Composition and Constitution of Compressed Strontium Polyhydrides

Article pubs.acs.org/JPCC

Composition and Constitution of Compressed Strontium Polyhydrides James Hooper,† Tyson Terpstra,‡ Andrew Shamp,‡ and Eva Zurek*,‡ †

Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, 30-060 Krakow, Poland Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000, United States

‡

S Supporting Information *

ABSTRACT: The structures of the strontium polyhydrides, SrHn with n > 2, under pressure are studied using evolutionary algorithms coupled with density functional theory calculations. A number of phases with even n are found to be thermodynamically stable below 150 GPa. Particularly interesting is the SrH4 stoichiometry, which comprises the convex hull at 50, 100, and 150 GPa. Its hydrogenic sublattice contains H2 and H− units, and throughout the pressure range considered, it adopts one of two configurations which were previously predicted for CaH4 under pressure. At 150 GPa, the SrH6 stoichiometry has the lowest enthalpy of formation. The most stable configuration assumes P3̅ symmetry, and its lattice consists of one-dimensional H2···H− hydrogenic chains. Symmetrization of these chains results in the formation of 1∞[Hδ−] helices, which are reminiscent of the trigonal phase of sulfur. The R3̅m-SrH6 phase, which is comprised of these helices, becomes dynamically stable by 250 GPa and has a high density of states at the Fermi level. We explore the geometric relationships between R3m ̅ -SrH6 and the Im3m ̅ -CaH6 and Imm2-BaH6 structures found in prior investigations.

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INTRODUCTION In 1935, Wigner and Huntington predicted that hydrogen would become an alkali-metal-like monatomic solid when compressed to P > 25 GPa.1 Just over thirty years later, Ashcroft prophesied that the large phonon frequencies in metallic hydrogen (a result of the small atomic mass), large electron−phonon coupling (which arises from the strong covalent bonds between the hydrogen atoms and lack of core electrons), and substantial density of states (DOS) at the Fermi level (EF) would render metallic hydrogen superconducting at high temperatures.2 This elusive state of matter3 has been coined the “holy grail” of high pressure research, and substantial experimental4−12 effort has been invested toward finding ways in which it may be attained. Experiments have been supplemented by extensive theoretical explorations of the potential energy landscape, electronic structure, and properties of hydrogen under pressure; a small portion of the plethora of recent examples includes refs 13−22. The work carried out to date illustrates that one way to metalize hydrogen is to access the appropriate region of the temperature/pressure phase diagram. However, because of the extreme conditions needed to achieve metalization (P > 250 GPa at 300 K) a chemical route toward this “holy grail” is also being sought out. One may wonder if compressed hydrogen can be metallized via doping by a particular element,23,24 if the resulting phases also have the propensity to be superconducting at high temperatures,25 and if they could be stabilized at 1 atm? Intense research, in diamond anvil cells and in silico, has been directed toward exploring chemical avenues toward metal© 2014 American Chemical Society

ization by combining hydrogen with other elements from the periodic table. Most of the transition metals in Groups 6−11 do not readily react with hydrogen at 1 atm, and high pressures are necessary to marry the two. Experiments and theory have been employed to study hydrides containing Ru, Pd, Ag, Os,26 Rh,26,27 W,28,29 Nb,30 Pt,26,31−33 and Cu,34 to name a few. Notably, around 100 GPa PtH was found to be a superconductor.31−33 Another set of widely studied systems are the Group 13 and Group 14 hydrides with the stoichiometries AlH3,35,36 GaH3,37 SiH4,38−46 Si2H6,47,48 GeH4,49−52 SnH4,53,54 and PbH4.55 Phases containing a main-group element and stoichiometries which, from a vantage point at 1 atm, may appear unusual have been explored as well. For example, computations have shown that BH may become preferred over BH3 under pressure,56 and H4O over H2O.57 The SiH4/H2 phases with ratios of 1:1, 1:2, and 1:5,58,59 Xe(H2)7,60 GeH4(H2)2,61 and (H2S)2H262 have all been experimentally characterized, with computational studies following suit.62−68 Herein we expand on explorations of the cold phase diagram of hydrogen combined with electropositive elements as a function of stoichiometry and pressure via first-principles theory.69−78 Due to the immense computational expense involved in calculating finite temperature effects, these have been neglected, as is often customary. We do note however that temperature Received: December 21, 2013 Revised: February 25, 2014 Published: March 3, 2014 6433

dx.doi.org/10.1021/jp4125342 | J. Phys. Chem. C 2014, 118, 6433−6447

The Journal of Physical Chemistry C

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evolutionary runs, including the SrH6 phase with helical hydrogenic chains. We hope our study provides guidance for experimental groups aiming to synthesize novel crystal stoichiometries under pressure. For example, recent experiments in diamond anvil cells (with and without laser heating) have resulted in the synthesis of unique phases such as NaCl3 and Na3Cl,81 SiH4(H2)n,58,59 Xe(H2)7,60 GeH4(H2)2,61 (H2S)2H2,62 and IrH3,82 to name a few.

may influence the structures of the most stable phases, as has recently been shown for pure hydrogen.16 A number of periodic trends have emerged from systematic calculations carried out on the alkali metal polyhydrides, MHn (n > 1 and M = Li, Na, K, Rb, Cs),69−72,74 and the alkaline earth polyhydrides MHn (n > 2 and M = Be, Mg, Ca, Ba).76−78 Summarized, the trends observed are as follows: • The pressure at which the polyhydrides start to become stabilized with respect to the “classic” MH or MH2 stoichiometries correlate roughly with the ionization potentials of the metals. • The hydrogenic sublattices present in the polyhydrides vary greatly and contain one or more of the following − − 1 − species: H2, Hδ− 2 , H , H3 , ∞[H3 ], and anionic atomistic cages. These structural motifs give rise to characteristic phonon modes which could potentially be employed to identify these phases via Raman or IR spectroscopy. • The DOS at EF and, therefore, the propensity for superconductivity are dependent upon the structure of the hydrogenic sublattice. • The structure of the hydrogenic sublattice is in turn dependent on the identity of the electropositive metal. The thermodynamically and dynamically stable lithium, sodium, and magnesium polyhydrides contain H2, H−, and Hδ− 2 motifs. The stable polyhydrides comprised of K, Rb, Cs, and Ba may in addition afford H−3 molecules, and 1 − ∞[H3 ] polymeric chains. Finally, Ca can sport negatively charged cage-like structures consisting of atomic hydrogen. • For the alkaline earth polyhydrides, MHn, the n with the most negative enthalpies of formation increase with increasing pressure, but for the alkali metal polyhydrides, they decrease. Out of the plethora of stable structures which were uncovered during these studies the CaH6 phase found by Tse and Ma using the particle-swarm-optimization technique as implemented in the CALYPSO code,79 stood out as a particularly promising candidate for high-temperature superconductivity.76 In this phase, the hydrogen atoms formed a unique, sodalite-like clathrate cage, which encapsulates the alkaline earth metal. This high-symmetry, atomistic, hydrogenic sublattice was negatively charged as a result of electron donation from the electropositive metal to hydrogen. The unique structure which the hydrogen atoms adopted gave rise to a high DOS at EF and an unprecedentedly strong electron phonon coupling, resulting in a remarkable superconducting critical temperature, Tc, of 220−235 K at 150 GPa. Herein, we complete our theoretical investigations of the alkaline earth polyhydrides under pressure by considering SrHn, n > 2. Evolutionary structure searches are carried out in order to computationally explore the potential energy landscape of the hydrogen rich region in the Sr/H phase diagram under pressure. We study in meticulous detail the geometries and electronic structures of the most stable phases, and compare them to those of their lighter77,80 and heavier78 brethren. We note that at the Study of Matter Under Extreme Conditions conference held in March 2013 (when our work was already in progress), we learned that Prof. John Tse, Prof. Yanming Ma, and their co-workers were also computationally investigating the high-hydrides of strontium under pressure. They found structures with unique hydrogenic sublattices in their studies, some which were similar to the ones identified in our

