Article pubs.acs.org/JPCC
High Pressure Potassium Polyhydrides: A Chemical Perspective James Hooper and Eva Zurek* Department of Chemistry, State University of New York at Buffalo, Buffalo, New York 14260-3000, United States S Supporting Information *
ABSTRACT: Doping hydrogen by an impurity has emerged as a possible route toward the metallization of hydrogen at experimentally achievable pressures. Evolutionary structure searches coupled with density functional theory calculations have been employed to determine the most stable stoichiometries and structures of potassium polyhydrides, KHn n > 1, under pressure. Stabilization occurs at pressures as low as 3 GPa, but KH5, the most stable stoichiometry throughout most of the pressure regime considered, does not become metallic until P > 300 GPa. There are, however, suggestions of metallicity in metastable phases at 100 GPa. Detailed structural, electronic, and chemical analyses of the emergent hydrogenic motifs are provided and related to the rest of the alkali series. The softness of the alkali metal cation is shown to be related to the formation of symmetrical H−3 molecules in compressed alkali metal polyhydrides.
■
rubidium polyhydrides, RbH5 and RbH3, contained a linear H−3 unit which underwent pressure-induced symmetrization.29 Metallization did not occur until above 200 GPa. In this study, we fill in the gap in the alkali series and explore the high−pressure potassium/hydrogen potential energy landscape. Our focus is on the 100 GPa regime because this is where signs of metallization are first observed in metastable species within non-hybrid density functional theory. There are clear similarities between the structures found in this work and those of the rubidium polyhydrides.29 KHn species stabilize at about the same pressure as their heavier cousins, RbHn, due to the similar ionization potentials. Whereas for lithium and sodium, the mole percent content of the most stable phase, LiH6 and NaH9, correlates with the size of the alkali metal cation, this is not the case for the heavier alkali metals. The presence of the ubiquitous H−3 structural motif in the latter is shown to be related to the softness of the heavier alkali metal cations. H2 is an extremely weak acid, and forcing it to form secondary bonding with an H− base in order to yield H−3 requires both pressure and the strongest MH base, i.e., the softest alkali metal.
INTRODUCTION The high temperature at which compressed hydrogen is predicted to become superconducting1,2 has long since driven the search for this elusive metallic allotrope.3,4 Recent advances have been made toward metallizing hydrogen at ambient temperatures and pressures around 300 GPa.5,6 It has been postulated that doping hydrogen with an impurity may decrease the external pressure required for metallization.7−9 For example, Si2H6 (disilane),10,11 GeH4,12 SnH413 GaH3,14 CaH6,15 and a number of MH3 hydrides16 have all been predicted to become metallic and superconducting at pressures attainable in a diamond anvil cell. In related efforts, hydrogen uptake in compressed metals with low hydrogen solubility has also been studied, for example RhH2,17 Re2H,18 noble metal hydrides,19 and superconducting PtH.20−22 And pressure induced structural transformations in hydrogen-rich systems, such as ammonia−borane23−25 and calcium borohydride,26 are under intense investigation. Our calculations have shown that the alkali metal polyhydrides, MHn with n > 1, become stable with respect to decomposition into MH and H2 at 100, 25, and 2 GPa for lithium,27 sodium,28 and rubidium,29 following the decreasing ionization potential of the metal. The lithiated species are particularly interesting because the most stable stoichiometry above 150 GPa, LiH6, was found to be metallic through the partial occupation of the H2 σ*-band and had a large density of states at the Fermi level, suggestive of a high Tc superconductor.27 Going down the group to NaHn, the most stable stoichiometry was found to be NaH9, which consisted of an Na+/H− sublattice and H2 molecules.28 Because the overlap of the Na 2p orbitals forestalls band gap closure between the H− and[H2 σ*]/[Na 3s, 3p] bands, a stable and metallic phase did not emerge until ∼300 GPa. Above 100 GPa, the most stable © 2012 American Chemical Society
■
RESULTS AND DISCUSSION The calculated enthalpies of formation, ΔHF, of the most favorable KHn structures found in our evolutionary runs are provided in Figure 1. The range of structures falls into categories similar to those which were uncovered for the rubidium polyhydrides: (1) K+, H2 molecules, and hydridic H− anions; (2) K+, H2, and H3− molecules; and (3) K+ and H−3 . Received: March 29, 2012 Revised: May 16, 2012 Published: May 25, 2012 13322
dx.doi.org/10.1021/jp303024h | J. Phys. Chem. C 2012, 116, 13322−13328
The Journal of Physical Chemistry C
Article
Figure 1. The enthalpy of formation, ΔHF, for the reaction KH + 1 /2(H2)n−1 → KHn versus the H2 composition at varying pressures. Filled symbols represent points at which evolutionary algorithm, EA, structure searches were explicitly run; open symbols represent structures which were reoptimized at said pressures from an EA search performed at another pressure. The dashed black line represents the convex hull at 100 GPa.
