Efficient systematic scheme to construct second-principles lattice dynamical models

Auteurs

C. Escorihuela-Sayalero, J. C. Wojdeł, and J. Íñiguez

Référence

Physical Review B, vol. 95, no. 9, art no. 094115, 2017

Description

We start from the polynomial interatomic potentials introduced by Wojdeł et al. [J. Phys.: Condens. Matter 25, 305401 (2013)] and take advantage of one of their key features—namely, the linear dependence of the energy on the potential's adjustable parameters—to devise a scheme for the construction of first-principles-based (second-principles) models for large-scale lattice-dynamical simulations. Our method presents the following convenient features. The parameters of the model are computed in a very fast and efficient way, as it is possible to recast the fit to a training set of first-principles data into a simple matrix diagonalization problem. Our method selects automatically the interactions that are most relevant to reproduce the training-set data, by choosing from a pool that includes virtually all possible coupling terms, and produces a family of models of increasing complexity and accuracy. We work with practical and convenient cross-validation criteria linked to the physical properties that will be relevant in future simulations based on the new model, and which greatly facilitate the task of identifying a potential that is simultaneously simple (thus computationally light), very accurate, and predictive. We also discuss practical ways to guarantee that our energy models are bounded from below, with a minimal impact on their accuracy. Finally, we demonstrate our scheme with an application to ferroelastic perovskite SrTiO₃, which features many nontrivial lattice-dynamical features (e.g., a phase transition driven by soft phonons, competing structural instabilities, highly anharmonic dynamics) and provides a very demanding test.

Lien

doi:10.1103/PhysRevB.95.094115