Efficient systematic scheme to construct second-principles lattice-dynamical models

Abstract

We start from the polynomic interatomic potentials introduced by Wojdeł et al. [J. Phys. Condens. Matt. 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 ({\em 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 SrTiO${}_3$, which features many non-trivial lattice-dynamical features (e.g., a phase transition driven by soft phonons, competing structural instabilities, highly anharmonic dynamics) and provides a very demanding test.

22 pages, 13 figures

References in corpus (13)

• Systematic treatment of displacements, strains and electric fields in density-functional perturbation theory
• First-principles theory of ferroelectric phase transitions for perovskites: The case of BaTiO3
• Phase transitions in BaTiO${}_3$ from first principles
• Finite-temperature properties of PZT alloys from first principles
• Lattice dynamics of BaTiO3, PbTiO3 and PbZrO3: a comparative first-principles study
• Ab initio statistical mechanics of the ferroelectric phase transition in PbTiO3
• Effect of quantum fluctuations on structural phase transitions in SrTiO_3 and BaTiO_3
• Phase diagram of Pb(Zr,Ti)O3 solid solutions from first principles
• Second-principles method including electron and lattice degrees of freedom
• First-principles model potentials for lattice-dynamical studies: general methodology and example of application to ferroic perovskite oxides
• Ferroelectricity at ferroelectric domain walls
• First-principles study of the temperature-pressure phase diagram of BaTiO3
• Atomistic simulations of the incipient ferroelectric KTaO${}_3$

Cited by in corpus (15)

• Ferroelectric/paraelectric superlattices for energy storage
• A phononic switch based on ferroelectric domain walls
• Electron-Lattice Interplays in LaMnO3 from Canonical Jahn-Teller Distortion Notations
• Brownian electric bubble quasiparticles
• Active learning of effective Hamiltonian for super-large-scale atomic structures
• Dynamical manipulation of polar topologies from acoustic phonon pumping
• Strain game revisited for complex oxide thin-films: Substrate-film thermal expansion mismatch in PbTiO${}_3$
• Liquid-crystal-like dynamic transition in ferroelectric/dielectric superlattices
• Influence of ferroelastic domain walls on thermal conductivity
• Role of long-range dipolar interactions in the simulation of the properties of polar crystals using effective atomic potentials
• Switchable Skyrmion-Antiskyrmion Tubes in Rhombohedral BaTiO${}_3$ and Related Materials
• Ferroelectric Properties and Topological Polar Textures of PbTiO${}_3$ from a Second-Principles Open-Source Interatomic Potential
• Finite-temperature properties and the hidden ferroelectric $R3c$ phase of bulk CaTiO${}_3$ from second principles
• Coexisting conventional and inverse mechanocaloric effects in ferroelectrics
• Combined cluster and atomic displacement expansion for solid solutions and magnetism