Figure 2. Supercells of the lowest enthalpy (a) KH9 and (b) KH5 phases recovered at 10 GPa. (c) The lowest enthalpy KH5 structure (Cmcm symmetry) recovered at 100 GPa. (d) The relative enthalpy of the structure shown in (b) to that shown in (c).
None of the low enthalpy configurations we observed, however, contained K+ and (H2)[−(2/n)] molecules as found in LiH6, RbH13, and RbH18. From Figure 1, it is possible to deduce which KHn species are thermodynamically stable at a given pressure by constructing the convex hull.30 The convex hull of KHn at 100 GPa in Figure 1 has been forged by drawing tielines between the various phases, and determining which points cannot fall below the lines connected to points on either side of it.31 The KH9 and KH5 stoichiometries are particularly stable in the sense that they are the global minima at some pressure as plotted in Figure 1. KH8 and KH11 also lie on the convex hull at 100 GPa, but the enthalpies of formation cluster at higher n values such that one cannot rule out other KHn structures which may also be thermodynamically stable. The geometries and electronic structures of the KH8 and KH11 phases are fairly representative of the systems containing a large mole percent of hydrogen, so they will be focused on in the discussion below. KH2 becomes stable at ∼150 GPa, preventing KH3 from falling on the convex hull at any pressure. Various KHn phases start to become stable with respect to decomposition into H2 and KH between 3−4 GPa, as compared to ∼2 GPa for the rubidium polyhydrides. The kindred pressures necessary for stabilization correlate well with the nearly equivalent ionization potentials: 4.2 vs 4.3 eV for Rb and K, respectfully. The potential energy landscape of the potassium polyhydrides also behaves much like their heavier brethren. For both alkalis, an MH9 stoichiometry first becomes the global thermodynamic minimum before being surpassed by MH5. One difference between the two metals is, however, that whereas KH5 remains the most stable stoichiometry through to 250 GPa, RbH5 is eventually overtaken by RbH3. All of the structures found in the evolutionary searches at 10 GPa were insulating and although there were always several enthalpically competitive configurations for KH9 and KH5, they all featured K+, H2 molecules, and hydridic H− anions. The lowest enthalpy structures of these phases both contained linear H−···H2 contacts similar to the ones observed in RbH5 and RbH9, as shown in Figure 2(a,b). One key difference between
KH5 and RbH5 is the local chemical environment of the alkali metal at 10 GPa. The latter is similar to the Cmcm-symmetry structure pictured in Figure 2(c), except the H3− unit asymmetrizes and becomes a single H−···H2 which lies adjacent to the alkali metal cation. There is no such structural motif in KH5 at 10 GPa and each hydride has several weak almost-linear H−···H2 contacts. The result is a much shorter H− to nearest H2 distance in the heavier analog: it is 1.28 Å in RbH5 and 1.70 Å in KH5 at 10 GPa. Stabilization of KH5: H3− Counteranions with H2 Bystander Molecules. The Cmcm-KH5 phase illustrated in Figure 2(c) does however become stable near 16 GPa (see Figure 2(d)), and remains so until the highest pressure considered in this study (250 GPa). This correlates with the finding that in elemental solids32 and simple hydrides,33 the heavier members of a group often follow the same structural changes as the lighter ones but at lower pressures. Both KH5 structures shown in Figure 2(b,c) are mechanically stable at 20 GPa and we find the ZPE corrections to favor the Cmcm system. The conventional unit cell of Cmcm-KH5 at 100 GPa along with its phonon densities of states (DOS) is shown in Figure 3(a, b).34 The phonon DOS confirmed KH5 was mechanically stable. As expected it is quite similar to that of RbH5 at 100 GPa, suggesting a softening of the H2 vibron (the highest frequency mode) relative to pure H2 at 1 atm.35 The second most stable KH5 structure we recovered from an EA search at 100 GPa was nearly 25 meV/atom higher in enthalpy than Cmcm-KH5. Like Cmcm-KH5, it was insulating and consisted of K+, H2, and H−3 molecules. At 250 GPa, the next lowest enthalpy structure found was very metallic, with chain-like arrangements of hydrogen atoms which were similar to an emergent RbH6 phase we recently reported near 250 GPa. Nevertheless, it was still 16 meV/atom less stable. The spread in enthalpy between the Cmcm and other KH5 structures suggest that the former is indeed particularly stable at high pressure. The PBE band gap of KH5 at 100 GPa measures 1.2 eV, which is ∼0.5 eV smaller than the corresponding gap in RbH5. 13323
dx.doi.org/10.1021/jp303024h | J. Phys. Chem. C 2012, 116, 13322−13328
The Journal of Physical Chemistry C
Article
the hydrogen sublattice of RbH5 agree with the molecular orbitals of H−3 29 and herein we find that the Wannier Functions of KH5 are similar. At 100 GPa, KH8 also lies on the convex hull and its lowest enthalpy C2/m-symmetry structure, shown in Figure 4(a),
Figure 3. (a) Unit cell of the Cmcm-symmetry KH5 structure at 100 GPa, and (b) its phonon densities of states. The modes corresponding to the symmetric and asymmetric H−3 stretch, as well as the H2 vibron are highlighted. (c) The total and site-projected densities of states (DOS) of Cmcm-KH5 at 100 GPa . In all of the plots, the Fermi energy is set to zero. (d) A sketch of the molecular orbital level diagram of a single H−3 molecule.
