Ziyue Lin(林子越), Hongyu Yu(于洪雨), Hao Song(宋昊), Zihan Zhang(張子涵),Tianxiao Liang(梁天笑), Mingyang Du(杜明陽), and Defang Duan(段德芳)

State Key Laboratory of Superhard Materials,College of Physics,Jilin University,Changchun 130012,China

Keywords: high pressure,crystal structure,electron properties,chemical bonds

1. Introduction

Pressure can greatly shorten interatomic distances, modify chemical properties of elements, overcome reaction barriers, and lead to the formation of some unusual stoichiometric compounds that are difficult to achieve under ambient conditions.[1–3]The new compounds appeared at high pressure usually exhibit novel properties and behaviors.[4–7]For example,mixed H and S can yield an H3S compound at high pressure with a high critical temperatureTcof 203 K.[8]Similarly, a large variety of atypical compounds, such as NaCl3with linear[Cl3]?species,[9]CsF3with high oxidation states have been predicted or synthesized under high pressure.[10]

In recent years, a large variety of atypical polyhalides with unusual bonding and electronic properties, such as NaCl3,KCl3,[11]KBr3,KBr5,[12]CsI3,[13]etc.,have been reported under high pressure. High pressure is a powerful tool to study the structure transformation.[14,15]NaCl3with linear[Cl3]?species has been reported to be stable withPnmaphase between 20 GPa and 48 GPa through theoretical prediction and experimental synthesis. At 48 GPa, it transforms fromPnmatoPm-3nphase. In the K–Br system, KBr3, which formed in a chemical reaction between KBr and Br2above 2 GPa at room temperature,has been reported to crystallize in the primitive orthorhombic structure(Pnma). On further compression,a monoclinic KBr5withP21space group has been reported at～6.0 GPa which decomposes to a trigonal (P-3c1) KBr3and Br2above 14 GPa and 1500 K. CsI3has a three-phase structural sequence at high pressure: orthorhombic(Pnma)to trigonal(P-3c1)to a cubic(Pm-3n)phase.

On the other hand, a large number of unexpected oxidation states of d-block elements have been identified in fluorides at high pressure, e.g., AuIVF4, AuVI,[16]HgIVF4, IrVIIIF8,[17]because fluorine(F)has a rather large electronegativity and a small atomic size. Of particular interest is the Cs–F system,at low pressure,some F3,F4,and F5species are formed in compounds CsF2,CsF3,and CsF5. At higher pressure,Cs exhibits a high oxidation state beyond the+1 in CsF3and CsF5,where Cs takes on the role of a 5p element by opening up its inert 5p shell via the aid of strong oxidant F.[10]The alkali-earth element Ba also shows high oxidation states in BaF3,BaF4,and BaF5at high pressure.[16]

Rb is adjacent to Cs,which may have some similar chemical properties. The only known RbF has a rocksalt-type(Fm-3m) structure, which becomes a cesium chloride-type (Pm-3m)structure at about 3 GPa.[10]The chemical reactions of Rb with fluorine under high pressures maybe exhibit even richer chemistry and new phenomena. Here, we explore the highpressure phase diagram of Rb–F systems for various RbFn(n=1,2,...7) compositions under high pressure via random structural prediction calculations. Our work shows that,in Frich RbFn(n=2,3, 4, 5)compounds,F3,F4, and F5species are stabilized at high pressure.We expect high oxidation states of Rb will be seen under extremely high pressure.

2. Computational details

To find stable RbFn(n= 1–7) compounds in which F has a high stoichiometric number, we conducted an extensive variable-composition structure search withab initiorandom structure searching (AIRSS) code[18,19]combining with Cambridge serial total energy package (CASTEP) code.[20]We performed structure searching and finally predicted about

72000 structures in total from 10 GPa to 300 GPa. Geometry optimization and electronic properties were calculated by Viennaab initiosimulation package(VASP)code.[21]The generalized gradient approximation(GGA)[22]within the framework of Perdew–Burke–Ernzerhof (PBE)[23]was used for the exchange–correlation functional, and projector augmented wave (PAW)[24]potentials were used. The cutoff energy was set to 900 eV, and Monkhorst–Packkmeshes were set to 2π×0.02 ?A?1to ensure that all enthalpy calculations would be converged to better than 1 meV/atom. Bader charges and ELFs were also calculated by VASP. The crystal orbital Hamilton populations (COHP)[25]were calculated with the LOBSTER[26]package. The phonon calculations were performed with PHONOPY[27]code.

