Understanding solid nitrogen through machine learning simulation

We construct a fast, transferable, general purpose, machine-learning interatomic potential suitable for large-scale simulations of $N_2$. The potential is trained only on high quality quantum chemical molecule-molecule interactions, no condensed phase information is used. The potential reproduces the experimental phase diagram including the melt curve and the molecular solid phases of nitrogen up to 10 GPa. This demonstrates that many-molecule interactions are unnecessary to explain the condensed phases of $N_2$. With increased pressure, transitions are observed from cubic ($\alpha-N_2$), which optimises quadrupole-quadrupole interactions, through tetragonal ($\gamma-N_2$) which allows more efficient packing, through to monoclinic ($\lambda-N_2$) which packs still more efficiently. On heating, we obtain the hcp 3D rotor phase ($\beta-N_2$) and, at pressure, the cubic $\delta-N_2$ phase which contains both 3D and 2D rotors, tetragonal $\delta^\star-N_2$ phase with 2D rotors and the rhombohedral $\epsilon-N_2$. Molecular dynamics demonstrates where these phases are indeed rotors, rather than frustrated order. The model does not support the existence of the wide range of bondlengths reported for the complex $\iota-N_2$ phase. The thermodynamic transitions involve both shifts of molecular centres and rotations of molecules. We simulate these phase transitions between finding that the onset of rotation is rapid whereas motion of molecular centres is inhibited and the cause of the observed sluggishness of transitions. Routine density functional theory calculations give a similar picture to the potential.