Figure 4. (a) Supercell of the C2/m-symmetry KH8 structure at 100 GPa, and (b) its phonon densities of states. The modes corresponding to the symmetric and asymmetric H−3 stretch, as well as the H2 vibron are highlighted. (c) The total and site-projected DOS of C2/m-KH8 at 100 GPa.
A single-point calculation on the negatively charged hydrogenic lattice of Cmcm-KH5, but with the metal atoms removed, showed it to be a good metal. The overlap of the core potassium 3p and 3s orbitals results in their broadening, shown in Figure 3(c), and inhibits the metallization of this phase. In elemental sodium the 2p cores overlap under pressure, and because of the Pauli principle and orthogonality36 the valence electrons are squeezed in the interstitial regions so that sodium becomes insulating.37 Since the Rb+ is larger than K+, the heavier polyhydride experiences a greater degree of core overlap, with a concomitantly larger band gap at the same pressure. Even by 250 GPa, the PBE band gap in KH5 has only decreased to just over 0.6 eV, and it does not close until 350 GPa. This phase is not a viable superconductor under pressure, and it is likely that, like RbHn, potassium polyhydrides as a whole are not promising materials in this regard. The siteprojected densities of states of KH5 are in-line with the presence of H−3 molecules; the simplest example of a threecentered four-electron (3c−4e) bond. The largest contribution to the valence bands just below the Fermi level arises from the terminal hydrogen atoms of the H−3 , consistent with the nonbonding molecular orbital of this species (see Figure 3(d)). The states between −11 and −4 eV, however, exhibit H2 and H−3 bonding character, so that every hydrogen atom contributes to the DOS in this energy range. Also, note the mixing of the K 3p bands with the hydrogenic states between −20 and −7 eV. We have previously shown that the Wannier Functions obtained for
consists of K+, H2 and H−3 molecules.38 It very much resembles the KH5 phase from Figure 3(a) except it has an extra layer of H2 molecules, highlighted in Figure 4(a), buffering the KH5 motifs. This phase was found to be mechanically stable at 100 GPa and the corresponding phonon densities of states is provided in Figure 4(b). The splitting of the H2 vibrational modes above 3500 cm−1 arises from their different environments: the lower frequency modes correspond to H2 molecules which reside within the KH5 motifs, whereas the higher frequency modes stem from those in the buffering layers. Like KH5, KH8 is also insulating at 100 GPa with a PBE band gap near 1.1 eV. Pressure-induced metallization does not occur until 250 GPa. The electronic structures of the two phases are similar as well, but in KH8 the presence of the “KH5” and “H2” layers leads to symmetry-breaking and a change in the local chemical environments. There are slight differences between the site-projected DOS of terminal H atoms within the same H−3 molecule (see Figure 4(c)), for example. Also, from their site-projected DOS the H2 molecules within the “H2 layer” can be divided into two groups which differ only in the direction along which they are pointed: the molecules generated from the 4g Wyckoff sites lie between H−3 species from opposite “KH5 layers”, and perpendicular to the other H2’s (those generated from the 4i Wyckoff sites) which are situated between K+ atoms. 13324
dx.doi.org/10.1021/jp303024h | J. Phys. Chem. C 2012, 116, 13322−13328
The Journal of Physical Chemistry C
Article
Hints of Metallicity in Metastable KHn Structures at High Pressure. Although KH5 is stubbornly insulating at every pressure considered, there are nonetheless suggestions of other KHn species becoming metallic near 100 GPa (within nonhybrid DFT). This is the reason why we focused on applying our EA to this pressure. One of the metallic phases uncovered which lies on the convex hull at 100 GPa is KH11. The lowest enthalpy candidate consists of K+, H2, and H− units, see Figure 5(a), and is representative of many of the potassium
