETHODS
7
beenpredictedinthemolecularphase[11],whereasthesuper-
4
. conducting transition temperature, Tc, may approach 764 K The structural searches were performed using the open–
1
formonoatomichydrogennear2TPa[12].
0 source evolutionary algorithm (EA) XtalOpt release 8 along
3 What are the structural motifs that compressed hydrogen with the default parameter set [21]. Evolutionary runs were
1 adoptswhendopedwithanelectropositiveelement? Theoret- carried out on the MgH2 stoichiometry at 0, 25, 50, 100,
v: ical work has predicted the presence of hydridic H− atoms, 150, 200 and 250 GPa with cells containing 2, 3, 4 and 8
i Hδ−molecules,H−···H motifs,symmetricH−molecules, formula units (FU). At 200 GPa additional searches on cells
X 2 2 3
polymeric (H−) chains, and sodalite cage structures, with with 5 and 6 FU were performed. Only the known α, (cid:15) and
3 ∞
ar the nature of the hydrogenic sublattice depending upon the ζ–phases were recovered, with the P63/mmc structure re-
identityofthealkalioralkalineearthmetal,andthepressure maining the most stable up to the highest pressures consid-
[13–20]. The latter clathrate–like cage which encapsulated ered. Exploratory searches at 200 GPa revealed that MgHn
thecalciumcationinCaH wasshowntobesusceptibletoa withn=2.5,3,3.5,4.5,5,...werenoticeablylessstablethan
6
Jahn–Teller distortion, giving rise to a remarkable electron– those with even n. Thus, a more refined search was carried
phonon coupling parameter of 2.69 at 150 GPa with a con- outat100and200GPawhichwasrestrictedtoevennrang-
comitantTcof∼225K[20]. ingfrom4-16with2-4FUforMgH4 andMgH6,2-3FUfor
MgH and 2 FU otherwise. Additional searches for n = 4
8
and n = 6 were carried out with 8 and 5 FU at 100 and
200GPa,respectively. Duplicatestructuresweredetectedus-
∗Electronicaddress:[email protected] ing the XtalComp [22] algorithm. The spglib package [23]
2
wasusedtodeterminespace–groupsymmetries. ple Ref. [35]. Plane wave basis set cutoff energies, which
Geometry optimizations and electronic structure calcula- gaveanenergyconvergencetobetterthan0.3mRy/atomwere
tions were performed using using density functional theory 55, 75 and 90 Ry for MgH2, MgH4 and MgH12, respec-
(DFT) as implemented in the Vienna ab-initio simulation tively, and a 16×16×16 Brillouin–zone sampling scheme
package (VASP) [24]. The exchange and correlation effects ofMethfessel–Paxton[36]withasmearingfactorof0.02Ry
were treated using the Perdew-Burke-Ernzerhof (PBE) func- wasemployed. Densityfunctionalperturbationtheory,which
tional [25] with plane–wave basis sets and a kinetic energy isimplementedinQE,wasusedforthephononcalculations.
cutoff of 600 eV. The hydrogen 1s1 and magnesium 2p63s2 The electron–phonon coupling matrix elements were calcu-
electronsweretreatedexplicitlyandtheprojector-augmented lated using a 16×16×16 k–mesh and 4×4×4 q–mesh
wave(PAW)method[26]wasusedtotreatthecorestates.The forMgH2andMgH4,alongwitha12×12×12k–meshand
k–pointgridswerechosenusingtheΓ–centeredMonkhorst– 3×3×3q–meshforMgH12. Theelectronphononcoupling
Packscheme. Thenumberofdivisionsalongeachreciprocal (EPC) parameter, λ, was calculated using a set of Gaussian
latticevectorwaschosensuchthattheproductofthisnumber broadeningsinstepsof0.005Ry.Thebroadeningforwhichλ
with the real lattice constant was 40 A˚ for the final geome- wasconvergedtowithin0.005was0.035,0.025and0.040Ry
try optimizations, as well as at least 50 A˚ for the electronic for MgH2, MgH4 and MgH12, respectively. The supercon-
densitiesofstates(DOS)andbandstructures. ducting transition temperature, Tc, has been estimated using
theAllen–DynesmodifiedMcMillanequation[37]as:
In situations where band gap closure occurs as a result
of pressure induced broadening, and eventual overlap of the
(cid:20) (cid:21)
ω 1.04(1+λ)
valence and conduction bands, standard density functionals T = logexp − (1)
predict too low metallization pressures. For this reason we c 1.2 λ−µ∗(1+0.62λ)
havecalculatedtheDOSofselectstructuresusingtheHSE06
whereω isthelogarithmicaveragefrequencyandµ∗ isthe
screened hybrid functional, which has been shown to give log
Coulombpseudopotential,oftenassumedtobebetween∼0.1-
goodaccuracyforbandgaps[27]. Duetotheimmensecom-
0.13.