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RESULTS AND DISCUSSION SrHn with n > 2: Keeping Up with Trends. In order to determine the pressure range where the strontium polyhydrides are stable, the geometries and enthalpies of solid molecular H2, and the “classic” hydride SrH2 must be known. For the former we employ the P63/m structure (an approximant for phase I of hydrogen, which consists of freely rotating molecules on a hexagonal close-packed lattice) below 105 GPa, and for P ≥ 105 GPa a layered C2/c structure. Both of these were found to be the global enthalpy minima in the cold (0 K) phase diagram using the ab initio random searching (AIRSS) technique.15 Under pressure SrH2 is observed to transform from the cotunnite (Pnma) → Ni2In (P63/mmc) → AlB2 (P6/mmm) structures at 8.3 and 115 GPa,83 respectively. In our computations these transitions occur at 8 and 104 GPa, in good agreement with experiment. Evolutionary searches were carried out to determine the global minima structures for SrH2 at 50, 100, and 150 GPa, and only the known phases were found. Next, we embarked on our computational quest to explore the hydrogen-rich region of the Sr/H phase diagram under pressure. The XtalOpt evolutionary algorithm (EA) was employed to search for the most stable crystal lattices of SrHn, with n = 3−12 at 50, 100, and 150 GPa. Geometry optimizations of the structures which were found allowed us to determine their enthalpies of formation, ΔHF, from the classic hydride and solid molecular hydrogen as a function of pressure. To locate the SrHn, which are thermodynamically stable with respect to decomposition into other polyhydride stoichiometries and H2 or SrH2 we plotted ΔHF versus %H2 composition and traced out the convex hull (see the Supporting Information, SI), as is customary. The convex hull can be defined as the set of line segments below which no other points lie,84 and the phases whose ΔHF comprise the hull are thermodynamically stable. At 50 GPa, SrH4 has the lowest ΔHF, SrH12 also lies on the hull, while SrH6 and SrH8 are close to it. In fact, no other structures except for SrH10 are stable at 100 or 150 GPa, and systems with odd n are ubiquitously absent from the hull. Because of this we focus on analyzing the SrHn crystal lattices with even n, whose enthalpies of formation are plotted in Figure 1. Theoretical studies of the alkali metal polyhydrides showed that the stoichiometries which were thermodynamically stable typically contained an odd number of hydrogens for every metal atom.70−72,74 The most notable exception was for the lightest alkali metal lithium, where LiH2, LiH6, and LiH8 were the only phases found on the convex hull up to 300 GPa.69 In stark contrast to the results that were obtained for a majority of the polyhydrides containing an alkali metal, computations illustrated that for MgHn, CaHn, and BaHn an even value of n is a requirement for stability.76−78 As noted above, our current work reveals that this is also the case for SrHn. Another pattern that emerges from computational investigations is that the 6434



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structural phase transitions as the lighter ones, but at lower pressures.85 This trend is in general observed in the classic MH alkali metal86 and MH2 alkaline earth metal hydrides as well.77,80 But does it also hold for polyhydrides of the Group 1 and Group 2 elements? In prior work we focused on analyzing the crystal lattices and electronic structures of the thermodynamically stable alkali metal polyhydrides which included LiH2, LiH6, LiH8, NaH7, NaH9, and NaH11. Because of the very different stoichiometries which lay on the convex hull, we did not attempt to compare in detail the lithium and sodium polyhydrides of a given composition. The only similarity which was noted was that the metastable Pm3̅m-NaH6 could be derived from R3̅m-LiH6 by setting all of the rhombohedral angles to 90°, but the most stable NaH8 lattice differed from LiH8.69,70 The heavier polyhydrides were unlike those containing lithium and sodium because many of their crystal lattices incorporated H−3 anions. However, a few of the stable KHn, RbHn, and CsHn structures bore a great resemblance to each other. For example, the I41/amd and Cmmm RbH3 and CsH3 phases were isotypic.71,74 Some of the magnesium, calcium, and strontium polyhydrides with a particular stoichiometry are indeed quite similar, and slight structural distortions are likely a result of the variation in the size of the metal cation. The barium polyhydrides, on the other hand, have a significantly greater diversity in the structures they can adopt.78 This is likely because Ba2+ is a relatively soft acid, akin to Cs+, Rb+, and K+, thereby facilitating the formation of H−3 anions within the hydrogenic sublattice. So, the chemistry of the electropositive element plays a non-negligible role in determining the preferred geometries of the alkali metal and alkaline earth polyhydrides under pressure. Let us proceed to discuss the crystal lattices and emergent electronic structures of the strontium polyhydrides whose enthalpies of formation are provided in Figure 1. SrH4 is the first of the polyhydrides predicted to resist decomposition into SrH2 and H2. This stoichiometry lies on the convex hull at all of the pressures we considered, exhibiting I4/mmm symmetry below and Cmcm symmetry above 84 GPa. Phonon calculations at 50, 100, and 150 GPa confirm the dynamic stability of the thermodynamically stable phases whose supercells are illustrated in Figure 2a,b. The CaH4 phase, which was a stable point on the convex hull between 50 and 200 GPa, also assumed these same I4/mmm and Cmcm crystal lattices, but the structural phase transition was calculated to occur at a higher pressure than in SrH4, 180 GPa, as expected.76 Between 100 and 200 GPa the most stable MgH4 lattice adopted Cmcm symmetry as well,77 but a structure with I4/mmm symmetry was not found. MgH4 was calculated as being unstable with respect to decomposition into MgH2 and H2 just under 100 GPa, so structure searches were not carried out at lower pressures. Because the MH4 stoichiometry is a common character appearing in the phase diagrams of a number of the stable polyhydrides, it is important to get a better understanding of the atomic arrangements within the two lattice types that are assumed, and the influence that the size of the metal cation has on the intricate details of their structures. In the I4/mmm arrangement, illustrated in Figure 2a, the alkaline earth metals are distributed in a body-centered tetragonal lattice. H2 molecules (whose intramolecular distance is somewhat longer than what would be expected for pure hydrogen at the given pressure) are found to either bisect the two square faces or to lie along each of the four long edges of the unit cell. Two H−

Figure 1. Enthalpy of formation, ΔHF, for the reaction SrH2 + 1/ 2(H2)n−2 → SrHn vs pressure for n = 4, 6, 10, and 12. The enthalpy of SrH2 and H2 are computed for the most stable structures from refs 83 and 15. We only illustrate the ΔHF for those SrHn stoichiometries which were found to lie on the convex hull at 50, 100, or 150 GPa (see the SI). The most stable SrHn phases did not stay constant throughout the pressure range studied, and the minima found at low (high) pressures are illustrated with closed (open) circles. Below 132 GPa two isoenthalpic SrH12 phases, one with C2/m and one with C2/c symmetry were found.

