Crystal structure prediction at finite temperatures

Crystal structure prediction is a central problem of crystallography and materials science, which until mid-2000s was considered intractable. Several methods, based on either energy landscape exploration or, more commonly, global optimization, largely solved this problem and enabled fully non-empirical computational materials discovery. A major shortcoming is that, to avoid expensive calculations of the entropy, crystal structure prediction was done at zero Kelvin, reducing to the search for the global minimum of the enthalpy rather than the free energy. As a consequence, high-temperature phases (especially those which are not quenchable to zero temperature) could be missed. Here we develop an accurate and affordable solution, enabling crystal structure prediction at finite temperatures. Structure relaxation and fully anharmonic free energy calculations are done by molecular dynamics with a forcefield (which can be anything from a parametric forcefield for simpler cases to a trained on-the-fly machine learning interatomic potential), the errors of which are corrected using thermodynamic perturbation theory to yield accurate results with full ab initio accuracy. We illustrate this method by applications to metals (probing the P–T phase diagram of Al and Fe), a refractory covalent solid (WB), an Earth-forming silicate MgSiO₃ (at pressures and temperatures of the Earth’s lower mantle), and ceramic oxide HfO₂.