Stabilization of H3 + in the high pressure crystalline structure of HnCl (n = 2–7)

Using the CALYPSO structure searching method, multicenter bonding H3 + ions were stabilized under high pressure in a hydrogen rich H–Cl system.


Introduction
The suggestion that the hydrides of main group elements at high pressure may be superconductors with high critical temperature has stimulated recent interest in the search for the possible existence of hydrogen-rich alloys by theoretical and experimental means. 1 The former has been greatly facilitated by the recent developments in practical strategies for the prediction of crystal structures. Although, the predicted hydrides have yet to be conrmed by experiment, the theoretical studies have revealed a myriad of novel structures for the high pressure hydrides and enriched the understanding of the nature of chemical bonding in the rarely explored high pressure regime.
The hydrides of group 1 and 2 elements formed from the reaction of the metal and hydrogen molecules have been the most studied. 2-6 Most of the structures and structural trends can be explained from the simple concept of electron transfer from the metal to the hydrogen due to the large electronegativity differences between the alkali and alkaline elements and hydrogen molecules. The predicted compounds display rich H species distinguished from the well-known H-ion in hydrides at traditional stoichiometric ratios. Perhaps one of the most exciting predictions is the emergence of symmetric and linear H 3 À at high pressures as observed in dense CsH 3 and BaH 6 . 7,8 Moreover, the formation pressures of these compounds of just a few tens of GPa are accessible by experiments. In comparison, the bonding pattern is quite different for group 14 and transition elements. For example, a Van der Waals solid with such molecular H 2 units was found experimentally in SiH 4 at low pressure. 9 At higher pressure, the atoms of group 14 elements tend to aggregate to form a 2D layered structure decorated with molecular like H 2 species as predicted for SiH 4 and SnH 4 . 10,11 In comparison, the high pressure chemistry of hydrogen with electron-rich group 17 halogens has not been investigated. In this paper, we present results on a study of the crystal structures and phase stabilities of hydrogen-rich HCl-

Computational details
The search for stable high pressure structures of the H n Cl system was based on global minimization of free energy surfaces using ab initio total energy calculations and the particle-swarm-optimization scheme as implemented in the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) code. 13,14 The performance and reliability of this method has been demonstrated on many known systems. An example is the success on the prediction 15-17 of an insulating orthorhombic (Aba2, Pearson symbol oC40) structure of Li and, more recently, two low-pressure monoclinic structures of Bi 2 Te 3 . In both cases, the predicted structures were later conrmed by experiments. 18,19 Structural searching was performed at 100, 200, and 300 GPa with a simulation cell consisting of 1-4 formula units. Ab initio electronic structure calculations and structural relaxations were carried out using density functional theory with the Perdew-Burke-Ernzerhof (PBE) exchangecorrelation 20 implemented in the Vienna ab initio Simulation Package (VASP) code. 21 The predicted stable structures were carefully optimized at a high level of accuracy. A plane wave energy cutoff of 1000 eV was employed. Large Monkhorst-Pack k point sampling grids 22 were used to ensure that all the enthalpy calculations were well converged to an accuracy of 1 meV per atom. The atomic charges were obtained from Bader topological analysis 23-25 with very large grids to ensure sufficient accuracy. We also performed additional calculations employing the DF-2 van der Waals (vdW) functional 26 to validate the results, in particular for the low pressure structures. Phonons were calculated with the supercell method 27 implemented in the PHONOPY program. 28 In essence, from nite displacements, the Hellmann-Feynman atomic forces computed at the optimized supercell by the VASP code were input to the PHONOPY code to construct the dynamical matrix. Diagonalization of the dynamical matrix gives the normal modes and their frequencies. Converged results were obtained with the use of a 2 Â 2 Â 1 supercell and 4 Â 4 Â 6 k-meshes for the Cc structure, and a 2 Â 2 Â 1 supercell and 4 Â 4 Â 6 k-meshes for the C2/c structure.

