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

## TL;DR

This paper introduces a machine learning method to improve predictions of phase transitions in silica using advanced computational techniques.

## Contribution

The novel contribution is a machine-learning-accelerated free-energy-perturbation method for evaluating exchange-correlation functionals.

## Key findings

- Machine learning improves accuracy in predicting transition temperatures for silica polymorphs.
- Only fifth-rung functionals achieve less than 5% relative error in temperature predictions.
- The method provides a framework for evaluating and developing new functionals.

## Abstract

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 SiO2, 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.