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Silane plus molecular hydrogen as a possible pathway to metallic
hydrogen
Yao, Yansun; Klug, Dennis D.
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Silane plus molecular hydrogen as a possible
pathway to metallic hydrogen
Yansun Yao1and 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 ab initio molecular dynamics to predict the structures and examine the physical origin of the pressure-induced drop in hydrogen intra-molecular vibrational (vibron) frequencies. A structural distortion is predicted 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 vibron frequencies reproduces well the experimental data (Strobel TA, Somayazulu M, Hemley RJ (2009) Phys Rev Lett 103:065701). The
bond weakening in H2 is induced by intermolecular interactions
between the H2and SiH4molecules. A significant feature of the
high-pressure structures of SiH4ðH2Þ2 is the dynamical behavior
of the H2molecules. It is found that H2molecules are rotating in
this pressure range whereas the SiH4 molecules remain rigid.
The detailed nature of the interactions of molecular hydrogen with
SiH4in SiH4ðH2Þ2is therefore strongly influenced by the dynamical
behavior of the H2molecules in the high-pressure structure. The
phase with the calculated structure is predicted to become metallic near 120 GPa, which is significantly lower than the currently suggested pressure for metallization of bulk molecular hydrogen. first principles ∣ hydrogen metallization ∣ structure prediction
O
ne 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 a metallic solid. The properties of metallic hydrogen could include high-temperature superconductivity (1), a liquid ground state (2), and conductivity at very high temperatures that gives rise to the strong magnetic fields of Jovian planets (3). The direct compres-sion of solid molecular hydrogen however may require a pressure in excess of 400 GPa to reach a metallic state and this pressure lies at the upper limit of the current experimental static compres-sion techniques (4, 5). There have been other approaches to this problem, including the study of hydrogen-rich molecular com-pounds (6). Compression of such comcom-pounds, in particular those involving group 14 elements, is predicted to lower the pressure required 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 elements or 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 be
formed near 7 GPa. This compound has unique properties under pressure including a surprising weakening of the molecular hydrogen stretching frequencies. Wang et al. (12) also recently presented experimental evidence that vibrational (vibron) fre-quencies are lowered at low pressures when hydrogen is added to SiH4. The behavior in SiH4ðH2Þ2contrasts with that of other
mixtures of simple materials (13–16) where hydrogen vibron frequencies increase with pressure in the pressure range below 100 GPa and they remain insulating. This observation indicates that the covalent bond in the H2 molecules can be effectively
modified at relatively low pressure with small change in chemical environment [there is only 11 atom percent Si in SiH4ðH2Þ2], and
would perhaps give rise to a unique metal with properties similar to metallic hydrogen.
X-ray diffraction (11) revealed the structure of SiH4ðH2Þ2to
have high symmetry, with the Si atoms forming an fcc framework. Ramzan et al. (17) subsequently estimated the metallization pressure for SiH4ðH2Þ2but the proposed structure was not
com-pletely described. In particular, the locations and orientations of hydrogen atoms in both SiH4and H2molecules were not given.
Theoretical understanding of the interesting physical properties of this and related compounds is therefore currently not yet in hand. In the current study, predictions of the locations and orientations of the hydrogen atoms in SiH4ðH2Þ2are made, along
with a suggestion of a possible lattice distortion at elevated pres-sure. The predicted structure shows a large decrease in the vibron frequency at pressures significantly lower than that observed in bulk molecular hydrogen (18). This finding is explained by the weakening of the H─H bonds at high pressure, resulting from strong intermolecular interactions between the H2 and SiH4
molecules. The phase with the predicted structure is calculated to undergo metallization near 120 GPa, which is about one-third the suggested pressure required for metallization of bulk mole-cular hydrogen.
Results and Discussion
The 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 (theSI Appendixpresents
com-putational details). The theoretical predictions show a good agreement with experiment. Because the EOS calculations do not include thermal expansion effects, they yield smaller volumes than the experimental data (obtained at room temperature). At low pressures, the structures obtained have slightly strained fcc frameworks of Si atoms, with four H2 molecules occupying all
four octahedral sites, and the other four occupying four out of eight 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 axes in the SiH4molecules all point to the nearest empty tetrahedral
sites, and therefore unambiguously fixes the orientation of SiH4
molecules. In terms of smallest volume (Fig. 1), there are two favorable structures, with space group I-4m2 and Imm2, obtained at pressures in the 5–15 GPa range. The main difference between these two structures is the orientation of H2 molecules. In the
I-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, analyzed data, 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 or
Dennis.Klug@nrc.ca.