be synthesized in experiments using appropriate metal to hydrogen ratios. The first of these is a C2/m-symmetry KH3 structure which becomes metallic around 70 GPa and, like all of the other low enthalpy KH3 structures, consisted of K+ cations and H−3 anions.39 Its extended structure was similar to the Cmcm-RbH3 geometry observed previously near 250 GPa, however the hydrogen layers buckled in the case of the lighter alkali, giving rise to pleated sheets rather than flat planes. When this phase is reoptimized with rubidium or cesium atoms replacing potassium, the sheets flatten and Cmcm symmetry is regained. In the case of potassium, the C2/m alternative has a smaller volume than Cmcm, suggesting that this structure is adopted to minimize the PV contribution to the enthalpy. The H−3 species themselves appear to become strained, however, bending slightly so that the intramolecular H−H−H angle is 170.2° (see Figure 5(b)). The phonon DOS of C2/m-KH3 at 100 GPa in Figure 5(c) differ from those of KH5 by the softening and increasing dispersion of the asymmetric H−3 stretching mode, which now lies between 1600 and 2300 cm−1, and the collective H3− bending modes near 1900 cm−1. The bending of the H−3 is also likely due in part to the Coulomb repulsion between adjacent molecules. The site-projected DOS at 100 GPa in Figure 5(d) is consistent with the presence of discrete H−3 molecules, and the metallicity stems from the pressure induced overlap of the H−3 non-bonding bands with the H−3 anti-bonding and K 3d bands. The shortest intra- and inter-H−3 H−H distances measure 0.93/0.91 Å and 1.66/1.87 Å in KH3/KH5 at 100 GPa, suggesting that KH5 may be favored over KH3 because the H2 molecules in KH5 help screen the negatively charged H−3 from one another. Moreover, the separation between an H−3 and an H2 is only 1.45 Å in KH5, considerably smaller than the nearest neighbor distance between adjacent H−3 motifs in KH3. In fact, if one subtracts the volume of the largest non-overlapping sphere that can be placed at the sites of the potassium atoms, then KH5 assumes 0.70 Å3 per H atom less space than does KH3, so that the former also minimizes the enthalpy by lowering the effective volume per hydrogen atom. The radius of these spheres ends up being ∼1.25 Å, since the shortest interalkali contacts measure only ∼2.51 Å in KH3 at 100 GPa (2.58 Å in KH5). C2/m-KH2, illustrated in Figure 6(a), was also found to be metastable and metallic at 100 GPa; the calculated zero point energy corrections (ZPE) stabilize KH2 (and KH3) relative to KH5 by roughly 15 meV/atom at 100 GPa.40 (The ZPE correction for pure H2 was taken from a linear extrapolation of the values reported in the literature at 75 and 150 GPa.49) The structure is unlike any discussed so far. Formally, it can be considered as containing K+ cations, H− anions, and H2 molecules. However, the H2 molecules do not form a linear H−···H2 contact with either of the hydridic atoms (the angle of the shortest contact measures 159.7° and the distance is 1.32 Å). Moreover, the site-projected DOS only show weak mixing of the hydridic states with the H2 molecular ones. This phase becomes metallic within non-hybrid DFT because of the pressure induced overlap of the H− and H2 bonding bands with the H2 anti-bonding and K 3d bands. Interestingly, the intramolecular H2 distances are longer than expected, near 0.83 Å, and the phonon modes corresponding to their vibration are found at lower frequencies than in either KH5 or KH8 at this pressure, near 3000 cm−1, see Figure 6(b).