putational expense involved in hybrid calculations, the ge-
The molecular calculations on Hδ− and MgH were per-
ometriesemployedhavebeenoptimizedwithPBE.Recently, 2 12
formedusingtheADFsoftwarepackage[38]andtherevPBE
it has been shown that inclusion of Hartree–Fock exchange
gradient density functional. The band structures of select
infunctionalssuchasHSE06orPBE0canhaveasignificant
phases (see the Supporting Information, SI) were calculated
impact upon the calculated transition pressures between dif-
usingthetight–bindinglinearmuffin–tinorbital(TB-LMTO)
ferent phases [28, 29]. Moreover, a study considering liquid
method [39], the VWN local exchange correlation potential
nitrogenatpressuresupto200GPa(andfinitetemperatures)
alongwiththePerdew–WangGGA.
has shown that the structural relaxations with a hybrid func-
tional can lead to large Peierls distortions (which inevitably
have an impact on the band gap) [30]. It has been proposed
thatnontrivialexchangecorrelationeffectscanbecomequite III. RESULTSANDDISCUSSION
important at extreme pressures, in particular when electron
localization occurs (“electride” behavior [31]), and/or when A. SqueezingMgH
2
thesemicoreelectronsinteract[29]. Sincewedonotobserve
significant broadening of the Mg 2p bands at the pressures The potential for reversible hydrogen storage has resulted
consideredhere,itmaybethatstructuralrelaxationwithahy- in much interest not only in crystalline MgH , but also in
2
bridfunctionalwillyieldsimilarresultsasPBE.Thiswillbe nanoparticles based on the structure of the various phases
consideredinfuturestudies.However,asexpected,ourcalcu- of this solid [40–44]. At 1 atm α-MgH assumes a TiO –
2 2
lationsshowthathybridfunctionalsincreasethepressuresat rutile–type geometry and it undergoes a series of structural
whichbandgapclosureispredictedtooccur. transitions, α (P4 /mnm) → γ (Pbcn) → β (Pa¯3) →
2
Phonon calculations were performed using VASP com- δ (Pbc2 ) → (cid:15) (Pnma), at 0.39, 3.84, 6.73 and 10.26 GPa
1
bined with the phonopy package [32] on supercells of 288 [45,46].Ataround165GPathePnmaphaseslightlydistorts
(MgH2),160(MgH4),351(MgH12)and272(MgH16)atoms. to a higher symmetry P63/mmc Ni2In–type configuration,
Theelectronicdensitiesofstatesandphononbandstructures ζ-MgH ,seeFig.1,whichwasshowntobedynamicallysta-
2
obtained with VASP for MgH2, MgH4 and MgH12 at 180, bleat180GPa. AtlowerpressuresBaH2[47,48],CaH2[49],
100and140GPashowedgoodagreementtothosecomputed andSrH [50]alsoadoptthisstructure. However,whereasthe
2
usingtheQuantumEspresso(QE)program[33],andthecom- heavier alkaline earth dihydrides with P6 /mmc symmetry
3
putationalsettingsdescribedbelow. areinsulating,inMgH metallizationispredictedtooccurby
2
IntheQEcalculationstheHandMgpseudopotentials,ob- 170 GPa at the PBE–level of theory [51]. Our evolutionary
tained from the QE pseudopotential library, were generated runsdidnotrevealanyotherphasesofMgH upto300GPa,
2
by the method of von Barth and Car with 1s1 and 3s23p0 apressureatwhichthemetallicityinζ-MgH persists.Calcu-
2
valence configurations, along with the Perdew–Zunger local lationsusingtheHSE06screenedhybridfunctional[27]con-
density approximation [34]. We choose this particular Mg firmthemetallicityat∼180GPa(seetheSI).