3. Results and discussion

Enthalpy difference per atom for RbFxis obtained by

Based on the above formula,we calculated the enthalpy difference of the most stable phase of RbFx(x=1–7)relative to RbF and F(Cmca)and constructed the convex hull at the pressures of 0, 10 GPa, 50 GPa, 100 GPa, 200 GPa, and 300 GPa presented in Fig.1(a). In general,structures falling on the convex hull line are thermodynamically stable against decomposition to elemental solids or other binary compounds. To provide more information relevant to experimental synthesis,we built a pressure–composition phase diagram of the Rb–F system,as depicted in Fig 1(b). At ambient pressure,we reproduced the experimentally known RbF structure with the space groupFm-3m. In additon to RbF,we found that RbF2, RbF3, and RbF5are thermodynamically stable at ambient pressure. However,RbF2and RbF3are dynamically unstable due to the imaginary frequencies in their phonon spectra(showed in Fig.S2).As pressure increases,RbF4appears on the convex hull in the pressure range between 4 GPa and 75 GPa indicating that it is thermodynamically stable. RbF2is stable up to 225 GPa,while RbF3and RbF5first decompose and then become stable at much high pressure. Both RbF6and RbF7are unstable within the pressure range studied.

All of the stable compounds undergo a series of phase transitions. The enthalpy difference of stable compounds as a function of pressure is shown in Fig.S1 of the supporting material. Except forI4/mmmphase of RbF2andPbam-0 phase of RbF3,all of these thermodynamically stable structures have been found to be dynamically stable within their stable pressure ranges,see Fig.S2 in the supporting material.

Fig. 1. (a) Convex hull diagram of Rb–F system from 0 to 300 GPa.Dotted lines connect data points, solid lines connect the convex hull. Solid squares represent stable compounds; open squares denote metastable compounds. (b) Pressure–composition phase diagram of Rb–F compounds from 0 to 300 GPa.

Fig.2. Crystal structures of RbF2. (a)Pbam RbF2 structure at 10 GPa,(b)Fd-3m RbF2 structure at 250 GPa.

First,let us look at RbF2,it is stable with tetragonalPbamsymmetry at 2 GPa containing F4species (Fig. 2(a)). Therefore, the compound can be viewed as [Rb]+2[F4]2?complex.The spacing between F and F atoms in the linear F?4species(Fa–Fb–Fc–Fd) is not equal. The distance between the middle two fluorine atoms(Fb–Fc)is 1.68 ?A,which has a weaker bonding than that in the pure F2molecule (F–F bond length 1.442 ?A). For two pairs of fluorine atoms on either side of the F4species(Fa–Fb,Fc–Fd),their distances are both 2.02 ?A,indicating there is a much weaker bonding than Fb–Fc. Our calculations for Bader charge showed that the charge transfer is 0.63efor Faor Fd,and 0.26efor Fbor Fc. This means that the F atom on the side is more likely to ionize. The calculated ICOHP values are?0.676 between Faand Fb(also Fcand Fd),?2.310 between Fband Fc. The latter value is much larger than the former one, indicating that the bonding between the two middle atoms are obviously stronger than the side ones.Interestingly, the configuration of F4species in RbF2is very similar to that of CsF2.RbF2becomes unstable above 15 GPa,then turns to be stable with aFd-3mphase at 225 GPa. This structure is a typical ionic phase(Fig.2(c)),and the ICOHP of the nearest F–F is?0.267, indicating none existence of F–F covalent bond.

