High-pressure Phase Stability andSuperconductivity of Pnictogen Hydrides andChemical Trends for Compressed Hydrides

Yuhao Fu,†,⊥ Xiangpo Du,‡,⊥ Lijun Zhang,∗,† Feng Peng,‡ Miao Zhang,‡ Chris J.Pickard,¶ Richard J. Needs,§ David J. Singh,∗,†,‖ Weitao Zheng,† and Yanming

Ma∗,‡

†College of Materials Science and Engineering and Key Laboratory of Automobile Materialsof MOE, Jilin University, Changchun 130012, China

‡State Key Laboratory of Superhard Materials, Jilin University, Changchun 130012, China¶Department of Materials Science & Metallurgy, University of Cambridge, 27 Charles

Babbage Road, Cambridge CB3 0FS, United Kingdom§Theory of Condensed Matter Group, Cavendish Laboratory, J J Thomson Avenue,

Cambridge CB3 0HE, United Kingdom‖Department of Physics and Astronomy, University of Missouri, Columbia, MO

65211-7010 USA⊥These two authors contributed equally to this work.

E-mail: lijun zhang@jlu.edu.cn; singhdj@missouri.edu; mym@jlu.edu.cn

ABSTRACT: The recent breakthrough dis-covery of unprecedentedly high temperaturesuperconductivity of 203 K in compressed sul-fur hydrides has stimulated significant interestin finding new hydrogen-containing supercon-ductors and elucidating the physical and chem-ical principles that govern these materials andtheir superconductivity. Here we report theprediction of high temperature superconduc-tivity in the family of pnictogen hydrides usingfirst principles calculations in combination withglobal optimization structure searching meth-ods. The hitherto unknown high-pressure phasediagrams of binary hydrides formed by the pnic-togens of phosphorus, arsenic and antimonyare explored, stable structures are identifiedand their electronic, vibrational and supercon-ducting properties are investigated. We predictthat SbH4 and AsH8 are high-temperature su-perconductors at megabar pressures, with criti-cal temperatures in excess of 100 K. The highly

symmetrical hexagonal SbH4 phase is predictedto be stabilized above about 150 GPa, whichis readily achievable in diamond anvil cell ex-periments. We find that all phosphorus hy-drides are metastable with respect to decom-position into the elements within the pressurerange studied. Trends based on our results anddata in the literature reveal a connection be-tween the high-pressure behaviors and ambient-pressure chemical quantities which providesinsight into understanding which elementsmay form hydrogen-rich high-temperaturesuperconducting phases at high pressures.

I. INTRODUCTION

Superconductivity, especially at high tempera-tures, continues to offer surprises both from ex-perimental discoveries and theoretical insightsoften stimulated by these experiments. These

1

findings include the Fe-based superconductors1

which have provided a large body of theoreti-cal work on spin-fluctuation pairing, nematic-ity and multiorbital physics,2–4 and recent re-ports of superconductivity in sulfur hydridesat pressures ∼200 GPa with a Tc of 203 K.5,6Superconducting sulfur hydrides show a strongisotope effect when deuterium is substitutedfor hydrogen, as expected for electron-phonon-based superconductivity.5 This breakthroughobservation has led to debate on the supercon-ducting mechanism, including discussion of thelimits of standard Migdal-Eliashberg electron-phonon coupling (EPC) theory,7–9 the role ofstrong covalent bonding,10,11 the effects of an-harmonicity on EPC,12 etc. These proposals,together with the pioneering work of Ashcroftand coworkers on predicted high-temperaturesuperconductivity in solid hydrogen13 and inhydrogen-rich hydrides14,15 may guide researchtowards the discovery of new high-temperaturesuperconductors based on materials containinglight elements.

High-temperature superconductors can bedivided into two classes: unconventional su-perconductors characterized by non-phononprimary pairing interactions, normally lead-ing to non-standard pairing states, and con-ventional superconductors, with dominantelectron-phonon pairing, and s-wave (or mainlys-wave for non-centrosymmetric cases) pair-ing states. In the latter case, methods existfor reliably evaluating superconducting proper-ties and analyzing the superconductivity, e.g.,through calculating the Eliashberg EPC spec-tral function α2F(ω). A general consensus hasbeen reached that the recently discovered su-perconducting sulfur hydrides belong to thiscategory.5,10,16–19 The experimental discoverywas motivated by a theoretical prediction ofhigh-Tc superconductivity in compressed solidH2S by some of us.

16 Two superconductingstates are observed in H2S: samples preparedat low temperature have a maximum Tc of ∼150 K at 200 GPa, while the superconductiv-ity at 203 K arises from samples prepared viaannealing at temperatures above 220 K. Thelatter phase originates from the decompositionof H2S into H3S.

6,12,17

Theoretical predictions of high-temperaturesuperconductivity rely on knowledge of the sta-ble structures of the system. Global optimiza-tion structure searching methods20 can iden-tify previously unknown ground-state struc-tures such as sulfur hydrides at high pres-sures.12,16,17,21 Calculations based on densityfunctional theory (DFT) allow an accurateenergetic evaluation of the structures foundwithin the potential energy landscape and anassessment of their potential for superconduc-tivity. The experimental discovery of high-temperature superconducting sulfur hydridesdemonstrates the predictive power of DFT-based structure searching and EPC calcula-tions, and suggests that more superconductorscould be discovered using this approach. Therole of theory is especially important since un-der such extreme conditions sample synthesisand in situ measurements of properties are usu-ally challenging. Recently, the sister systemsof selenium and tellurium hydrides were pre-dicted to exhibit high-Tc superconductivity inhydrogen-rich compounds stabilized above 100GPa.22,23 These proposals await experimentaltesting.