pressures at which Group 1 and Group 2 polyhydrides become preferred over the classic stoichiometries tend to correlate with the ionization potential of the electropositive metal. Again, this tendency is corroborated by the present study. The first structure to become stable with respect to decomposition into SrH2 and H2, I4/mmm-SrH4, does so at ∼20 GPa. In comparison, Cmcm-MgH4 became viable around 100 GPa,77 I4/mmm-CaH4 below 50 GPa,76 and Fddd-BaH6 at ∼16 GPa.78 The potassium, rubidium, and cesium polyhydrides were calculated to become stable below 5 GPa,71,72,74 and the sodium70 and lithium69 polyhydrides around 25 and 100 GPa, respectively. It should be noted that because these stabilization pressures are based on structure searches carried out at higher pressures, they should be treated only as rough estimates. Prior theoretical work on hydrogen-rich systems containing “a little bit” of Mg,77 Ca,76 and Ba78 illustrated that a wide variety of hydrogenic sublattices are possible, and we find SrHn to be no exception. The structural motifs present in the stable phases consisted mostly of either strontium cations and H2 molecules with hydridic H− anions, or molecular hydrogen bearing a slight net negative charge, Hδ− 2 . Even though lattices containing an H−3 anion never lay on the convex hull, a few (likely metastable) phases incorporating this unit were found in our evolutionary searches. For example, at 50 GPa, an SrH6 structure made up entirely of strontium cations and H−3 was found to have an enthalpy only 2 meV/atom higher than the lowest enthalpy alternative (which contained a mixture of H− and H2 units). At higher pressures, however, a new motif consisting of nonmolecular, one-dimensional hydrogenic helices, 1∞[Hδ−], is observed within SrH6. These chain-like spirals are reminiscent of other nonmolecular motifs such as the one-dimensional polymeric units composed of condensed H−3 anions, 1∞[H−3 ], found in RbH6 at 250 GPa,71 and the clathratelike hydrogenic cage comprising CaH6 at 150 GPa.76 The First Stable Polyhydride: SrH4. In elemental solids the heavier members of a group often undergo the same 6435



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H− ions in MgH4, in SrH4 and CaH4 the square of H− is distorted into a polygon with an H2 nearby and perpendicular to the midpoint of each of the polygon’s long edges such that it helps form a hexagon between nearest neighbor metal ions as illustrated in Figure 2c. Whereas I4/mmm-CaH4 is predicted to be metallic within PBE by 50 GPa, the PBE band gap for the strontium analogue was calculated to be 0.47 eV at 80 GPa. At 150 GPa CmcmSrH4 was computed to be a semimetal via the PBE functional, see Figure 2d. Calculations with the HSE06 screened hybrid functional, which has been shown to give good accuracy for band gaps,89 confirmed its metallicity (see the SI). For comparison, the PBE functional predicted that Cmcm-CaH4 would have a relatively high DOS at EF by 200 GPa,76 and MgH4 would metalize by 20 GPa.77 Even though the alkaline earth tetrahydrides are predicted to be metallic and stable at pressures lower than those necessary to metalize hydrogen, it is likely they will not have a high DOS at EF. This means that even though they may be superconducting under pressure, Tc is not expected to be remarkably high. For example, we estimated that MgH4 would become superconducting below 29−37 K at 100 GPa using the Allen-Dynes modified McMillan equation.77 Hydrogenic Helices in SrH6. Theoretical work has illustrated that the most stable point in the convex hull of the alkaline earth metal polyhydrides moves toward stoichiometries with a higher hydrogen content as pressure increases. For example, CaH4 had the most negative ΔHF from 50 to 150 GPa and CaH6 thereafter;76 and whereas BaH6 was the minimum point on the hull at 50 GPa, this distinction was claimed by BaH10 at 150 GPa.78 Unsurprisingly, the same trend is observed in the strontium polyhydrides. The enthalpy of formation of SrH4 and SrH6 becomes nearly equivalent at 100 GPa, the first pressure at which the latter stoichiometry is thermodynamically stable. And, by 150 GPa a mesmerizing SrH6 phase containing hydrogenic helical motifs becomes the minimum point on the convex hull. At 100 GPa SrH6 adopts the C2/c symmetry structure shown in Figure 3a. The most representative motifs of its hydrogenic sublattice are the highlighted zigzag arrangements of H2 and H− ions. There are two such chain-like formations running through the structure at directions which are perpendicular to each other, and an example of each is outlined in Figure 3a. At 100 GPa the lengths of the H2 molecules which belong to these chains are 0.79 Å and 0.80 Å (which is slightly elongated relative to the 0.76 Å in pure molecular hydrogen at this pressure), and their respective H2···H− distances measure 1.37 and 1.46 Å. This structure has a small band gap of 0.03 eV at 100 GPa as calculated with the PBE functional, see Figure 3c. It is dynamically stable at 100 GPa, and the H2 vibron is found just under 3500 cm−1. At 108 GPa the C2/c structure is overtaken by another configuration containing H2···H− motifs. The most striking structural evolution which occurs under pressure in this phase is the gradual transformation of a hydrogenic sublattice containing discrete building blocks (molecular hydrogen and hydridic hydrogen) to one without, see Figure 3b, so that by 150 GPa all of the H−H distances along the corkscrew-like chains measure 1.07 Å. The one-dimensional chains comprised of atomic hydrogen bear a slight net negative charge as a result of electron donation from the electropositive strontium atoms, and can therefore be represented by the formula 1∞[Hδ−]. These helical hydrogenic chains are the distinguishing feature of R3̅m-

Figure 2. Supercells of the lowest enthalpy SrH4 structures at (a) 50 GPa (I4/mmm) and (b) 100 GPa (Cmcm). Strontium is colored blue, hydridic (H−) hydrogens are white, and atoms within dihydrogen are represented as red. The green lines are the unit cell boundaries. (c) The zigzag formations adopted by the nearest neighbor Mg−Mg and Sr−Sr contacts in Cmcm MgH4 and SrH4 at 150 GPa, as well as the hydrogenic motifs which form between them. The colored purple and blue lines represent nearest neighbor metal−metal contacts. The red lines are bonds within a single H2 (0.81 Å in SrH4), whereas the dashed lines represent nonbonded contacts between neighboring hydrogens (H2···H− 1.59 Å, and H−···H− 1.82 Å in SrH4). (d) Total electronic DOS for SrH4 at 50 GPa (I4/mmm) and 150 GPa (Cmcm). The Fermi energy is set to zero. (e) Phonon DOS of Cmcm-SrH4 at 150 GPa. The peak arising from the H2 vibron is highlighted.

anions are positioned on each of the rectangular faces of the cell, forming a cube around the central metal ion. The Cmcm structure, shown in Figure 2b, is comprised of buckled sheets of metal cations separated by layers containing H2 and H− ions. The free H2 vibronic mode87 of 4161 cm−1 is reduced to nearly 3100 cm−1, see Figure 2e, as a result of the elongation of the H−H intramolecular bond to 0.81 Å in Cmcm-SrH4 at 150 GPa. The Cmcm configurations are remarkably similar for CaH4 and SrH4, whereas the MgH4 structure is noticeably different as a result of the significantly smaller ionic radius (0.72, 1.00, and 1.16 Å for six-coordinate Mg2+, Ca2+, and Sr2+88). One common feature all of the Cmcm structures share is the buckled sheets formed between the nearest neighbor metal atoms. The key difference between them is that whereas the shortest contacts between metal atoms zigzag through square arrangements of 6436