pseudopotential as it has been employed in numerous lattice ζ-MgH is metallic as a result of the closure of an indi-
2
dynamicalstudiesofmaterialsunderpressure, seeforexam- rect band gap. A flat band displaying H− s–character rises
3
above the Fermi level, EF, around Γ−A, and a steep band 0 λ(ω) 1
that boasts primarily Mg s and a little bit of Mg p–character λ = 0.01
falls below EF around the H–point, as illustrated in Fig. 1. 2000 2.1%
ζ-MgH2containshalfthenumberofvalenceelectronsperfor- total DOS
m39uKla[u5n2i]t.aTshdeoBesσM–ganBd2,Hwsh–ibcahnbdescaormeecsomsuppaerracbolne,diuncptianrgtica-t -1y (cm )1500 tλo(tωa)l α2F
ularthe“holes”atthetopofthebandspanningfromΓtoA. nc
e
HwoitwheMvegr2,+wihneterercaaslMategdBi2ncthoenshiestxsagoofnhaelxhaogloensa,lthbeohroenxasghoeneatsl Frequ1000 λ = 0.35
59.9%
networkinζ-MgH ismadeupofalternatingMg2+ andH−
2
ions,withthesecondsetofhydrideslocatedinthehexagonal 500
holes. So the Fermi surfaces arising from the B σ– [53] and
λ = 0.22
the H s–bands [51] are not identical. We also noticed some 38.0%
similarities between ζ-MgH2 and the most stable CsH phase Γ K M Γ A H L A PDOS, α2F(ω)
above 160 GPa [54]. Whereas the former can be thought of
aslayersofgraphiticsheetsofalternatingMg2+andH−ions
FIG. 2: Phonon band structure, phonon density of states and the
arranged in an ABABA... stacking with H− sandwiched in Eliashbergspectralfunction,α2F(ω),ofζ-MgH at180GPa. Cir-
2
betweenthetwolayers, inCsHhalfoftheH− havebeenre- cles indicate the phonon linewidth with a radius proportional to
movedsothatonlylayersofCs+andH−arefound. the strength. At this pressure λ = 0.58, ω = 1111 K, and
log
ThedensityofstatesattheFermilevel,g(E ),ofζ-MgH Tc =16−23Kassumingµ∗ =0.13−0.1.
F 2
is0.01eV−1/electronat170GPaandby300GPaitdecreases
onlyslightly,seetheSI.Despitetherelativelylowg(E )we
F
modestg(E )thetotalEPCparameteriscalculatedasbeing
were intrigued in the possibility of superconductivity in this F
0.58, and along with an ω of 1111 K gives rise to a T of
system.Fig.2plotsthephononbandstructureanddensitiesof log c
16-23Kforµ∗ rangingfrom0.13−0.1,respectively,viathe
states,phononlinewidths(γ(ω)),Eliashbergspectralfunction
(α2F(ω)), and λ(ω) of ζ-MgH at 180 GPa. 38% ofthe to- Allen–Dynes modified McMillan equation. For comparison,
2
theEPCparameterandω forBaH inthesimplehexagonal
talEPCparameter,λ,isaresultofthelow–frequencymodes log 2
below ∼700 cm−1 which are associated primarily with the structure at 60 GPa have been calculated as being 0.22 and
780 K, respectively, giving rise to T on the order of only a
motionsoftheheavier Mgions, whereastheregionbetween c
750-2400 cm−1, which is mostly due to motions of the H− fewmK[47].
anions, contributes 62% towards the total λ with the modes Given the recent interest in compressed hydrogen–rich
alongΓ−K −M andH −L−Aplayingadominantrole. solidsaspotentialsuperconductors,webegantowonderifH2
Themodesabove2100cm−1 areprimarilycausedbytheset maymixwithMgH2 underpressureand whatothermetallic
ofH−anionswhichareclosertotheMg2+cations(theMg–H systemsmaybefound. Aswillbeshowninamoment,while
distances at 180 GPa measure 1.58 and 1.81 A˚). Despite the theζ phaseispreferredforMgH2above165GPa,itisnotthe
moststablepointonthehydrogen–richMg/Hphasediagram
atthesepressures.
-10
B. StabilizationofthePolyhydrides
-5
H- s
Thefirstionization–potentialofmagnesiumis∼2eVlarger
0
thanthatoflithium,suggestingthatstabilizationofthemag-
eV) Mg sp nesiumpolyhydrideswilloccuratasomewhathigherpressure
gy (-5 than the lithium polyhydrides (that is, above 100 GPa [13]).
ner The ionic radius of Mg2+ is about 30% smaller than that of
E
-10 Ca2+, and since CaH was found to be the most stable stoi-
4
chiometryatP = 50−150GPaandCaH at200GPa[20],
6
-15 wemayexpectthatthemostfavorableMgHncombinationhas
2 < n < 6. Howdothesepredictions—baseduponchem-
icalintuitionthatwasdevelopedbyanalyzingcomputational
-20Γ K M Γ A L H A studiesofcompressedpolyhydrides[13–20]—comparewith
theresultsfromourevolutionarystructuresearches?