This article contains supporting information online at www.pnas.org/lookup/suppl/ doi:10.1073/pnas.1006508107/-/DCSupplemental.
PHY
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 H2molecules at tetrahedral
and octahedral sites are aligned along the [101] and ½101 direc-tions of the fcc lattice, respectively, and slightly strain the cell along the these two directions (orthorhombic distortion, Fig. 2B). These two structures have very close volumes and enthalpies in this 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 ¼ 1SiH4þ 2H2) and 0.006 eV∕f:u: less than the values of Imm2 structure.
The structural search shows that near 15 GPa, the fcc frame-work of Si atoms experiences a more radical rhombohedral distortion (Fig. 2C) with a small volume drop (ca. 3.3%), and the amount of distortion goes up with pressure (Fig. 1). The Si atoms remain highly ordered, and would have a R-3m space group if all
H atoms were removed from the cell. The original fcc unit cell changes from a orthogonal lattice to a triclinic cell with angles between lattice vectors varying from 86.1° to 94.3°. The distortion changes the orientations of H2molecules. The H2molecules at
tetrahedral and octahedral sites are aligned along the ½111 and [111] directions of the (distorted) fcc unit cell, respectively (Fig. 2C). The SiH4molecules also deviate from the perfect
tet-rahedrons, as the sp3orbitals interact with the nearby H 2
mole-cular orbitals. These distortions, being in SiH4and H2molecules,
reduced the space group of SiH4ðH2Þ2to P1. In terms of enthalpy
(SI Appendix, Figs. S3 and S4), the P1 structure becomes more
favorable than the I-4m2 structure at pressures higher than 22 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 structure
is about 0.11 eV∕f:u: higher than that of the I-4m2 structure. A rough estimate of Gibbs free energy by adding Fvibto 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 the enthalpy of I-4m2 structure goes up rapidly relative to that of P1 structure with increasing pressure (SI Appendix, Fig. S4), one can expect, when entropy is considered, that the P1 structure is energetically favorable at pressures somewhat greater than 30 GPa.
The structural details of the I-4m2, Imm2, and P1 structures are listed inSI Appendix, Table S1. The calculated X-ray diffrac-tion patterns for both the I-4m2 and Imm2 structures are close to that of the fcc structure, as the Si frameworks in these two structures are only slightly strained (Fig. 2D). These diffraction patterns are in agreement with the experimentally reported diffraction pattern (11). The calculated P1 diffraction pattern however already deviates from that of the fcc lattice at 15.5 GPa (Fig. 2D). As will be discussed in detail later, the H2molecules
in SiH4ðH2Þ2rotate in their original site over the pressure range
studied in Fig. 1. Any orientation of H2molecules derived from a
static calculation in this pressure range therefore only corre-sponds to an instantaneous configuration, and the properties of SiH4ðH2Þ2represent the collective effects of all possible
con-figurations.
The calculated pressure dependences of H2vibron frequencies
for the I-4m2, Imm2, and P1 structures are shown in Fig. 3. For all three structures, the vibron frequencies undergo a remarkable weakening in the 5–40 GPa pressure range as was observed in the experimental report (11) except for a single vibron frequency in the experiment that has much lower frequency than in bulk hydrogen but does not weaken up to 35 GPa and could arise from another higher energy structure (12). This weakening of H2
vi-bron frequencies in SiH4ðH2Þ2 is significantly greater than that
observed in the bulk solid hydrogen (18) over a similar pressure
10 20 30 40 40 50 60 70 SiH4(H2)2 I-4m2 SiH4(H2)2 Imm2 SiH4(H2)2P1 Experiment Experiment Vo lu m e ( Å 3 /f.u.) Pressure (GPa)
Fig. 1. Calculated and experimental EOS as functions of pressure. The experimental EOS (11) are shown for compression (filled circles) and decom-pression (empty circles). The pressure at which the slight strained fcc cell distorts to a rhombohedral cell is marked by an arrow. Below 15 GPa, a full optimization on the P1 structure yields the I-4m2 space group.
