Silane plus molecular hydrogen as a possiblepathway to metallic hydrogenYansun Yao1 and Dennis D. Klug1

Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, ON, Canada K1A 0R6

Edited* by Russell J. Hemley, Carnegie Institution of Washington, Washington, DC, and approved October 11, 2010 (received for review May 10, 2010)

The high-pressure behavior of silane, SiH4, plus molecular hydro-gen was investigated using a structural search method and abinitio molecular dynamics to predict the structures and examinethe physical origin of the pressure-induced drop in hydrogen intra-molecular vibrational (vibron) frequencies. A structural distortion ispredicted at 15 GPa from a slightly strained fcc cell to a rhombohe-dral cell that involves a small volume change. The predicted equa-tion of state and the pressure-induced drop in the hydrogen vibronfrequencies reproduces well the experimental data (Strobel TA,Somayazulu M, Hemley RJ (2009) Phys Rev Lett 103:065701). Thebond weakening in H2 is induced by intermolecular interactionsbetween the H2 and SiH4 molecules. A significant feature of thehigh-pressure structures of SiH4ðH2Þ2 is the dynamical behaviorof the H2 molecules. It is found that H2 molecules are rotating inthis pressure range whereas the SiH4 molecules remain rigid.The detailed nature of the interactions of molecular hydrogen withSiH4 in SiH4ðH2Þ2 is therefore strongly influenced by the dynamicalbehavior of the H2 molecules in the high-pressure structure. Thephase with the calculated structure is predicted to become metallicnear 120 GPa, which is significantly lower than the currentlysuggested pressure for metallization of bulk molecular hydrogen.

first principles ∣ hydrogen metallization ∣ structure prediction

One of the main challenges for condensed matter experimen-talists and theoreticians for many decades has been to find

the conditions where molecular hydrogen can be transformed to ametallic solid. The properties of metallic hydrogen could includehigh-temperature superconductivity (1), a liquid ground state (2),and conductivity at very high temperatures that gives rise to thestrong magnetic fields of Jovian planets (3). The direct compres-sion of solid molecular hydrogen however may require a pressurein excess of 400 GPa to reach a metallic state and this pressurelies at the upper limit of the current experimental static compres-sion techniques (4, 5). There have been other approaches to thisproblem, including the study of hydrogen-rich molecular com-pounds (6). Compression of such compounds, in particular thoseinvolving group 14 elements, is predicted to lower the pressurerequired for metallization compared to pure bulk hydrogen (7, 8).In these systems, the hydrogen can be viewed as perturbed by“impurities” in the material and “chemically precompressed” (6).

An extension of this approach is to study mixtures of elementsor simple molecules with hydrogen under pressure (9, 10). Re-cently, Strobel et al. (11) reported that by mixing silane (SiH4)and hydrogen, a stoichiometric compound, SiH4ðH2Þ2, can beformed near 7 GPa. This compound has unique properties underpressure including a surprising weakening of the molecularhydrogen stretching frequencies. Wang et al. (12) also recentlypresented experimental evidence that vibrational (vibron) fre-quencies are lowered at low pressures when hydrogen is addedto SiH4. The behavior in SiH4ðH2Þ2 contrasts with that of othermixtures of simple materials (13–16) where hydrogen vibronfrequencies increase with pressure in the pressure range below100 GPa and they remain insulating. This observation indicatesthat the covalent bond in the H2 molecules can be effectivelymodified at relatively low pressure with small change in chemicalenvironment [there is only 11 atom percent Si in SiH4ðH2Þ2], and

would perhaps give rise to a unique metal with properties similarto metallic hydrogen.

X-ray diffraction (11) revealed the structure of SiH4ðH2Þ2 tohave high symmetry, with the Si atoms forming an fcc framework.Ramzan et al. (17) subsequently estimated the metallizationpressure for SiH4ðH2Þ2 but the proposed structure was not com-pletely described. In particular, the locations and orientations ofhydrogen atoms in both SiH4 and H2 molecules were not given.Theoretical understanding of the interesting physical propertiesof this and related compounds is therefore currently not yetin hand. In the current study, predictions of the locations andorientations of the hydrogen atoms in SiH4ðH2Þ2 are made, alongwith a suggestion of a possible lattice distortion at elevated pres-sure. The predicted structure shows a large decrease in the vibronfrequency at pressures significantly lower than that observed inbulk molecular hydrogen (18). This finding is explained by theweakening of the H─H bonds at high pressure, resulting fromstrong intermolecular interactions between the H2 and SiH4

molecules. The phase with the predicted structure is calculatedto undergo metallization near 120 GPa, which is about one-thirdthe suggested pressure required for metallization of bulk mole-cular hydrogen.