Figure 5. Supercell of the (a) Cmc21-symmetry KH11, and the (b) C2/ m-symmetry KH3 structure at 100 GPa. (c) The phonon densities of states, and the (d) total and site−projected DOS of C2/m-KH3 at 100 GPa. The modes corresponding to the symmetric and asymmetric H−3 stretch at the Γ-point, as well as a bending mode, are highlighted.
polyhydride structures that contain a large mole percent of hydrogen. The hydridic atoms lie only 1.09 Å from the nearest H2, forming an asymmetric linear H−···H2 motif. Another enthalpically competitive and metallic KH11 structure was similar, except it contained symmetric H3− molecules. Unfortunately, none of these phases were mechanically stable within the harmonic approximation and the imaginary phonon modes often included an asymmetric H−3 stretch. At this pressure, many of the polyhydrides with n > 8 lie quite close to the convex hull. Two of these, KH12 and KH14, contained structural motifs comparable to those found in KH11, but also afforded imaginary phonon modes. Two metallic but metastable structures were located in the evolutionary searches at 100 GPa. They both fell above the convex hull at 100 GPa, but phonon calculations revealed they were mechanically stable. Provided that the barriers to decomposition into other phases are high, they may potentially 13325
dx.doi.org/10.1021/jp303024h | J. Phys. Chem. C 2012, 116, 13322−13328
The Journal of Physical Chemistry C
Article
Figure 7. The difference between the z and d distances in an H−···H2 fragment (see inset) within a given alkali or alkaline earth metal polyhydride (see legend) vs pressure. The polyhydrides were reoptimized starting from structures obtained at 2 GPa using successive pressure increments, corresponding to the points marked in the plot. The structures with symmetrized H−3 molecules are shown above (M = Na, K, Rb, and Cs).
Figure 6. (a) Unit cell of the C2/m-symmetry KH2 structure at 100 GPa, and (b) its phonon densities of states. The H− atoms are colored blue, and the H2 vibron mode is highlighted. (c) The total and siteprojected DOS of C2/m-KH2 at 100 GPa.
The Driving Force Behind Making an H2 Interact with H−. Our calculations suggest that the stabilization of KH5 over KH3 under pressure is the result of increasing the H−H distances between H−3 molecules in order to minimize the Coulomb repulsion between them, and in decreasing the volume per hydrogen so as to lower the destabilizing PV contribution to the enthalpy. But the symmetric H−3 observed in rubidium and potassium polyhydrides are not stable at ambient pressures. Ab initio computations, however, have shown that an asymmetric H−3 whose H−H distances measure 0.75 and 2.84 Å41 is a minimum on the gas phase potential energy surface. This species exhibits a double-well minimum, with the lowest energy barrier being a symmetric configuration with H−H lengths of 1.06 Å. The pressures at which equalized H−3 units start to appear in the heavy alkali polyhydrides is inversely proportional to the size of the alkali metal cation. This is evident in Figure 7, wherein the difference between the intramolecular separations in the H−3 species, z−d, observed in KH5, RbH5, and CsH5 with Cmcm symmetry is plotted as a function of pressure. At mild compression, the motif displays an H−···H2 configuration like the one shown in the inset, and z−d approaches zero as H−3 symmetrizes. Note that when z−d goes to zero in Figure 7, it is showing the pressure at which the H−···H2 configuration ceases to be a minimum on the calculated potential energy surface, i.e., there is a barrierless transition to the symmetric H−3 species. The volume increments used to compress the MH5 and BaH4 species are depicted by symbols in Figure 7. In the low pressure KH5 structure the hydrogen molecules rearrange so they are no longer parallel, this is why the difference between the two H−H distances is longer than in RbH5 and CsH5 at 2 GPa. The pressure at which symmetrization of the simple 3c−4e bond occurs correlates with the softness of the not-so-innocent bystander cation found in the cell; Cs+ > Rb+ > K+. Chemically, this trend is quite intuitive by considering that we are trying to
force a soft base, H−, to interact with an extremely weak acid, H2, and form a symmetric H3− in this computational experiment. Because of the M+−H− interaction, the basicity of the hydride is decreased in the presence of the alkali metal cation, and thereby hindered relative to the gas-phase. This is illustrated in Figure 8, where the difference between the length of the two H−H contacts in H−3 in a number of alkali
Figure 8. The difference between the z and d distances in an H−···H2 fragment (see inset) is plotted vs their sum for an isolated H−3 molecule in the gas phase. During the optimization, the total length of the molecule was constrained and the central atom was allowed to relax freely. These values are also illustrated for an H−···H2 contact in NaH5, KH3, KH5, CsH3, CsH5, and BaH4. These phases were reoptimized starting from structures obtained at 2 GPa in order to determine the effect of pressure on the sum and difference of the H− H contacts in an H−3 unit. 13326
dx.doi.org/10.1021/jp303024h | J. Phys. Chem. C 2012, 116, 13322−13328
The Journal of Physical Chemistry C
Article
polyhydrides is plotted versus their sum. The total length of the fragment at which symmetrization occurs gives an idea of the effective pressure felt by the H−3 . It is readily seen that the two bonds equalize most easily in the gas−phase, followed by CsH5 (CsH is the strongest base out of any of the alkali hydrides). In order to reference other examples of hard and soft cations, calculations on hypothetical NaH5 and BaH4 structures are also included in Figures 7 and 8. The BaH4 structure employed was one of the most stable configurations found in an evolutionary search at 50 GPa. Several enthalpically competitive structures were recovered, but the one selected resembles Cmcm-MH5 except the H2 is replaced by an H− in order to balance the charge. The BaH4 system, illustrated in Figure 7, is stable with respect to decomposition into BaH2 and H2 at 50 GPa, but a full analysis of the BaHn potential energy landscape is beyond the scope of this work. The hydrogen sublattice of both NaH5 and BaH4 rearrange substantially at low pressures so, for the purpose of comparison, the hydrogen molecules were constrained to remain parallel to one another in order to enforce the H−···H2 contact. The behavior of H−3 in lattices containing Ba2+ and Na+ is as expected: symmetrization occurs at a very low pressure for BaH4 and much higher pressure, corresponding to a decrease in the total fragment length, for NaH5.