Here we explore the thermodynamic stabil-ity of pnictogen hydrides of P, As and Sbat high pressures and their superconductingproperties. This investigation is in part mo-tivated by the fact that the strength of the co-valent H–P bond (with a bond energy of 322kJ/mol) is rather similar to that of the H–Sbond (bond energy of 363 kJ/mol) in the molec-ular gas phase. It is therefore reasonable to con-jecture, within the scenario that strong cova-lent bonding favors superconductivity,10,11 thatphosphorus hydrides containing strong covalentbonds to H atoms and becoming metallic un-der compression might exhibit similarly strongEPC and potentially high-Tc superconductiv-ity. To the best of our knowledge, solid pnicto-gen hydrides, even at ambient conditions, haveonly rarely been studied,24–27 although the cor-responding molecular gases (e.g., PH3, P2H4,AsH3, and SbH3) are well known in chemistry.

We find that thermodynamic stability of thegas molecules (PH3 > AsH3 > SbH3) is re-versed at high pressures, resulting in decompo-

2

sition enthalpies that decrease from P, As toSb hydrides. Except for the molecular solidphases stabilized by weak van der Waals in-teractions at low pressures,24–27 P hydrides arefound to exhibit thermodynamic instability todecomposition into the elements under pres-sures up to 400 GPa. For As hydrides, stablecompounds emerge only above 300 GPa. Sb hy-drides are the most easily stabilized compoundsabove 150 GPa, which is readily achievable indiamond anvil cells. We have identified two sta-ble hydrogen-rich compounds, SbH4 and AsH8,as possible high-temperature superconductorswith a Tc of 102 K at 150 GPa and 141 K at350 GPa, respectively. Based on analysis ofcurrent and prior theoretical work on other bi-nary hydrides, we have established a connectionbetween ambient-pressure chemical propertiesand energetic stability, structural features, su-perconducting properties, etc. of hydrides uponpressures. The trends implied by this connec-tion may help in discovering new binary andmultinary high-pressure hydrogen-rich super-conductors, since it does not require knowledgeof the very different chemistries of elements athigh pressures. Using trends in behavior tohelp in discovering superconductors has longbeen recognized, starting with the rules set outby Matthias.28,29 Finally, we mention the puz-zling fact that although there have been morethan a dozen predictions of high-temperaturesuperconductivity in compressed hydrogen-richcompounds,16,17,19,22,23,30–39 sulfur hydride is theonly system to date that has been demonstratedto exhibit a higher superconducting tempera-ture than the record of 164 K set by cuprates.40

The second higher-Tc material identified in ex-periments is silicon hydride with Tc = 17 Karound 100 GPa,,41 although the origin of thesuperconductivity is still under debate (likelyfrom platinum hydride).42,43 The chemical andphysical properties of sulfur hydride that makeit the highest-Tc superconductor found so farare not yet fully understood. Here we provideinsight into this puzzle based on trends derivedfrom data for a wide range of high-pressure hy-drides.

II. COMPUTATIONAL AP-

PROACHES

Our investigation consists of determination ofstable stoichiometries and crystalline struc-tures, and calculation of their superconduct-ing and related properties. The hitherto un-known high-pressure phase diagrams (at 0 K)of pnictogen (X) hydrides were explored by per-forming very extensive structure searches for aset of stoichiometries XnHm, and the most sta-ble structure and low-lying enthalpy metastablestructures were identified for each XnHm. Thesecalculations were performed using two leadingcodes for first-principles structure prediction,CALYPSO44,45 and AIRSS.46,47 The energeti-cally stable stoichiometries and the most stablestructure at each stoichiometry obtained fromthe two searching methods are in agreement.Over 100 stoichiometries were searched and atotal of about 100,000 structures were relaxedby minimizing the total energy within the P/H,As/H and Sb/H systems.

DFT calculations were performed using theVASP code48 with projected-augmented-wave(PAW)49 potentials, and the CASTEP codewith ultrasoft pseudopotentials. The 1s (H),3s and 3p (P), 4s and 4p (As), and 5s and 5p(Sb) electrons were treated explicitly as valenceelectrons. We used the generalized gradient ap-proximation exchange-correlation functional ofPerdew, Burke and Ernzerhof.50 Medium qual-ity computational parameters were used whenevaluating the enthalpies of structures duringthe searches. The low-lying enthalpy structureswere then further optimized using the PAWmethod and more accurate computational pa-rameters consisting of kinetic energy cutoff en-ergies of 650 eV (P/H and As/H) and 510 eV(Sb/H), and k-point meshes of spacing 2π×0.03 Å−1 or less. We checked the energy con-vergence with respect to these parameters andfound convergence of the enthalpy differencesto better than 1 meV/atom level.

We calculated the phonon dispersion relationsand EPC using linear response theory as imple-mented in the Quantum ESPRESSO package.51

These calculations were performed using norm-

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conserving pseudopotentials and a kinetic en-ergy cutoff of 100 Ry. For reliable evaluation ofthe double-delta function integrals in the EPCcalculations, dense k-point meshes with a spac-ing of about 2π× 0.015 Å−1 were used, in com-bination with the Methfessel-Paxton broaden-ing scheme52 with a broadening parameter of0.05 Ry. For the Brillouin sampling of phononmomentum, a q-point mesh with a grid spacingof ∼2π× 0.06 Å−1 was adopted.

