Prediction of new thermodynamically stable aluminum oxides

Recently, it has been shown that under pressure, unexpected and counterintuitive chemical compounds become stable. Laser shock experiments (A. Rode, unpublished) on alumina (Al2O3) have shown non-equilibrium decomposition of alumina with the formation of free Al and a mysterious transparent phase. Inspired by these observations, we have explored the possibility of the formation of new chemical compounds in the system Al-O. Using the variable-composition structure prediction algorithm USPEX, in addition to the well-known Al2O3, we have found two extraordinary compounds Al4O7 and AlO2 to be thermodynamically stable in the pressure ranges 330-443 GPa and above 332 GPa, respectively. Both of these compounds at the same time contain oxide O2− and peroxide O22− ions, and both are insulating. Peroxo-groups are responsible for gap states, which significantly reduce the electronic band gap of both Al4O7 and AlO2.

), and oxide (O 22 ) ions. It was not clear whether AlO 2 or other unusual oxides are stable at any pressure-temperature conditions. Very recently, it has been shown that even in seemingly extremely simple systems, such as Na-Cl, totally unexpected compounds (Na 3 Cl, Na 2 Cl, Na 3 Cl 2 , NaCl 3 and NaCl 7 ) become stable under pressurethese have been predicted using evolutionary crystal structure prediction method USPEX and verified by experiments 9 . If such unusual compounds exist in the ''trivial'' Na-Cl system, one can expect similarly unusual compounds in nearly any other system under pressure. Here we test this hypothesis on the Al-O system, and indeed predict that Al 4 O 7 and AlO 2 become thermodynamically stable under high pressure.

Computational Methodology
To predict stable Al-O oxides and their structures, we used the evolutionary algorithm USPEX [10][11][12] in its variable-composition mode 13 at pressures 0, 50, 100, 150, 200, 300, 400, 500 GPa. The reliability of USPEX has been demonstrated many times beforee.g. Ref. 9, 14-18. Modern methods have shown remarkable power to predict novel unexpected compoundse.g. in the Na-Cl 9 , Mn-B 19 , Mg-C 20 and Na-Si 21 systems. Stable compositions were determined using the convex hull construction: a compound is thermodynamically stable when its enthalpy of formation from the elements and from any other compounds is negative. Enthalpy calculations and structure relaxations were done using density functional theory (DFT) within the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) 22 , as implemented in the VASP code 23 . These calculations were based on the all-electron projector-augmented wave (PAW) method 24 and plane wave basis sets with the kinetic energy cutoff of 600 eV and uniform C-centered k-point meshes with reciprocal-space resolution of 2p*0.02 Å 21 . The first generation of structures/compositions was produced randomly with the use of space group symmetries (using algorithm 12 ); the lowest-fitness 60% of the structures/compositions were allowed to produce child structures/compositions (fitness being defined as the difference between enthalpy of the structure and the convex hull). Initial structures were allowed to have up to 20 atoms in the unit cell, but this range was allowed to change in subsequent generations as a result of evolution. Child structures/compositions were created in the following manner: 20% by random symmetric generator, 40% by heredity, 20% by softmutation, and 20% by atomic transmutation. In this work, we first performed searches in the entire Al-O system with up to 20 atoms/cell, and have found only Al 2 O 3 and oxygen-enriched phases Al 4 O 7 and AlO 2 . Then we did additional focused searches in a narrower compositional range Al 2 O 3 -O, and obtained the same result.
After USPEX predictions, we selected structures on the convex hull and close to it, and relaxed them carefully at pressures 0, 10, ..., 520 GPa. These calculations have confirmed stability of three oxideswell-known Al 2 O 3 and non-classical AlO 2 and Al 4 O 7 . For these compounds, we also computed their electronic band structures. For accurate estimates of the band gaps, we have used the HSE hybrid functional 25 . Phonon frequencies throughout the Brillouin zone were calculated using the finite displacement approach as implemented in the Phonopy code 26,27 , and these calculations confirmed that these phases are dynamically stable at pressure ranges where our enthalpy calculations predict their thermodynamic stability.

Results
Stable compounds in the Al-O system. At all pressures in the range 0-500 GPa, the known compound -Al 2 O 3 -is found to be thermodynamically stable. In agreement with previous works we find the same sequence of phase transitionsfrom corundum to the Rh 2 O 3 (II)-type structure at 100 GPa, then to the CaIrO 3 -type structure at 130 GPa, and then to the U 2 S 3 -type phase at 394 GPa.
The computed thermodynamics of Al-O compounds are shown in Fig. 1. Al 4 O 7 and AlO 2 begin to show competitive enthalpies of formation at pressures above 300 GPa and have stability fields at      Table 1.