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order to help minimize the interaction energy of lone electron pairs with one another. But hydrogen does not have lone pairs of electrons, adding further to the intrigue of this phase. Nonmolecular structural motifs have previously been found in RbH6 at 250 GPa71 (which contained polymeric chains of H−3 anions, 1∞[H−3 ]) and the clathrate-like hydrogenic cage comprising CaH6 at 150 GPa.76 Perhaps, not unexpectedly R3̅m-SrH6 can be derived via a minor distortion of the latter. The structure and electronic structure of these two alkaline earth hexahydrides makes them quite special indeed. An MgH6 stoichiometry did not lie on the convex hull at either 100 or 200 GPa,77 and two out of the three BaH6 structures which were predicted to be stable between 50 and 150 GPa did not have a high DOS at EF because of the structure of their hydrogenic sublattices.78 R3̅m-SrH6, on the other hand, is a very good metal like CaH6 and Imm2-BaH6. The DOS calculated with both the PBE, see Figure 3c, and the screened hybrid HSE06 functionals89 (see the SI) confirm the metallicity at 150 GPa. Phonon calculations on R3̅m-SrH6 at 150 GPa revealed a number of unstable modes, so we did not attempt to calculate the Tc of this phase. The vibration with the largest imaginary frequency recreated the H2···H− motifs discussed above, as illustrated by the inset in the phonon DOS in Figure 3d. Optimization of this phase to lower pressures in 10 GPa increments resulted in the atomistic helical chains transforming into H2···H− configurations at 120 GPa. When an 84-atom supercell was created at 150 GPa and the atoms were shifted to follow the imaginary frequency, the structure optimized to one with P3̅ symmetry, which was 0.009 eV/atom lower in enthalpy. This structural distortion led to the formation of H2···H− units (whose H−H and H2···H− distances measured 0.89 and 1.16 Å) along the hydrogenic chains and a slight elongation of the shortest Sr−Sr contact (from 2.95 to 3.02 Å). The distortion of the hydrogenic chains resulted in a substantial decrease in the DOS at the Fermi level, such that it was nearly vanishing. We calculated the DOS of select structures obtained from recreating the H2···H− units starting from R3̅m-SrH6, and even though the DOS was perturbed, all remained metallic. At 150 GPa the difference in enthalpy between the R3̅m and P3̅ phases is surpassed by the zero-point-energy of R3̅m-SrH6, estimated to be 0.224 eV/atom, suggestive of potential melting of the hydrogenic sublattice. Liquid-like behavior of the hydrogenic sublattice has previously been proposed for metallic hydrides containing a heavy element.55,71 At higher pressures the imaginary frequency with the largest magnitude decreased (∼1000 cm−1 at 150 GPa to ∼625 cm−1 at 180 GPa) and at 250 GPa the R3̅m-SrH6 phase was found to be dynamically stable, with a high DOS at the Fermi level. Herein, we employ the R3̅m structure as a model for SrH6 at 150 GPa, keeping in mind that slight distortions of its hydrogenic sublattice are likely to give rise to a number of nearly isoenthalpic phases with decreased metallicity. Our goal is to develop an understanding of the electronic structure of R3̅m-SrH6, since it becomes dynamically stable at higher pressures, and to assess the relationship between its structure and the structures of the other alkali metal polyhydrides. And we will analyze the electronic structure of this unique strontium polyhydride in an effort to unveil the origins of its pronounced metallicity. The remarkable resemblance between R3m ̅ -SrH6 and CaH6 hint that the former may also be superconducting with a high critical temperature, at a pressure at which it becomes dynamically stable.

Figure 3. Supercells of SrH6 structures at (a) 100 GPa (C2/c) and (b) 150 GPa (R3̅m). Strontium is colored blue, atomistic (Hδ−) hydrogen atoms are colored white, and atoms within dihydrogen are represented as red. Structural data for P3̅-SrH6 is provided in the SI. (c) Total electronic DOS and (d) phonon DOS for SrH6 at 100 GPa (C2/c) and 150 GPa (R3̅m-SrH6). In the electronic DOS, the Fermi energy is set to zero. Only the phonon DOS for modes with real positive frequencies is shown in the 150 GPa plot. The inset provides a simplified sketch of the phonon mode with the largest computed imaginary frequency. R3̅m-SrH6 becomes dynamically stable by 250 GPa, and the phonon DOS at this pressure is provided in the SI.

SrH6 and are another example of multicenter bonding in compressed solids.90 Perhaps the most famous examples of helical structural motifs in monatomic extended systems are the Group 16 elements like tellurium, selenium, and sulfur91−94 (which happen to be isoelectronic with SrH6). In fact, the atomic arrangements within the individual helices in R3̅m-SrH6 resemble those present in the trigonal S, Se, and Te structures.92 The major difference between the extended crystal lattices of the polyhydride and the elemental phases is that in the former every third helix is replaced by a linear chain of strontium ions and, in addition, the handedness of neighboring helices is reversed in SrH6 but they are all the same in the Group 16 structures. Helices are often cited as examples of a local chemical motif which lowers the enthalpy of an extended structure when incorporated into the lattice. For example, the cubic gauche structure of polymeric nitrogen under pressure95 can be derived from helical arrangements of nitrogen molecules,96 which tend to favor gauche dihedral angles in 6437



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Increasing the Hydrogen Content: SrH8 and Beyond. We now move on to discuss the structures of the higher hydrides of strontium, and compare them with those which were found in prior studies for magnesium, calcium and barium. The hydrogenic motifs in the calcium polyhydrides were rationalized by considering the “formal” effectively added electrons (EAE) donated to each H2 molecule from calcium.76 Assuming full electron transfer the EAE in CaH4 and CaH12 would be 1e/H2 and (1/3)e/H2, respectively. Because these electrons are donated into the antibonding σ* orbital, the H−H bond elongates. Tse and Ma pointed out that if the filling of the σ* bands is large enough, the bond would be severed with a − concomitant fragmentation of Hδ− 2 into two H units. This argument can be used to explain the M(2H−)(H2) makeup of MH4 (M = Mg, Ca, Sr), and the absence of hydridic hydrogens in the thermodynamically stable MgH12, MgH16,77 and CaH1276 structures. The lowest enthalpy BaH10 phase we found at 150 GPa, on the other hand, was comprised of a two-dimensional hydrogenic sublattice with H2···H− contacts, and BaH12 contained bent H−3 anions because of the softness of the Ba2+ cation. We wondered what the structures of SrHn with n > 6 might look like? Would their hydrogenic lattices consist solely of slightly elongated dihydrogen molecules like in MgH12 and CaH12, or would the soft strontium cation facilitate the formation of H−3 -containing motifs akin to BaH12, and could H− anions be incorporated in the lattice as in BaH10? The SrH8 stoichiometry does not lie on the convex hull; however, it is never quite far from it. Phonon calculations for the most stable structure found at 100 GPa (which was composed of H2 and H− units) revealed numerous imaginary frequencies. Furthermore, since this phase was not metallic we did not analyze this stoichiometry any further. SrH10 comprises the convex hull at 100 GPa where two phases, one with Cm and the other with C2/c symmetry, were nearly isoenthalpic, differing by less than 1 meV/atom (the phase transition between the two is calculated to occur at 103 GPa). The hydrogenic motifs in both SrH10 phases are difficult to classify since they consist of (H2···H−)n and (H2···H−···H2)n contacts of varying shapes and lengths, and at 100 GPa both had a small but finite DOS at E F . The SrH 12 stoichiometry was thermodynamically stable at 50 and 150 GPa. At 50 GPa two isoenthalpic structures were found, one with C2/m and one with C2/c symmetry, and both of the hydrogenic sublattices were comprised of a 5:1 mixture of H2 to H− units. Since these crystal lattices are quite similar, only the C2/c structure and its DOS is illustrated in Figure 4a, the corresponding data for the C2/m alternative is provided in the SI. The PBE band gap of both phases was 1.6 eV at 50 GPa, and metallization did not occur below 150 GPa. But, by this pressure, another structure with C2/m symmetry was lower in enthalpy, see Figure 4b. The hydrogenic sublattice of this phase was composed entirely of Hδ− 2 molecules leading to a relatively sizable DOS at EF, see Figure 4d. Because of the substantial computational cost involved we did not compute the full phonon DOS of any of the aforementioned SrH10 or SrH12 phases. However, both Cm and C2/c-SrH10 at 100 GPa, as well as the two SrH12 structures, which were found to be isoenthalpic at 50 GPa, and C2/mSrH12 at 150 GPa exhibited only real frequencies at the Γ-point. Our quick survey shows that a wide variety of hydrogenic sublattices are possible for SrHn, with n ≥ 8, and only the highpressure C2/m-SrH 12 structure could be explained by considering the number of EAE alone. In fact, this structure is related to the previously studied MgH1277 and CaH1276

