Ice Ih anomalies: Thermal contraction, anomalous volume isotope effect, and pressure-induced amorphization
Ice Ih displays several anomalous thermodynamic properties such as thermal contraction at low temperatures, an anomalous volume isotope effect (VIE) rendering the volume of D{sub 2}O ice greater than that of H{sub 2}O ice, and a pressure-induced transition to the high-density amorphous (HDA) phase. Furthermore, the anomalous VIE increases with temperature, despite its quantum-mechanical origin. Here, embedded-fragment ab initio second-order many-body perturbation (MP2) theory in the quasiharmonic approximation (QHA) is applied to the Gibbs energy of an infinite, proton-disordered crystal of ice Ih at wide ranges of temperatures and pressures. The quantum effect of nuclei moving in anharmonic potentials is taken into account from first principles without any empirical or nonsystematic approximation to either the electronic or vibrational Hamiltonian. MP2 predicts quantitatively correctly the thermal contraction at low temperatures, which is confirmed to originate from the volume-contracting hydrogen-bond bending modes (acoustic phonons). It qualitatively reproduces (but underestimates) the thermal expansion at higher temperatures, caused by the volume-expanding hydrogen-bond stretching (and to a lesser extent librational) modes. The anomalous VIE is found to be the result of subtle cancellations among closely competing isotope effects on volume from all modes. Consequently, even ab initio MP2 with the aug-cc-pVDZ and aug-cc-pVTZ basis sets has difficulty reproducing this anomaly, yielding qualitatively varied predictions of the sign of the VIE depending on such computational details as the choice of the embedding field. However, the temperature growth of the anomalous VIE is reproduced robustly and is ascribed to the librational modes. These solid-state MP2 calculations, as well as MP2 Born–Oppenheimer molecular dynamics, find a volume collapse and a loss of symmetry and long-range order in ice Ih upon pressure loading of 2.35 GPa or higher. Concomitantly, rapid softening of acoustic phonons is observed starting around 2 GPa. They constitute a computational detection of a mechanical instability in ice Ih and the resulting pressure-induced amorphization to HDA.