FIG.1: Theelectronicbandstructureofζ-MgH2 at180GPa. The The calculated enthalpies of formation, ∆HF, of the im-
character of the bands which cross the Fermi level is highlighted. portant MgHn structures found in our searches are provided
The Fermi energy is set to zero in all of the plots. A side and top in Fig. 3 (see the SI for the plot of ∆H vs. H composi-
F 2
viewofζ-MgH2isshownontheright,withtheMg/Hatomscolored tion). At 100 GPa only MgH4 is predicted to resist decom-
inred/white. position into MgH and H . In fact, MgH persists as hav-
2 2 4
4
ing the most negative ∆H as the pressure is increased. By (a)
F
200 GPa all stoichiometries except for MgH , MgH and
2.5 3
MgH have a negative ∆H . Because MgH , MgH and
3.5 F 4 12 Cmcm
MingtHhe16SIli,ethoenythaerectohnevremxohduylnlaamti2c0a0llyGPstaa,bwlehwicihthisrepsrpoevcidtetdo Swaanp d MHg'2'ss optimize
decomposition into other phases and MgH /H . Fig. 3 illus-
2 2 H atom -- H-
tratesthatwhereasthe∆H ofMgH startstobecomeneg-
F 4 I4/mmm H atom -- H2 Cmcm
ativenear92GPa, forMgH12 andMgH16 thisoccursat122 (CaH4 structure) Mg atom (MgH4 structure)
and117GPa,respectively. Comparisonofthesefindingswith
thepredictionsbaseduponournewlydevelopedchemicalin-
tuition under pressure illustrates that we did reasonably well
in predicting the stabilization pressures and most stable stoi- (b)
chiometrywithoutperforminganycomputations. Now,letus 5 5
begin ourexploration of thestructural peculiaritiesand elec- Mg s H- s
0 0
tronicstructuresofthemagnesiumpolyhydridesfallingonthe
Mg p
convex–hull. V) H s
y (e-5 2 -5
g
ner-10 -10
E
C. MgH :H moleculesandhydridicatoms
4 2
-15 -15
H-
The phase with the most negative enthalpy of formation 0.1 Å-1 H2
throughoutthepressurerangestudied,Cmcm–MgH4,forms -20Γ Z T Y Γ S R-200 0.10 0
adistortedCsClbcclatticewithH− atomstakingupthever- DOS H PDOS
(eV -1 electron -1) (arb. units)
tex positions of the underlying cube–like cages. The body–
centeredpositionsareoccupiedbya1:1mixofMg2+cations
and H2 molecules with slightly elongated bonds, as high- FIG. 4: (a) A schematic illustration of the structural similar-
lighted by the red and blue polyhedra in Fig. 4(a). The size ity between Cmcm–MgH (right) and the I4/mmm–symmetry
4
mismatch between the two results in the hydrides forming CaH structure from Ref. [20] (left). The hydride cages around
4
differentsizedcagesaroundthem. ThesameCmcm–MgH Mg2+/Ca2+ and the H molecules are colored red and blue, re-
4 2
structure was discovered in evolutionary runs carried out at spectively[56]. (b)ThePBEelectronicbandstructureofMgH4 at
100and200GPa,andphononcalculationsat100GPashowed 100 GPa. The character of the bands which cross the Fermi level
ishighlighted. Alsoshownontherightarethetotalelectronicand
itwasdynamicallystable.
hydrogensite–projecteddensitiesofstates(DOS).
Interestingly, the lowest enthalpy I4/mmm–symmetry
CaH structure found using the particle–swarm optimization
4
technique[55]inarecentstudy[20]canbedescribedthesame
wayasCmcm–MgH . Thedifferencebetweenthetwoisthe
4
manner in which the cations and the H molecules are dis-
2
tributed: in CaH they are dispersed homogeneously, but in
4
MgH theyarearrangedintointerwovenzig–zagchains. Ad-
4
m) MgH12 ditionally, the hydride cages are more distorted in the MgH4
o structurewiththesmallestfacewhichsurroundsanMg2+be-
at
V / MgH16 ingtheonewhichlinksonemagnesiumcationtoanother.Ac-
e tually,thestructurecanalsobeviewedassheetsofMgH2with
m
H molecules trapped in the larger gaps between the sheets,
H (f on2esuchsheetisshownattherightofFig.4(a).
∆ MgH4
WithinPBEthetotaldensityofstatesofCmcm–MgH at
4
100 GPa is quite small; in fact it is lower than that of the
I4/mmmanalogue. Theformeris42meV/atommorestable
thanthelatteratthispressure,butthevolumeofI4/mmm–
MgH is 0.04 A˚3 per atom smaller than that of Cmcm–
4
MgH . The formation of the zig–zag like chains illustrated
4
Pressure (GPa) in Fig. 4(a) must therefore have a substantial impact on the
electroniccontributiontotheenthalpy.