Fig. 2. The (A) I-4m2, (B) Imm2, and (C) P1 structures shown with their lattice vectors (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 H2molecules at the octahedral and tetrahedral sites
are shown in dark and light gray, respectively. Simulated X-ray diffraction patterns (D) at 15.5 GPa (X-ray wavelength ¼ 0.5 Å) for the I-4m2, Imm2, P1, and undistorted fcc structures.
0 5 10 15 20 25 30 35 40 122 124 126 128 130 I-4m2 (T) I-4m2 (O) P1 (T) P1(O) Imm2 (T) Imm2 (O) Frequenc y (THz) Pressure (GPa)
Fig. 3. Calculated pressure dependences of the H2vibron frequencies of the
I-4m2, Imm2, and P1 structures of SiH4ðH2Þ2. The notations T and O refer to
the H2molecules at tetrahedral and octahedral sites.
range. For bulk hydrogen, the vibron frequency weakening occurs at much higher pressures (above 40 GPa) and over a much larger pressure range, from 40 to 120 GPa. This observation suggests that a unique interaction between H2 and SiH4 molecules is
present in SiH4ðH2Þ2. The H2molecules at the tetrahedral sites
always have more prominent bond weakening than their counter-parts at the octahedral sites (Fig. 3), which indicates the former experience stronger interaction with the SiH4molecules than the
latter. One may explain the difference in interaction strengths by applying a “short distance ¼ strong interaction” paradigm (20), as the tetrahedral sites are closer to the nearest fcc SiH4sites than
are the octahedral sites.
A qualitative analysis of the intermolecular interactions in SiH4ðH2Þ2 is provided through the calculated valence charge
density for I-4m2 and P1 structures at selected pressures (Fig. 4). At low pressure (6.9 GPa), the intermolecular interactions in the entire system are relatively weak. The SiH4molecules remain as
tetrahedrons. As the pressure increases, the free space within the cell decreases and forces the molecules (H2and SiH4) to more
strongly interact with each other. This interaction goes up rapidly with compression and the valence electrons from neighboring molecules would have to migrate toward the region between molecules to minimize the unfavorable repulsions. As a result, the bonding within the molecules will weaken. For example, at 15.7 GPa (Fig. 4), notable electron density is already built up in the region between SiH4molecules and H2molecules at the
tetrahedral sites, indicating a strong orbital overlap. The interac-tion with H2molecules at the octahedral sites, on the other hand,
is much weaker. The orbital overlap distorts the sp3 hybridized
orbital and the SiH4molecules start to deform progressively from
perfect tetrahedrons. This trend is even more prominent at higher pressure. As seen from the valence charge density at 99.2 GPa (Fig. 4), the H2 molecules at tetrahedral sites are already very
close to the Si atoms. The high pressure brings H2 molecules
at tetrahedral sites into the coordination shell of the Si atoms and the SiH4 tetrahedrons distort significantly. The interaction
between SiH4 and the H2 molecules at octahedral sites also
strengthens.
Another measure of the interactions between SiH4 and H2
molecules in SiH4ðH2Þ2 is reflected by the H─H bond length changes. Because phonon frequencies are correlated with the in-teratomic force constants, the softening of the vibron frequency in 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 bond lengths in the H2molecules at tetrahedral and octahedral sites
are 0.750 and 0.748 Å, respectively. At 42.6 GPa, the two bond lengths increase to 0.756 and 0.749 Å. Here again one notices that the bond weakening is more prominent for the H2molecules at
the tetrahedral sites than for their counterparts at octahedral sites. Once the pressure increases to 99.2 GPa, the H─H bond lengths 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 hydrogen at 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 the I-4m2 structure and 0.0055 Å over the pressure range 9.6–37.7 GPa for the Imm2 structure.
