Novel Superconducting Phases of HCl and HBr under High Pressure

Article pubs.acs.org/JPCC

Novel Superconducting Phases of HCl and HBr under High Pressure: An Ab Initio Study Changbo Chen,* Ying Xu, Xiuping Sun, and Sihan Wang School of Science, Changchun University of Science and Technology, Changchun 130022, P. R. China ABSTRACT: The novel superconducting C2/m phases of HCl and HBr were predicted using the developed particle swarm optimization algorithm for crystal structure prediction. The calculated results showed that the phase transition from P1 to C2/m phases occurred at 250 and 120 GPa for HCl and HBr, respectively. Hydrogen bond symmetrization was observed in the newly predicted C2/m phase. No imaginary phonon frequencies in the whole Brillouin zone indicated that the C2/m phases of HCl and HBr were dynamically stable. In addition, the C2/m phase of HBr was the most stable structure, which rejected the earlier hypotheses of elemental decomposition into bromine and hydrogen. Perturbative linear response calculations predicted that the critical temperature Tc of the C2/m phase of HCl could reach 20 K at 250 GPa.

I. INTRODUCTION Over the past decades, among the simplest diatomic molecules forming hydrogen bonds in solid states, hydrogen chloride (HCl) and hydrogen bromide (HBr) have attracted a great deal of attention.1−5 Systematic studies on these compounds can greatly help in understanding the intriguing nature of hydrogen bonds. High pressure can effectively modify interatomic interactions and revise the bonding properties of materials.6−9 Therefore, the variations in hydrogen bonds under high pressure play an important role in phase transition. Pressureinduced hydrogen bond symmetrization in hydrogen halides (HBr, HCl, and DCl) has also been observed from Raman and infrared measurements,10−13 which is an important highpressure phenomenon. In addition, hydrogen compounds are verified to metallize at lower pressures than pure hydrogen, and they are expected to be high-temperature superconductors.14−21 The aforementioned interesting results prompted investigations on the metallization of HCl and HBr under high pressure, which might help in understanding metallic hydrogen. At high temperature, HCl and HBr have weak hydrogen bonds, adopting the orientationally disordered molecular phases (I and II).22−24 However, at very low temperature, HCl and HBr are proposed to be in an ordered orthorhombic phase III (space group: Cmc21), which shares the same structure with hydrogen fluoride.24,25 At room temperature, pressure-induced phase transitions from I to III for HCl and HBr were observed experimentally.10−12,26 With increasing pressure, phase III was suggested to further transform into phase IV (space group: Cmcm) at 51 and 39 GPa for HCl12 and HBr,10 respectively. Hydrogen bond symmetrization occurs in phase IV. Surprisingly, phase IV of HBr is unstable and decomposes, as verified by experiments.10,12 In addition, Zhang et al.27 investigated the structures at the pressure range of 0− 100 GPa by first principles. A post-Cmcm phase was uncovered as the P-1 phase with symmetric hydrogen bonds at 108 and 59 © XXXX American Chemical Society

GPa for HCl and HBr, respectively. The dissociation of HBr occurs at rather high pressures (above 120 GPa) with the formation of monatomic Br and solid H2. Another post-Cmcm phase was revealed by Duan et al.,28 which is considered to be the P21/m phase with symmetric hydrogen bonds above 233 GPa for HCl and at the range of 134−196 GPa for HBr; HBr is predicted to decompose into Br2 and H2 above 196 GPa. As described above, the stability of the P-1 and P21/m phases for HCl and HBr under high pressure remains controversial. In addition, the existence of other stable structures under high pressure remains unclear. Therefore, these issues encouraged us to search for new high-pressure structures and study the properties of the new phases. In this paper, we performed a first-principles study to predict high-pressure structures using the developed particle swarm optimization algorithm. New C2/m phases with hydrogen bond symmetrization for HCl and HBr were predicted at 250 and 120 GPa, respectively. Surprisingly, the C2/m phase of HBr could not decompose into bromine and hydrogen, which rejected the previous work. Moreover, perturbative linear response calculations predicted that the critical temperature Tc of the C2/m phase of HCl could reach 20 K at 250 GPa.

