Formation of Stoichiometric CsFn Compounds

Alkali halides MX, have been viewed as typical ionic compounds, characterized by 1:1 ratio necessary for charge balance between M+ and X−. It was proposed that group I elements like Cs can be oxidized further under high pressure. Here we perform a comprehensive study for the CsF-F system at pressures up to 100 GPa, and find extremely versatile chemistry. A series of CsFn (n ≥ 1) compounds are predicted to be stable already at ambient pressure. Under pressure, 5p electrons of Cs atoms become active, with growing tendency to form Cs (III) and (V) valence states at fluorine-rich conditions. Although Cs (II) and (IV) are not energetically favoured, the interplay between two mechanisms (polyfluoride anions and polyvalent Cs cations) allows CsF2 and CsF4 compounds to be stable under pressure. The estimated defluorination temperatures of CsFn (n = 2,3,5) compounds at atmospheric pressure (218°C, 150°C, -15°C, respectively), are attractive for fluorine storage applications.

stable in the entire pressure range up to 100 GPa. However, all of the stable compounds undergo a series of phase transitions, with dramatic changes of the electronic structure.
Let us first look at CsF 3 phases. At ambient pressure, we find CsF 3 adopts a rhombohedral structure (space group R 3m), which is made of Cs 1 and linear symmetric [F 3 ] 2 species. The F-F distance in the [F 3 ] is 1.736 Å , indicating, as expected, weaker bonding than in the F 2 molecule (F-F bond length 1.442 Å ). Bader analysis also supports this conclusion: there is a charge transfer of 0.950 e from Cs to F 3 species, very close to the value in CsF (0.928 e), but the charge distribution within F 3 is not even: two end F atoms have the charge of -0.406 e, while the central atom only has -0.138 e. Trihalide anions [X 3 ] 2 (X5Br, I) are well known, but the [F 3 ] 2 species has only been experimentally found as CsF 3 complexes in argon matrix 12,13 . Here, we for the first time report its existence in a thermodynamically stable crystalline phase. According to DFT calculation, R 3m-CsF 3 is stable against decomposition to CsF and F 2 (the formation energy is about -0.189 eV/atom at T 5 0 K, P 5 1 atm). At 27 GPa, CsF 3 undergoes a phase transition to a monoclinic phase C2/c. More interestingly, this structural transition coincides with a striking increase in Cs's Bader charge, as shown in Fig. 2     can be also found in Miao's work 5 . But his previously proposed C2/m structure is less stable than the C2/c structure found here. Similar to CsF 3 , CsF 5 is also stable in the entire investigated pressure range between 0-100 GPa. At 0 GPa, we found a monoclinic P2 1 phase is stable against decomposition to any other stable compositions (Cs, CsF, CsF 3 , F). P2 1 -CsF 5 can be described as packing of Cs 1 and [F 5 ] 2 species. [F 5 ] 2 ion has a V-shape and F-F bond lengths are 1.617, 1.953, 1.858, 1.617 Å , and F-F-F bond angle at central F atom is 98.592u. Bader analysis in Fig. 3 shows that the entire F 5 group has charge -0.958 e. The hypothetical pentafluoride anion [F 5 ] 2 has also been proposed by Riedel 12 5 , we found a structure based on the packing of CsF 5 molecules. We again plot the variation of Cs's Bader charge in stable CsF 5 compounds with pressure. Indeed, analysis indicates a two-step oxidation of Cs 11 R 13 R 15, coinciding with the transition sequence (from C2/c to C2/m at 21 GPa, and from C2/m to Fddd at 47 GPa).
Our results show CsF 3 and CsF 5 are stable alongside the known compound CsF in the whole investigated pressure range (0-100 GPa). Unlike the recently discovered exotic sodium chlorides 14 ,  ). Note that this is different from the previous study 5 , in which the latter factor was overlooked, along with a large number of stable phases. Due to these two competing mechanisms, one can expect other stoichiometries can be stabilized as well. Indeed, we found CsF 2 and CsF 4 can be stable at intermediate pressure ranges.
Previously, a tetragonal (I4/mmm) XeF 2 -like molecular structure was proposed to be stable at 5-20 GPa 5 . Our search found molecular CsF 2 crystal to be unstable against decomposition to CsF 3 and CsF at all pressures. A class of CsF 2 compounds, however, has been found to be stable at low pressures in our prediction. At 0 GPa, another I4/mmm CsF 2 phase is found to be stable. As shown in Fig. 4c 22 anions appear again!). Miao investigated the possibility of CsF 4 molecule structurally similar to XeF 4 , which is contradictory to chemical intuition (CsF 4 can be neither isostructural nor isoelectronic to XeF 4 ). Indeed, our results suggest that Cs 41 based compound is energetically unfavored. But we found that the most stable CsF 4 structure above 57 GPa shows the oxidation state higher than 13.
Light halogens, fluorine (F) and chlorine (Cl), at normal conditions are highly reactive and toxic gases. For chemical industry and laboratory use, this presents great inconvenience. Their storage in the gaseous form (even as liquefied gases) is very inefficient, and compressed gas tanks may explode, presenting great dangers. At normal conditions, the volume of 22.4 litres (L) of pure fluorine gas weighs just 36 grams (g), illustrating the dismal inefficiency of storage in this form. To the best of our knowledge, no effective and safe fluorine storage materials are known. Both F and Cl have a huge range of industrial applications, which would benefit from such storage materials, especially if they can achieve high storage capacity, stability and reversibility. Table I | Investigated reactions of the CsF-F system at ambient pressure conditions. wt% gives the weight content of released F 2 gas. DH 0K and DH 300K are the calculated enthalpies at T50 K and 300 K, including the vibrational energies in (kJ/mol). DS 300K is the corresponding formation entropy in J/(K?mol). T c is the predicted decomposition temperature at standard atmosphere (1 bar In this work, we found that a series of CsF n (n51, 2, 3, 5) compounds can be stable at zero temperature and ambient pressure. One mole of CsF 5 (227.9 g, occupying the volume of 0.07 L) contains 2 moles of F 2 gas (which in the free state would occupy the volume of 44.8 L -hence, storage in the form of CsF 5 is three orders of magnitude more efficient, and much safer, than in the form of pure F 2 gas). The reaction CsF 5 5 CsF 1 2F 2 (gas), is thermodynamically unfavourable at zero temperature (the enthalpy of this reaction is 88.41 kJ/mol), but will be favourable on increasing temperatures, due to the higher entropy of the F 2 gas (202.8 J/(mol?K) at standard conditions) 16 . The calculated thermodynamic properties of these defluorination reactions are given in Table I. It can be seen that such compounds as CsF 3 can be thermally decomposed, and then again be synthesized at lower temperatures at nearly room temperature window. CsF 5 , having the highest F content, can be used for fluorine storage at low temperature conditions. Thermodynamic stability of the predicted polyfluorides at atmospheric pressure means that there will be ways to ''recharge'' them with fluorine after defluorination, and such reversibility is a strong advantage of the proposed fluorine storage materials.
We have presented a comprehensive study of possible stable compounds in the CsF-F binary system under pressure. CsF n phases show extremely rich chemistry. At ambient pressure, novel and unexpected compounds CsF 2 , CsF 3 , CsF 5  ), and neutral molecular species (CsF 5 ). Our hope is that this report will stimulate further experimental studies and serve as a guide for the design of fluorine storage materials.

