Emergence of novel hydrogen chlorides under high pressure

HCl, a 'textbook' example of a polar covalent molecule, is a well-known compound of hydrogen and chlorine. Inspired by the discovery of unexpected stable stoichiometries of sodium chlorides, we performed systematic searches for all stable compounds in the H-Cl system from ambient pressure to higher pressures up to 500 GPa using variable-composition ab initio evolutionary algorithm USPEX. We found several compounds that are stable under pressure, i.e. HCl, H$_2$Cl, H$_3$Cl, H$_5$Cl and H$_4$Cl$_7$, which display a rich variety of chemical bonding types. At ambient pressure, H$_2$, Cl$_2$ and HCl molecular crystals are formed by weak intermolecular van der Waals interactions and adjacent HCl molecules connect with each other to form asymmetric zigzag chains, which become symmetric under high pressure. In hydrogen-rich chlorides, H$_2$ and HCl react to form the thermodynamically stable H$_3$Cl crystalline compound in which molecular cyclic H$_3^+$ cations are stabilised by the Cl$^-$ sublattice. Increasing the amount of hydrogen leads to stable solid-state H$_5$Cl, in which H$_2$ formally combines with H$_3^+$ to form H$_5^+$ cations. Additionally, chlorine-based Kagom\'e layers are formed with intercalated zigzag HCl chains in chlorine-rich hydrides. These discoveries help to understand how varied bonding features can co-exist and evolve in one compound under extreme conditions.


Introduction
In 1935, Wigner 1 proposed an insulator-to-metal transition in solid hydrogen under pressure. The dissociation, rebonding and polymeriztion, and eventual metalization of molecular systems under high pressure provide conditions for producing novel physical and chemical phenomena. Chemical bonding is the key to understanding the structure and properties of materials, and impacts a broad range of fields including physics, chemistry, biology, materials and earth sciences. It is known that very unusual and unexpected compounds can become stable under pressure, and the chemical nature of many of these compounds are still not understood 2,3 . For example, under pressure, the simple Na-Cl system contains stable compounds such as Na 3 Cl, Na 2 Cl, Na 3 Cl 2 , NaCl 3 and NaCl 7 , as well as 'normal' NaCl 4

. While
NaCl is a 'textbook' example of an ionic crystal, HCl is an archetypal polar covalent molecule. One can expect large differences between the Na-Cl and H-Cl systems; however, we can imagine that the HCl system is even more diverse due to its increased variety of intermolecular and intramolecular interactions. In addition, hydrogen adds extra excitement: the high-pressure metallic phase of hydrogen has been predicted to possess a nearly room-temperature superconductivity (T c ~240K) 5 , and while superconducting metallic hydrogen remains elusive, recent calculations using USPEX predicted the high-pressure stability of the compound H 3 S 6 with a T c reaching 190-200 K; this prediction was subsequently verified experimentally 7 .
It has been suggested 8 that alloying hydrogen with other elements can greatly reduce the pressure required for stability of the superconducting state, and one may think not of only metal hydrides, but also of compounds with more electronegative atoms, such as the aforementioned H 3 S, or the H-Cl compounds studied here. Several H-Cl compounds were predicted in a recent work, but we still found some results [9][10][11] are in contradiction with our findings. Besides the structure prediction, the bonding features and superconductivity were not fully explored. Here, we attempt to give an exhaustive picture of the H-Cl system under pressure.