The valence charge density in Fig. 4 also reveals that, under high pressure, some valence electrons are delocalized and move off atoms to interstitial regions (charge density between 0.2 and 0.3 e−∕Å3). The “delocalizing” of electrons at high pressure is rather general (23). It is helpful for further understanding to consider the behavior of bulk Si under high pressure. At ambient pressure, bulk solid Si forms a cubic diamond structure (Si-I) through sp3 covalent bonds. With increasing pressure, the 3d
orbital energy approaches that of the sp3 orbital, and valence
electrons start to fill up the 3d orbital. This results in an orbital rehybridization to a sp2orbital once sufficient electrons are
pro-moted to 3d orbitals. As a result, the Si structure transforms from a cubic diamond structure to a two-dimensional (sp2) structure
(for example, Si-XI) at high pressure (24). A similar electron reordering 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 metallic character in SiH4ðH2Þ2increases with pressure. The next
ques-tion to address is at what pressure will SiH4ðH2Þ2become
metal-lic. The answer can be provided from the examination of the calculated electronic density of states (DOS). As shown in SI
Appendix, Fig. S7, the band gap of P1 structure starts to close near
120 GPa (the accurate pressure for band gap closure depends on the detailed orientation of the H2molecules; see discussion
be-low). It is encouraging to see that the calculated metallization pressure for SiH4ðH2Þ2is well within the reach of current
dia-mond–anvil techniques. On the other hand, it should be noted that, due to systematic defects for treating the excited states in density functional theory (DFT) calculations (as used in the pre-sent study) band gaps are in general underestimated. Thus, it is very likely that actual pressure for band gap closure in SiH4ðH2Þ2
is higher than the DFT estimated values (17). Nevertheless, the metallization pressure calculated here is more than a factor of 3 lower 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 gap closure for SiH4ðH2Þ2with increasing pressure. Close to the
am-bient pressure (0.27 GPa, Fig. 5A), van der Waals interactions predominate in the system. The SiH4molecules, H2molecules
at tetrahedral and octahedral sites, have well-separated valence bands. The valence bands for the H2 molecules at tetrahedral
sites interact slightly with their counterparts at the octahedral sites. The rather weak intermolecular interactions, in reality, can-not maintain the SiH4ðH2Þ2structure 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 structure already 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 SiH4ðH2Þ2in the (110) plane of
the fcc lattice (distorted accordingly) for I-4m2 structure at 6.9 GPa, and P1 structure at 15.7 and 99.2 GPa. For a clearer presentation, atoms are removed from the right half of planes. The atoms that are not surrounded by charge densities belong to the nearest plane above. The notations T and O refer to H2molecules at tetrahedral and octahedral sites.
PHY
several noteworthy points. As the compression delocalizes the orbitals, the orbitals of the neighboring molecules (being either H2or SiH4) would therefore overlap (Fig. 4) and result in a broad
valence band (Fig. 5 A–D). With increasing pressure, the strengthening 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 ingredient for the metallization. A sufficiently large bandwidth expansion eventually forces valence and conduction bands to overlap, and increases 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 H2molecules, through mixing with the
SiH4conduction band, moves below the Fermi level and overlaps
with the occupied DOS, and therefore the system becomes weakly 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 antibonded
states (σu), respectively. Once H─H bonds weaken, the energy
of bonded states will increase and those of the antibonded states will decrease. Thus, the energy separation between the bonded states and antibonded states, in other words the energy gap, decreases. The same band overlap and band gap closure will also occur in bulk solid hydrogen, but at much higher pressure.