Figure 4. Supercells of the lowest enthalpy SrH12 structures at (a) 50 GPa (C2/c) and (b) 150 GPa (C2/m). Strontium is colored blue, atomistic (H−) hydrogen atoms are white, and atoms within dihydrogen are represented as red. Two “Sr(H2)2” sheets are outlined in green and purple. An Hδ− 2 is outlined in black. (c) A top and side view of an isolated sheet containing strontium cations and H2δ− extracted from the SrH12 structure at 150 GPa. Note that in the top view the dihydrogens form a slightly distorted honeycomb like sheet. (d) Total electronic DOS for SrH12 structures at 50 GPa (C2/c) and 150 GPa (C2/m). The Fermi energy is set to zero.

phases. Each one of these lattices contains Hδ− 2 molecules, which are oriented “side-on” with respect to the metal atom and surround it in a hexagonal fashion. In MgH12 and CaH12 at 150 GPa six Hδ− 2 envelope each metal atom, giving rise to M(H2)6 hexagonal units that are the building blocks of the extended crystal. In SrH12, the metal cations are also encircled by six Hδ− 2 molecules in a “side-on” arrangement, but each dihydrogen is shared between three strontiums. This gives rise to two distinct sheets with an Sr(H2)2 stoichiometry, which can be described in terms of a slightly distorted honeycomb lattice of Hδ− 2 , with strontium cations situated in the middle of the pseudohexagonal voids. The two sheets are oriented perpendicular to each other, as outlined in purple and green in Figure 4b and each Sr belongs to both sheets. A top and side view of one such sheet is illustrated in Figure 4c. The H−H distances are 0.87 Å within one sheet and 0.79 Å in the other. In addition, there are 2Hδ− 2 molecules per primitive cell, which do not belong to these sheets (outlined in black), that measure 0.85 Å. Because the aforementioned MH12 phases are metallic as a result of the partial filling of the H2 σ* bands, they are all relatively good metals. The DOS at EF of SrH12 at 150 GPa is quite comparable to that of MgH12 between 140 and 300 GPa. The latter was predicted to become superconducting below 47−60 K at 140 GPa.77 Metallicity in R3̅m-SrH6. Our studies of the alkali metal and alkaline earth polyhydrides revealed a variety of paths 6438



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Figure 5. Electronic structure of R3̅m-SrH6 at 150 GPa. (a) The H and Sr site-projected densities of states (PDOS). The Sr PDOS is decomposed into (top) px, py, and pz contributions and (bottom) 5s and 4d (σ {dz2−r2}, π {dxz, dyz}, and δ {dxy, dx2−y2}) contributions. The black dashed line provides the sum of the Sr s, p, and d PDOS. The Fermi energies are set to zero. Note that different scales are employed in these plots. The total DOS of this phase is provided in Figure 3. (b) An isosurface plot (isovalue = 0.07 e/Å3) of the charge density difference between the crystal lattice at 150 GPa and the sum of its constituent atoms. (c) An isosurface (ELF = 0.75), and contour plot of the electron localization function. The plane of the contour passes through the hydrogenic chains and strontium cations. (d) Band structure of (left to right) SrH6, as well as the same system but with the hydrogen and strontium atoms removed.

comparable with that of CaH6 and a number of the hydrides that did not contain H− or H−3 anions. This phase remains a good metal up to pressures of at least 250 GPa, where it is also dynamically stable. We therefore proceeded to explore the relationship between the electronic structure of SrH6 and the helical hydrogenic chains within its crystal lattice at 150 GPa, so that the results could be more easily compared to those previously obtained for CaH6 at this pressure.76 The site-projected densities of states (PDOS) onto the H and Sr atoms in R3̅m-SrH6 are shown in Figure 5a. The metallic bands are primarily due to hydrogen, and the occupied hydrogen PDOS is mostly of s-character throughout. The H s-bands mix substantially with the Sr semicore 4p bands between −22 and −16 eV and, additionally, with Sr 5s and 4d between −15 and 0 eV. The Sr 4p character is split into two contributions, one from px and py and the other from pz; the zcoordinate is that which points along the direction of the

toward metalization. Which road was taken depended upon the nature of the hydrogenic sublattice. Phases comprised solely of Hδ− 2 molecules, like C2/m-SrH12, were metallic even at 1 atm as a result of the partial filling of the H2 σ*u bands, and the high DOS at EF persisted as the structure became a stable phase. Systems containing H− and H2 units, like both of the SrH4 phases we found, became metallic due to pressure-induced overlap of the H− band with the H2 σ*u and (n − 1)d or n(sp) bands. If H−3 anions were present instead (as in KH5, RbH5, and CsH3), metallization was caused by pressure-induced overlap of the H−3 nonbonding bands, with bands that contained metal (n − 1)d and H−3 antibonding character. Phases that metallized as a result of band broadening generally had a lower DOS at EF as compared to those that were conducting because of electron transfer. At 150 GPa, the density of states at the Fermi level of R3̅m-SrH6, 0.023 eV−1/(valence electron), is higher than a majority of the polyhydrides we have encountered and is 6439



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Structural Relationships of CaH6, SrH6, and BaH6 to the Classic Dihydrides. MH6 is a stoichiometry familiar on the convex hulls of the alkaline earth polyhydrides, with CaH6 (150, 200 GPa), SrH6 (100, 150 GPa) and BaH6 (50, 150 GPa) appearing on it at the pressures provided in the braces (and potentially higher pressures where explicit calculations have not yet been performed). Above we have alluded to the fact that the R3̅m-SrH6 and Im3̅m-CaH6 phases (which are among the lowest enthalpy phases at 150 GPa) are linked by a small distortion. Actually, one of the two isoenthalpic BaH6 structures which is thermodynamically stable at 150 GPa exhibits a number of features which are reminiscent of these two phases as well. In order to get a better understanding of the local coordination environment around the metal ions in R3̅m-SrH6, Im3m ̅ -CaH6, and Imm2-BaH6, we have extracted fragments from their crystal lattices, see Figure 7.

shortest Sr−Sr contact. Because Sr undergoes pressure-induced s → d hybridization, the occupied bands contain both 5s and 4d-character. The Sr d-bands are also split into groups which represent their symmetry with respect to rotation around the zaxis: σ {dz2−r2}, π {dxz, dyz}, and δ {dxy, dx2−y2}. In order to further analyze the modification of the electronic structure upon compound formation, we calculated the charge density difference between the total electronic charge density of R3m ̅ -SrH6 at 150 GPa and the sum of its constituent atoms, see Figure 5b. The blue regions, which are localized around strontium and along the shortest Sr−Sr contacts, represent a loss of charge relative to the sum of the atomic fragments. The red regions surrounding the hydrogens are indicative of a gain of charge. But, even though electron density is donated from the electropositive metal to the helical hydrogenic chains, a number of the occupied bands exhibit Sr 4d and 5s character suggesting that the alkaline earth metal assumes an oxidation state somewhat lower than +2. In fact, a Bader charge analysis97 assigned charges of +1.07 to the strontium and −0.17 to each hydrogen, in-line with previous estimates of an oxidation state of +1.02 on the calcium in CaH6 at 150 GPa.76 The electron localization function (ELF) of SrH6, see Figure 5c, illustrates that the strongest bonding interactions occur along the helical hydrogen chains, as expected from the ∼1.07 Å H−H distances. There was no evidence of bonding between the strontium cations or between strontium and hydrogen. But charge transfer from the strontium atoms to the hydrogenic sublattice is not the only reason why R3̅m-SrH6 is metallic. In Figure 5d we provide the band structure of this phase, along with hypothetical structures which assume the same lattice but where all of the hydrogen or strontium atoms have been removed. Not surprisingly, the lattice consisting of pure hydrogen is quite a good metal too. And its metallicity can be traced back the one-dimensional chains comprised of atomic hydrogen, as illustrated in Figure 6. Without the presence of

Figure 7. Shortest (thick gray line), second shortest (red dotted line), and third shortest (blue dotted line) M−M distances in R3̅m-SrH6, Im3̅m-CaH6, and Imm2-BaH6 at 150 GPa. The alkaline earth atoms are shown as large green spheres and hydrogen atoms as small white spheres. For CaH6, one of the shortest distances is denoted by a red dashed line in order to better link it to the other structures.