Results and discussion
Before embarking on a detailed discussion of the structures of the predicted high pressure H n Cl polymers, the relative energetics of the H-Cl system with H-rich stoichiometry from 100 to 300 GPa are summarized in the convex hull plot shown in Fig. 1. The enthalpies of formation were evaluated as the difference in the enthalpy of the predicted H n Cl structure with solid HCl and H 2 at the selected pressures. Since hydrogen has a small atomic mass, the zero point energy (ZPE) may be important. To investigate the vibrational effects on the phase stability, ZPEs for H 2 Cl and H 5 Cl were estimated at 100-300 GPa from the corresponding phonon spectra using the quasi-harmonic approximation. 29 It is found that the ZPEs are quite small and the inclusion of ZPEs in the phase diagram only resulted in a slight shi in the formation pressures but the stability of both phases remains unaltered. Structures lying on the convex hull are thermodynamically stable or metastable and, in principle, can be synthesized. Fig. 1 reveals that only two HCl-H 2 complexes, H 2 Cl and H 5 Cl are stable at 100 GPa. At this pressure H 2 Cl has the most negative enthalpy of formation. With increasing pressure, the stability of H 5 Cl relative to H 2 Cl increases and becomes the most stable phase at 300 GPa. vdW effects may play an important role in the stabilization of a molecular solid. We have thus performed additional calculations on the H-Cl system with the vdW-DF2 method. 26 The results show that the differences between calculations with and without vdW corrections on the formation enthalpies of the structures considered in Fig. 1 are small. The formation pressures were found to change slightly. For example, the stabilized pressure of H 2 Cl increased from 21.2 to 21.3 GPa, while for H 5 Cl it increased from 50 to 60 GPa. Otherwise, the energetic order remains the same. Now we examine the development of the high pressure crystal structures in H n Cl (n ¼ 2-7). The starting point is the crystal structure of HCl under ambient pressure. At low temperature, X-ray and neutron diffraction show HCl crystallized in an orthorhombic structure (Bb2 1 m). 30 In the crystal, HCl molecules are linked via the H atoms forming zigzag chains running parallel to the crystallographic b axis. The nearest neighbour Cl-H and second nearest neighbour Cl/H distances are 1.25Å and 2.44Å, respectively. The Cl/Cl separation is 3.88 A and the H-Cl/H valence angle is 93.6 . The predicted crystalline phase of H 2 Cl at 100 GPa has a C2/c space group and the structure is shown in Fig. 2. The crystal is formed from HCl chains interposed with H 2 molecules. In this case, the H in the HCl chain is midway between the two Cl atoms with an H-Cl  distance of 1.45Å. The H-Cl-H angle has opened to 97.9 and the Cl/Cl separation is shortened to 2.90Å. The H 2 units in the structure all have a H-H distance of 0.74Å, which is almost identical to that of the isolated molecule. The Bader charges for the H in the chain and Cl atoms are +0.44 and À0.35, respectively and 0.0 for the H atoms in the H 2 units. The closest contact between a Cl atom and the H 2 molecule is 1.98Å. The crystal structure of H 2 Cl at 300 GPa differs little from that at 100 GPa. The H atoms in the H-Cl chains are still situated at the middle of the two neighbouring Cl atoms with a H-Cl distance of 1.35Å. The H-Cl-H angle is 95.5 and the shortest separation between two Cl atoms has reduced further to 2.69Å. The H-H bond length in the H 2 unit is 0.73Å. The closest H 2 /Cl distance is. 1.70Å. Compression has a signicant effect on the interatomic distances of the H-Cl chains but does not alter fundamentally the underlying bonding pattern. A longer H-Cl distance in the chain suggests increased ionicity of the Cl-H bonds.
Although H 3 Cl and H 4 Cl are only metastable, it is instructive to examine the evolution of the crystal structure with increasing H 2 concentration. The structures of H 3 Cl at 100 and 300 GPa are shown in Fig. 3. Both are composed of zigzag H-Cl chains. Like H 2 Cl, the H atom is equidistant from the two nearest Cl atom with H-Cl bond distances of 1.44Å at 100 GPa and 1.43Å at 300 GPa. The most signicant difference between the low and high pressure structures is that the Cl-H-Cl angle is almost linear at 100 GPa but bends to 135 at 300 GPa. At 300 GPa, the closest contact between the H 2 and the H in the chain is 1.27Å. However, in both cases, the H-H distance of the H 2 molecule remains 0.73Å. The structure of H 4 Cl at 100 GPa differs dramatically from all the structures within this series of compounds. Instead of H-Cl chains, the structure is composed of isolated HCl and H 2 molecules. The H-Cl distance is 1.38Å and the