Accuracy of first-principles interatomic interactions and predictions of ferroelectric phase transitions in perovskite oxides: Energy functional and effective Hamiltonian

While first-principles density functional theory (DFT)-based models have been effective in capturing the physics of ferroelectric phase transitions in ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$, quantitative estimates of the transition temperatures (${T}_{C}$) suffer from errors that are believed to originate from the errors in estimating lattice constants obtained within the local density approximation (LDA) and generalized gradient approximation (GGA) of DFT. The recently developed strongly constrained and appropriately normed (SCAN) meta-GGA functional has been shown to be quite accurate in the estimation of lattice constants. Here, we present a quantitative analysis of the estimates of ferroelectric ground-state properties of eight perovskite oxides and transition temperatures of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$ obtained with molecular dynamics simulations using an effective Hamiltonian derived from the SCAN meta-GGA-based DFT. Relative to LDA, we find an improvement in the estimates of ${T}_{C}$, which arises from the changes in the calculated strain-phonon, anharmonic coupling constants, and strength of ferroelectric instabilities, i.e., frequencies of the soft modes. We also assess the errors in ${T}_{C}$ originating from approximately integrating out the high-energy phonons during construction of the model Hamiltonian through estimates of the effects of fourth-order couplings between the soft mode and higher-energy modes of ${\mathrm{BaTiO}}_{3}, {\mathrm{PbTiO}}_{3}$, and ${\mathrm{KNbO}}_{3}$. We find that inclusion of these anharmonic couplings results in deeper double-well energy functions of ferroelectric distortions and further improvement in the estimates of transition temperatures. Consistently improved estimates of lattice constants and transition temperatures with the SCAN meta-GGA calculations augur well for their use in simulations of superlattices or heterostructures of perovskite oxides, in which the effects of lattice matching are critical.