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Ab Initio Bulk Free Energy Surface of Proper Ferroelectrics

Pinchen Xie1,2, Yixiao Chen2, Xinyu Xu3, Zhi Yao1, Weinan E2,*, and Roberto Car4,2,†

  • *Present address: AI for Science Institute, Beijing, China and Center for Machine Learning Research and School of Mathematical Sciences, Peking University, Beijing, China.
  • †Contact author: rcar@princeton.edu
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Phys. Rev. Lett. 136, 056801 – Published 4 February, 2026

DOI: https://doi.org/10.1103/bpz5-2pyw

Abstract

We report a systematic and accurate approach for deriving the bulk free energy surface (FES), a function of temperature, polarization, and strain, from the first-principles density functional theory (DFT) of proper ferroelectrics. The core of our approach is the metadynamics algorithm that extracts the polarization dependence of the FES from all-atom molecular dynamics simulations without an a priori ansatz. The rest of the FES is derived from the metadynamics trajectories that span the relevant phase space. We demonstrate our approach in the case of lead titanate. The errors across the phase transition, due to DFT numerics, all-atom molecular dynamics, and free energy evaluation by enhanced sampling, can be systematically controlled and are of the order of 1  meV/atom. The accuracy of the resulting ab initio FES is only limited by the adopted functional approximation of DFT.

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Phys. Rev. Lett. 136, 056801– Published 4 February, 2026
  • Received 21 June 2025
  • Accepted 11 December 2025
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