3.3 Ammonia

Bonding in NH$_3$ is intermediate between hydrogen bonded tetrahedral structure of H$_2$O, and vdW-bonded close-packed structure of CH$_4$. Weak hydrogen bonding between neighboring ammonia molecules results in a pseudo-close-packed arrangement in the solid state 96. It is extremely interesting to understand the nature of hydrogen bonding in crystalline ammonia, and the properties of ammonia under pressure are of fundamental interest, as compressed ammonia has a significant role in planetary physics90.

At room temperature, ammonia crystallizes at 1 GPa in a rotationally disordered, face-centered-cubic phase (phase III) 96; 97; 98. X-ray and neutron studies have yielded information about the equation of state and structures of solid ammonia. The low-P, T phase I of ammonia undergoes a first-order phase transition into phase IV at about 3 - 4 GPa and then into phase V at about 14 GPa. Phase I has a cubic structure with space group P2$_1$3, while phase IV has been identified as the orthorhombic structure with space group P2$_1$2$_1$2$_1$. Phase V might have the same space group as phase IV (an isosymmetric phase transition).

We carried out variable-cell structure prediction calculations at 5, 10, 25, 50 GPa. At low pressures (5 GPa), we found that the P2$_1$3 structure to be stable (Fig. 3.7a), in good agreement with the experiment. At high pressures, USPEX without applying symmetry in the initialization still easily found P2$_1$3 structure, however, failed to get the ground state structure P2$_1$2$_1$2$_1$ phase in a simulation with up to 20 generations. The energies of whole-molecule rotation are very small compared to intra-molecular bonding energies, thus making the process of finding correct molecular orientations extremely difficult. This indicates that the energy landscape of ammonia is actually very flat. To enhance the searching efficiency, we initialized the first generation using random symmetric structures. And to retain diversity of the population, 30% of the population of each new generation was produced by random symmetric mechanism. In this case, the ground state structure (Fig. 3.7c) would appear within 6 generations or $\scriptsize {\sim }$210 structural relaxations. In addition, we also found the P2$_1$/c phase (Fig. 3.7b) reported before 99.

Figure 3.7: Crystal structures of ammonia. a) P2$_1$3 phase (stable at 1 - 6 GPa, Z=4); b) P2$_1$/c phase (stable at 6 - 8.5 GPa, Z=4); c) P2$_1$2$_1$2$_1$ phase (stable at 8.5 - 60 GPa, Z=4)