FIG.3: ∆H oftheMgH ,MgH ,andMgH phasesasafunc- As the pressure increases from 100 to 300 GPa, the short-
F 4 12 16
tionofpressure. Theplotalsoillustratestheenthalpyofthevarious estdistancebetweenthemetalcationsdecreasesfrom2.56A˚
MgH2 phases with respect to the most stable structure at a given to 2.32 A˚, and the Mg 2p core bands broaden from 0.19 to
pressure,withtheregionbelow15GPamagnifiedintheinset. 0.58 eV due to core overlap. The shortest Mg–H− distance
5
decreases from 1.74 A˚ to 1.55 A˚, as does the Mg–H2 sep- a) b)
aration (1.92 A˚/1.68 A˚). The molecular H bonds lengthen
2
somewhatfrom0.78A˚ to0.79A˚.Thisisslightlylongerthan
the intramolecular distance in pure compressed H at these
2
pressures,0.73A˚ and0.75A˚,respectively.
SinceMgH containsH−units,itbecomesmetallicasare-
4
sult of pressure induced band broadening and eventual over-
lap, like LiH and NaH . Metallization occurs within PBE
2 9
already by 20 GPa, even though Cmcm–MgH is not stable
4
withrespecttodecompositionintoH andMgH atthispres-
2 2
sure. A band displaying H− s–character rises above EF at H atom
theY–point,whereasbandsexhibitingpredominantlyMgsp Mg atom
and a little bit of H σ∗–character fall below it at the Z and
2
T–points(seeFig.4(b),andthe“fatbands”intheSI).Calcu-
FIG.5:(a)A2×2×2supercellofR3–MgH wherethepolyhedral
12
lationsusingtheHSE06functionalincreasethemetallization
unitsarehighlightedtoemphasizetheABCABC... close-packedar-
pressureto∼150GPa(seetheSI).
rangement.TheMgH buildingblocksarecoloredsuchthatthered
12
polyhedraalllieinthesameplane.(b)AsupercellofP−1–MgH .
16
TheMgH buildingblocksarecoloredtoemphasizethesimilarity
12
D. MgH andMgH :theHδ−belt tothestructurein(a).Theblockscoloredredorgreenlieinthesame
12 16 2
plane,andthehydrogenscoloredinbluedonotbelongtoanMgH
12
The absence of H− anions in the other structures lying on buildingblock[56].
the convex hull at 200 GPa, MgH and MgH , has impor-
12 16
tant consequences for their electronic structure. The hydro-
genicsublatticesofthesephasesarecomposedsolelyofHδ− ThelowestenthalpyMgH16configurationwefound,which
2
molecules with slightly stretched bonds, just like the CaH exhibited P − 1 symmetry and was dynamically stable at
12
structurepredictedinapreviousstudy[20]. Thepresenceof 130 GPa, could be thought of as being made up of similar
hydridic hydrogens in systems with a small mole fraction of MgH12 unitswithexcessHδ2− moleculesstuffedbetweenthe
hydrogen, and their absence in phases with a high hydrogen hexagons,asillustratedinFig.5(b). These‘interstitial’dihy-
content was rationalized by Wang and co–workers by con- drogenslieontopoftheMg2+cationsintheMgH12building
sidering the formal number of ‘effectively added electrons’ blocks. The intramolecular distance in H−1/4 at 1 atm was
2
(EAE) which are donated from the alkaline earth metal va- calculated as being 0.78 A˚, whereas the bond lengths of the
lencebandsintotheH2σ∗–bands[20]forvariousCaHnstoi- dihydrogensinMgH16rangefrom0.76to0.85A˚ at130GPa,
chiometries. IftheEAEissmall,thedihydrogenbondsimply with the interstitial hydrogen molecules being shorter (0.76-
stretchesasaresultofthepopulationofH2 σ∗,andhydridic 0.78A˚)thanthoseinthebelt(0.79-0.85A˚).Theunequalbond
hydrogens are not formed. If the EAE is large enough, the lengths in the Hδ− units may be a result of different charge
moleculedissociatesintotwoH−units. states,orbedue2totheirlocalbondingenvironments,orboth
The most stable MgH12 structure found in our evolution- [57]. Asthepressureincreases,theintramolecularH–Hbond
ary searches had R3–symmetry and was shown to be dy- lengthsdecrease,withtheinterstitialandbelthydrogensmea-
namically stable at 140 GPa. The hexagonal building block suring0.74-0.76A˚ and0.78-0.84A˚,respectively,at300GPa.
