Comparing the weighted density approximation with the LDA and GGA for ground-state properties of ferroelectric perovskites

First-principles calculations within the weighted density approximation (WDA) were performed for ground-state properties of ferroelectric perovskites ${\mathrm{PbTiO}}_3$, ${\mathrm{BaTiO}}_3$, ${\mathrm{SrTiO}}_3$, ${\mathrm{KNbO}}_3$, and ${\mathrm{KTaO}}_3$. 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 ${\mathrm{PbTiO}}_3$ 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

Figure 1

Total energy as a function of soft-mode displacement in tetragonal ${\mathrm{PbTiO}}_3$ $\left(c∕a=1.063\right)$, rhombohedral ${\mathrm{BaTiO}}_3$ and ${\mathrm{KNbO}}_3$ with the LDA, GGA, and WDA (uniform electron gas $G$). Here $\delta$ is the displacement relative to experiment.

Figure 2

Four types of function $G(r,n)$ with $r_s=1.0$ $\left(n=0.2387\right)$. (a), (b), (c), and (d) correspond to the types defined in the last subsection of Sec. 3.

Figure 3

Energy as a function of volume for the cubic and the relaxed tetragonal ${\mathrm{PbTiO}}_3$, with the LDA, GGA, and WDA (two types of $G$). Dashed lines are cubic structures and solid lines are tetragonal structures.