Results and DiscussionThe structural search results are presented in Fig. 1 where equa-tions of state (EOS) of the most energetically competitive struc-tures are shown and compared with the experimental data (11)over the pressure range 5–40 GPa (the SI Appendix presents com-putational details). The theoretical predictions show a goodagreement with experiment. Because the EOS calculations donot include thermal expansion effects, they yield smaller volumesthan the experimental data (obtained at room temperature). Atlow pressures, the structures obtained have slightly strained fccframeworks of Si atoms, with four H2 molecules occupying allfour octahedral sites, and the other four occupying four out ofeight tetrahedral sites. To minimize the interactions among H2

molecules, alternate tetrahedral sites are occupied. The SiH4

molecules form tetrahedrons through sp3 hybridized orbitals.In order to reduce unfavorable repulsive interactions with H2

molecules in the occupied interstitial sites, the four Si-H axesin the SiH4 molecules all point to the nearest empty tetrahedralsites, and therefore unambiguously fixes the orientation of SiH4

molecules. In terms of smallest volume (Fig. 1), there are twofavorable structures, with space group I-4m2 and Imm2, obtainedat pressures in the 5–15 GPa range. The main difference betweenthese two structures is the orientation of H2 molecules. In theI-4m2 structure, all H2 molecules are aligned along the [001]direction of the fcc unit cell (Fig. 2A). This alignment results

Author contributions: Y.Y. and D.D.K. designed research, performed research, analyzeddata, and wrote the paper.

The authors declare no conflict of interest.

*This Direct Submission article had a prearranged editor.1To whom correspondence may be addressed. E-mail: Yansun.Yao@nrc.ca orDennis.Klug@nrc.ca.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1006508107/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1006508107 PNAS ∣ December 7, 2010 ∣ vol. 107 ∣ no. 49 ∣ 20893–20898

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in minor modified force field along the [001] direction and there-fore slightly shortens the c axis of the fcc lattice (tetragonal dis-tortion). In the Imm2 structure, the H2 molecules at tetrahedraland octahedral sites are aligned along the [101] and ½101� direc-tions of the fcc lattice, respectively, and slightly strain the cellalong the these two directions (orthorhombic distortion, Fig. 2B).These two structures have very close volumes and enthalpies inthis pressure range. For example, at 15 GPa, the volume and en-thalpy of I-4m2 structure is 0.03 Å3∕f:u: (1 formula unit ðf:u:Þ ¼1 SiH4 þ 2H2) and 0.006 eV∕f:u: less than the values of Imm2structure.

The structural search shows that near 15 GPa, the fcc frame-work of Si atoms experiences a more radical rhombohedraldistortion (Fig. 2C) with a small volume drop (ca. 3.3%), and theamount of distortion goes up with pressure (Fig. 1). The Si atomsremain highly ordered, and would have a R-3m space group if all

H atoms were removed from the cell. The original fcc unit cellchanges from a orthogonal lattice to a triclinic cell with anglesbetween lattice vectors varying from 86.1° to 94.3°. The distortionchanges the orientations of H2 molecules. The H2 molecules attetrahedral and octahedral sites are aligned along the ½111� and[111] directions of the (distorted) fcc unit cell, respectively(Fig. 2C). The SiH4 molecules also deviate from the perfect tet-rahedrons, as the sp3 orbitals interact with the nearby H2 mole-cular orbitals. These distortions, being in SiH4 and H2 molecules,reduced the space group of SiH4ðH2Þ2 to P1. In terms of enthalpy(SI Appendix, Figs. S3 and S4), the P1 structure becomes morefavorable than the I-4m2 structure at pressures higher than22 GPa. The vibrational contribution to free energy, Fvib, is es-timated (19), for example, at 30 GPa and 300 K (SI Appendix,Fig. S6) and the results shows that the Fvib of the P1 structureis about 0.11 eV∕f:u: higher than that of the I-4m2 structure.A rough estimate of Gibbs free energy by adding Fvib to the en-thalpy indicates that the I-4m2 structure is only 0.02 eV∕f:u:more stable than the P1 structure at 30 GPa. Given that theenthalpy of I-4m2 structure goes up rapidly relative to that ofP1 structure with increasing pressure (SI Appendix, Fig. S4),one can expect, when entropy is considered, that the P1 structureis energetically favorable at pressures somewhat greater than30 GPa.