Another important issue to address is the stability and dynamics of SiH4ðH2Þ2. The calculated phonon dispersion curves
for 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 Γ directions (SI Appendix, Fig. S5A). The same calculation, how-ever, shows that at elevated pressures, i.e., 30 GPa, the imaginary phonon frequencies disappear and I-4m2 structure becomes stable (SI Appendix, Fig. S5B). The calculations of phonon DOS for both I-4m2 and P1 structures confirmed their mechanical stabilities at 30 GPa (SI Appendix, Fig. S6). There are multiple reasons to account for the phonon softening at low pressure. At low pressure, long-distance weak interactions dominate in the system, which makes the DFT evaluation of the force constants difficult. 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 of SiH4ðH2Þ2, and recognizing that the instability of SiH4ðH2Þ2at
low 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 molecular dynamics (CPMD) (28) were preformed on the I-4m2 and P1 structures at 12 and 34 GPa, respectively. The calculated time evolutions of the dimensions and angles of the simulation cells are 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 and angles of the simulation cells remaining near their equilibrium values. The static structure factor Ssð q
⇀
Þfor I-4m2 and P1 struc-tures were evaluated (29) from the NPT CPMD trajectories and the results are shown in Fig. 6C (computational details in SI
Appendix). The Ssð q
⇀
Þ for both structures resembles closely to the calculated X-ray diffraction patterns in Fig. 2D, indicating that the molecules in the NPT CPMD trajectories remain at their equilibrium sites, which therefore suggests structural stability at room temperature. The Ssð q
⇀
Þof the I-4m2 structure (Fig. 6C), is clearly associated with that of a fcc cell and agrees very well with the experimentally reported diffraction pattern (11). The slight tetragonal distortion (arising from the alignment of H2molecules
along c axis) from the static calculation (Fig. 2A), is not readily
B
A
D
C
0.0 0.2 0.4 0.6 0.8 1.0 1.2 99.2 GPa SiH 4 H2 (O) H2 (T)DOS per f.u. (states/eV)
Energy (eV) -20 -15 -10 -5 0 5 0.0-25 -20 -15 -10 -5 0 5 0.2 0.4 0.6 0.8 1.0 152.7 GPa SiH 4 H2 (O) H2 (T)
DOS per f.u. (states/eV)
Energy (eV) 0 10 20 30 40 50 0.27 GPa SiH 4 H 2 (O) H2 (T)
DOS per f.u. (states/eV)
Energy (eV) -6 -5 -4 -3 -2 -1 0 1 0-10 -8 -6 -4 -2 0 2 2 4 6 8 6.9 GPa SiH4 H 2 (O) H 2 (T)
DOS per f.u. (states/eV)
Energy (eV)
Fig. 5. Calculated electronic DOS projected on SiH4and H2molecules for
(A) I-4m2 structure at 0.27 GPa, (B) I-4m2 structure at 6.9 GPa, (C) P1 structure at 99.2 GPa, and (D) P1 structure at 152.7 GPa. The notations T and O refer to the H2molecules at tetrahedral and octahedral sites. The origin “0” in energy
corresponds to the highest energy of the occupied states.
B
0 2 4 6 8 10 12 14 10.5 11.0 11.5 a b c Angles (degree) Dimensions (Å) Simulation Time (ps) 80 90 100 α β γA
0 2 4 6 8 10 12 14 11.5 12.0 12.5 13.0 a b c Angles (degree) Dimensions (Å) Simulation Time (ps) 85 90 95 α β γC
5 10 15 20 25 I-4m2 P1 q (Å-1)Intensity (arb. unit)
2θ (degree)
2 3 4 5
Fig. 6. Evolution of the simulation cell dimensions and angles for the (A) I-4m2 and (B) P1 structures of SiH4ðH2Þ2at 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 from the calculations indicated in A and B. See text andSI Appendix.
apparent at room temperature and is obscured by hydrogen molecular motions.
The dynamics of both SiH4and H2molecules are seen from
visualization of their individual atomic trajectories. The equili-brated CPMD trajectories were obtained in a microcanonical (NVE) ensemble after an additional temperature equilibration in a canonical (NVT) ensemble and the pressure equilibration in the NPT ensemble described above. In Fig. 7 A and C, the trajectories of SiH4 components are depicted for the I-4m2
and P1 structures, respectively. The SiH4molecules remain
ba-sically fixed at their original sites and both the H and Si atoms undergo thermal motions about their respective crystallographic symmetry. In contrast, H2 molecules undergo clear rotation at
these pressures (Fig. 7 B and D). The rotation of H2molecules
implies a sampling of many possible structures in addition to the lowest enthalpy ones and is the reason that average cell constants and angles in Fig. 6A remain at those for an fcc structure. The CPMD trajectories for the P1 structure indicates that this basic structure is preserved (Fig. 7C and D). In both cases, the H2
mo-lecules remain rotating in their original sites and the structure appears to be stable. The rotation of H2molecules is also a
struc-tural feature of the low-pressure phase I of solid bulk hydrogen that is stable up to pressures of about 110 GPa (18). The clear rotation of H2molecules seen in the CPMD simulations indicates
that the structure is sampling a variety of low-energy sites and therefore a variety of structures which would lead to the complex and somewhat broad Raman spectrum observed in the experi-ment (11). With increasing pressure, the strong interaction with the SiH4molecules will reduce the mobility of the H2molecules
and, in particular, the mobility of the H2molecules at the
tetra-hedral sites. Additional CPMD calculations show that, at 100 GPa, the H2molecules at the tetrahedral sites stopped
rotat-ing and the ones at octahedral sites have rotations confined mostly to the (110) plane. The rotation of H2molecules will
in-fluence the properties of SiH4ðH2Þ2including the metallization.
