High-pressure ionic and molecular phases of ammonia within density functional theory

We have studied ammonia under pressure using density functional theory (DFT) methods. We have used four density functionals; the local density approximation (LDA) and Perdew-Burke-Ernzerhof (PBE) semilocal functionals, the $\mathrm{PBE}+\mathrm{G}06$ semilocal functional which includes an empirical dispersion correction, and the PBE0 hybrid functional, finding results in reasonable agreement with the available experimental data in each case. Using a combination of DFT and a random-structure-searching technique, we have found a molecular phase of ammonia of space group symmetry $Pa\overline{3}$ which has not been reported in experimental studies. This phase is calculated to have a region of thermodynamic stability at low pressures with each of the four density functionals. Results with both the PBE and PBE0 functionals indicate that ammonium amide (NH${{}_4}^{+}$NH${{}_2}^{-}$) proton transfer ionic solids are stable at pressures above about 100 GPa.

Figure 1

Enthalpy relative to the $P{2}_{1}3$ phase as a function of pressure, calculated with the PBE semilocal functional. Solid lines correspond to ionic structures, and dashed lines to molecular structures.

Figure 2

Enthalpy relative to the $P{2}_{1}3$ phase as a function of pressure, calculated with the PBE0 hybrid exchange-correlation functional. Solid lines correspond to ionic structures, and dashed lines to molecular structures. The enthalpy differences between the phases were calculated using the PBE structures, with the exception of the enthalpy difference between the $P{2}_{1}3$ and $Pa\overline{3}$ phases, which was calculated using structures relaxed with the PBE0 functional, as described in the main text.

Figure 3

Enthalpies of the low-pressure molecular phases of ammonia, relative to the $P{2}_{1}3$ phase as a function of pressure, with the PBE, PBE0, $\mathrm{PBE}+\mathrm{G}06$ and LDA functionals. The PBE0 enthalpy differences between the phases were calculated using the PBE structures, exception of the enthalpy difference between the $P{2}_{1}3$ and $Pa\overline{3}$ phases, which was calculated using structures relaxed with the PBE0 functional, as described in the main text.

Figure 4

The $Pa\overline{3}$ structure at 5 GPa calculated with the PBE functional. The white spheres indicate hydrogen atoms, and the blue (dark gray) spheres indicate nitrogen atoms. Dashed lines denote hydrogen bonding; those in red (thicker) emphasize the parallelepiped of ammonia molecules in the structure. Each ammonia molecule both donates and accepts three hydrogen bonds.

Figure 5

EDoS of the $P{2}_{1}3$ molecular structure of phase I of ammonia at 1 GPa with the top of the valence band at zero energy. Note that the lowest energy region is almost entirely $s$ like while the highest energy occupied region is predominantly $p$ like.

Figure 6

EDoS of the $Pma2$ proton transfer structure of ammonia at 100 GPa. The occupied EDoS shows the same three regions present in $P{2}_{1}3$ at low pressures, but they are substantially broadened. The top of the valence band is at zero energy.

Figure 7

Minimum band gaps of various phases as a function of pressure with (a) the PBE functional and (b) PBE0. Solid lines correspond to ionic structures and dashed lines to molecular structures.