Comparing the Weighted Density Approximation with the LDA and GGA for Ground State Properties of Ferroelectric Perovskites

TL;DR

This study compares the weighted density approximation (WDA) with LDA and GGA for calculating ground state properties of ferroelectric perovskites, showing WDA's improvements in volume predictions and discussing potential enhancements.

Contribution

The paper introduces a detailed comparison of WDA with LDA and GGA for ferroelectric perovskites, highlighting WDA's advantages and limitations in predicting structural properties.

Findings

WDA improves equilibrium volume predictions over LDA and GGA.

WDA's ferroelectric instability results align well with LDA and GGA.

WDA overestimates strain and volume in some structures.

Abstract

First-principles calculations within the weighted density approximation (WDA) were performed for ground state properties of ferroelectric perovskites PbTiO$_3$, BaTiO$_3$, SrTiO$_3$, KNbO$_3$ and KTaO$_3$. We used the plane-wave pseudopotential method, a pair distribution function $G$ based on the uniform electron gas, and shell partitioning. Comparing with the local density approximation (LDA) and the general gradient approximation (GGA), we found that the WDA significantly improves the equilibrium volume of these materials in cubic symmetry over both the LDA and GGA; Ferroelectric instabilities calculated by the WDA agree with the LDA and GGA very well; At the experimental ferroelectric lattice, optimized atom positions by the WDA are in good agreement with measured data; However the WDA overestimates the strain of tetragonal PbTiO$_3$ at experimental volume; The WDA overestimates the volume of fully relaxed structures, but the GGA results are even worse. Some calculations were also done with other models for $G$. It is found that a $G$ with longer range behavior yields improved relaxed structures. Possible avenues for improving the WDA are discussed.