The role of nuclear quantum effects in the relative stability of hexagonal and cubic ice.

At atmospheric pressure, hexagonal ice (Ih) is thermodynamically stable relative to cubic ice (Ic), although the magnitude and underlying physical origin of this stability difference are not well defined. Pure Ic crystals are not accessible experimentally, and hence computer simulations have often been used to interrogate the relative stabilities of Ih and Ic; however, these simulations are dominated by molecular interaction models that ignore the intramolecular flexibility of individual water molecules, do not describe intermolecular hydrogen-bonding with sufficient accuracy, or ignore the role of nuclear quantum effects (NQEs) such as zero-point energy. Here, we show that when comparing the relative stability of Ih and Ic using a flexible, anharmonic molecular interaction model, while also accurately accounting for NQEs, a new picture emerges: Ih is stabilized relative to Ic as a result of subtle differences in the intramolecular geometries and intermolecular interactions of water molecules which are modulated by NQEs. Our simulations hence suggest that NQEs are a major contributor to the stabilization of Ih under terrestrial conditions and thus contribute to the well-known hexagonal (sixfold) symmetry of ice crystals.

Accelerated path-integral simulations using ring-polymer interpolation.

Imaginary-time path-integral (PI) molecular simulations can be used to calculate exact quantum statistical mechanical properties for complex systems containing many interacting atoms and molecules. The limiting computational factor in a PI simulation is typically the evaluation of the potential energy surface (PES) and forces at each ring-polymer "bead"; for an n-bead ring-polymer, a PI simulation is typically n times greater than the corresponding classical simulation. To address the increased computational effort of PI simulations, several approaches have been developed recently, most notably based on the idea of ring-polymer contraction which exploits either the separation of the PES into short-range and long-range contributions or the availability of a computationally inexpensive PES which can be incorporated to effectively smooth the ring-polymer PES; neither approach is satisfactory in applications to systems modeled by PESs given by on-the-fly ab initio calculations. In this article, we describe a new method, ring-polymer interpolation (RPI), which can be used to accelerate PI simulations without any prior assumptions about the PES. In simulations of liquid water modeled by an empirical PES (or force field) under ambient conditions, where quantum effects are known to play a subtle role in influencing experimental observables such as radial distribution functions, we find that RPI can accurately reproduce the results of fully-converged PI simulations, albeit with far fewer PES evaluations. This approach therefore opens the possibility of large-scale PI simulations using ab initio PESs evaluated on-the-fly without the drawbacks of current methods.