structure calculations were performed by using Density Functional Theory as implemented in the Vienna ab initio Simulation Package (VASP) version 4.6.31,45 with the gradient−corrected exchange and correlation functional of Perdew−Burke−Ernzerhof (PBE).46 The projector augmented wave (PAW) method47 was used to treat the core states, and a plane−wave basis set with an energy cutoff of 600 eV was employed. The K 3s/3p/4s electrons were treated explicitly in all of the calculations. The k-point grids were generated using the Γ-centered 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 structural searches, and 40 Å otherwise. For the calculation of the enthalpies of formation, the KH and H2 enthalpies were computed for the most stable structures from refs 33, 48, and 49. Phonons and thermodynamic properties of select KH2, KH3, KH5, KH8, KH11, and KH12 phases as described in the text were calculated using the PHON50 package. The supercells used for the phonon calculations were chosen such that the number of atoms in the simulation cell was always between 96 and 216 atoms.
CONCLUSIONS Our first-principles computations predict that potassium polyhydrides, KHn with n > 1, become stable at pressures as low as 3 GPa. Like their heavier brethren, RbHn, there is a wide variety in their structures and their hydrogenic sublattice can be viewed as being composed of H−, H2, and H−3 molecules. The appearance of H−3 is likely primarily driven by the inclination of pressure to favor delocalized, multi-centered bonding,42 but also by the softness of the alkali metal cation. H−3 was not observed in lithium or sodium polyhydrides simply because the alkali−hydride interaction was too strong to allow a weak H2 base to attack an H−, even under pressure. Potassium is the first alkali in the series to allow the stabilization of a symmetric H−3 at modestly low pressures (∼20 GPa), but never without H2 molecules present in the lattice as well. We attribute this to the need for H2 molecules to screen the negatively charged H−3 species from one another. This is the makeup of KH5, the most stable KHn structure between 15 and 250 GPa. The broadened K 3p bands hybridize with hydrogenic bands, but to a lesser extent than observed in RbH5 at similar pressures, and the overlap of the K 3s/3p orbitals makes this phase an insulator at least until 250 GPa. Metastable KH2 and KH3 structures which become metallic at 100 and 70 GPa, respectively, at the PBE level of theory were also found in our evolutionary runs. However, KH2 does not become a thermodynamically stable phase up until ∼150 GPa.
Phonon band structures of KH2, KH3, KH5, and KH8. This material is available free of charge via the Internet at http:// pubs.acs.org.
■
■
ASSOCIATED CONTENT
S Supporting Information *
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: ezurek@buffalo.edu. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS We acknowledge the NSF (DMR-1005413) for financial support, and the Center for Computational Research at SUNY Buffalo for computational support. We thank an insightful referee of a prior publication for useful comments.