The structure of the hydrogenic sublattice around the shortest Sr−Sr contact in R3m ̅ -SrH6 is illustrated in Figure 7. The one-dimensional helical chains of hydrogen atoms running in the z-direction are highlighted by the purple dotted lines. Even though these are the only contacts between hydrogen atoms which are close enough to covalently bond, it is instructive to visualize the polyhedra, which are formed by drawing lines connecting the second nearest-neighbor hydrogen atoms too. From this perspective we see that strontium is enclathrated within a sodalite-like hydrogenic cage, similar to calcium in CaH6. In SrH6 a hexagonal face bisects each one of the two shortest Sr−Sr contacts, and a pseudohexagonal face forms along the four second nearest-neighbor ones as well. A square face lies perpendicular to the third shortest Sr−Sr distance. The alkaline earth metals within Im3̅m-CaH6 and Imm2-BaH6 are also found within very similar chemical environments. The main difference between SrH6 and CaH6 is that in the latter all of the hexagonal faces display perfect 6fold symmetry, and there are six shortest equidistant Ca−Ca contacts. In fact, SrH6 can be derived from CaH6 by elongating four out of the six closest metal−metal contacts, and slightly distorting the face which bisects them so it is no longer an ideal hexagon. Another difference is that in CaH6 evidence of covalent bonding interactions was found between all nearestneighbor hydrogens,76 whereas in SrH6 bonds are formed only between the hydrogens comprising a single helix. Hydrogenic polyhedra composed of hexagonal and square faces encompassing a central barium atom can also be observed in the Imm2symmetry BaH6 structure. The biggest difference between BaH6

Figure 6. (Left) Supercell of R3̅m-SrH6 at 150 GPa highlighting the one-dimensional spirals of hydrogen, 1∞[Hδ−]. (Right) These chains give rise to a metallicity at 1 atm, even without electron donation from strontium. As pressure is applied, the bands broaden.

strontium and the persistence of pressure, these chains would surely undergo a Peierls distortion to form molecular hydrogen, H2, thereby opening up a gap at EF. This hypothetical H6 phase is metallic because each hydrogen in the chain has two equidistant neighbors, and electron donation from the strontium atoms to the hydrogenic sublattice does not destroy its highly metallic character. CaH6 is metallic for the same reason that SrH6 is: both structures are comprised of atomistic hydrogen which arranges to make a three-dimensional clathrate-like lattice in the former and one-dimensional spirals in the latter. 6440



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and CaH6/SrH6 is the presence of H−3 ions in the former. The length of the H−3 molecules is comparable to the length of the edges of the hexagonal faces bridging the shortest Ba−Ba contacts. Because of this a single H−3 can be used to form the edge of a hexagonal face that bisects the second-shortest Ba−Ba distances, thereby integrating smoothly into the lattice. Note that this H−3 edge belongs to two faces, one of which is hexagonal and the other which is square. When the metal atoms in CaH6, SrH6, or BaH6 are swapped for each other, they optimize back to their native structures, reaffirming that the nature of the alkaline earth atom is crucial in determining their crystal lattices. While exploring the structural relationships between these hexahydrides, we realized that they could all be traced back to the P6/mmm-MH2 lattice (AlB2 structure). This phase is adopted by the classic alkaline earth hydrides under pressure, and the structural transition is predicted to occur at 40, 115, and 178 GPa for BaH2, SrH2, and CaH2 in our calculations. The AlB2 structure contains layers of hydrogen anions in a honeycomb lattice separated by layers of metal cations which are situated directly beneath the centers of the hexagons. This means that below and above each metal one finds a hexagon composed of hydrogens, reminiscent of the MH6 structures in Figure 7. In Figure 8 we illustrate how SrH6 could be

Figure 9. (a) R3̅m-SrH6 colored so that the hexagonal prisms encapsulating the strontium cations can be mapped onto the modified MH2 + 2H2 lattice illustrated in Figure 8. On the far right we illustrate a single layer which is comprised of hydrogen ions. (b) The Im3̅mCaH6 and Imm2-BaH6 structures. The one-dimensional rows of hexagonal prisms are colored to differentiate polyhedra which have metal and hydrogen ions that belong to specific layers. The layers of hydrogen ions are illustrated on the right. The average H−H distances within the hexagonal faces which form between the shortest M−M contacts at 150 GPa are shown in the box to the right (note that the variation in these distances is less than 0.015 Å). The minimum/ maximum distances between the hydrogens in a given “honeycomblike” plane are 1.24/2.48, 1.55/2.31, and 1.71/3.11 Å in CaH6, SrH6, and BaH6.

The CaH6 structure can also be represented in terms of edgesharing polyhedra which are constructed from distorted hexagonal prisms, see Figure 9b. However, whereas in SrH6 the polyhedra of a given color (red, green, or gray) form onedimensional chains running along the z-axis, in CaH6, the representation is not unique and can be constructed in three different ways. That is, the colored one-dimensional polyhedral chains can be drawn so that they run along either the x-, y-, or z-direction. The reason for the difference is that in CaH6 each calcium is in an octahedral environment comprised of six calciums cations (with each Ca−Ca contact measuring 3.04 Å at 150 GPa), whereas in SrH6 there are only two nearestneighbor Sr−Sr contacts (which measure 2.94 Å at 150 GPa). Each pair of contacts represents an axis which can be used to define the chains of hexagonal prisms surrounding the metal, so there are three ways to map CaH6 to the MH2 structure, one of which is illustrated in Figure 9b. Imm2-BaH6 can also be represented in terms of one-dimensional chains of hexagonal prisms which encapsulate the barium cations. One difference between the lighter hexahydrides and BaH6 is that in the former there are three distinct layers of metal ions, but in the latter there are only two such layers, as denoted by the coloring in Figure 9b. Furthermore, in BaH6 some of the polyhedral edges are constructed from H−3 units, but in SrH6 and CaH6, hydrogen ions are only found on the vertices of the polyhedra. The extended hydridic sheets that correspond to the honeycomb lattice in the AlB2 structure are shown to the right of the

Figure 8. Schematic illustration of how one could construct a structure resembling R3̅m-SrH6 from P6/mmm-SrH2. The hexagonal prisms encompassing the strontium cations are displaced along the Sr−Sr axis such that the red ones move up, the green ones move down, and the gray ones remain fixed. Adding hydrogen allows one to retain the hexagonal prisms in the structure.

constructed starting from P6/mmm-SrH2. First, the 1-D chains of strontium cations and their nearest-neighbor hydrogens are divided into three groups, as denoted by the coloring (gray, green, and red) in the middle panel. Next, the hexagonal prisms that encompass strontium and bisect the hydrogen atoms are moved along the vertical z-axis such that the red polyhedra move up, the green ones move down, and the gray ones stay fixed, so that the strontiums no longer lie in the same plane. Adding hydrogen to remake the hexagonal prisms surrounding each strontium results in an SrH6 stoichiometry, since triple the amount of hydrogen is needed to create three sheets instead of one. This construction indeed replicates, minus some significant distortions of the hydrides around the alkaline earth metal cations, the SrH6 structure shown in Figure 9a. 6441



