Weighted-density-approximation description of rare-earth trihydrides

Density-functional calculations within the weighted density approximation (WDA) are presented for ${\mathrm{YH}}_3$ and ${\mathrm{LaH}}_3.$ We investigate some commonly used pair-distribution functions G. These calculations show that within a consistent density-functional framework a substantial insulating gap can be obtained while at the same time retaining structural properties in accord with experimental data. Our WDA band structures agree with those of $\mathrm{GW}$ approximation very well. It shows that there is no strong correlation in H $1s$ states, and the absence of self-interaction in $\mathrm{H}1s$ is crucial to obtain correct band structures of these rare-earth trihydrites. But the calculated band gaps are still 1.0–2.0 eV smaller than experimental findings.