Quantum anharmonic effects in hydrogen bond symmetrization of high-pressure ice

The nuclear quantum effects of hydrogen play a significant role in determining the phase stability of water ice. Hydrogen bond symmetrization occurs as hydrogen atoms tunnel in a double-well potential, ultimately occupying the midpoint between oxygen atoms and transforming ice VIII into ice X under high pressure. Quantum fluctuations lower this transition from classical predictions of more than 100 to $60\phantom{\rule{4pt}{0ex}}\text{GPa}$. We reveal that the Perdew-Burke-Ernzerhof functional underestimates the hydrogen double-well barrier, thus resulting in a transition pressure more than $10\phantom{\rule{4pt}{0ex}}\text{GPa}$ lower than the strongly constrained and appropriately normed functional, which is validated against quantum Monte Carlo calculations. By treating nuclear quantum anharmonicity with neural canonical transformation (NCT), we find that the transition pressure is temperature independent. Moreover, non-Gaussian flow-based wave functions predict a reduction of about $2\phantom{\rule{4pt}{0ex}}\text{GPa}$ relative to the self-consistent harmonic approximation. Although increasing pressure typically shortens chemical bonds and hardens phonon modes, NCT calculations reveal that the hydrogen bond softens hydrogen-oxygen stretching in ice VIII under pressure.