Hypervalent Iodine with Linear Chain at High Pressure

Iodine is an element of fascinating chemical complexity, and numerous hypervalent iodine compounds reveal vital value of applications in organic synthesis. Investigation of the synthesis and application of new type of hypervalent iodine compound has extremely significant meaning. Here, the formation of CsIn (n > 1) compounds is predicted up to 200 GPa using an effective algorithm. The current results show that CsI3 with space group of Pm-3n is thermodynamically stable under high pressure. Hypervalence phenomenon of iodine atoms in Pm-3n CsI3 with endless linear chain type structure appears under high pressure, which is in sharp contrast to the conventional understanding. Our study further reveals that Pm-3n CsI3 is a metallic phase with several energy bands crossing Fermi-surface, and the pressure creates a peculiar reverse electron donation from iodine to cesium. The electron-phonon coupling calculations have proposed superconductive potential of the metallic Pm-3n CsI3 at 10 GPa which is much lower than that of CsI (180 GPa). Our findings represent a significant step toward the understanding of the behavior of iodine compounds at extreme conditions.

Swarm Optimization) method [32][33][34][35] , which has been successfully used in numerous predictions regarding compounds and structures over the past few years [36][37][38][39][40][41][42][43][44][45][46] . Our work shows that CsI 3 has the simple Pmnb structure at ambient pressure and undergoes a complicated transition to high symmetric cubic Pm-3n phase at high pressure. The current Pm-3n phase of CsI 3 is a metal phase, and the pressures create a peculiar reverse electron donation from iodine to cesium. In addition, the iodine atoms of Pm-3n phase forming into several completely linear chains show an attractive hypervalence phenomenon, which cannot be simply explained by traditional three-center-four-electron (3c-4e) scheme [47][48][49] . This work presents significant concerning on the synthesis and the fundamental structural properties of the simplest and most representative polyiodide materials with implications for an entire family of similar materials.

Calculation Methods
To obtain stable structures for CsI n , we carried out a structural search using a global minimization of free energy surfaces based on the CALYPSO methodology [32][33][34][35] and the first-principles calculations. The remarkable feature of this methodology is the capability of predicting the stable structure with only the knowledge of the chemical composition at given external conditions (for example, pressure). The underlying ab initio structural relaxations, electron localization function (ELF) and electronic band structure calculations were performed within the framework of density functional theory (DFT) as implemented using by VASP (Vienna ab initio simulation package) code 50 . The generalized gradient approximation (GGA) within the framework of Perdew-Burke-Ernzerhof (PBE) 51 was used for the exchange-correlation functional. And the projector augmented wave method (PAW) 52 has been adopted, with 5s 2 5p 6 6s 1 and 5s 2 5p 5 treated as valence electrons for cesium and iodine, respectively. The cutoff energy for the expansion of the wavefunction into plane waves was set at 400 eV and fine Monkhorst-Pack (MP) k meshes of 0.025 Å −1 have been chosen to ensure that all the enthalpy calculations are well converged. The phonon calculations have been carried out by using a supercell approach as implemented in the Phonopy code 53 . This method uses the forces obtained by the Hellmann-Feynman theorem calculated from the optimized 3 × 3 × 3 supercell. The Bader's quantum theory of atoms in molecules (QTAIM) analysis 54 was used for charge calculation.
Electron-phonon coupling (EPC) calculations have been performed using the pseudo-potential plane-wave method and density-functional perturbation theory 55,56 as implemented in the Quantum-ESPRESSO package 57 . EPC calculation has been performed on 4 × 4 × 4 MP q meshes in the first Brillouin zone with a kinetic energy cutoff of 60 Ry. 16 × 16 × 16 MP k meshes are chosen to ensure k-point sampling convergence with Gaussians of 0.025 Ry, which approximates the zero-width limit in this calculation.

