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

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.