0

40

80

120

P H2

(a) 100GPa200GPa

300GPa

400GPa

-50

0

50

100

∆H (meV/atom)

AsHAsH8

As H2

(b)

0.0 0.2 0.4 0.6 0.8 1.0x[nH2/(nX+nH2)]

-300

-200

-100

0

100

SbH4SbH SbH3Sb H2

(c)AsH

Figure 1: (color online) Calculated formationenthalpies ∆H (in meV/atom) of various pnic-togen hydrides with respect to decompositioninto the elemental solids at 100 (squares), 200(triangles), 300 (circles) and 400 (diamond)GPa, respectively. The data for each stoi-chiometry corresponds to the lowest enthalpystructures from the searches. The structures ofphases VI (Pm3̄m) and VIII (Im3̄m) of P,53 IV(Im3̄m) of As,53 III (Im3̄m) of Sb,53 and theP63m and C2/c structures of solid H2

54 wereused for evaluating ∆H.

III. RESULTS AND DIS-

CUSSION

3.1 Phase stabilities and stable crystallinestructures of pnictogen hydrides at high

pressures. Since H-rich compounds are poten-tially more favorable for high-temperature su-perconductivity,14 we focused our CALYPSOsearches on the XnHm (n=1∼3 and m=1∼8)stoichiometries with higher H contents (m ≥ n)containing up to 4 formula units per simulationcell. More diverse stoichiometries (with m up to13) were considered in the AIRSS searches. Themain results from these cross-checking searchcalculations are depicted in the hull diagramsof Fig. 1, which each contain data for pres-sures of 100–300 GPa. For As hydrides (Fig.1b), searches at the higher pressure of 400 GPawere performed to demonstrate the stability ofthe AsH and AsH8 structures above 300 GPa.Only the lowest enthalpy structure at each sto-ichiometry studied is shown.

We find a surprising trend in that at highpressures the thermodynamic stability of pnic-togen hydrides increases with the atomic num-ber of the pnictogen. The P hydrides (Fig.1a) are found to be unstable against decom-position into the elements, and pressure doesnot have a noticeable effect on their stability.The predicted lowest-energy structures of sev-eral metastable stoichiometries are shown inSupplementary Fig. S1 and Table S1. As andSb hydrides (Fig. 1b and 1c) show a clear ten-dency to be stabilized by increasing pressure;for As hydrides, a single stoichiometry stableagainst elemental decomposition into the ele-ments emerges at 300 GPa, while for Sb hy-drides, all the stoichiometries become stableabove 200 GPa. These results indicate thatthe relative stabilities of the pnictogen hydridesobtained from the known chemical bondingstrengths at ambient conditions (P > As > Sb)are opposite to those found at high pressures (P< As < Sb). We find two stable binary As hy-drides on the convex hull at 400 GPa, AsH andAsH8. We find three compounds on the convexhull for Sb hydrides at 300 GPa and two at 200GPa. These are SbH, SbH3 (at 300 GPa only)and SbH4. Note that the much lower forma-tion enthalpies of Sb hydrides (∼200 meV/atommore stable) demonstrates their high stabilityunder compression. We evaluated the effect ofzero point energy (ZPE) on the phase stabilityby calculating harmonic phonon spectra for Sb

4

hydrides, as shown in Supplementary Fig. S2.Inclusion of the ZPE gives rise to a negligiblechange in the convex hulls.

The structures of the predicted stable com-pounds are shown in Fig. 2a-e (see Supple-mentary Table S2 for detailed structural in-formation), and the pressure ranges withinwhich they are stable are depicted in Fig. 2f.The stable structures of the compounds re-main unchanged throughout their stable pres-sure ranges. The AsH hydride (Fig. 2a) adoptsa structure of Cmcm symmetry which is sta-ble above 300 GPa. It consists of a three-dimensional As-H network in which both Asand H atoms are approximately five-fold co-ordinated. The lowest enthalpy structure ofAsH8 (Fig. 2b) of C2/c symmetry is stabilizedabove 350 GPa. It is formed from the pri-mary motifs of irregular AsH16 polyhedra, con-nected with each other in a three-dimensionalnetwork. Each corner H atom of the AsH16polyhedron is linked to another H from the ad-jacent polyhedron. The short contact betweentwo H atoms leads to formation of an intrigu-ing quasi-molecular H2-unit with a bond lengthof ∼0.8–0.9 Å. The formation of such H2-unitsin compressed hydrides is also seen in systemswith Si, Ge, Sn, Li, Ca, Te,23,30,32,33,55,56 etc.

The energetically favored structure of SbH(Fig. 2c, stable above 175 GPa) has spacegroup Pnma and is composed of chain-like Sb-H motifs with each Sb coordinated by three Hatoms. The H-rich compounds SbH3 (Fig. 2d)and SbH4 (Fig. 2e) have Pmmn and P63/mmcsymmetries, respectively. While the former ismarginally stable (very close to the convex hullformed by SbH and SbH3 in Fig. 1c) at 300GPa, the latter is robustly stable above 150GPa. SbH3 is composed of irregular polyhe-dral SbH10 and SbH12 motifs which form itsthree-dimensional topology. Bridging the ad-jacent SbH12 motifs in a two-dimensional fash-ion gives rise to quasi-molecular H2-units (inred) with a rather long bond length of ∼0.91 Å,compared with the molecular H2 bond length of0.74 Å. SbH4 is a highly symmetrical hexagonalcompound that consists of SbH14 octadecahe-dra connected via shared H atoms at the cornersto form a three-dimensional network. There are