for this phase consists of an Mg2+ cation surrounded by six
SinceMgH andMgH aremetallicasaresultofthepar-
H−21/3 molecules, as illustrated in Fig. 5(a). The dihydro- tial filling of1th2e H2 σ∗–b16ands like LiH6, they have a high
genmoleculesinthesehexagonsappeartoarrangeina‘belt’ densityofstatesatE ,seeFig.6. Bothphasesremaingood
F
around the metal cation in a side–on fashion. The hexagons metalsuponcompressionuptoatleast300GPa,andtheMg
are tiled in parallel sheets forming an ABCABC... close– 2pbandsbroadenonlyslightlyto∼0.15-0.2eVat300GPaas
packedstructure.Thisdescriptionis,however,somewhatmis- aresultofcoreoverlap. AcomparisonoftheDOSofMgH
12
leading as the distance between Mg2+ and a hydrogen atom at140GPacalculatedwithPBEandtheHSE06screenedhy-
withintheMgH12 buildingblockiscomparabletotheshort- brid functional showed that latter valence DOS was slightly
estdistancebetweenthemetalionandahydrogenatomina broader (as expected for metallic systems [58, 59]), and the
different building block. For example, the intra– and inter– core Mg 2p bands shifted to lower energies. However, the
buildingblockMg–Hmeasurementsare1.76and1.81A˚,re- g(E ) computed with the two functionals was essentially
F
spectively,at140GPa. ThedihydrogenbondsinMgH12 are the same (see the SI). This is in–line with our previous re-
substantiallyelongatedto0.82and0.81A˚ at140and300GPa, sultswhichshowedthatg(E )isrelativelyinsensitivetothe
F
when compared with the typical bond lengths of pure H2 at choice of the functional in sodium polyhydrides that did not
these pressures (0.74/0.75 A˚). A gas phase geometry opti- containhydridichydrogens[14].Thenearlyfree–electronlike
mizationonaH−1/3 moleculeat1atmshowedthatthebond valence bands of MgH and MgH exhibit primarily H s–
2 12 16
stretched from 0.75 to 0.79 A˚. So the expansion of the H–H character,withalittlebitofMgspspanningthroughout(see
bondobservedinMgH isconsistentwiththepartialfilling the fat bands in the SI). Nonetheless, the computed DOS of
12
oftheH σ∗–bands. these structures match quite well with a hypothetical system
2
6
(a)
0.12 (a) MgH12 (b) MgH16 -0.8
140 GPa 130 GPa
300 GPa 300 GPa -1.9
V)
e 0.1
n
o
ectr -4.3
el 0.08
e
c
n
e
val 0.06
E) / ( -7.6
g(
0.04
-10.1
0.02
0-30 -20 -10 0 -30 -20 -10 0 5 GPa
Energy (eV) Energy (eV) -13.4
1 atm
FIG.6: ThePBEvalencedensitiesofstatesof(a)MgH ,and(b)
12 -15.4
MgH . NotethattheFermilevelliesjustbelow(directlyafter)a
16
140 GPa
sharppeakintheDOSinMgH at140GPa(MgH at130GPa). (b)
12 16
S nits) MgH12 at 5 GPa H Mg s Mg p
Ou
(wHh1e6r)e2−thelamttiecteasl(csaeteiotnhsehSaIv)e,sbuegegnesretimveovoefda,lmthoes(tHfu1l2l)2io−niaznad- PD(arb.
tionoftheMgvalence3selectronsintotheH2σ∗–bands. OS units) MgH12 at 140 GPa H Mg s Mg p
PDarb.
(
E. TheMgH12BuildingBlocks -20 -15 -10 -5 0 5 10
Energy (eV)
AnumberofMH clusters,whereMisatransitionmetal
12
FIG.7: (a)CalculatedmolecularorbitalleveldiagramofanMgH
atom,havebeenpredictedasbeingstableinthegasphaseby 12
cluster when optimized in the gas phase at 1 atm (left) and in the
quantum chemical calculations [60]. Moreover WH (H ) ,
4 2 4 geometrywhichitadoptsintheR3–MgH solidat5GPa(center)
12
whichcontainsfourhydridichydrogensandfourdihydrogens
and140GPa(right). TheenergiesoftheMOsat140GPaaregiven
bonded to the metal center in a side–on fashion, has been totherightineV.(b)Calculatedsite–projecteddensitiesofstatesof
madeinaneonmatrix[61]. Unsurprisingly,molecularcalcu- R3–MgH at5and140GPa.