The structural details of the I-4m2, Imm2, and P1 structuresare listed in SI Appendix, Table S1. The calculated X-ray diffrac-tion patterns for both the I-4m2 and Imm2 structures are closeto that of the fcc structure, as the Si frameworks in these twostructures are only slightly strained (Fig. 2D). These diffractionpatterns are in agreement with the experimentally reporteddiffraction pattern (11). The calculated P1 diffraction patternhowever already deviates from that of the fcc lattice at 15.5 GPa(Fig. 2D). As will be discussed in detail later, the H2 moleculesin SiH4ðH2Þ2 rotate in their original site over the pressure rangestudied in Fig. 1. Any orientation of H2 molecules derived from astatic calculation in this pressure range therefore only corre-sponds to an instantaneous configuration, and the propertiesof SiH4ðH2Þ2 represent the collective effects of all possible con-figurations.

The calculated pressure dependences of H2 vibron frequenciesfor the I-4m2, Imm2, and P1 structures are shown in Fig. 3. For allthree structures, the vibron frequencies undergo a remarkableweakening in the 5–40 GPa pressure range as was observed inthe experimental report (11) except for a single vibron frequencyin the experiment that has much lower frequency than in bulkhydrogen but does not weaken up to 35 GPa and could arise fromanother higher energy structure (12). This weakening of H2

vibron frequencies in SiH4ðH2Þ2 is significantly greater than thatobserved in the bulk solid hydrogen (18) over a similar pressure

10 20 30 40

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.u.)

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Fig. 1. Calculated and experimental EOS as functions of pressure. Theexperimental EOS (11) are shown for compression (filled circles) and decom-pression (empty circles). The pressure at which the slight strained fcc celldistorts to a rhombohedral cell is marked by an arrow. Below 15 GPa, a fulloptimization on the P1 structure yields the I-4m2 space group.

Fig. 2. The (A) I-4m2, (B) Imm2, and (C) P1 structures shownwith their latticevectors (a, b, and c) in the accordingly distorted fcc unit cell. The Si atoms(larger spheres) are located at the fcc sites and bonded to four H atoms(smaller spheres). The H2 molecules at the octahedral and tetrahedral sitesare shown in dark and light gray, respectively. Simulated X-ray diffractionpatterns (D) at 15.5 GPa (X-ray wavelength ¼ 0.5 Å) for the I-4m2, Imm2,P1, and undistorted fcc structures.

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Fig. 3. Calculated pressure dependences of the H2 vibron frequencies of theI-4m2, Imm2, and P1 structures of SiH4ðH2Þ2. The notations T and O refer tothe H2 molecules at tetrahedral and octahedral sites.

20894 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1006508107 Yao and Klug

range. For bulk hydrogen, the vibron frequency weakening occursat much higher pressures (above 40 GPa) and over a much largerpressure range, from 40 to 120 GPa. This observation suggeststhat a unique interaction between H2 and SiH4 molecules ispresent in SiH4ðH2Þ2. The H2 molecules at the tetrahedral sitesalways have more prominent bond weakening than their counter-parts at the octahedral sites (Fig. 3), which indicates the formerexperience stronger interaction with the SiH4 molecules than thelatter. One may explain the difference in interaction strengths byapplying a “short distance ¼ strong interaction” paradigm (20),as the tetrahedral sites are closer to the nearest fcc SiH4 sites thanare the octahedral sites.