Results and Discussions
The high-pressure synthesis and structural information of CsI n . Structural predictions for CsI n (n = 2 − 5) have been performed with CALYPSO methodology 32-35 using simulation sizes with 1-4 formula per primitive cell under a series of pressure points (0, 50, 100, 150 and 200 GPa). The enthalpy of formation per atom is calculated using the following formula: where Δ H f is the enthalpy of formation per atom and H is the calculated enthalpy per chemical unit for each compound. From the convex hull shown in Fig. 1a (solid lines), only CsI 3 with space group of Pm-3n is thermodynamically stable under high pressure. However, previous experimental work shows that CsI 4 can be synthesized at ambient pressure, and a P2 1 /a phase with 4 formulas per primitive cell has been proposed by X-ray analysis 29 . The currently predicted Pnma phase is energetically much superior to the monoclinic P2 1 /a structure, while the formation enthalpy of Pnma is positive value and thus does not support its thermodynamic stability. We note that the experimentally synthesized CsI 4 was heated in a closed vessel at 90 °C, and was then cooled slowly to 25 °C 29 . Therefore, the P2 1 /a CsI 4 structure is a metastable phase. CsI 3 is stable at ambient pressure and adopts an orthorhombic lattice with Pmnb symmetry (Fig. 2a). The optimized lattice parameter of Pmnb phase at 0 GPa is a = 7.2366 Å, b = 11.2631 Å and c = 10.4905 Å. At 0 GPa, this actually Cs + [I 3 ] − phase contains linear type I 3 − ions with two I-I bonds length of 2.901 and 3.019 Å, which are similar to the experimental data of 2.820 and 3.100 Å 28 , respectively. Such typical hypervalent iodine moiety of orthorhombic Pmnb structure can be conventionally explained by traditional theory. For I 3 − ion of Pmnb phase, the central iodine atom shares two electrons with two adjacent iodine atoms by forming one 3c-4e bond, and meanwhile it gets one electron from cesium atom to keep the other two iodine atoms following Lewis octet rule 23 . On the other hand, Pauling 58 and Cartmell 59 interpreted the hypervalence phenomenon of this ion in terms of the trigonal-bipyramidal orbitals of the central atom (sp 3 d hybridization). The central iodine atom has 10 electrons in valence shell which supports the conventional hypervalence phenomenon. The Pmnb structure remains stable up to 7.8 GPa, where undergoes a complicated first-order phase transition to cubic Pm-3n structure with volume collapse of 7.19% (Fig. 1b). The optimized lattice parameters of Pm-3n phase at 10 GPa is a = 6.2865 Å. Atoms occupy the Wyckoff 2a (0, 0, 0) for cesium and 6d (0, 0.5, 0.75) for iodine. Surprisingly, the Scientific RepoRts | 5:14393 | DOi: 10.1038/srep14393 enthalpies of Pm-3n phase at least up to 200 GPa from convex hull (Fig. 1a) show that Pm-3n phase tends to decompose as the increasing pressure.
Comparing with orthorhombic Pmnb structure, a striking feature of this modification is that all the iodine atoms form endless linear chains (Fig. 2b). And these endless chains just locate on the surface of the Pm-3m Cs lattice. The lattice dynamics calculations with no imaginary phonon frequencies support the dynamic stability of Pm-3n structure over the pressure range studied here (Fig. 3a). Remarkly, the endless chain structure has rarely been found in inorganic compounds before. One previous work shows that the B atoms of Li 2 B can form kinked chains along the c axis under high pressure 38 . However, such kinked chains of B is clearly different from iodine chains which are thoroughly linear without any tortuosity. The similar crystal structures with Pnma and Pm-3n space groups have been reported for NaCl 3 31 . NaCl 3 is stable in the Pnma containing almost linear asymmetric Cl 3 groups at 20 to 48 GPa, and then transforms into a metallic Pm-3n structure. NaCl 3 and CsI 3 are clearly analogous compounds and even adopt the same structures, and Cl-Cl bonds in Pm-3n NaCl 3 similar with our predicted I-I bonds by forming extended monatomic chains running along the three mutually perpendicular axes 31 . In addition, the Cs-I bond length in CsI 3 is close to that in CsI as pressures change, indicating the forming of Cs-I ionic bond (Fig. 3b). And the I-I bond length in CsI 3 is 2.764 Å at 60 GPa, significantly shorter than the shortest I-I distances of 3.021 Å in solid I 2 (Fig. 3b), showing a stronger bonding character. The ELF of CsI 3 at 150 GPa shows that the strongest electron localization area are located between iodine and iodine atoms (Fig. 3c), suggesting covalent bond forms between the iodine atoms. As we well know, pressure-induced molecular dissociation of solid I 2 has been reported from theoretical or experimental studies, but iodine in Pm-3n phase can held together by strong chemical bonds at least until 200 GPa. We have calculated the charges using Bader's quantum theory of atoms in molecules (QTAIM) analysis 54 for  CsI 3 at high pressure. From Fig. 3d, the electrons devoted from cesium to iodine are gradually reduced as the increasing pressure, indicating a peculiar reverse electron donation from iodine to cesium, and thus naturally gives rise to suppress the strength of Cs-I bonds, which is responsible for tendency of the decomposition at higher pressure. Each iodine atom of CsI 3 gets two shared electrons from the nearest-neighbor iodine and averagely 0.3 electrons from cesium atom, and frankly the valence shell of iodine has 9.3 electrons with hypervalence character. Generally, several hypervalent compounds such as hypervalent P, S, I and Xe in PCl 5 , SF 6 , IF 7 and XeF 4 always have integral electrons in valence shell of 10, 12, 14 and 12, respectively 60 . For conventional hypervalent iodine compounds, only one central atom possesses hypervalence property which being surrounded by other several ligands. While in the current ionic CsI 3 compound, all the iodine atoms possess such character, which broadens conventional understanding of hypervalent iodine. Therefore, high pressure induces the attractive hypervalent phenomenon in CsI 3 iodine with specific endless linear chain structure.
At ambient pressure, the prototypical ionic crystal of CsI 3 is an insulator. Interestingly, CsI 3 becomes metallic after the first-order phase transition at 7.8 GPa. The calculated electronic band structures of Pm-3n phase at 10 GPa show it is metallic with several bands crossing Fermi level (Fig. 4a). Pressure induces CsI 3 to exhibit increasingly shorter interatomic distances, which is accompanied by an increase in the bandwidth, especially those near the Fermi-surface, thus leading to the 5p bands of iodine expand along conductive band direction (Fig. 4b). Furthermore, the calculated projected density of states (PDOS) of CsI 3 show that the 5d states of Cs have more electronic occupation as the pressure increasing (Fig. 4c,d).
It should be mentioned that the superconducting behaviors in CsI have been extensively explored through experimental measurement and theoretical calculations [12][13][14] . It is suggested that the formation of several electrons and hole Fermi-surface pockets in CsI is due to a dramatic increase of the electron donation from I − to Cs + , thus leading to more electrons to be involved in the electron-phonon coupling which is responsible for superconductivity and the larger EPC potential, thereby contributing to the increase in T C