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start to interact, so these bands broaden. For example, the 4p bandwidth in the most stable SrH4 phase increases from 2.5 to 7 eV when the pressure goes from 50 to 150 GPa, see Figure 2d. Because of the larger radius of Sr2+ as compared to Mg2+, this greatly exceeds the dispersion of the Mg 2p bands in MgH4, which measures 1, under pressure.103 We therefore wondered whether the hydrogenic motifs adopted by the polyhydrides could be influenced, at least in part, by the electron density associated with the atomic cores of the metal atoms? The schematic drawing in Figure 10a illustrates that hydrogen atoms, which arrange so that they form a hexagon bisecting an M−M contact (as in Cmcm-CaH4 and SrH4), would be able to more effectively avoid a region in the center between two metal ions than ones which form a square (as in Cmcm-MgH4). This is the region where the electron density from the metallic cores would meet. To study this further we would ideally like to compare the electron densities of MgH4 and SrH4 optimized in both structure types illustrated in Figure 2c at 150 GPa. Unfortunately, when Mg is substituted into the lowest enthalpy SrH4 structure at 150 GPa, it reoptimizes back to its native Cmcm-MgH4. When Sr is substituted into the MgH4 structure, however, the hydrogenic motifs remain intact in the sense that the square face composed of hydrogens bisecting nearest neighbor Sr−Sr contacts is preserved. This allows us to compare two SrH4 structures which differ in the way that their hydrogenic sublattices arrange between the shortest Sr−Sr contact. Plots of the occupied charge density which contains H s/p and Sr 4s/4p/5d character are shown in Figure 10b. The plane chosen contains the hexagonal or square hydrogenic motifs discussed. At this pressure, significant electron density is found throughout the lattice, but, as expected the lowest isovalues are found in this plane (colored in dark blue near the center of the square and hexagons). The most apparent differences between the two structure types is that the density between the hydrogens constituting the hexagons is higher than between those making up the square. This is because the H−H distances in the square motifs comprising the MgH4-based SrH4 phase are longer (1.90−2.00 Å) than the H−H measure along the hexagonal edges (1.50−1.85 Å) in the native SrH4 configuration. This suggests that the hydrogen atoms in the hexagonal faces are more tightly packed, and coincides with how the difference between the enthalpy of the two structures (∼2.0 eV) is almost entirely due to their volumes, with the pV contribution being ∼1.8 eV lower in the more compact SrH4 lattice (21.4 vs 22.3 Å3 per SrH4 unit). By shifting the plane by ∼0.3 Å along the Sr−Sr contact, as plotted in Figure 10c, it can be seen that the electron density of the hydrogens encroaches upon the density resulting from the metallic cores. The drawing in Figure 10a is used to schematically illustrate this situation. This suggests that the overlap of the electron density around the hydrogens with the density originating from the metallic cores forces them further apart in the MgH4-based SrH4

colored polyhedra in Figure 9. The distortion from the ideal honeycomb structure is, in fact, more pronounced in CaH6 and BaH6, as compared to SrH6. Metallic Cores and Hydrogenic Sublattices. In the preceding sections we have shown that, despite the structural similarities between a number of the alkaline earth tetrahydrides and hexahydrides, there are subtle differences in the make-up of their hydrogenic sublattices that are caused by the size of the metal cation and the strength of its interaction with the hydrogenic motifs. Another set of binary phases where the identity of the alkaline earth metal yields important differences in the emergent crystal lattices are the intermetallic compounds Ca2Ag7 and SrAg5. Ca2Ag798 prefers to adopt the Yb2Ag7 structure-type in lieu of the CaCu5 lattice, which SrAg5 assumes.99 The alkaline earth atoms are embedded in large extended networks of Ag, similar to how they are surrounded by a hydrogenic lattice within the polyhydrides. Recently, Hü ckel100 and DFT calculations101 were employed to investigate the chemical pressures (CP) acting on the atoms within these systems. The term “chemical pressure” refers to local pressures induced by the constraints of a crystal lattice (as opposed to the application of an external force). This concept is often used in discussions concerning how substituting one element within a crystal by an element of a different size influences the properties of the system.100,101 The CP analysis showed that in SrAg5 and (a hypothetical) CaAg5 the Ag−Ag contacts are compressed beyond the distances optimal for their pairwise interactions, but both Ca and Sr would prefer to be closer to Ag (i.e., the Ca/Sr atoms are too small for the cages they are in). This creates a tug-of-war between the two opposing structural tendencies, such that stabilizing one destabilizes the other.101 Ultimately, the analysis confirms in a new light that by adopting the Yb2Ag7 as opposed to the CaCu5 structure-type, CaAg7 relieves the negative CP on the Ca atom by creating a more compact coordination environment around it. One of the morals of the study is that local chemical bonds cannot be independently optimized within a crystal; they are optimized in a collective manner. Since the enthalpy is a sum of the internal energy and the pressure multiplied by the volume (H = U + pV), in the polyhydrides both the chemical and the physical pressures are important in determining which structures are assumed. Below we look a little bit more closely at some of the forces that may be driving the adoption of various structural motifs in the polyhydrides. Covalent bonds are formed between the hydrogens comprising the Hδ− 2 molecules found in all of the MH4 phases, and some degree of bonding is likely present between the negatively charged hydrogens comprising the clathrate cages within Im3̅m-CaH6, the helical 1∞[Hδ−] chains in R3̅m-SrH6, and the H−3 molecules found in Imm2-BaH6. The number of EAE has been employed to rationalize the CaH4 and CaH6 structures,76 and we have shown that the softness of the alkali metal cation may facilitate the formation of multicentered bonds in H−3 .72 These motifs coalesce into lattices, and in our discussion above we alluded to the fact that the nonbonded hydrogenic interactions may also be dependent on the nature of the alkaline earth element. For example, whereas a square planar arrangement of H− ions bisects the shortest M−M contact in MgH4 at 150 GPa, in SrH4 and CaH4, the shortest contact between the metal ions zig-zags through six-sided hydrogenic polygons at this pressure, see Figure 2c. At sufficiently high pressures, atoms can be pushed close enough together so that their semicore and even core states 6442



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Figure 11. (a) Computed energies, ΔErxn, for the reaction shown for varying M−M distances and H−H distances constrained to 1.3 Å. The metal complexes are treated with either a +2 charge (top) or are neutral (bottom). The square and hexagon outlined in blue represent the H4 and H6 motifs. The reaction energy computed with the charged hydrogen motifs (2− charge) in the absence of metal centers is shown by the dashed black line. (b) Structure models used to compute the reaction energy of [M3(H4)2]+2 + 2(H2) → [M3(H6)2]+2, as discussed in the main text.

Figure 10. (a) Schematic illustration showing that when the hydrogen atoms in the hydrogenic lattice adopt a hexagonal as opposed to a square configuration, they are able to more effectively avoid the regions in the center between the two metals. The hexagonal and square edges (shortest H−H distances) measure the same length. (b) δ− The valence charge density which contains the Hδ− 4 or the H6 motifs in (left) SrH4 when optimized in the most stable MgH4 structure at 150 GPa, and (right) the native Cmcm-SrH4 structure at 150 GPa. (c) Planes parallel to those shown in (b), but shifted by 0.32 Å along the Sr−Sr contact. (d) The valence charge density which contains the Hδ− 4 motif in the most stable MgH4 structure at 150 GPa. In all plots, the isovalues are given in e/Bohr3 and the contour lines are drawn every 0.003 units from 0.03 to 0.08 e/Bohr3.