A qualitative analysis of the intermolecular interactions inSiH4ðH2Þ2 is provided through the calculated valence chargedensity for I-4m2 and P1 structures at selected pressures (Fig. 4).At low pressure (6.9 GPa), the intermolecular interactions in theentire system are relatively weak. The SiH4 molecules remain astetrahedrons. As the pressure increases, the free space within thecell decreases and forces the molecules (H2 and SiH4) to morestrongly interact with each other. This interaction goes up rapidlywith compression and the valence electrons from neighboringmolecules would have to migrate toward the region betweenmolecules to minimize the unfavorable repulsions. As a result,the bonding within the molecules will weaken. For example, at15.7 GPa (Fig. 4), notable electron density is already built upin the region between SiH4 molecules and H2 molecules at thetetrahedral sites, indicating a strong orbital overlap. The interac-tion with H2 molecules at the octahedral sites, on the other hand,is much weaker. The orbital overlap distorts the sp3 hybridizedorbital and the SiH4 molecules start to deform progressively fromperfect tetrahedrons. This trend is even more prominent at higherpressure. As seen from the valence charge density at 99.2 GPa(Fig. 4), the H2 molecules at tetrahedral sites are already veryclose to the Si atoms. The high pressure brings H2 moleculesat tetrahedral sites into the coordination shell of the Si atomsand the SiH4 tetrahedrons distort significantly. The interactionbetween SiH4 and the H2 molecules at octahedral sites alsostrengthens.

Another measure of the interactions between SiH4 and H2

molecules in SiH4ðH2Þ2 is reflected by the H─H bond lengthchanges. Because phonon frequencies are correlated with the in-teratomic force constants, the softening of the vibron frequencyin Fig. 3 indicates that the H─H bond lengths increase with pres-

sure. For the P1 structure at 15.7 GPa, the calculated H─H bondlengths in the H2 molecules at tetrahedral and octahedral sitesare 0.750 and 0.748 Å, respectively. At 42.6 GPa, the two bondlengths increase to 0.756 and 0.749 Å. Here again one notices thatthe bond weakening is more prominent for the H2 molecules atthe tetrahedral sites than for their counterparts at octahedralsites. Once the pressure increases to 99.2 GPa, the H─H bondlengths at tetrahedral sites increases significantly to 0.815 Å,while the bond lengths at octahedral sites remain at 0.749 Å.For comparison, the calculated H─H bond lengths in the pre-dicted C2∕c structure (21, 22) for phase III of bulk hydrogenat a much higher pressure of 154 GPa are 0.743 and 0.750 Å. Ex-amination of the changes in the H─H bond length show length-ening of 0.0064 Å over a pressure range 7.8–33.7 GPa for theI-4m2 structure and 0.0055 Å over the pressure range 9.6–37.7GPa for the Imm2 structure.

The valence charge density in Fig. 4 also reveals that, underhigh pressure, some valence electrons are delocalized and moveoff atoms to interstitial regions (charge density between 0.2 and0.3 e−∕Å3). The “delocalizing” of electrons at high pressure israther general (23). It is helpful for further understanding toconsider the behavior of bulk Si under high pressure. At ambientpressure, bulk solid Si forms a cubic diamond structure (Si-I)through sp3 covalent bonds. With increasing pressure, the 3dorbital energy approaches that of the sp3 orbital, and valenceelectrons start to fill up the 3d orbital. This results in an orbitalrehybridization to a sp2 orbital once sufficient electrons are pro-moted to 3d orbitals. As a result, the Si structure transforms froma cubic diamond structure to a two-dimensional (sp2) structure(for example, Si-XI) at high pressure (24). A similar electronreordering also occurs in SiH4ðH2Þ2. As shown in SI Appendix,Fig. S8, there is already a significant promotion of valence elec-trons in Si atoms to 3d orbital in the P1 structure at 99.2 GPa.

With the accumulation of valence electrons on the more dif-fuse interstitial regions, the overall electron mobility and metalliccharacter in SiH4ðH2Þ2 increases with pressure. The next ques-tion to address is at what pressure will SiH4ðH2Þ2 become metal-lic. The answer can be provided from the examination of thecalculated electronic density of states (DOS). As shown in SIAppendix, Fig. S7, the band gap of P1 structure starts to close near120 GPa (the accurate pressure for band gap closure depends onthe detailed orientation of the H2 molecules; see discussion be-low). It is encouraging to see that the calculated metallizationpressure for SiH4ðH2Þ2 is well within the reach of current dia-mond–anvil techniques. On the other hand, it should be notedthat, due to systematic defects for treating the excited states indensity functional theory (DFT) calculations (as used in the pre-sent study) band gaps are in general underestimated. Thus, it isvery likely that actual pressure for band gap closure in SiH4ðH2Þ2is higher than the DFT estimated values (17). Nevertheless, themetallization pressure calculated here is more than a factor of 3lower than the currently suggested pressure required for metal-lization of bulk molecular hydrogen.