Then we look at RbF3, it adopts aR-3mspace group at 2 GPa, and transforms to aPnmaphase at the pressure of

40 GPa,and keeps stable up to 225 GPa. TheR-3mstructure contains linearly symmetric F3species with the configuration of Rb+[F3]?. Through Bader analysis,Rb+transfers 0.93eto[F3]?,and F atoms at both ends of the F?3species are equivalent. In such a linear structure, the distance of F–F is 1.71 ?A at 10 GPa, with the ICOHP value of?2.02. The F–F bond here is obviously weaker than the F–F bond in the pure F2molecule(1.442 ?A),but a little stronger than the F–F bond inR-3mCsF3(1.736 ?A).[28]

For thePnmastructure, the [F3]?species is not linear with the F–F–F angle of 174.267?and its Bader charge is 0.88e. We also calculated ICOHPs of the two F–F bonds in F3species. Between them, the ICOHP is?2.169 with bond length of 1.68 ?A,and the ICOHP is?2.280 with bond length of 1.67 ?A.

We found that RbF4compound is stable in the pressure range of 4–75 GPa withC2/msymmetry that contains both[F3]?and [F2]?species. In such a structure, the nearest distance of F–F is 1.54 ?A in a[F2]?species,the second and third nearest distance between F atoms is 1.58 ?A and 1.76 ?A in a[F3]?species, and their ICOHP values are?3.838,?3.206,and?1.502, respectively. Shorter bonds have significantly larger ICOHP values, which is consistent with our common knowledge of the relationship between bond length and bond strength. The Bader charges are?0.89efor[Rb]+, 1.25efor[F2]?,and 1.14efor[F3]?,suggesting the formation of[Rb]+,[F2]?, and [F3]?. Here, the simultaneous presence of [F2]?and[F3]?species has been predicted for the first time in alkali metal fluorides.This is in line with Miao’s work,which shows that there are multiple different clusters of homonuclear bonds in the same compound.[29]

Fig.3. Crystal structures of RbF3. (a)R-3m RbF2 structure at 10 GPa,(b)Pnma RbF3 structure at 50 GPa.

Fig.4. Crystal structures of RbF4 and RbF5. (a)C2/m RbF4 structure at 10 GPa,(b)P21 RbF5 structure at ambient pressure,(c)Pnma RbF5 structure at 150 GPa.

In the case of RbF5, its stable pressure intervals are 0–8 GPa and 150–225 GPa, with the symmetries ofP21andPnma, respectively. TheP21structure contains F3and F2species which have different F–F distances and ICOHPs between atoms: 1.60 ?A, ICOHP:?3.182 and 1.82 ?A, ICOHP:?1.295 in F3species;1.54 ?A,ICOHP:?4.078 in F2species.The F3group accepts 0.67e, F2group accepts 0.25e, and the Rb atom loses 0.92e. ThePnmastructure has a symmetrical V-shaped[F5]?species. This configuration also appears in the CsF5with aP21symmetry.[28]The Rb transfers 0.86eto the F5species, suggesting the existence of Rb+cation and[F5]?anion.We use Fa–Fb–Fc–Fd–Feto represent a F5unit.The distance and ICOHP value between F atoms at 0 GPa are,Fa–Fb:1.49 ?A,ICOHP:?4.363;Fb–Fc:1.79 ?A,ICOHP:?1.041;Fc–Fd:1.79 ?A,ICOHP:?1.041;Fd–Fe:1.49 ?A,ICOHP:?4.363.The F5species here is symmetric, and the whole compound can be viewed as Rb+[F5]?.

From partial density of states (PDOS), we can tell whether a compound is a conductor, a semiconductor, or an insulator, and can also make a preliminary estimate of the likelihood of bonding between different atoms by the degree of orbital overlap. We calculated PDOS for multiple crystal structures containing F2, F3, and F5species (Fig. 5). First of all, according to the PDOS values at Fermi level, except forFd-3mRbF2,these predicted stable compounds are insulators(Fig.S3). On the other hand,there is a little overlap between Rb 5p and F 2p states around the Fermi level (Fig. 3(a)), indicating that 5p electrons of Rb are not involved in bonding.From the analysis of Bader charges and PDOS, we can see that there is no potential for finding new oxidation states in our predicted stable Rb–F compounds up to 300 GPa, and a high oxidation state will appear at much higher pressure.