Figure 2: (color online) Structures of the pre-dicted stable pnictogen hydrides: (a) AsH(space group Cmcm), (b) AsH8 (C2/c), (c)SbH (Pnma), (d) SbH3 (Pmmn); (e) SbH4(P63/mmc). The As/Sb–H bonds are depictedby dashed lines and H–H covalent bonds as redsticks. The corresponding stable pressure rangeof each compound is shown in (f).

two types of H atoms occupying the 4e (black)and 4f (red) Wyckoff sites, respectively. Each4e H atom is coordinated by three Sb atoms,and the 4f H atom, while coordinated by twoSb atoms, has a close contact with another 4fH atom, forming quasi-molecular H2-units witha bond length of ∼0.83 Å. SbH4 resembles theTeH4 compound with the same stoichiometrywhich adopts the R3̄m phase.23

A Bader charge density analysis57 shows sub-stantial charge transfer from As/Sb to H (seeSupplementary Table S3). This indicates thatthe As/Sb–H bonds have substantial ionic char-acter. On the other hand, plots of the electronlocalization function (ELF) (see SupplementaryFig. S5) show material-dependent (see below)

5

charge concentration between As/Sb and Hatoms. Hence the predicted stable compoundsare dominated by mixed covalent and ionic in-teractions.

3.2 Electronic structure, phonons,electron-phonon coupling and supercon-ductivity of identified stable pnictogenhydrides. The DFT calculations indicate thatall of the compounds are metallic within theirstable pressure ranges. Fig. 3 shows band struc-tures and projected densities of states (DOS)for three H-rich compounds, AsH8, SbH3 andSbH4 (see Supplementary Fig. S3 for resultsfor H-poor AsH and SbH). The Fermi levels(Ef ) of AsH8 (Fig. 3a-b) and SbH4 (Fig. 3e-f)are located at shoulders of a peak in the DOS,leading to a rather large value of the DOS atEf (N(Ef )). Moreover, substantial H-derivedstates exist in proximity to Ef , which mimicssolid metallic hydrogen. These features arepotentially favorable for high-temperature su-perconductivity. This is, however, not the casefor SbH3 (Fig. 3c-d) in which Ef lies near thebottom of a broad valley in the DOS, whichgives a low N(Ef ), and only a small amount ofH derived states at Ef .

As shown in the phonon spectra of Fig. 4 (a:AsH8, d: SbH3 and g: SbH4) and Supplemen-tary Fig. S4 (AsH and SbH), all of the com-pounds are dynamically stable as demonstratedby the absence of imaginary phonon frequen-cies. The projected phonon DOS of SbH4 (Fig.4h) shows three well separated regions: thelow-frequency vibrations associated with heavySb atoms (below 15 THz), higher frequencywagging, bending and stretching modes derivedfrom the H atom bonded to Sb (between 15 and65 THz) and high-frequency intra-molecular H–H stretching modes from the quasi-molecularH2-units (around 80 THz). The H–H stretchingmodes of SbH3 (Fig. 4e) are lower in frequencyand they merge into the medium-frequency re-gion because of the larger bond lengths of theH2-units. In AsH8 (Fig. 4b), two groups of H–H stretching modes appear, which correspondto two types of H2 unit with different bondlengths.

We performed EPC calculations for the pre-dicted stable compounds to probe their super-

Figure 3: (color online) Calculated band struc-tures and projected densities of states of stableH-rich pnictogen hydrides: (a,b) AsH8 at 350GPa, (c,d) SbH3 at 300 GPa and (e,f) SbH4 at150 GPa. The green circles in the band struc-tures represent the orbital projections of theelectronic states onto H atoms.

conducting properties. Fig. 4 shows the EPCparameters for each phonon mode (a,d,g), theEliashberg EPC spectral function α2F(ω) andits integral λ(ω) (c,f,i) for AsH8, SbH3 andSbH4 (results for AsH and SbH are shownin Supplementary Fig. S4). Fig. 5a summa-rizes data for the total EPC parameters λand their pressure dependence. AsH8 andSbH4 are H-rich compounds with rather highλ values above 1.0, while SbH3 has a lowervalue of about 0.5. For all three H-rich com-pounds the intermediate-frequency H-derivedwagging, bending and stretching phonons andlow-frequency vibrations from the heavy As/Sbatoms, rather than the high-frequency phononsderived from the H2-units, dominate the contri-butions to the total EPC.

Within the framework of strong-coupling BCStheory,58 the total EPC parameter is propor-tional to the product of N(Ef ) and the squaredelectronic matrix element < I2 > averaged overthe Fermi surface. The calculated values of

6

L M A Γ Z V0

20

40

60

80

100(a) AsH8 (b)

As

H

(c)

α2 Fλ

Γ Z T Y S X U R0

20

40

60

80

ω(THz)

(d) SbH3 (e)

Sb

H

(f)

α2 Fλ

Γ A H K Γ M L H0

20

40

60

80

100(g) SbH4

PHDOS

(h)

Sb

H

0 1 2

(i)

α2 Fλ

Figure 4: (color online) Calculated phonon dis-persion curves (a,d,g), projected phonon den-sity of states (PHDOS) (b,e,h), Eliashberg EPCspectral functions α2F(ω) and its integral λ(ω)(c,f,i) of AsH8 at 350 GPa, SbH3 at 300 GPaand SbH4 at 150 GPa, respectively. The pro-portion of red color in the phonon dispersioncurves represents the magnitude of the EPC pa-rameter λn,q(ω) at each phonon mode (n, q).