II. COMPUTATIONAL METHOD We carried out high-pressure structure searches for HCl and HBr based on variable-cell PSO simulations with the CALYPSO code.29,30 The efficiency of this method has been demonstrated on many systems.31−35 Each structure obtained was fully relaxed to the minimum energy at selected pressures with the Vienna ab initio simulation package.36 During Received: February 17, 2015 Revised: June 30, 2015

A

DOI: 10.1021/acs.jpcc.5b01653 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C calculations, the projector-augmented wave37 method within the generalized gradient approximation (GGA) of Perdew− Burke−Ernzerhof (PBE)38 was adopted with the choices of 3s23p5 and 1s1 valence electrons for Cl (Br) and H atoms, respectively. To obtain reliable results, accurate convergence tests were performed. We chose a cutoff energy of 1000 eV for wave function expansion into plane waves and a k-mesh of 0.03 × 2π Å−1 within the Monkhorst−Pack scheme39 for sampling the Brillouin zone to ensure that the error bars of total energies were less than 1 meV/atom. Moreover, in the subsequent geometry optimizations, all forces on atoms were converged to less than 1 meV/Å, and the total stress tensor was reduced to the order of 0.001 GPa. The convergence tests have been described elsewhere.40−42 Phonon dispersion was performed, and the electron−phonon coupling (EPC) parameter λ of HCl and HBr was measured using density functional perturbation theory43,44 as implemented in the QUANTUM-ESPRESSO package.45 The plane-wave pseudopotential method within the GGA of PBE38 was adopted, and the electronic wave functions and electron density were expanded by the plane-wave basis sets with a cutoff energy of 60 Ry. Q-point mesh (4 × 4 × 2) was used for EPC calculations for the C2/m phase of HCl and HBr. Moreover, at each Q point, the EPC matrices were calculated using a 4 × 4 × 2 Q-point mesh.

Table 1. Predicted Lattice Constants and Atomic Coordinates Based on the Conventional Cell of the Newly Predicted Structures at Selected Pressures pressure (GPa) 250 (HCl)

space group C2/m

P4/nmm 120 (HBr)

C2/m

P4/nmm

lattice parameter (Å)

atomic coordinates (fractional)

a = 3.923, b = 2.763 c = 6.098 a = 2.870, c = 2.409

Cl 4i (0.5328, 0, 0.2299)

a = 4.506, b = 3.130 c = 6.981 a = 3.273, c = 2.776

H 4i (0.7905, 0, 0.6258) Cl 2c (0.5, 0, 0.7967) H 2b (0, 0, 0.5) Br 4i (0.5351, 0, 0.2331) H 4i (0.7851, 0, 0.6210) Br 2c (0.5, 0, 0.7914) H 2b (0, 0, 0.5)

calculated at finite temperature. In the present work, all total energy calculations of the competing structures for HCl and HBr were performed at zero temperature. Therefore, the Gibbs free energy becomes the enthalpy, H = E0 + PV, where E0 is the internal energy of the system. The calculated enthalpy difference (ΔH) (relative to Cmc21 phase) as a function of the pressure for HCl and HBr is shown in Figures 2(a) and

III. RESULTS AND DISCUSSION To probe high-pressure structures, a structure search was performed for HCl and HBr based on variable-cell PSO simulations with the CALYPSO code. Simulated cells with up to 16 atoms were allowed at the pressure range of 0−300 and 0−200 GPa for HCl and HBr, respectively. Five energetically competing structures for HCl and HBr were selected, which had the space groups Cmc21 (4 f.u./cell), Cmcm (4 f.u./cell), P1 (4 f.u./cell), P4/nmm (2 f.u./cell), and C2/m (4 f.u./cell), as depicted in Figure 1. Structural information on HCl and HBr

Figure 2. (a, b) Enthalpy curves relative to the Cmc21 phase of HCl and HBr as a function of pressure, respectively. (c) Formation enthalpy curves of HBr as a function of pressure.