Fig. 5 A–D show the evolution of valence bands and band gapclosure for SiH4ðH2Þ2 with increasing pressure. Close to the am-bient pressure (0.27 GPa, Fig. 5A), van der Waals interactionspredominate in the system. The SiH4 molecules, H2 moleculesat tetrahedral and octahedral sites, have well-separated valencebands. The valence bands for the H2 molecules at tetrahedralsites interact slightly with their counterparts at the octahedralsites. The rather weak intermolecular interactions, in reality, can-not maintain the SiH4ðH2Þ2 structure at this pressure (11, 12).For the initial pressure range where weak interactions dominate,compression occurs easily, after which intermolecular interac-tions increase rapidly. At 6.9 GPa, the volume of I-4m2 structurealready decreases to about 54% of the initial value at 0.27 GPa,and the intermolecular interactions begin to increase (Fig. 5B).The behavior of the DOS with pressure from Fig. 5 A–D reveals

Fig. 4. Calculated valence charge density of SiH4ðH2Þ2 in the (110) plane ofthe fcc lattice (distorted accordingly) for I-4m2 structure at 6.9 GPa, and P1structure at 15.7 and 99.2 GPa. For a clearer presentation, atoms are removedfrom the right half of planes. The atoms that are not surrounded by chargedensities belong to the nearest plane above. The notations T and O refer toH2 molecules at tetrahedral and octahedral sites.

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several noteworthy points. As the compression delocalizes theorbitals, the orbitals of the neighboring molecules (being eitherH2 or SiH4) would therefore overlap (Fig. 4) and result in a broadvalence band (Fig. 5 A–D). With increasing pressure, thestrengthening orbital overlap stabilizes the bonding interactions(lower in energy) and destabilizes the antibonding interactions(higher in energy), and therefore increases the overall bandwidth(25). The bandwidth expansion in energy is a key ingredientfor the metallization. A sufficiently large bandwidth expansioneventually forces valence and conduction bands to overlap, andincreases the electron velocity near the Fermi level, which is ex-actly as found for SiH4ðH2Þ2. As seen in Fig. 5D, at 152.7 GPa,some unoccupied DOS of H2 molecules, through mixing with theSiH4 conduction band, moves below the Fermi level and overlapswith the occupied DOS, and therefore the system becomesweakly metallic. The weakening of the H─H bonds in the H2 mo-lecules (Fig. 3) is also closely correlated with the metallization(9). The valence and the nearest conduction bands of H2 mole-cules are constructed from bonded states (σg) and antibondedstates (σu�), respectively. Once H─H bonds weaken, the energyof bonded states will increase and those of the antibonded stateswill decrease. Thus, the energy separation between the bondedstates and antibonded states, in other words the energy gap,decreases. The same band overlap and band gap closure will alsooccur in bulk solid hydrogen, but at much higher pressure.

Another important issue to address is the stability and dy-namics of SiH4ðH2Þ2. The calculated phonon dispersion curvesfor the I-4m2 structure at 10 GPa shows weak instability at 0 K,as indicated by the imaginary frequencies in the Z to Γ and N to Γdirections (SI Appendix, Fig. S5A). The same calculation, how-ever, shows that at elevated pressures, i.e., 30 GPa, the imaginaryphonon frequencies disappear and I-4m2 structure becomesstable (SI Appendix, Fig. S5B). The calculations of phonon DOSfor both I-4m2 and P1 structures confirmed their mechanicalstabilities at 30 GPa (SI Appendix, Fig. S6). There are multiplereasons to account for the phonon softening at low pressure.At low pressure, long-distance weak interactions dominate in thesystem, which makes the DFT evaluation of the force constantsdifficult. The small proton mass also poses a problem. The mo-lecular motions (i.e., from quantum effects) can deviate from a