N(Ef ) for each compound are shown in Fig.5b. While AsH8 and SbH4 have rather highvalues of N(Ef ), SbH3 exhibits quite a lowN(Ef ). These results accord with their sig-nificantly different λ values. The high N(Ef )in H-poor AsH arises predominantly from As-induced states (Supplementary Fig. S3b) andresults in a small value of λ similar to that of su-perconducting solid As under compression.59,60

Besides the difference in N(Ef ), we find that thestrengths of the covalent components of As/Sb–H bonds (with mixed covalent and ionic nature)vary considerably among the compounds, as in-dicated by the ELF data shown in Supplemen-tary Fig. S5. The Sb–H bonds in SbH3 are muchweaker than those of SbH4 and the As-H bondsin AsH8. The weaker Sb–H bonds in SbH3 inprinciple correspond to a low deformation po-tential, i.e., a smaller modification of the elec-tronic structure, with respect to the motion of

H atoms. This leads to a relatively small <I2 >, and thus a low λ.

0.0

0.5

1.0

1.5

2.0

λ

(a)

0.010

0.012

0.014

0.016

N(E

f)(states/eV/Å

3)

(b)

150 200 250 300 350 400 450P (GPa)

0

40

80

120

160

Tc(K)

(c)AsH

AsH8SbH

SbH3SbH4

Figure 5: (color online) The total EPC param-eter λ (a), electronic DOS at the Fermi levelN(Ef ) (b) and superconducting critical temper-ature Tc (c) as a function of pressure for thepredicted stable compounds. For the Tc calcu-lations, two different screened Coulomb repul-sion parameters of µ∗ = 0.1 (filled symbols andsolid lines) and 0.13 (open symbols and dashedlines) are used for comparison.

The superconducting Tc values of the sta-ble compounds are evaluated using the Allen-Dynes modified McMillan equation61 with cal-culated logarithmic average frequency (ωlog)and a typical choice of screened Coulomb repul-sion parameter of µ∗ = 0.1. The results shownin Fig. 5c (see Supplementary Table S4 for nu-merical values) are consistent with the trends inλ (Fig. 5a). AsH8 and SbH4 exhibit quite highTc values of around 150 K and 100 K, respec-tively. The other compounds have moderateTc values of ∼20 K or below. The value of Tcin SbH4 decreases slightly with pressure, whileAsH8 shows an increase. Using a standard valueof µ∗ = 0.13 for metallic hydrides,14 we find asmall decrease in Tc with pressure, ∼8–11% inthe higher-Tc compounds of AsH8 and SbH4.

3.3 Deduced general chemical trends

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of high-pressure hydrogen-containing su-perconductors. Gathering data for pnicto-gen hydrides and other hydrides12,22,23,30–38,62,63

allows us to deduce useful physical princi-ples about the phase stability and occurrenceof high-temperature superconductivity in H-containing materials under pressure. For clar-ity, here we consider only the binary hydridesMnHm formed by main-group elements M withsp bonding. We find that the Pauling elec-tronegativity difference between M and H atambient pressure, χM −χH , is a good “descrip-tor” of high-pressure phase stability, structuralfeatures and superconducting properties of thehydrides. Specifically, we find that the follow-ing properties of MnHm are related to χM−χH :

(i) Energetic stability against elemental de-composition. Fig. 6 shows formation enthalpiesof various hydrides at 200 GPa as a functionof χM − χH . For cases in which more than onestable stoichiometry exists, the averaged forma-tion enthalpy (among all the stoichiometries) isshown, accompanied by an error bar indicatingthe maximum and minimum enthalpy. The di-ameter of the circular symbol is proportionalto the atomic radius of M.64 This divides hy-drides into two classes with negative and pos-itive χM − χH , respectively. Considering theextreme cases, H2O with χM − χH � 0 hasstrong covalent O–H bonds, whereas LiH withχM−χH � 0 has strong ionic Li–H bonding. Itmay thus be reasonable to conjecture that thehydrides with χM−χH > 0 prefer to form cova-lent M–H bonds, while those with χM−χH < 0are more ionic in nature. In the regions of bothχM − χH > 0 and χM − χH < 0, we observe ageneral trend that the formation enthalpy de-creases (i.e., stability increases) with |χM−χH |.For χM − χH > 0, this can be explained by thelarger electronegativity of M which correspondsto strongly covalent M–H bonds, and thereforeto higher stability of the hydrides. In this re-gion, the atomic radius can also affect the co-valent bond strength, and therefore have a crit-ical role in determining the stability. For in-stance, despite the similar electronegativities ofS and Se, S hydrides have much lower formationenthalpies than Se hydrides (by about 50∼150meV/atom). We attribute this to the smaller

atomic radius of S favoring stronger covalentH–S bonds. In the region χM − χH < 0, thesmaller electronegativity of M and larger valueof |χM−χH | leads to substantial charge transferfrom the cationic M to anionic H. On the onehand, this increases the Madelung energy of theionic component of the M–H bonding, which in-creases the stability. On the other hand, thecharge transfer is favorable for the formation ofquasi-molecular H units in the interstitial re-gions (see below). This lowers the enthalpy ofhydrides and make them more stable. This ex-planation accords with the increased thermo-dynamic stability of P, As, and Sb hydrides, asdemonstrated above.

Figure 6: (color online) Formation enthalpies∆H (in meV/atom) of main-group-element (M)binary hydrides12,22,23,30–38,62 at 200 GPa withrespect to decomposition into the constituentelemental solids, plotted against the electroneg-ativity difference between M and H at ambientpressure, χM−χH . The electronegativity valuesare taken from Pauling’s scale.65 When severalstable phases with different stoichiometries ex-ist, the averaged formation enthalpy is shown,and the endpoints of the error bars representthe minimum and maximum values of ∆H. Thesizes of the circles are proportional to the empir-ical atomic radii.64 The regions correspondingto positive and negative χM − χH are shown inthe background colors of pink and gray, respec-tively.

