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Density functional theory plus $U$ (DFT+$U$) is one of the most efficient first-principles methods to simulate the cold pressure properties of strongly-correlated materials. However, the applicability of DFT+$U$ at ultra-high pressure is not sufficiently studied, especially in the widely-used augmented schemes [such as projector augmented wave (PAW) and linearized augmented plane wave (LAPW)]. This work has systematically investigated the performance of DFT+$U$ in PAW and LAPW at the pressure up to several hundred GPa for the lanthanide metals, which is a typical strongly-correlated series. We found DFT+$U$ simulation in PAW exhibits an unphysical underestimating of force at high pressure. By delicate analysis and comparison with local-orbital-independent hybrid functional results, we have demonstrated that this unphysical behavior is related to a normalization problem on the local density matrix caused by the overlap of local orbitals in PAW under high pressure. Additionally, we observed a slight softening of force in DFT+$U$ in heavy lanthanides (Tm, Yb and Lu) at high pressure comparing with the DFT results without the influence of local orbital overlap, and it might be related to the enhancement of bonding effect in correlation correction methods at high pressure. Our work reveals the underestimating of high pressure in DFT+$U$ simulation, analyses two sources of this unusual behavior and proposes their mechanism. Most importantly, our investigation highlights the breakdown of DFT+$U$ for high pressure simulation in VASP package based on PAW framework., Comment: 20 pages, 8 figures

The formation of precipitated zirconium (Zr) hydrides is closely related to the hydrogen embrittlement problem for the cladding materials of pressured water reactors (PWR). In this work, we systematically investigated the crystal structures of zirconium hydride (ZrHx) with different hydrogen concentrations (x = 0~2, atomic ratio) by combining the basin hopping algorithm with first principles calculations. We conclude that the P3m1 {\zeta}-ZrH0.5 is dynamically unstable, while a novel dynamically stable P3m1 ZrH0.5 structure was discovered in the structure search. The stability of bistable P42/nnm ZrH1.5 structures and I4/mmm ZrH2 structures are also revisited. We find that the P42/nnm (c/a > 1) ZrH1.5 is dynamically unstable, while the I4/mmm (c/a = 1.57) ZrH2 is dynamically stable.The P42/nnm (c/a < 1) ZrH1.5 might be a key intermediate phase for the transition of {\gamma}->{\delta}->{\epsilon} phases. Additionally, by using the thermal dynamic simulations, we find that {\delta}-ZrH1.5 is the most stable structure at high temperature while ZrH2 is the most stable hydride at low temperature. Slow cooling process will promote the formation of {\delta}-ZrH1.5, and fast cooling process will promote the formation of {\gamma}-ZrH. These results may help to understand the phase transitions of zirconium hydrides.

Metal halide perovskites are ideal candidates for indoor photovoltaics (IPVs) because of their easy-to-adjust bandgaps, which can be designed to cover the spectrum of any artificial light source. However, the serious non-radiative carrier recombination under low light illumination restrains the application of perovskite-based IPVs (PIPVs). Herein, polar molecules of amino naphthalene sulfonates are employed to functionalize the TiO2 substrate, anchoring the CsPbI3 perovskite crystal grains with a strong ion-dipole interaction between the molecule-level polar interlayer and the ionic perovskite film. The resulting high-quality CsPbI3 films with the merit of defect-immunity and large shunt resistance under low light conditions enable the corresponding PIPVs with an indoor power conversion efficiency of up to 41.2% (P-in: 334.11 & mu;W cm(-2), P-out: 137.66 & mu;W cm(-2)) under illumination from a commonly used indoor light-emitting diode light source (2956 K, 1062 lux). Furthermore, the device also achieves efficiencies of 29.45% (P-out: 9.80 & mu;W cm(-2)) and 32.54% (P-out: 54.34 & mu;W cm(-2)) at 106 (P-in: 33.84 & mu;W cm(-2)) and 522 lux (P-in: 168.21 & mu;W cm(-2)), respectively.