harmonic description, which would be important for hydrogen-rich materials (18, 26). To investigate further the stability ofSiH4ðH2Þ2, and recognizing that the instability of SiH4ðH2Þ2 atlow pressure may be a result of an insufficient harmonic approx-imation of vibrations in analogy with results reported for elemen-tal Ca (27), room temperature (300 K) Car–Parrinello moleculardynamics (CPMD) (28) were preformed on the I-4m2 and P1structures at 12 and 34 GPa, respectively. The calculated timeevolutions of the dimensions and angles of the simulation cellsare shown in Fig. 6 A and B obtained from 15 ps isothermal-isobaric (NPT) CPMD trajectories. Both the I-4m2 and P1 struc-tures appear to be stable at 300 K with the dimensions andangles of the simulation cells remaining near their equilibriumvalues. The static structure factor Ssðq⇀Þ for I-4m2 and P1 struc-tures were evaluated (29) from the NPT CPMD trajectories andthe results are shown in Fig. 6C (computational details in SIAppendix). The Ssðq⇀Þ for both structures resembles closely tothe calculated X-ray diffraction patterns in Fig. 2D, indicatingthat the molecules in the NPT CPMD trajectories remain at theirequilibrium sites, which therefore suggests structural stability atroom temperature. The Ssðq⇀Þ of the I-4m2 structure (Fig. 6C), isclearly associated with that of a fcc cell and agrees very well withthe experimentally reported diffraction pattern (11). The slighttetragonal distortion (arising from the alignment of H2 moleculesalong c axis) from the static calculation (Fig. 2A), is not readily

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Fig. 5. Calculated electronic DOS projected on SiH4 and H2 molecules for(A) I-4m2 structure at 0.27 GPa, (B) I-4m2 structure at 6.9 GPa, (C) P1 structureat 99.2 GPa, and (D) P1 structure at 152.7 GPa. The notations T and O refer tothe H2 molecules at tetrahedral and octahedral sites. The origin “0” in energycorresponds to the highest energy of the occupied states.

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Fig. 6. Evolution of the simulation cell dimensions and angles for the(A) I-4m2 and (B) P1 structures of SiH4ðH2Þ2 at 12 and 34 GPa, respectively,from NPT CPMD simulations at 300 K. (C) Calculated static structure factor(X-ray wavelength ¼ 0.5 Å), Ssðq

⇀Þ, for the I-4m2 and P1 structures fromthe calculations indicated in A and B. See text and SI Appendix.

20896 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1006508107 Yao and Klug

apparent at room temperature and is obscured by hydrogenmolecular motions.

The dynamics of both SiH4 and H2 molecules are seen fromvisualization of their individual atomic trajectories. The equili-brated CPMD trajectories were obtained in a microcanonical(NVE) ensemble after an additional temperature equilibrationin a canonical (NVT) ensemble and the pressure equilibrationin the NPT ensemble described above. In Fig. 7 A and C, thetrajectories of SiH4 components are depicted for the I-4m2and P1 structures, respectively. The SiH4 molecules remain ba-sically fixed at their original sites and both the H and Si atomsundergo thermal motions about their respective crystallographicsymmetry. In contrast, H2 molecules undergo clear rotation atthese pressures (Fig. 7 B and D). The rotation of H2 moleculesimplies a sampling of many possible structures in addition to thelowest enthalpy ones and is the reason that average cell constantsand angles in Fig. 6A remain at those for an fcc structure. TheCPMD trajectories for the P1 structure indicates that this basicstructure is preserved (Fig. 7C and D). In both cases, the H2 mo-lecules remain rotating in their original sites and the structureappears to be stable. The rotation of H2 molecules is also a struc-tural feature of the low-pressure phase I of solid bulk hydrogenthat is stable up to pressures of about 110 GPa (18). The clearrotation of H2 molecules seen in the CPMD simulations indicatesthat the structure is sampling a variety of low-energy sites andtherefore a variety of structures which would lead to the complexand somewhat broad Raman spectrum observed in the experi-ment (11). With increasing pressure, the strong interaction withthe SiH4 molecules will reduce the mobility of the H2 moleculesand, in particular, the mobility of the H2 molecules at the tetra-hedral sites. Additional CPMD calculations show that, at100 GPa, the H2 molecules at the tetrahedral sites stopped rotat-ing and the ones at octahedral sites have rotations confinedmostly to the (110) plane. The rotation of H2 molecules will in-fluence the properties of SiH4ðH2Þ2 including the metallization.