Methods
Searches for the stable compounds and structures were performed using an evolutionary algorithm, as implemented in the USPEX code [8][9][10][11] . The most significant feature of USPEX we used in this work is the capability of optimizing the composition and crystal structures simultaneously -as opposed to the more usual structure predictions at fixed chemical composition 1,14 . The compositional search space is described via building blocks (for example, search for all compositions in a form of [xCsF 1 yF]). During the initialization, USPEX samples the whole range of compositions of interest randomly and sparsely. Chemistry-preserving constraints in the variation operators are lifted and replaced by the block correction scheme which ensures that a child structure is within the desired area of compositional space, and a special ''chemical transmutation'' operator is introduced. Stable compositions are determined using the convex hull construction: a compound is thermodynamically stable if the enthalpy of its decomposition into any other compounds is positive. Structure prediction was done in conjunction with ab initio structure relaxations based on density functional theory (DFT) within the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) 17 as implemented in the VASP code 18 . For structural relaxation, we used the all-electron projector-augmented wave (PAW) method and the plane wave basis set with the 600 eV kinetic energy cutoff; the Brillouin zone was sampled by uniform Gamma-centered meshes with the resolution 2p 3 0.06 Å 21 . For post-processing, the selected low-enthalpy structures were treated by using hard PAW potential of F (F_h), using a energy cut off of 1000 eV. Such calculations provide an excellent description of the known structures (CsF and F 2 ) and their energetics. To ensure that the obtained structures are dynamically stable, we calculated phonon frequencies throughout the Brillouin zone using the finite-displacement approach as implemented in the Phonopy code 19 . The vibrational entropies and enthalpies are obtained by directly summing over the calculated phonon frequencies, in order to calculate the free energy (see online supporting information, similar methods have been widely used for simulation of dehydration reactions for hydrogen storage materials 20,21 ). Charge transfer was investigated on the basis of the electron density using Bader's analysis 22 as implemented in a grid-based algorithm without lattice bias 23 . Electron localization function (ELF) 24 is also calculated in order to analyze chemical bonding for the selected compounds.