H-H bond length is 0.74Å. For comparison, the H-Cl bond of a free molecule is 1.276Å. Therefore, the distance in the solid state at 100 GPa is slightly longer. The structure of H 4 Cl at 300 GPa again is different from that at 100 GPa. The basic building units are isolated Cl atoms, H 2 molecules with H-H distance of 0.74Å and a novel 2-D layer of slightly puckered fused hexagonal rings formed from 3 HCl units with additional H atoms attached to the Cl atoms. Each H atom in the ring is bonded to three Cl atoms. In addition, each Cl is bonded to an extra H atom which is not coordinated to other species in the crystal. The H-Cl distances in the fused ring are 1.59Å and the terminal H-Cl is substantially shorter at 1.49Å. Interestingly, the terminal H-Cl-H (ring) angles are 77 and the in-plane H-Cl-H and Cl-H-Cl angles are between 114-115 .
An interesting structure was observed in H 5 Cl at 100 GPa. Although chains formed from Cl and H atoms are still clearly visible, the detailed construction of the chain is very different. In H 5 Cl, instead of placing one H atom midway between the two nearest neighbour Cl atoms, it is replaced by an H 3 unit. The H 3 is a distorted isosceles triangle and can be described as a loosely bound unit of an H atom and an elongated H 2 with an apical angle of 63.8 . The apical H atom is linked to the two nearest Cl atoms in the chain with H-Cl distances of 1.47Å. The distances from the apical H atom to the two H forming the H 2 are 1.01Å and 0.97Å, respectively and the intermolecular H-H distance is 0.81Å. The remaining H 2 units in the structure have H-H distances of 0.74Å. Moreover, the shortest distance from these H 2 to the H 3 is 1.36Å and, therefore, may be considered as noninteracting molecules.
Compression of H 5 Cl to 300 GPa does not change the space group symmetry. The chain pattern with interpose H 3 units is still maintained, but the local H/H interactions have changed dramatically. The H 3 unit now approaches an equilateral triangle. The H-H lengths are 0.87, 0.87 and 0.88Å with bond angles 59.7, 59.7 and 60.5 . The Cl-H distance has elongated from 1.47Å at 100 GPa to 1.60Å! The large lengthening of the Cl-H clearly suggests a substantial change in the Cl-H bonds. More signicantly, the isolated H 2 molecules are now pushed towards the H 3 units and interact with one of the H atoms forming almost two H/H bonds at 1.15Å. Concomitantly, the distance in H 2 is lengthened to 0.76Å. The Bader charges for the H atom in the H 3 and H 2 units and for the Cl atom are +0.16 and +0.014 and À0.48 respectively. In comparison to H 2 Cl the ionicity on both the H and Cl atoms have increased substantially. The plot of the electron localization function (ELF) shown in Fig. 4 shows localized spin paired electron density within the H 3 ring and in the H 2 molecule (ELF over 0.8). Weak pairing is also observed between one of the H in the H 3 ring with the two H atoms of H 2 .   The nature of the bonding in the group 17 hydrides at high pressure is different from group 1 and 2 and group 14 hydrides. One observed a gradual shi in the chemical interaction from electron transfer in electropositive group 1 and 3 compounds to covalent bonding group 14 and nally the ionic bonding in group 17 elements. Although this study was focused on Cl, we anticipate a similar bonding mechanism is applicable to other halogen hydrides.

Conclusions
We have investigated the phase stability of the HCl-H 2 system at high pressure using the PSO algorithm in combination with ab initio density functional based electronic calculations. Between 100-300 GPa, two stable phases with the H 5 Cl and H 2 Cl stoichiometries were found. The basic structure of the high pressure phases is similar to the low temperature ambient pressure structure of HCl. H 2 Cl consists of zigzag H-Cl chains and noninteracting H 2 molecules. The most usual and informative nding is that while the chain like structure is preserved in H 5 Cl, the H atoms connecting the Cl in the chains are replaced by units consisting of weakly interacting H 2 /H 3 . The H 3 + is positively charged and stabilized from the formation of multicenter bonds. The similarity in the local structure, vibrational frequencies and electronic charge compel us to relate the unit to the isolated H 3 + molecule. It is also found that the effect of pressure on the electronic structure of group 17 hydrides is very different from the more electropositive group 1 and 2 elements: the electron-rich Cl atom and anion do not transfer their electrons into interstitial space of the crystal under very high compression. In fact electrons are removed from the H atoms leading to the formation of cationic clusters that benet from multicenter bonding.