Capturing nuclear quantum effects in high-pressure superconducting hydrides and ice with nuclear-electronic orbital theory

Abstract

Nuclear quantum effects are essential for correctly describing hydrogen-rich materials at high pressures. Superconducting hydrides and ice are prime examples of such systems, requiring the inclusion of lattice anharmonicity and nuclear quantum effects to correctly predict and describe the structures and phase transition pressures observed experimentally. Herein, we show that the nuclear-electronic orbital density functional theory (NEO-DFT) method, which treats specified nuclei quantum mechanically on the same level as the electrons, is capable of accurately describing nuclear quantum effects in superconducting hydrides and ice. NEO-DFT predicts the hydrogen-bond symmetrization pressure in H$_3$S and D$_3$S, benchmarking against the more expensive stochastic self-consistent harmonic approximation (SSCHA) method, and predicts the correct symmetric Fm$\bar{3}$m structure for LaH$_{10}$ at a wide range of pressures. NEO-DFT also predicts the ice VIII to ice X phase transition pressures for H$_2$O and D$_2$O in agreement with experimental measurements. The accuracy, computational efficiency, and broad applicability of the NEO method opens the door for expanded large-scale studies into these types of systems.

Figures (3)

• Figure 1: (a) Asymmetric to symmetric phase transition calculated for H$_3$S with conventional periodic DFT (black) and for H$_3$S/D$_3$S (blue/maroon) with periodic NEO-DFT. The green region indicates the region corresponding to the symmetric Im$\bar{3}$m phase. The pink dashed line indicates the pressure corresponding to the highest experimental T$_c$, which occurs at 155 GPa. The $y$-axis corresponds to the difference between S--H distances for two sulfur atoms and the intervening hydrogen. The symmetric phase is defined as this distance being less than 0.02 Angstroms. Crystal structures in the conventional bcc cell of the Im$\bar{3}$m (bottom) and R3m (top) phases of H$_3$S are shown. Solid lines indicate covalent bonds, while the dashed lines in the R3m phase indicate hydrogen bonds. Note that conventional DFT geometry optimizations do not distinguish between H$_3$S and D$_3$S. (b) Electronic band structure of Im$\bar{3}$m H$_3$S at 200 GPa performed using conventional DFT and NEO-DFT for H$_3$S and D$_3$S using the same color scheme as part a.
• Figure 2: (a) Lattice angle for the lowest energy LaH$_{10}$ structure optimized at different pressures using conventional DFT (black) and NEO-DFT (blue). The asymmetric phase has lattice angles between 62 and 63 degrees, whereas the symmetric phase has lattice angles near 60 degrees. Cage-like structures of LaH$_{10}$ for the Fm$\bar{3}$m (symmetric) and R$\bar{3}$m (asymmetric) phases are shown. The experimental pressure range where superconductivity is observed, implicating the symmetric Fm$\bar{3}$m structure, is indicated by yellow shading. (b) Lattice angle of LaH$_{10}$ structures at each step of the periodic NEO-DFT structural optimization starting at the asymmetric structure optimized with conventional DFT at different pressures. In both panels, the green shaded area indicates the region corresponding to the symmetric Fm$\bar{3}$m structure.
• Figure 3: Ice VIII (grey) to ice X (green) phase transition calculated with conventional periodic DFT (black) and NEO-DFT (blue for H, maroon for D) as a function of pressure. In both ice structures, the simulation cell contains 16 water molecules divided into two networks (indicated in red and blue). The green shaded area indicates the region considered to belong to the ice X phase. The blue and maroon shaded areas indicate the experimentally predicted ice VIII to ice X phase transition pressure range for H and D, respectively.