12
. Therefore, it is intriguing to determine whether Pm-3n CsI 3 will possess superconducting property under high pressure. Figure 5 shows the phonon density of states (PHDOS) and Eliashberg spectral function α 2 F (ω) 61 for Pm-3n CsI 3 at 10 GPa. It is found that α 2 F (ω) contains two parts of which the low and high frequency where ω log is the logarithmic average frequency calculated directly from the phonon spectrum and μ * is the Coulomb pseudopotential. ω log is obtained to be 97.33 K at 10 GPa and 322.96 K at 150 GPa. Using a μ * of 0.1, the estimated T C is 0.15 K at 10 GPa but it disappears at 150 GPa. It is noteworthy that the estimated T C in  CsI 3 is noticeably larger than the value in CsI of 0.03 K, and the pressure is significantly lower than that of CsI (180 GPa).

Conclusions
In summary, we have systematically investigated compounds CsI n up to 200 GPa using an effective CALYPSO algorithm. Strikingly, CsI 3 with space group of Pm-3n is thermodynamic stability under high pressure. Within the cubic Pm-3n CsI 3 phase, iodine atoms arranging into several endless linear chains show an attractive hypervalence phenomenon under high pressure, which is in sharp contrast to the conventional understanding. We further discovered that Pm-3n CsI 3 is a metallic phase with several energy bands crossing Fermi-surface, and the pressure creates a peculiar reverse electron donation from iodine to cesium. The electron-phonon coupling calculations have proposed superconductive potential of the metallic Pm-3n CsI 3 at 10 GPa, which are analogous to the known CsI 12 . This work has wide implications for other inorganic compounds that likely harbor similar high-pressure behavior, and the significance for synthetic chemistry is highlighted.