12
lationsonboththeoptimizedMgH buildingblocksaswell
12
as(MgH )2+withD symmetryrevealednumerousimagi-
12 6h
naryfrequencies,sotheseclusterswillnotbestableat1atm. Thefrontierorbitalsofthe1atmclustercontainsubstantial
Nonetheless, itisinstructivetocomparetheelectronicstruc- characterarisingfromH,andtheHOMOalsohasanimpor-
tureoftheMgH12buildingblockwiththeDOScomputedfor tantcontributionfromtheMg3pandtheLUMOfromtheMg
R3–MgH12atvariouspressures. 3sorbitals. Ourfragmentorbitalanalysis[62]showsthatthe
Whereas in an optimized MgH cluster the Mg–H and LUMO+1 contains primarily H–character with less than 4%
12
intramolecular H–H distances were calculated as being 2.20 of Mg 3d states mixed in. In the ‘less–compressed’ cluster
and0.79A˚,thesevaluesmeasure2.34-2.58/1.76-1.78A˚ and extracted from the solid at 5 GPa the frontier orbitals swap
0.79/0.82 A˚ in R3–MgH at 5/140 GPa. So the gas phase positions so that the HOMO displays Mg 3s and the LUMO
12
clusterisactuallyalittlebitmore‘compressed’thanthebuild- Mg 3p–character. This is in–line with the projected densi-
ingblockwithinthesolidat5GPa.Theenergyleveldiagrams tiesofstateswhichillustratethatthepredominantcontribution
and canonical molecular orbitals (MOs) of these clusters are aroundtheFermilevelisduetoMgsat5GPa.At140GPathe
illustratedinFig.7(a). ThesixMOslowestinenergyresem- gapbetweenthehydrogenicandthemetallicbandsbetween-6
ble the canonical MOs of benzene, except that they do not to-3eVclosesinthesolid,andtheHOMOandHOMO-1or-
contain a node which bisects the dihydrogen molecules. A bitalsintheclustercomeclosertogetherinenergy. Moreover,
large gap is found between the highest occupied molecular asaresultofthepressureinduceds→ptransitioninMg,the
orbital(HOMO)andHOMO-1oftheoptimizedcluster,buta states around the Fermi level contain about an equal amount
smallgapseparatestheHOMOandlowestunoccupiedmolec- of Mg s and p–character. In the cluster the energy ordering
ularorbital(LUMO).TheHOMO–HOMO-1gapdecreasesas of the molecular orbitals also changes, so that the HOMO is
theclusteriscompressed,asdotheanalogoussetsofbandsin moreMgp–like,andtheLUMOdisplaysprimarilyHschar-
theextendedsystem,asillustratedinFig.7(b). acter. Sothegasphaseclustersareabletomimicsomeofthe
7
0 λ(ω) 1 0 λ(ω) 1
3500
λ = 0.01 3000
3000 1.5% λ = 0.08
11.1%
total DOS 2500 total DOS
-1ncy (cm )22050000 tλo(tωa)l α2F -1ncy (cm )2000 tλo(tωa)l α2F
e e
qu qu1500
e1500 e
Fr Fr
1000 λ = 0.58
1000 λ = 0.48 78.8%
65.4%
500 λ = 0.24 500 λ = 0.07
33.0% 10.0%
0Γ Z R S Y T Γ PDOS, α2F(ω) 0Γ T L Γ PDOS, α2F(ω)

FIG. 9: Phonon band structure, phonon density of states and the
FIG. 8: Phonon band structure, phonon density of states and the
Eliashberg spectral function, α2F(ω), of MgH at 100 GPa. Cir- Eliashberg spectral function, α2F(ω), of MgH12 at 140 GPa. Cir-
4 cles indicate the phonon linewidth with a radius proportional to
cles indicate the phonon linewidth with a radius proportional to
the strength. At this pressure λ = 0.73, ω = 1554 K, and
the strength. At this pressure λ = 0.74, ω = 941 K, and log
T =29−37Kassumingµ∗ =0.13−0.1. log Tc =47−60Kassumingµ∗ =0.13−0.1.
c
essentialfeaturesoftheprojectedDOSofthesolidatdifferent
pressures.
Despitetheincreasedhydrogencontentandhigherdensity
F. Superconductivityinthepolyhydrides
of states at the Fermi level, the total EPC parameter of R3–
MgH at 140 GPa is almost the same as of Cmcm–MgH
12 4
Our computations have estimated the Tc of the classic al- at 100 GPa. However, a comparison of the λ(ω) in Fig. 9
kaline earth hydride, P63/mmc–MgH2, as being ∼20 K at andFig.8showsthattherelativecontributionstotheoverall
180 GPa. We wondered what the Tc of the aforementioned λ are quite different in the two polyhydrides. MgH12 does
hydrogen–rich phases would be in comparison, and if Tc not contain any hydridic hydrogens, and is metallic because
wouldbeinfluencedbythehydrogenicsublatticeofthepoly- of the partial filling of the H σ∗–bands. In contrast to what
2
hydride. Computations have been carried out on Cmcm– wasfoundforMgH ,theH vibroncontributesabout11.1%
4 2
MgH4 and R3–MgH12 at 100 and 140 GPa, respectively, to the total λ. This corresponds quite well to the 11.3% cal-
sincethesearepressuresslightlylargerthanwhen∆HF was culated for a compressed KH6 phase [19] whose hydrogenic
computedasbecomingnegative,andsincebothsystemswere sublattice only contained Hδ− motifs. The EPC associated
2
foundtobemetallicwithinPBEatthesepressures. with the low–frequency modes below 400 cm−1, which are
Within PBE the density of states at the Fermi level of dominatedbythemotionsoftheheaviermetalatoms,isabout
Cmcm–MgH at 100 GPa is comparable to the one calcu- athirdoftheamountcalculatedforthephasescontainingH−
4
lated for ζ-MgH at 180 GPa. The total EPC parameter is units. Themaincontributiontoλ,79%,arisesfromtheinter-
2
nearly28%larger,however.Inbothphasesthelow–frequency mediate frequency regime, which is primarily due to the H
2
modeswhicharemostlyduetothevibrationsoftheMgatoms motions. ThereasonwhytheT ofMgH isestimatedasbe-
c 12
contribute∼0.2tothetotalλ;compareFig.8andFig.2. The ing∼20KhigherthanthatofMgH isduetothelargerω .