(ii) Key structural features. For the hydrideswith χM − χH < 0, for example our predicted

8

AsH8, SbH3 and SbH4 phases, there is sub-stantial charge transfer from the relatively elec-tropositive M to the electronegative H (Sup-plementary Table S3). The M–H bonds havemixed covalent and ionic nature. With suchweaker M–H bonding, the H atoms are proneto move to the interstitial regions under pres-sures. Therefore, substantial energy gain maybe achieved via the formation of H–H cova-lent bonds in the interstitial regions. This isespecially the case under pressure where largenon-bonded anions are unfavorable. This leadsto the formation of intriguing quasi-molecularH-units in H-rich compounds.23,30–33,55,66 Turn-ing to χM − χH > 0, for instance S12,16,17 andSe19,22 hydrides, the strong polar covalent M–H bonds dominate. Under such conditions, allcationic H atoms are tightly bonded by the Matoms with large electronegativity, and thus theformation of H–H bonds is energetically un-favourable. The quasi-molecular H-unit is ab-sent in the hydrides. The distinction betweenthis key structural behavior in the two regions isreflected in Fig. 7, which shows the evolution ofthe CALYPSO search for SbH4(χM − χH < 0)and SeH3(χM − χH > 0) at 200 GPa. Usuallytens of generations are required to determinethe global minimum in the CALYPSO calcu-lations. The structures at each generation aresorted according to their enthalpy. The colorcoding represents the minimum distance be-tween two H atoms in each structure. All of thelow enthalpy structures of SbH4 contain quasi-molecular H2 units with short contacts (0.8∼0.9Å) between neighboring H atoms. In contrast,in SeH3 the low-lying structures exhibit largeminimum H–H distances (over 1.5 Å) as three-dimensional covalent H-Se networks are formed.

(iii) Density of states at the Fermi level. Asdemonstrated in Fig. 5b, N(Ef ) is a criticalparameter in determining the strength of theEPC. Fig. 8 shows the values of N(Ef ) forthe binary hydrides that are predicted to besuperconductors,12,22,23,30–35,37–39,62,63 as a func-tion of χM − χH at 200 GPa. To make a faircomparison and avoid potential errors arisingfrom different theoretical calculations, we takestructural data from Ref. 12,22,23,30–35,37–39,62,63, and perform full structural optimiza-

Figure 7: (color online) The structures gener-ated are sorted according to enthalpy during theCALYPSO structure searches for SbH4 (a) andSeH3 (b) at 200 GPa, as a function of searchgenerations. The color-coding represents theminimum distance between two H atoms, whichis also proportional to the size of the circle. Theinsets show the predicted ground-state struc-tures of SbH4 and SeH3.

tions and calculate N(Ef ) using the plane-wavePAW method. In general, we find that highvalues of N(Ef ) appear in the region with rela-tively small magnitudes of χM −χH . The com-pounds with higher values of N(Ef ) in the tworegions are TeH4, SbH4 (χM−χH < 0) and SH3,SeH3 (χM − χH > 0), respectively. The highlysymmetric structures of these hydrides (TeH4:P6/mmm; SbH4: P63/mmc; S/SeH3: Im3̄m),which in principle give rise to high degener-acy of the band structure at special k-points,may be responsible for the high values of N(Ef ).They are all predicted to be good superconduc-tors with values of λ above 1.12,17,19,22,23

(iv) Features of the electron-phonon coupling.Fig. 9 shows the Eliashberg spectral functionα2F(ω) (black lines), its normalized integralλ(ω) (divided by the total λ, colorful scale),and logarithmic average frequency ωlog (blackscale) of typical compounds from the two re-

9

Figure 8: (color online) Calculated electronicDOS at the Fermi level N(Ef ) of main-group-element binary hydrides12,22,23,30–35,37–39,62,63 at200 GPa, as a function of the electronegativitydifference between M and H at ambient pres-sure, χM − χH . When several stable phaseswith different stoichiometries exist, we choosethe one with the highest predicted supercon-ducting Tc. Similar to Fig. 6, the regions ofχM −χH > 0 and χM −χH < 0 are in pink andgrey, respectively.

gions. In the χM − χH < 0 region (AsH8and SbH4), the total EPC originates mainlyfrom the medium-frequency phonons, predomi-nantly wagging, bending, and stretching modesderived from the H bonded to As/Sb. Thehigher frequency H–H stretching modes of thequasi-molecular H2-units make fairly small con-tributions to the EPC. Therefore the integralλ(ω) becomes saturated (in blue) at the upper-middle part of the ω range. Turning to theregion of χM − χH > 0 (SH3 and SeH3), theEPC arises mainly from the high-frequency H-derived phonons of covalent M–H networks.The integral λ(ω) thus becomes saturated closeto the upper boundary of ω. These featuresof the EPC can be ascribed to the differentchemical bonding and structural features ofthe hydrides in the two regions. Note that

ωlog, the important quantity determining thesuperconducting Tc, shows higher values in theχM − χH > 0 region than in the χM − χH < 0region, despite the evidently lower maximumω of the former region than that of the latter.This demonstrates that simply hardening thephonons is not always effective in raising Tc.The reason originates from the distinct depen-dence of α2F(ω) on ω in the two regions, sinceonly the phonons contributing to the EPC arecounted when evaluating Tc.