SI Appendix, Fig. S7Ashows the calculated band gaps of the P1
structure as functions of pressure with the H2molecules at the
octahedral sites rotating on the (110) planes. The rotation angles at instantaneous trajectory snapshots are described by the angle θ between the H2molecular axes at tetrahedral sites and those at
octahedral sites. The initial angle, as in the predicted P1 struc-ture, is close to 90° (SI Appendix, Fig. S7B). SI Appendix,
Fig. S7A shows that, with H2molecules at the octahedral sites
oriented at various angles θ, the pressure where band gap closure first occurs is calculated to be about 120 GPa. For θ ¼ 45°, the band gap is not yet closed at 140 GPa so the actual predicted pressure for metallization may therefore be determined by all possible hydrogen orientations.
Conclusions
In summary, the results of this study of the structure of SiH4ðH2Þ2
indicate that interaction of SiH4with molecular hydrogen at high
pressure 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 and takes place in a structure where H2molecules rotate at
tetrahe-dral and octahetetrahe-dral sites of a distorted fcc lattice of SiH4units in
the pressures in the experimental report. The rotation of hydro-gen molecules become partially hindered near the metallization pressure of about 120 GPa. H2 molecules at tetrahedral sites
show significantly greater bond weakening than H2 molecules
at octahedral sites. This rapid weakening of the H2bond is also
consistent with a predicted metallization pressure near 120 GPa. These results demonstrate that the metallization of SiH4ðH2Þ2
may be achieved at relatively low pressure and with properties similar to metallic hydrogen.
Methods
Searches for candidate structures of SiH4ðH2Þ2 were performed with a
experimental reported fcc lattice (details inSI Appendix). The EOS, valence charge densities, and electronic DOS were calculated using the Vienna ab initio 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). An energy cutoff of 910 eV was used. An 8 × 8 × 8 and a 32 × 32 × 32 k-point mesh (33) for Brillouin zone (BZ) samplings were used in the EOS and electronic 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 energy cutoff of 70 Hartree. A 4 × 4 × 4 q-point and a 10 × 10 × 10 k-point mesh was 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 of 60 Rydberg. A fictitious electron mass of the electronic wave function of 50 a.u. and a time step of 4 a.u. were used for the time integration of the ionic motions (38). The BZ sampling was restricted to the zone center. To check the structural stability, the supercells were first examined for 15 ps in an isothermal-isobaric (NPT) ensemble, after an initial 3-ps tempera-ture equilibration in a canonical (NVT) ensemble. The static structempera-ture factor Ssðq
⇀
Þ was calculated (seeSI Appendixfor 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 a canonical (NVT) ensemble to avoid temperature drifting. The temperature in the CPMD calculations is controlled by a Nosé thermostat (39). Note Recently there were several additional reports appearing after our submission (40–42) that address several other properties of SiH4ðH2Þ2.
ACKNOWLEDGMENTS.Y.Y. thanks Yunfeng Liang for valuable suggestions on CPMD and Jianjun Dong for fruitful discussions on electronic structures. We also thank the Editor and reviewers for very constructive and helpful comments.
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Fig. 7. Depicted trajectories of Si (yellow) and H atoms (white) in SiH4
molecules in the (A) I-4m2 and (C) P1 structures of SiH4ðH2Þ obtained from
NVE CPMD simulations. Depicted trajectories for hydrogen molecules at the octahedral (green) and tetrahedral (blue) sites in the (B) I-4m2 and (D) P1 structures of SiH4ðH2Þ2from simulations for A and C. The distorted fcc unit
cells are identified by solid lines.
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