2(b). The Cmc21 phase had the lowest enthalpy below 50 and 40 GPa for HCl and HBr, respectively. With increasing pressure, although the enthalpy between the Cmc21 and Cmcm phases was indistinguishable, the phase transition from the Cmc21 to Cmcm phases occurred with hydrogen bond symmetrization, which has been verified by previous studies.10,12 The Cmcm structure transformed into the P-1 structure for HCl and HBr at 104 and 58 GPa, respectively, which was consistent with the results of Zhang et al.27 For HCl, the enthalpy difference between the C2/m and P4/nmm phases was so small above 250 GPa that it became negligible. However, for HBr, the C2/m phase was the most stable above 120 GPa. In addition, experimental and theoretical studies have indicated that HBr decomposes under high pressure. To further analyze the stability of HBr under high pressure, the formation enthalpy of the C2/m phase of HBr was calculated as a function of pressure, as shown in Figure 2(c). The formation enthalpy was calculated by adopting corresponding structures to pressures for Br246 and H2.47 The C2/m phase of HBr could not decompose until 200 GPa. Zero-point energy (ZPE) usually plays a non-negligible role in the total energy of hydrogen-rich materials, and the ZPE of the structures concerned was evaluated using the quasi-harmonic model.48 The calculated ZPE of the C2/m phase of HBr was 0.272 eV/f.u. at 200 GPa. For Br2 and H2, the ZPEs were 0.053 and 0.293 eV/atom, respectively. Considering ZPE adjustment, the enthalpy of

Figure 1. Predicted structures of HCl and HBr under high pressure. The green and gray balls represent Cl (Br) and H atoms, respectively.

predicted at the selected pressures is listed in Table 1. The predicted Cmc21, Cmcm, and P-1 phases have been observed by experimental10−12,26 and theoretical studies.27 Meanwhile, the P21/m phase obtained by Duan et al.28 was also considered in our calculations. The P4/nmm and C2/m structures were predicted at 250 and 150 GPa for HCl and HBr, respectively. Hydrogen atoms were located midway between the neighboring Cl or Br atoms, as shown in Figures 1(e) and 1(f). As mentioned above, hydrogen bond symmetrization could occur in the high-pressure structures predicted for HCl and HBr, which might be indispensable for the stable phases of HCl and HBr under high pressure. To check the stability of the structures predicted from a thermodynamic perspective, the Gibbs free energy must be B

DOI: 10.1021/acs.jpcc.5b01653 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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Figure 3. (a−d) Phonon dispersion curves and density of states of C2/m for HCl and HBr at 250 and 120 GPa, respectively. (e) Phonon dispersion curves of the P4/nmm phase of HCl at 250 GPa.

formation with respect to Br2 and H2 was −0.171 eV/f.u. The trend of undecomposition of the C2/m phase of HBr was influenced by the ZPE, which rejected the earlier hypotheses of elemental decomposition into bromine and hydrogen.10,12,27,28 The phonon spectra of the crystal, which give information on dynamic stability, should be calculated. The phonon dispersion curves of the C2/m phase of HCl and HBr are shown in Figures 3(a) and 3(c). No imaginary phonon frequencies were observed, which indicated that the C2/m phase of HCl and HBr was dynamically stable. The phonon densities of states (DOS) of the C2/m phases of HCl and HBr depicted in Figures 3(b) and 3(d) show that low-energy phonon modes were associated with the Cl or Br atom, and the phonon modes with high frequencies mainly corresponded to the H atom. Moreover, the phonon frequencies of the C2/m phase of HCl and HBr increased with pressure up to 300 and 200 GPa, respectively. However, imaginary phonon frequencies were observed in the phonon dispersion curves of the P4/nmm phase of HCl (Figure 3(e)), which indicated that the P4/nmm phase of HCl was not dynamically stable. Therefore, above 250 GPa, the C2/m phase of HCl was the most stable. To explore the electronic properties of the C2/m phase of HCl and HBr, the electronic band structure and projected DOS were calculated at 250 and 120 GPa for HCl and HBr, respectively (Figure 4). The large dispersion bands crossed the Fermi level for HCl (Br), revealing its metallic character. Moreover, a flat band in the vicinity of EF close to the Γ point was found. The simultaneous occurrence of flat and steep bands