1.75 Å. In order to assess the sensitivity of the trends to the total electron density, we have used a model with a +2 electronic charge, which results in a formal electron count on the hydrogens which agrees with the crystalline structures, as well as a neutral charge. In the neutral model, as the M−M length decreases, MH6M becomes more stable (ΔErxn is negative) for Ba, Sr, and Ca. Moreover, MgH6Mg is never stable. This model suggests that hexagonal hydrogenic arrangements are energetically preferred for all of the alkaline earth metals other than Mg when the distance between the metals is less than ∼3.1 Å, which agrees with the motifs noted above in MgH4, CaH4, SrH4, CaH6, SrH6, and BaH6 at 150 GPa. In the charged model the hexagonal arrangements become more stable for Sr and Ba below 3.0 Å. We have also considered the reaction energies for a hypothetical three-layer system, [M3(H4)2]+2 + 2(H2) → [M3(H6)2]+2 and M = Mg, Ba, using the model systems illustrated in Figure 11b. Whereas the left-hand side of the reaction was computed to be energetically preferred over the right for Mg (5.3 eV), the opposite was the case for Ba (−2.7 eV) using H−H distances constrained to fall within 0.1 Å of those present in the lowest enthalpy MgH4 and BaH6 structures at 150 GPa. The left-hand side of the reaction was found to yield a lower energy only when the H−H distances were allowed to relax. When the M−M contact was held fixed at 3.0

structure. The resulting volume increase destabilizes the structure compared to the native SrH4 lattice. The isovalue of the electron density between the hydrogens within the native MgH4 (Figure 10d) structure is similar to the one in the most stable SrH4 structure. It is also likely that the interaction of the metal d-orbitals with the hydrogen 4s/4p has an influence on the structures which are adopted by the compressed alkaline earth polyhydrides. To further explore how the interaction of the ionic cores influences the preferred hydrogenic motifs, we considered the reaction energy (computed in the gas phase via a molecular program) for the addition of H2 to a hypothetical MH4Mq model system yielding MH6Mq (q = +2, 0). MH4Mq consists of two metal atoms bridged by four hydrogens which form a square, whereas in MH6Mq, a hexagon bisects the M−M contact, as illustrated in Figure 11a. We have considered M−M measuring from 3.0 to 3.4 Å and H−H fixed at 1.3 Å. These values are typical for the polyhydrides at 150 GPa; for example, the shortest M−M distances in MH6 measure around 3 Å and the H−H distances within the hexagonal faces are all less than 6443



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Å, the H−H distances expanded to ∼2.6 Å in Ba3(H4)2+2, once again illustrating that the hydrogens want to avoid the regions where their electron density may overlap with the metal ion cores.

in the Vienna Ab Initio Simulation Package (VASP) versions 4.6.31 and 5.2,107 with the gradient-corrected exchange and correlation functional of Perdew−Burke−Ernzerhof (PBE).108 The reliability of generalized gradient approximation (GGA) type functionals such as PBE, and functionals which include Hartree−Fock exchange such as HSE06 or PBE0 in predicting transition pressures between different phases109,110 and in characterizing Peierls distortions111 in solids under pressure is an active area of investigation. The projector augmented wave (PAW) method112 was used to treat the core states, and a plane−wave basis set with an energy cutoff of 500 eV was employed for the structure searches, and 600 eV otherwise. The Sr 4s/4p/5s electrons were treated explicitly in all of the calculations. The k-point grids were generated using the Γcentered Monkhorst−Pack scheme, and the number of divisions along each reciprocal lattice vector was chosen such that the product of this number with the real lattice constant was 30 Å in the structure searches, and 45−60 Å otherwise. For the calculation of ΔHF, we used the enthalpies of the most stable SrH2 and H2 structures from refs 83 and 15, respectively. The DOS of select structures was computed using the HSE0689 screened hybrid functional, wherein the k-points were determined using a 40 Å product. Phonon calculations of the SrHn, n = 4, 6, and 8 phases, were performed using VASP combined with the phonopy113 package. The supercells were chosen such that the number of atoms in the simulation cell was always greater than or equal to 84 atoms, typically being 2 × 2 × 2 or 3 × 3 × 3 representations of the standard primitive cells generated from the AFLOWLIB web site (http://aflowlib.org/). Γ-Point phonons were carried out for the phases with n = 10 and 12. The molecular calculations on the model systems illustrated in Figure 11 were performed using the ADF software package,114 the revPBE gradient density functional,108 and triple-ζ Slatertype basis sets with polarization functions from the ADF basis set library, and for the metals the (n − 1)sp/ns electrons were treated explicitly. XCRYSDEN115 was employed to render many of the structures shown in the main text, and the charge densities in Figure 10b were generated using the VESTA visualization software package.116

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CONCLUSIONS Our density functional theory investigation of SrHn, with n = 3−12, predicts that the polyhydrides will become stable with respect to decomposition into H2 and the classic hydride, SrH2, by 20 GPa. In accord with the results previously obtained for the Mg,77 Ca76 and Ba78 polyhydrides, we find that n is even in the thermodynamically stable phases, and that the stoichiometry with the most negative ΔHF has a larger hydrogen content at higher pressures. SrH4 lies on the convex hull at 50, 100, and 150 GPa and this phase becomes metallic due to pressureinduced band broadening and overlap of the H− bands with the Sr sd and the H2 σ* bands by 150 GPa. The structures adopted by SrH4 in this pressure range are isotypic with those previously predicted for CaH4.76 At 150 GPa the lowest point on the convex hull was SrH6. Our evolutionary searches found a phase with R3̅m symmetry, which could be viewed as a distorted version of the clathrate− like CaH6 structure whose Tc was calculated to be 220−235 K at 150 GPa.76 The distortion leads to the formation of helical 1 chains of hydrogens, ∞ [Hδ−], with interatomic distances measuring ∼1.07 Å along the chains. Even without electron donation from the metal, these chains would be metallic as a result of their one-dimensional, atomistic structure. Electron donation from strontium to the hydrogenic sublattice does not destroy the metallicity of this phase. We find a plethora of similarities between R3̅m-SrH6 and Im3̅m-CaH6, including the high DOS at EF, the phonon DOS, and perhaps most importantly the fact that the hydrogenic sublattices present in both structures are atomistic (chains in SrH6, and cages in CaH6). At 150 GPa, R3̅m-SrH6 is not dynamically stable, and following the imaginary phonon mode leads to a P3̅ symmetry phase with a larger unit cell and slightly lower enthalpy. The vibration perturbs the symmetric helical hydrogenic chains giving rise to H2···H− motifs and lowering the DOS at EF. By 250 GPa, however, R3m ̅ -SrH6 is found to be dynamically stable and it has a high density of states at the Fermi level. We illustrated that Im3̅m-CaH6, R3̅m-SrH6, and Imm2-BaH6 can all be derived from the AlB2-type alkaline earth dihydride, MH2, structure. And finally we took a look at how the interaction between the metal cations and the hydrogen anions may influence the motifs observed in the hydrogenic sublattices.

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ASSOCIATED CONTENT

S Supporting Information *

Structure search details, structural coordinates, and convex hulls of SrHn, as well as the phonon DOS, projected electronic DOS, and electronic DOS calculated using the HSE06 functional for select phases. This material is available free of charge via the Internet at http://pubs.acs.org.

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COMPUTATIONAL DETAILS The structure searches were performed using the open-source evolutionary algorithm, EA, XtalOpt Release 8.104,105 EA runs were carried out on the SrH2 stoichiometry to confirm known phases and SrHn, with n = 3−12 at 50, 100, and 150 GPa, employing simulation cells with 2−4 formula units. In the Supporting Information we provide further details regarding the EA searches. Duplicate structures were detected via the XtalComp106 algorithm, and the SPGLIB package was used to determine space-group symmetries. The lowest enthalpy structures from each search were relaxed in a pressure range from 10 to 150 GPa. Geometry optimizations and electronic structure calculations were performed by using Density Functional Theory as implemented

AUTHOR INFORMATION

Corresponding Author

*E-mail: ezurek@buffalo.edu. Tel.: +1-716-645-4332. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the NSF (DMR-1005413) for financial support, and the Center for Computational Research at SUNY Buffalo for computational support. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0002006. E.Z. thanks the Alfred P. Sloan 6444



Article

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Foundation for a research fellowship (2013-2015). J.H. acknowleges support from the Homing Plus Program (HOMING PLUS/2012-6/4) granted by the Foundation for the Polish Science and cofinanced by the European Regional Development Fund.

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