3.4 More relevant discussion. SinceAshcroft first proposed metallic hydrides as po-tentially good superconductors at high pres-sures,14 high-Tc (above 100 K) superconductiv-ity has been predicted in a number of high-pressure H-rich compounds.12,17,22,23,30,31 The Shydride is one of these predictions16,17 that hasbeen confirmed experimentally.5,6 In other sys-tems, either low temperature superconductiv-ity41,67 or no superconductivity68,69 was found.While the underlying reasons for this are notyet settled, one possibility is that the predictedsuperconducting compounds did not form inhigh-pressure experiments. Confining hydridesor mixtures of hydrogen and other substancesin diamond anvil cells up to ultrahigh pressureconditions is technically challenging and, due tothe technical limitations, experimental synthe-ses may fail even though the theoretically pre-dicted structures are energetically stable. Thisis highly likely for hydrides with small forma-tion enthalpies, such as those of Si, Ge, B, Se,etc., as indicated in Fig. 6.

It is also possible that kinetic processes un-der pressure inhibit formation of some of thepredicted compounds. If so, a highly symmet-ric structure may be more likely to be syn-thesised because the energetic barrier for thetransition between the symmetric structure andother isomers is usually large. This suggestsa strong kinetic stability with respect to vari-ations in the external conditions. From thispoint of view, S hydrides are indeed favorablefor experimental synthesis since the stable SH3structure has simultaneously a large formationenthalpy (∼135 meV/atom at 200 GPa) andhigh symmetry (space group Im3̄m). In thissense, the SbH4 phase predicted in the present

10

Figure 9: (color online) The Eliashberg EPCspectral function α2F(ω) (black lines), its in-tegral λ(ω) (colorful scale), and logarithmicaverage frequency ωlog (black scale) for typi-cal hydrides in the regions of χM − χH > 0(SH3 and SeH3) and χM − χH < 0 (AsH8 andSbH4). For comparison among different com-pounds, the λ(ω) is normalized and divided bythe total λ (indicated for each compound).

work is quite promising for possible experimen-tal synthesis, in view of its large formation en-thalpy (∼90 meV/atom at 200 GPa) and highlysymmetric structure (space group P63/mmc).Certainly the larger barrier associated with thehighly symmetric structure may make its syn-thesis challenging. This can be basically over-come by for instance sufficient thermal energyor catalytic assistant.

Turning to trends, results from the currentand previous theoretical studies reveal a con-nection between the thermodynamic stability,structural features and superconducting prop-erties of high-pressure hydrides, and the Paul-ing electronegativity differences between H andthe other elements. This is a remarkable and atfirst sight strange finding, since high-pressurechemistry is well known to be radically differ-ent from that at ambient pressure.70 Our find-ings indicate that the ambient-pressure chemi-cal properties determine to a large extent thehigh-pressure behavior.

Electropositive elements (with χM − χH � 0in our classification), such as alkaline and al-kaline earth metals, form highly ionic ambient-

pressure hydrides characterized by large chargetransfers and structures similar to fluorides. Inparticular, the crystals are stabilized by theMadelung energy of the cationic M and anionicH ions. The anionic H in these materials arewell separated from other H ions and the Hvibrational frequencies are relatively low. Athigh pressures the distances between H anionsare significantly shortened, but the weak ionicM–H bonds allow H atoms to move to the in-terstitial regions. These lead to stabilizationof the H–H covalent bonds in the interstitialregion. Thus quasi-molecular aggregation ofH emerges30,55,63,66 and high H vibrational fre-quencies occur in the high-pressure phases.

Non-metallic strongly electronegative ele-ments (with χM − χH � 0) often form weaklybound insulating H-containing molecular solidsat ambient pressure, e.g., NH3, H2O, H2S, etc.While strong covalent M–H bonds dominatemolecules, the intermolecular bonds character-izing cohesion of molecular solids are weak vander Waals bonds and hydrogen bonds. Undercompression, with decreasing intermoleculardistances and accompanying hydrogen-bondsymmetrization,71–73 solids with covalent M–Hbonding networks eventually become energeti-cally favored. Because of the strong polar cova-lent M–H bonds, the H–H bonds and aggrega-tion of H atoms are energetically unfavourable.

As for the elements with moderate electroneg-ativities comparable to that of H (χM − χH ∼0), the hydrides formed are intermediate be-tween the above two cases. The M–H bondshave mixed covalent and ionic characters, andthe former is not strong enough to stabilize co-valently bonded M–H networks. In the hydrideswith χM−χH < 0 (Si, Ge, Sn, Te, Sb, etc.), theanionic nature of H atoms (due to the chargetransfer from M to H) and the tendency of Hatoms to move to interstitial regions (due tothe relatively weak M–H bonds) under pressureallows aggregation of H via formation of H–Hcovalent bonds in H-rich phases. This mecha-nism helps to stabilize hydrides. The stabilityincreases with the magnitude of χM − χH (asin Fig. 6), which determines the Madelung en-ergy of the ionic interaction and the capabilityof hydrides to form aggregates of H. For As and

11

P hydrides with small |χM − χH |, only limitedcharge transfer from As/P to H can occur dueto the small electronegativity difference. Onthe other hand, the fairly strong As/P–H co-valent bonds hinder H atoms from moving tointerstitial regions. Hence H–H covalent bondsare unlikely to form. This may be responsiblefor their positive formation enthalpies in Fig. 6.