near the Fermi level has been suggested as a favorable condition for enhancing electron pairing, which is essential for superconductivity.49 The C2/m phase of HCl or HBr exhibited metallic behavior, which mainly came from the Cl-s,p or Br-s,p states and H-s states, as shown in the projected DOS at the Fermi level depicted in Figures 4(b) and 4(d). Meanwhile, strong hybridization between Br or Cl and H orbitals was found, which indicated the formation of Cl (Br)−H bonds. The superconductivity of hydrogen compounds has always been focused on because of its scientific significance, and it has been verified in H2S,50 (H2S)2H2,51 and AlH3H2.52 To study the superconductivity of C2/m in HCl and HBr, the EPC parameter λ, logarithmic average phonon frequency ωlog, and Eliashberg function α2F(ω) were obtained using density functional perturbation theory. The calculated λ of HCl was 0.56, and the phonon frequency logarithmic average ωlog calculated directly from the phonon spectrum was 1094 K at 250 GPa. By contrast, the resulting λ of HBr was 0.27, and the phonon frequency logarithmic average ωlog was 834 K at 120 GPa. The theoretical spectral function α2F(ω) and integrated λ as a function of frequency are depicted in Figure 5. These results showed that the Cl translational vibrations at low frequency contributed 52% to EPC λ, whereas the contribution from the high-frequency H made up the remaining 48%. For HBr, the low-frequency Br translational vibrations and phonon modes at high frequency corresponding to H atoms

Figure 5. (a, b) Eliashberg phonon spectral function α2F(ω) and the electron phonon integral λ(ω) of C2/m for HCl and HBr at 250 and 120 GPa, respectively.

Figure 4. (a−d) Electronic band structure and projected density of states of C2/m for HCl and HBr at 250 and 120 GPa, respectively. C

DOI: 10.1021/acs.jpcc.5b01653 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C contributed 30% and 70% to EPC λ, respectively. The critical temperature Tc was estimated from the Allen−Dynes modified McMillan equation,53 Tc = (ωlog/1.2)exp[(1.04(1 + λ))/(λ − μ*(1 + 0.62λ))]. This equation has been found to be highly accurate for materials with λ < 1.5. μ* is the Coulomb pseudopotential, which can be best chosen in the range of 0.1− 0.13 by Ashcroft.54 On the basis of our calculations, the value of μ* chosen was 0.1−0.13. Tc for the C2/m phase of HCl at 250 GPa could reach 13−20 K. Using the same method, the calculated Tc for the C2/m phase of HBr at 120 GPa was in the range of 0.12 to 9.7 × 10−3 K. The higher Tc for the C2/m phase of HCl may be attributed to stronger EPC λ.

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IV. CONCLUSION In summary, we performed a first-principles study to predict high-pressure structures using the developed particle swarm optimization algorithm. Hydrogen bond symmetrization was found in the high-pressure structures predicted for HCl and HBr, which might be indispensable for the stable phases of HCl and HBr under high pressure. The C2/m phase with hydrogen bond symmetrization for HCl and HBr was the most stable at 250 and 120 GPa, respectively. Meanwhile, the C2/m phase of HBr was the most stable, which rejected the earlier hypotheses of elemental decomposition into bromine and hydrogen. The results of the electronic band structure and partial DOS calculations suggested that the C2/m phase was metallic, whereas perturbative linear response calculations predicted that Tc of the C2/m phase of HCl could reach 20 K at 250 GPa.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (No 11104019). Parts of calculations were performed in the Scientic Computation and Numerical Simulation Center of Changchun University of Science and Technology.

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REFERENCES

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