Methods
Searches for stable compounds in the H-Cl system from ambient pressure up to 500 GPa were performed using the variable-composition ab initio evolutionary algorithm USPEX 12,13 . In these variable-composition searches, all H-Cl compositions were allowed, under the constraint that the total number of atoms in the unit cell should not be greater than 30 atoms. The first generation contained 80 candidate structures, while all subsequent generations contained 60 structures. In each new generation, 40% of the structures were produced by heredity, 20% by softmutation, 20% by transmutation and 20% were produced randomly. Local geometry relaxations were performed using density-functional calculations with the help of the VASP code 14 . These calculations are based on the Perdew-Burke-Ernzerhof (PBE) functional 15 , which ascribes to the generalised gradient approximation (GGA) level of theory. We used the all-electron projector-augmented wave method (PAW) 16 , with an outermost core radii of 1.1a.u. for the H atom and 1.9 a.u. for the Cl atom ([Ne] core). The plane-wave kinetic-energy cutoff was set to 900 eV, and uniform -centred k-meshes with a reciprocal space resolution of 2π × 0.06 Å −1 were used for sampling the Brillouin zone. These settings enabled excellent convergence of the energy differences, stress tensors, and structural parameters. Denser k-point meshes in reciprocal space with a resolution of 2π × 0.03 Å −1 were used for further calculations.
All compounds presented here were confirmed to be dynamically stable at their predicted pressure ranges of stability (SM, Fig. S2). Phonon calculations were performed using density-functional perturbation theory (DFPT) 17 . Detailed structural information is given in Supplementary Materials (SM ,   Table S1).
All molecular species were optimised at different levels of theory (B3PW91, PBEPBE, MP2, CCSD(T)). A triple-zeta basis set was employed for all atoms, which was increased using both polarized and diffuse functions, aug-cc-pVTZ 18,19 . For each structure, the analytic Hessian was calculated to obtain the vibrational frequencies and determine the nature of the stationary point (local minimum). Calculations were performed using the Gaussian 09 computational programs 20 . As the results followed the same trend, we present here only the electrostatic potential results based on the B3PW91 functional. The surface potentials, V S (r), were obtained using the Wave Function Analysis-Surface Analysis Suite (WFA) 21 . Figure 1 shows the convex hulls of the H-Cl system in the pressure range 0-500 GPa. Elemental hydrogen and chlorine in their most stable forms, i.e., the P6 3 /m, C2/c, Cmca-12, Cmca and I4 1 /amd structures for H 2 22 and Cmca, Fmm2-28, Immm and FCC structures for chlorine 23 , were adopted as the reference states in their pressure ranges of their stability. The convex hull is a set of thermodynamically stable states, which are stable with respect to disproportion into other phases or pure elements. Any structure, for which the enthalpy of formation lies on the convex hull, is considered to be thermodynamically stable and -in principle -can be synthesised from any isochemical mixture.

Results and Discussion
Besides reproducing the well-known HCl phase (space group Cmc2 1 ), we also found the stable stoichiometries 2:1, 3:1, 5:1 and 4:7. After analysing their crystal structures, we identified a rich variety of structures with symmetric and asymmetric zigzag HCl chains, host-guest inclusion compounds, chlorine Kagomé layers, H 3 + and H 5 + units, interpenetrating graphene-like chlorine nets, and other structures, which will be illustrated in the following text.
The pressure-composition phase diagram of the H-Cl system is shown in Fig. 2. We find that HCl remains a stable compound in the pressure ranges 0-160 GPa and >251 GPa, but decomposes into H 2 Cl and H 4 Cl 7 at the pressures between these ranges. Similar reentrant behaviour is also observed for H 3 Cl.

