Potential energy surface trekking: Application to carbon at terapascal pressures

We have developed a structure searching technique, which is referred to as “potential energy surface trekking”. In this method, the system is forced to climb up a potential energy surface to its ridges by the inversion of restoring forces and then to climb down toward other local minima of the surface by the release from the inversion across the ridges. One quickly obtains multiple stable structures existing around a starting point of the simulation by increasing the number of trekking paths. We have combined the technique with first-principles calculations based on the density functional theory and applied it to carbon at terapascal pressures. As a result, distorted simple hexagonal, distorted simple cubic, β -tin, and bc8-like structures have been obtained in addition to earlier-predicted bc8, r8, and simple cubic structures. While each structure has its own mechanically stable pressure region within 0.7–3.2 TPa, Gibbs free energy comparisons show that the earlier-predicted sequence of the phase transitions, cubic diamond → bc8 → simple cubic, eventually emerges up to at least 6000 K.