Discussion
Properties of the new phases. Phonon dispersion curves of Al 4 O 7 and AlO 2 , computed at 400 and 500 GPa, respectively, are shown in Fig. 5. Both phases are dynamically stable and display a continuum of phonon energies, i.e. absence of decoupled O-O vibrational modes of peroxo-groups, because at high pressure Al-O modes have frequencies comparable to O-O modes. At the same time, in the electronic structure, there are clearly defined dispersive bands of peroxo-groups, and these play an important role, as we discuss below. Both phases are dynamically and mechanically stable, as shown by their computed phonons, elastic constants, and evolutionary metadynamics 29 simulations, also enabled in the USPEX code and allowing one to explore possible phase transitions. We have confirmed that there are indeed no distortions or modulations that could lead to more stable structures.
All the predicted phases are insulating and show very distinct electronic structure compared with Al 2 O 3 . At 400 GPa, the computed DFT band gaps are 6.93 eV for Pnma-Al 2 O 3 , 2.51 eV for Al 4 O 7 , 2.92 eV for AlO 2 . We recall that DFT calculations significantly underestimate band gaps, while hybrid functionals and GW approximation give much better band gaps, typically within 5-10% of  the true values. Fig. 6 shows band gaps as a function of pressure, computed using the GGA (PBE functional), hybrid HSE functional 25 and GW approximation 30,31 ; one can see that GGA band gaps are ,30% underestimates; HSE band gaps practically coincide with the most accurate GW values for AlO 2 , but are 0. This band gap reduction for Al 4 O 7 and AlO 2 originates from the additional low conduction band in the middle of the band gap. Our calculations (Fig. 7) show that these low conduction bands can be unequivocally assigned to the peroxo-groups. In both Al 4 O 7 and AlO 2 , both gap states -the HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) -come from peroxo-groups. Together with low compressibility of the peroxo-groups (between 300 GPa and 500 GPa, the O-O distance changes from 1.37 to 1.38 Å and from 1.46 to 1.42 Å in AlO 2 and Al 4 O 7 , respectively), this explains why the band gaps of Al 4 O 7 and especially AlO 2 are practically independent of pressure in a wide pressure range (Fig. 6). As Fig. 8 shows, projected densities of states show only small contributions from Al, thus indicating a high degree of ionicity. Indeed, Bader charges 32 are 12.44 of Al, 20.83 of O1 (peroxide anion) and 21.61 of O2 (oxide anion) in AlO 2 at 400 GPa.
While the band gaps computed by DFT (PBE functional) are, as expected, significantly underestimated, the energetics are accurate. We have tested this by computing the energy and enthalpy of the reaction Al 2 O 3 z1=2O 2~2 AlO 2 using the combined exact exchange (EXX) and random phase approximation (RPA) technique [33][34][35] . At 300 GPa we obtained the  (1) In both PBE and EXX1RPA the new compounds are stabilized by the P*V-term in the free energy, rather than by the internal energy. This originates from the low packing efficiency in elemental oxygen, which remains a molecular solid in the entire pressure range studied here. For this reason we can expect increased reactivity of oxygen, and stabilization of oxygen-rich compounds (such as peroxides) at high pressures. (2) Results of the PBE and EXX1RPA are quantitatively similar, especially at 500 GPa, where the difference is only 5 meV/ atom. (3) At the EXX1RPA level of theory the new compounds predicted here are even more stable than at the PBE level.

Conclusions
Systematic search for stable compounds in the Al-O system at pressures up to 500 GPa revealed two new stable compounds (AlO 2 and Al 4 O 7 ); their stability fields are above 332 GPa and in the range 330-443 GPa, respectively. Our analysis reveals that insulating compounds AlO 2 and Al 4 O 7 exhibit significantly ionic character, both contain peroxide [O-O] 22 and oxide O 22 anions and therefore belong to the exotic class of ''peroxide oxides''. Electronic levels of the peroxo-groups form gap states (''low conduction band'') that lead to a twofold lowering of the band gap relative to Al 2 O 3 . Our preliminary results show that the formation of peroxo-ions and stabilization of peroxides under pressure occur in many oxide systems, and this phenomenon may play an important role in planetary interiors, with their high pressures and abundance of oxygen atoms.