Once metallic hydrides are stabilized by highpressure, one can ask whether or not they aregood superconductors. Our current results indi-cate that three features of hydrides are essentialfor strong EPC and a high Tc. The first is a highN(Ef ). While this quantity certainly dependson the specific band structure and electronicoccupation, highly symmetric structures are inprinciple favorable for high values of N(Ef ). In-terestingly this occurs with small magnitudesof |χM − χH | (Fig. 8). The second feature isthe appearance of substantial H-derived statesin proximity to Ef , mimicking pure metallichydrogen. H-rich compounds are more likelyto satisfy this criterion. The third feature isthe large electronic deformation potential withrespect to motion of H atoms. The hydrideswith strong chemical bonding, especially cova-lent bonding, are more favored by this feature.In this regard, the Tc of S hydrides are pre-dicted to be enhanced by alloying with moreelectronegative elements (e.g., P and O)11,74 tofurther strengthen the covalent bonding. Forthe hydrides containing quasi-molecular assem-blies of H atoms,23,30–34,55,63,66,75 the deforma-tion potential associated with intra-molecularH–H stretching motion is fairly large (due to thestrong H–H covalent bonds). Unfortunately,as demonstrated in Fig. 9, the correspondingphonon modes make a quite limited contribu-tion to the EPC. An even higher superconduct-ing Tc would be expected if these phonon modeswere involved in the EPC, for example, underfurther compression.

While preparing this manuscript, our atten-tion was drawn to two reports on superconduc-tivity in pnictogen hydrides. One is a prelim-inary observation of high Tc superconductivityin P hydrides from ∼30 K increasing continu-ously to more than 100 K up to pressures above200 GPa.76 While more experimental data are

required to verify this finding, the basic idea co-incides with the main motivation of this work.However, based on our structure searching re-sults, P hydrides are predicted to be unsta-ble against elemental decomposition up to 400GPa. Our results point to the possibility thatP hydrides formed in the experiments76 may bemetastable and could be stabilized by kineticprocesses at high pressures. The conclusionthat the P hydrides are thermodynamically un-stable at megabar pressures is consistent withrecent theoretical reports.77,78 Further analysisof the metastability, energy barriers related tokinetic stability, as well as superconductivitycalculations for P hydrides, will be publishedelsewhere. Another is the theoretical predic-tion of 106 K superconductivity in SbH4 at 150GPa by Ma et al.79 Using a structure search-ing method based on a genetic algorithm,80

they obtained the same high-symmetry struc-ture (space group P63/mmc) of SbH4 that wehave found in our work. Their calculationsof superconducting properties also agree withours. Experimental attempts to synthesise Sbhydrides at high pressures and explore theirsuperconducting properties are eagerly antici-pated to test this theoretical prediction.

IV. CONCLUSIONS

We have used first principles structure search-ing methods to study the hitherto unknownphase diagram of solid pnictogens (i.e., P, As,Sb) hydrides at high pressures with the aim ofpredicting new high-Tc superconductors. Sur-prisingly, except for the molecular solid phasesstabilized by weak van der Waals interactionsnear ambient pressure, we did not find any Phydrides to be stable with respect to decompo-sition into the elements up to 400 GPa. Thehydrides containing the heavy element Sb arefound to be the most stable at high pressures.This was unexpected because at ambient pres-sure the lighter pnictogen hydrides are the moststable.

We have predicted several stable supercon-ducting hydrides (AsH, AsH8, SbH, SbH3 andSbH4). Among them, two H-rich compounds,

12

AsH8 and SbH4 are predicted to exhibit Tc val-ues of ∼150 K above 350 GPa, and ∼100 Kabove 150 GPa, respectively. SbH4 is energeti-cally very stable and adopts a highly symmet-rical hexagonal structure, and the stabilizationpressure is well within reach of modern diamondanvil cell experiments. Finally, through sys-tematic analysis of current and previous studiesof binary hydrides, we determined a close con-nection between the high-pressure behavior ofhydrides and ambient pressure chemical quan-tities. In particular we found that the elec-tronegativity difference between the constituentelements is a good descriptor for characteriz-ing the structure, chemical bonding, thermo-dynamic stability and superconducting proper-ties of hydrides at high pressures. Analysingthese trends could provide further insights intothe intriguing and diverse chemical and physicalproperties of compressed hydrides. Our workprovides a useful roadmap for discovering morestable compressed hydrides and exploration oftheir superconducting properties.

ASSOCIATED CONTENT

Supporting Information. Effect of zeropoint energy on phase stabilities, Electronicstructure, phonon, electron-phonon couplingresults of H-poor compounds, Electron localiza-tion function and Bader charge analysis results,Explicit structural information and calculatedsuperconducting properties of the identified sta-ble hydrides.

ACKNOWLEDGMENTS

The authors thank Eva Zurek for sharing struc-ture data for iodine hydride. The work atJilin Univ. is supported by the funding ofNational Natural Science Foundation of Chinaunder Grant Nos. 11274136 and 11534003,2012 Changjiang Scholar of Ministry of Edu-cation and the Postdoctoral Science Founda-tion of China under grant 2013M541283. L.Z.acknowledges funding support from the Re-cruitment Program of Global Youth Expertsin China. Part of calculations was performed

in the high performance computing center ofJilin Univ. R.J.N. acknowledges financial sup-port from the Engineering and Physical Sci-ences Research Council (EPSRC) of the UK[EP/J017639/1]. R.J.N. and C.J.P. acknowl-edge use of the Archer facility of the U.K.’s na-tional high-performance computing service (forwhich access was obtained via the UKCP con-sortium [EP/K013564/1]).

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Figure 10: For Table of Contents Only

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