Free-energy perturbation in the exchange-correlation space accelerated by machine learning: application to silica polymorphs

We propose a free-energy-perturbation approach accelerated by machine-learning potentials to efficiently compute transition temperatures and entropies for all rungs of Jacob's ladder. We apply the approach to the dynamically stabilized phases of SiO(2), which are characterized by challengingly small transition entropies. All investigated functionals from rungs 1-4 fail to predict an accurate transition temperature by 25-200%. Only by ascending to the fifth rung, within the random phase approximation, an accurate prediction is possible, giving a relative error of 5%. We provide a clear-cut procedure and relevant data to the community for, e.g., developing and evaluating new functionals.