■
REFERENCES
(1) Ashcroft, N. W. Phys. Rev. Lett. 1968, 21, 1748−1749. (2) Cudazzo, P.; Profeta, G.; Sanna, A.; Floris, A.; Continenza, A.; Massidda, S.; Gross, E. K. U. Phys. Rev. Lett. 2008, 100 (257001), 1−4. (3) Narayana, C.; Luo, H.; Orloff, J.; Ruoff, A. L. Nature 1998, 393, 46−49. (4) Loubeyre, P.; Occelli, F.; LeToullec, R. Nature 2002, 416, 613− 617. (5) Eremets, M. I.; Troyan, I. A. Nat. Mater. 2011, 10, 927−931. (6) Howie, R. T.; Guillaume, C. L.; Scheler, T.; Goncharov, A. F.; Gregoryanz, E. Phys. Rev. Lett. 2012, 108 (125501), 1−5. (7) Carlsson, A. E.; Ashcroft, N. W. Phys. Rev. Lett. 1983, 50, 1305− 1308. (8) Ashcroft, N. W. Phys. Rev. Lett. 2004, 92 (187002), 1−4. (9) Klug, D. D.; Yao, Y. Phys. Chem. Chem. Phys. 2011, 13, 16999− 17006. (10) Jin, X.; Meng, X.; He, Z.; Ma, Y.; Liu, B.; Cui, T.; Zou, G.; Mao, H. K. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 9969−9973. (11) Flores-Livas, J. A.; Amsler, M.; Lenosky, T. J.; Lehtovaara, L.; Botti, S.; Marques, M. A. L.; Goedecker, S. Phys. Rev. Lett. 2012, 108 (117004), 1−5. (12) Gao, G.; Oganov, A. R.; Bergara, A.; Martinez-Canales, M.; Cui, T.; Iitaka, T.; Ma, Y.; Zou, G. Phys. Rev. Lett. 2008, 101 (107002), 1− 4.
■
COMPUTATIONAL DETAILS The structural searches were performed using the open−source evolutionary algorithm, EA, XtalOpt Release 7,43 and the parameter set suggested in ref 44. EA searches were carried out employing simulation cells with at least two KHn formula units (four formula units for KH2 and KH3 and two formula units for the rest) at 10, 100, and 250 GPa as shown in Figure 1. A supplemental EA search was run on four formula units of KH5 at 100 GPa to help confirm its stability. The lowest enthalpy structures from each search were relaxed in the pressure range from 0 to 250 GPa. Geometry optimizations and electronic 13327
dx.doi.org/10.1021/jp303024h | J. Phys. Chem. C 2012, 116, 13322−13328
The Journal of Physical Chemistry C
Article
(13) Tse, J. S.; Yao, Y.; Tanaka, K. Phys. Rev. Lett. 2007, 98 (117004), 1−4. (14) Gao, G.; Wang, H.; Bergara, A.; Li, Y.; Liu, G.; Ma, Y. Phys. Rev. B 2011, 84, 064118. (15) Wang, H.; Tse, J. S.; Tanaka, K.; Iitaka, T.; Ma, Y. Proc. Nat. Acad. Soc. 2012, 109, 6463. (16) Kim, D. K.; Scheicher, R. H.; Mao, H. K.; Kang, T. W.; Ahuja, R. Proc. Natl. Acad. Sci. U.S.A. 2010, 107, 2793−2796. (17) Li, B.; Ding, Y.; Kim, D. Y.; Ahuja, R.; Zou, G.; Mao, H. K. Proc. Natl. Acad. Sci. 2011, 108, 18618−18621. (18) Scheler, T.; Degtyareva, O.; Gregoryanz, E. J. Chem. Phys. 2011, 135, 214501. (19) Gao, G.; Wang, H.; Zhu, L.; Ma, Y. J. Phys. Chem. C 2012, 116, 1995. (20) Kim, D. Y.; Scheicher, R. H.; Pickard, C. J.; Needs, R. J.; Ahuja, R. Phys. Rev. Lett. 2011, 107, 117002. (21) Zhou, X.-F.; Oganov, A. R.; Dong, X.; Zhang, L.; Tian, Y.; Wang, H.