The electron localization function(ELF)is used to characterize the localized distribution of electrons, determine the type of bonding, and find out the lone pair electron distribution.The ELFs of the stable phases were calculated.Red areas(ELF≈1.0)around Rb and F atoms indicate the lone electron pairs, and green areas (ELF≈0.5) between the F atoms indicate strong covalent bonding. Blue areas in ELFs typically indicate non-covalent bonding,for example,delocalized electrons in metals.Through this judgment,we further confirm the F3, F4, and F5species in these structures. We calculated the ELF of all the stable compounds shown in Fig.6 and Fig.S4.First let us look at the ELF ofPbamRbF2at ambient pressure,the F4cluster exists in a linear form which was also found in the structure ofPbamCsF2.[28]ForR-3mRbF3,there are linear equivalent F3units(Fig.6(b)).This form of the F3unit has been found in other fluorides such as CsF3.[28]InC2/mRbF4,the ELF and structure diagram show asymmetric F2and F3units (Fig. 6(d)). InPnmaRbF5(Fig. 6(e)), it tends to form symmetrical V-shaped F5units, which was also predicted in the work of CsF5.[28]

Fig. 5. The calculated PDOS of (a) Pbam RbF2 at 10 GPa, (b) R-3m RbF3 at 10 GPa,(c)Pnma-h RbF3 at 50 GPa,(d)C2/m RbF4 at 10 GPa,(e) Pnma RbF5 at 150 GPa. The states are aligned at the Fermi level(vertical dashed lines).

In this work,homonuclear covalent bonds like F3,F4,and F5species form in the Rb–F system,which has been explained by Miaoet al.using the H¨uckel model.[29]The atomic orbital energies of the different elements in the heterogenous bond are different, whereas in the homonuclear bond, the two atomic orbitals forming the chemical bond have the same energy, so the bond energy of heterogenous bond formed will be greater than the energy in the homonuclear bond. For the system we study, the case happens to be that F–F bonds are generated preferentially under pressure.

Under the action of pressure,the energy of the inner electron orbital will also increase, and eventually, the inner electrons may achieve enough energy to participate in bonding.Also,the effect of pressure will reduce the energy of electron orbitals that are not occupied, and make such orbitals likely to be involved in bonding.[29]In the case of cesium fluoride,inner-shell electrons become the main components of chemical bonds in a lower pressure range.[10]In the investigation below 300 GPa, we just only found F3, F4, and F5species in the Rb–F system. If the pressure increases further, high oxidation state of rubidium beyond the+1 state would appear in the novel rubidium fluorides, which will be discussed in the future.

Fig. 6. The ELFs of (a) Pbam RbF2 at 10 GPa, (b) R-3m RbF3 at10 GPa,(c)Pnma RbF3 at 50 GPa,(d)C2/m RbF4 at 10 GPa,(e)Pnma RbF5 at 150 GPa.

4. Conclusion

In summary,four new compounds of RbF2,RbF3,RbF4,and RbF5were predicted to be stable at experimentally accessible pressures. Based on the bond lengths, Bader charges,ICOHP values,ELFs,and PDOS,we found that the stable rubidium fluorides behave as ionic compounds containing[F3]?,[F4]2?,and[F5]?species under high pressure,and Rb has not been oxidized beyond+1 states up to 300 GPa. The homonuclear bonding of F–F is easily formed at low pressure. After further pressurization, it is prospect for the possibility of the future discovery of Rb with high oxidation states in which inner orbital electrons participate in bonding.

Acknowledgements

Parts of the calculations were performed in the High Performance Computing Center (HPCC) of Jilin University and TianHe-1(A) at the National Supercomputer Center in Tianjin.