4 log
main reason why the overall EPC parameter is larger for the Unfortunately, the computational expense precluded us from
polyhydride than the classic hydride is a result of the total calculatingtheEPCparameterofcompressedP −1–MgH ,
16
coupling provided by the modes between ∼500-2500 cm−1, orfromexploringthepressuredependenceofT .
c
whichareprimarilyduetothemotionsofthehydrogenatoms.
Whereas the classic hydride contains only hydridic hydro-
gens, there is an equal number of H and H− hydrogens in The values we calculate for the total EPC parameter and
2
MgH .TheH vibron,locatedaround3500cm−1contributes the T of the magnesium polyhydrides falls within the range
4 2 c
only 1.5% to the total coupling strength in the polyhydride. of0.5-1.6and10-139K,respectively,computedforanumber
Thisisnotsurprising,sincethebandscrossingtheFermilevel of hydrogen–rich systems [20]. We show that comparable λ
displayedonlyasmallamountofH s–character. Despitethe values may be obtained for polyhydrides with very different
2
higherλthatMgH hasascomparedtoMgH ,theprefactor hydrogenic sublattices, but their ω and therefore T may
4 2 log c
inthemodifiedMcMillanequation, ω , iscalculatedasbe- differ. The magnesium polyhydrides are predicted to have a
log
ing15%smallersothetotalT ofMgH isestimatedasbeing largerT thanMgH underpressure,andphaseswithalarger
c 4 c 2
∼14Khigherthanthatoftheclassicalkalineearthhydride. molepercentratiowilllikelyhaveahigherT .
c
8
IV. CONCLUSIONS moleculeswithslightlystretchedbonds,emergeasbeingther-
modynamically stable. MgH and MgH are metallic in
12 16
Evolutionarystructuresearchescoupledwithdensityfunc- part as a result of the partial filling of the H2 σ∗–bands and
tional theory calculations are used to predict the most sta- have a high density of states at the Fermi level. Their elec-
ble structures and stoichiometries of the magnesium polyhy- tronicstructureatvariouspressurescanbetracedbacktothe
drides,MgHnwithn≥2,underpressure.Thethermodynam- molecularorbitaldiagramoftheirbuildingblock,theMgH12
icallystablestructuresfoundinthisstudyhaveahydrogenic cluster.Despitetheverydifferenthydrogenicsublattices,both
sublatticecontainingH− anionsandH2 units(MgH4),orH2 MgH4 andMgH12 arefoundtohavesimilarelectronphonon
moleculeswhicharelessstronglybondedthanthosefoundin couplingparameters. ThemainreasonwhytheTc ofMgH12
puremolecularhydrogenat1atm(MgH12andMgH16). at140GPaiscalculatedasbeinglargerthanthatofMgH4 at
MetallizationinP6 /mmc–MgH occursasaresultofan 100GPa,47-60Kvs.29-37Kassumingtypicalvaluesofµ∗,
3 2
H− s–band rising above, and a Mg sp band falling below is because of the larger average logarithmic frequency com-
the Fermi level. Tc is estimated as being between 16-23 K putedforMgH12.
at 180 GPa, with a sizable contribution to the total electron
phononcouplingparameterarisingfromvibrationsrelatedto
boththehydrogenandmagnesiumatoms. Acknowledgments
MgH , which starts to become thermodynamically sta-
4
ble with respect to decomposition into MgH and H near We acknowledge the NSF (DMR-1005413) for financial
2 2
100GPaisfoundtocontainoneH moleculeandtwohydridic support,andtheCenterforComputationalResearchatSUNY
2
hydrogensper Mg2+ cation. Metallization occursas aresult Buffalo for computational support. B.A. was supported by
ofpressure–inducedbandgapclosure,butthedensityofstates a postdoctorate scholarship of CoHE (Turkish Council of
at the Fermi level is quite low. Around 120 GPa other stoi- Higher Education), and acknowledges ULAKBIM-TR-Grid
chiometries, whose hydrogenic sublattices contain only Hδ− forcomputationaltime.
2
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