SI Appendix, Fig. S7A shows the calculated band gaps of the P1structure as functions of pressure with the H2 molecules at theoctahedral sites rotating on the (110) planes. The rotation anglesat instantaneous trajectory snapshots are described by the angle θbetween the H2 molecular axes at tetrahedral sites and those atoctahedral sites. The initial angle, as in the predicted P1 struc-ture, is close to 90° (SI Appendix, Fig. S7B). SI Appendix, Fig. S7Ashows that, with H2 molecules at the octahedral sites oriented atvarious angles θ, the pressure where band gap closure first occursis calculated to be about 120 GPa. For θ ¼ 45°, the band gap isnot yet closed at 140 GPa so the actual predicted pressure formetallization may therefore be determined by all possible hydro-gen orientations.

ConclusionsIn summary, the results of this study of the structure of SiH4ðH2Þ2indicate that interaction of SiH4 with molecular hydrogen at highpressure is unexpectedly strong, in agreement with recent experi-mental findings. The rapid weakening and lengthening in the H2

bond occurs at pressures far below that seen in bulk hydrogen andtakes place in a structure where H2 molecules rotate at tetrahe-dral and octahedral sites of a distorted fcc lattice of SiH4 units inthe pressures in the experimental report. The rotation of hydro-gen molecules become partially hindered near the metallizationpressure of about 120 GPa. H2 molecules at tetrahedral sitesshow significantly greater bond weakening than H2 moleculesat octahedral sites. This rapid weakening of the H2 bond is alsoconsistent with a predicted metallization pressure near 120 GPa.These results demonstrate that the metallization of SiH4ðH2Þ2may be achieved at relatively low pressure and with propertiessimilar to metallic hydrogen.

MethodsSearches for candidate structures of SiH4ðH2Þ2 were performed with aexperimental reported fcc lattice (details in SI Appendix). The EOS, valencecharge densities, and electronic DOS were calculated using the Vienna abinitio simulation code (30) and projector-augmented plane-wave potentials(31). The Si and H potentials employed 3s3p and 1s as valence states, respec-tively, with the Perdew–Burke–Ernzerhof exchange-correlation functional(32) (same for all three pseudopotentials used in the present study). Anenergy cutoff of 910 eV was used. An 8 × 8 × 8 and a 32 × 32 × 32 k-pointmesh (33) for Brillouin zone (BZ) samplings were used in the EOS andelectronic DOS calculations, respectively. Phonon calculations were per-formed using the ABINIT program (34) employing the linear response meth-od, Hartwigsen–Goedecker–Hutter pseudopotentials (35) with an energycutoff of 70 Hartree. A 4 × 4 × 4 q-point and a 10 × 10 × 10 k-point meshwas used for phonon calculations. The CPMD calculations (28) were per-formed with a supercell of 288 atoms, using the Quantum ESPRESSO package(36) with norm-conserving pseudopotentials (37) with an energy cutoff of60 Rydberg. A fictitious electron mass of the electronic wave function of50 a.u. and a time step of 4 a.u. were used for the time integration ofthe ionic motions (38). The BZ sampling was restricted to the zone center.To check the structural stability, the supercells were first examined for15 ps in an isothermal-isobaric (NPT) ensemble, after an initial 3-ps tempera-ture equilibration in a canonical (NVT) ensemble. The static structure factorSsðq

⇀Þ was calculated (see SI Appendix for details) from the NPT CPMD trajec-tory. The equilibrated trajectories were then obtained in a microcanonical(NVE) ensemble after an additional temperature equilibration (3 ps) in acanonical (NVT) ensemble to avoid temperature drifting. The temperaturein the CPMD calculations is controlled by a Nosé thermostat (39).

Note Recently there were several additional reports appearing after oursubmission (40–42) that address several other properties of SiH4ðH2Þ2.

ACKNOWLEDGMENTS. Y.Y. thanks Yunfeng Liang for valuable suggestions onCPMD and Jianjun Dong for fruitful discussions on electronic structures. Wealso thank the Editor and reviewers for very constructive and helpfulcomments.

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Fig. 7. Depicted trajectories of Si (yellow) and H atoms (white) in SiH4

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20898 ∣ www.pnas.org/cgi/doi/10.1073/pnas.1006508107 Yao and Klug