HCl: A brief revisit of the pressure-induced symmetrisation of the zigzag chains
At ambient conditions, HCl adopts the orthorhombic Cmc2 1 structure (Fig. 3a) and typical of hydrogen bond.
The structure of the orthorhombic Cmcm phase is shown in Fig. 3b. In this condensed phase, HCl-HCl contacts have an L-shaped geometry, with the H-Cl bond axis of one molecule perpendicular to the other one. A similar herringbone pattern is also observed in solid X 2 (X, halogen) 25,26 . Fig. 4a illustrates why the HCl chain possesses a zigzag shape (L-shaped geometry) rather than a linear or all-trans one.
Electrostatic arguments can be used to find the answer. The computed electrostatic potential V S (r) on the 0.001 a.u. surface of HCl is displayed in Fig. 4b, computed at the B3PW91/aug-cc-pVTZ level using the WFA surface analysis suite [18][19][20][21]  When pressure increases, the difference between the alternating short and long H-Cl separations becomes smaller. Eventually, this difference disappears and symmetric hydrogen bonds appearsymmetric HCl-based zigzag chains are encountered in several phases at different compositions.
Hydrogen bond symmetrisation in HCl under high pressure is well studied, both experimentally and theoretically 11,29 . In HCl, symmetrisation occurs experimentally at 51 GPa at T = 300 K, which can be attributed to softening of the symmetric stretch A 1 mode. A Cmc2 1 →Cmcm transformation is predicted to occur at ~40 GPa, then a Cmcm→P2 1 /m transition occurs above 233 GPa 11 . The Cmc2 1 →Cmcm structural transformation is calculated to occur at about 35 GPa, in good agreement with Duan et al. 28 .
Recall that HCl experimentally adopts the disordered phase I at room temperature while it requires 19 GPa to transform into phase III (Cmc2 1 ) 30 .
In Our variable-composition search showed that above 160 GPa and below 251 GPa, the 1:1 stoichiometry is unstable and HCl will decompose into a mixture of H 2 Cl and H 4 Cl 7 . This founding is contradict to others research 10 . The tetragonal P4/nmm-HCl possesses a layered mackinawite-type structure, and becomes stable at pressures above 251 GPa. In this structure, adjacent HCl-based zigzag chains get close to form 2D-layers (Fig. 3c). The shortest interlayer Cl-Cl distance is 2.  (Fig. 3d). Previous reported results proposed the following transition sequence Cmc2 1 ->(35 GPa) Cmcm ->(108 GPa) P-1 from ab initio evolutionary search 11 . This triclinic P-1 structure is always higher in energy than our predicted thermodynamically stable Cmcm (39-160 GPa) and P4/nmm-HCl (251-500 GPa) structures.

H 2 Cl: HCl zigzag chains + H 2 units
The hydrogen-rich compound H 2 Cl crystallizes in the monoclinic structure C2/c (Fig. 5a). This

H 3 Cl
The first phase of the hydrogen-rich compound H 3 Cl phase crystallizes in the monoclinic C2/c structure (Fig. 6a) At 59 GPa, the monoclinic C2/c phase transforms into an orthorhombic structure with the space group P2 1 2 1 2 1 (Fig. 6b)  HCl and H 2 is calculated as -0.07 eV/atom at 100 GPa.

H 5 Cl: the existence of H 3 + units
At 106 GPa, the hydrogen-rich compound H 5 Cl becomes stable. Its lowest-pressure structure Pc ( in the Pc phase (0.748 Å) or the experimental free gas phase H 2 distance (0.74 Å). Such elongation is expected for an electron-deficient system (Fig. 7c). The molecular orbital diagram for symmetric (D 3h ) H 3 + is reproduced in Fig. 7d four-electron bonding scheme (5c-4e) is assigned: such a bonding mode has previously been observed in protonated hydrogen-based clusters 37 , the global-minimum structure of which is, however, non-planar. The calculated DOS of H 5 Cl (Fig. S2) shows that this compound is an insulator upto 479 GPa. Obviously, H-rich system is not easily metallised compare to Cl-rich system.

H 4 Cl 7 : chlorine-based Kagomé layers intercalated with zigzag HCl chains
Besides hydrogen-rich H-Cl compounds, we also uncovered a chlorine-rich compounds H 4 Cl 7 , which has never been reported before. C2/m-H 4 Cl 7 was found to be stable in the pressure range 90-278 GPa, and it transforms to another monoclinic structure with the space group C2 at 278 GPa (Fig. 2). In the low-pressure C2/m phase, three different networks can be found. The first is two (HCl) 2  electrons may be formally assigned to each chlorine centra, thus Cl is the AX 4 E 3/2 type, a rectangular planar AX 4 unit (one electron less than that of XeF 4 ) 3 . The zigzag chains are oriented in such a way that the chlorine atoms are located in the six-and three-membered ring-based channels made by the stacked Kagomé layers (Fig. 8a).