Insights into the high-pressure behavior of solid bromine from hybrid density functional theory calculations

Understanding the properties of molecular solids at high pressure is a key element in the development of new solid-state theories. However, the most commonly used generalized gradient approximation of the density functional theory (DFT) often fails to describe the behavior of these systems correctly at high pressure. Here we utilize the hybrid DFT approach to model the properties of elemental bromine at high pressure. The calculations reproduce in very good agreement with experimentation the properties of molecular phase I ($Cmca$ symmetry) and its pressure-induced transition into nonmolecular phase II $\left(Immm\right)$. The experimentally yet unobserved transition into phase III $\left(I4/mmm\right)$ is predicted to occur at 128 GPa, followed by subsequent formation of an fcc lattice at 188 GPa. Analysis of the structure and electronic properties of the modeled phases indicates that the molecular $Cmca$ phase becomes metallic just at the borderline of its stability, and that both the $Immm$ and $I4/mmm$ phases are metallic and quasi–two-dimensional. Finally, we show that the incommensurate phases of bromine postulated from experimentation are transient species that can be viewed as intermediates in the dissociation process occurring at the boundary of the transition from phase I to phase II.

Figure 1

(a) Crystal structure of solid bromine in the $Cmca$ molecular structure (phase I). (b) Difference between calculated and experimental geometry of the $Cmca$ phase at 1 atm.

Figure 2

Pressure dependence of the enthalpies of high-pressure phases of bromine relative to the $I4/mmm$ structure. Vertical lines denote the phase transition pressures (at 0 K).

Figure 3

(a) Comparison of experimental lattice constants (blue/gray stars for $Cmca/Immm$, data from Ref. [37]) with those calculated with the HSE06 functional (red/yellow lines for $Cmca/Immm$). (b) Comparison of experimental frequencies of Raman bands for the $Cmca$ phase (blue solid and open circles for data from Refs. [33] and [38], respectively) and those calculated with HSE06 (gray line).

Figure 4

(a) The crystal structures of the high-pressure phases of solid bromine: phase I, $Cmca$; phase II, $Immm$; phase III, $I4/mmm$; and phase IV, $Fm\overline{3}m$. (b) Calculated pressure dependence of the Br—Br distances in these phases (red/yellow/gray/green lines for phases I/II/III/IV). Stars denote experimental values (blue, Ref. [69]; pink, Ref. [68]). (c) ICOBI for Br—Br distances. Dashed vertical lines in (b) and (c) indicate the predicted transition pressures between ground-state structures of solid bromine.

Figure 5

(a) Pressure dependence of the calculated electronic band gap for the $Cmca$ phase of bromine with the HSE06 + D3 method (red line) and previous results based on the PBE + D2 approach (blue stars, Ref. [44]). (b) Electronic density of state near the Fermi level (indicated by a vertical line) for the $Cmca$ phase of bromine between 60 and 90 GPa.

Figure 6

(a) Relative enthalpy of the $Immm, Cm\text{−}10$, and $Fmm2\text{−}28$ structures with respect to $Cmca$. (b) Br—Br distances in the $Cmca/Immm$ structures (red/yellow solid lines) and $Cm\text{−}10/Fmm2\text{−}28$ phases (blue/violet dashed lines).