-T. Phys. Rev. B. 2011, 84, 054543. (22) Scheler, T.; Degtyareva, O.; Marques, M.; Guillaume, C. L.; Proctor, J. E.; Evans, S.; Gregoryanz, E. Phys. Rev. B. 2011, 83, 214106. (23) Liu, A.; Song, Y. J. Phys. Chem. C 2012, 116, 2123−2131. (24) Liang, Y.; Tse, J. S. J. Phys. Chem. C 2012, 116, 2146−2152. (25) Lin, Y.; Ma, H.; Matthews, C. W.; Kolb, B.; Sinogeikin, S.; Thonhauser, T.; Mao, W. L. J. Phys. Chem. C 2012, 116, 2172−2178. (26) Liu, A.; Xie, S.; Dabiran-Zohoory, S.; Song, Y. J. Phys. Chem. C 2010, 114, 11635−11642. (27) Zurek, E.; Hoffmann, R.; Ashcroft, N. W.; Oganov, A. R.; Lyakhov, A. O. Proc. Natl. Acad. Sci. 2009, 106, 17640−17643. (28) Baettig, P.; Zurek, E. Phys. Rev. Lett. 2011, 106 (237002), 1−4. (29) Hooper, J.; Zurek, E. Chem−Eur. J. 2012, 18, 5013. (30) Trimarchi, G.; Freeman, A. J.; Zunger, A. Phys. Rev. B 2009, 80 (092101), 1−4. (31) Feng, J.; Hennig, R. G.; Ashcroft, N. W.; Hoffmann, R. Nature 2008, 451, 445−448. (32) McMahon, M. I.; Nelmes, R. J. Chem. Soc. Rev. 2006, 35, 943− 963. (33) Ahuja, R.; Eriksson, O.; Johansson, B. Physica B 1999, 265, 87− 91. (34) Cmcm-KH5 at 100 GPa: a = 2.97 Å, b = 6.88 Å, and c = 4.69 Å with its constituent atoms generated from H 8 f (0.000, 0.276, 0.333), H 8 f (0.000, 0.130, −0.057), H 4c (0.000, −0.0.125, 0.25), and K 4c (0.000, 0.578, 0.250) Wyckoff sites. (35) Stoicheff, B. P. Can. J. Phys. 1957, 35, 730. (36) Neaton, J. B.; Ashcroft, N. W. Phys. Rev. Lett. 2001, 86, 2830− 2833. (37) Ma, Y. M.; Eremets, M.; Oganov, A. R.; Xie, Y.; Trojan, I.; Medvedev, S.; Lyakhov, A. O.; Valle, M.; Prakapenka, V. Nature 2009, 458, 182−185. (38) C2/m-KH8 at 100 GPa: a = 6.82 Å, b = 3.03 Å, c = 6.09 Å, α = 90.0°, β = 78.4°, and γ = 90.0° with its constituent atoms generated from H 4i (0.326, 0.000, 0.257), H 4i (0.290, 0.000, 0.385), H 4i (0.152, 0.000, 0.030), H 4i (−0.117, 0.000, 0.457), H 4i (0.067, 0.000, −0.152), H 4i (−0.089, 0.000, 0.302), H 4i (0.248, 0.000, 0.073), H 4g (0.000, −0.375, 0.000), and K 4i (−0.387, 0.000, 0.298) Wyckoff sites. (39) [C2/m-KH3 at 100 GPa: a = 6.06 Å, b = 4.92 Å, c = 2.96 Å, α = 90.0°, β = 61.4°, and γ = 90.0° with its constituent atoms generated from H 2h (0.000, −0.316, 0.500), H 4j (0.412, 0.200, 0.318), and K 2i (0.201, 0.000, 0.057) Wyckoff sites. (40) [C2/m-KH2 at 100 GPa: a = 4.83 Å, b = 6.01 Å, c = 2.87 Å, α = 90.0°, β = 125.2°, and γ = 90.0° with its constituent atoms generated from H 2i (0.462, 0.000, −0.402), H 2i (0.242, 0.000, −0.272), and K 2g (0.000, 0.200, 0.000) Wyckoff sites. (41) Ayouz, M.; Dulieu, O.; Guerout, R.; Robert, J.; Kokoouline, V. J. Chem. Phys. 2010, 132 (194309), 1−11. (42) Grochala, W.; Hoffmann, R.; Feng, J.; Ashcroft, N. W. Angew. Chem., Int. Ed. 2007, 46, 3620−3642. (43) Lonie, D. C.; Zurek, E. Comput. Phys. Commun. 2011, 182, 2305−2306.
(44) Lonie, D. C.; Zurek, E. Comput. Phys. Commun. 2011, 182, 372− 387. (45) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558−561. (46) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (47) Blöchl, P. Phys. Rev. B 1994, 50, 17953. (48) Gou, Q.; Pei, C.; Wang, X. High Pressure Res. 1993, 11, 299− 307. (49) Pickard, C. J.; Needs, R. J. Nat. Phys. 2007, 3, 473−476. (50) Alfè, D.; Price, G. D.; Gillan, M. J. Phys. Rev. B 2001, 64, 045123.
13328
dx.doi.org/10.1021/jp303024h | J. Phys. Chem. C 2012, 116, 13322−13328
