Importance of zero-point energy for crystalline ice phases: A comparison of force fields and density functional theory

New Insights into the Volume Isotope Effect of Ice Ih from Polarizable Many-Body Potentials

The anomalous volume isotope effect (VIE) of ice Ih is calculated and analyzed based on the quasi-harmonic approximation to account for nuclear quantum effects in the Helmholtz free energy. While a lot of recently developed polarizable many-body potential functions give a normal VIE contrary to experimental results, we find that one of them, MB-pol, yields the anomalous VIE in good agreement with the most recent high-resolution neutron diffraction measurements─better than DFT calculations. The short-range three-body terms in the MB-pol function, which are fitted to CCSD(T) calculations, are found to have a surprisingly large influence. A vibrational mode group decomposition of the zero-point pressure together with a hitherto unconsidered benchmark value for the intramolecular stretching modes of H₂O ice Ih obtained from Raman spectroscopy data unveils the reason for the VIE: a delicate competition between the latter and the librations.

Transferable Potential Function for Flexible H2O Molecules Based on the Single-Center Multipole Expansion

A potential function is presented for describing a system of flexible H₂O molecules based on the single-center multipole expansion (SCME) of the electrostatic interaction. The model, referred to as SCME/f, includes the variation of the molecular quadrupole moment as well as the dipole moment with changes in bond length and angle so as to reproduce results of high-level electronic structure calculations. The multipole expansion also includes fixed octupole and hexadecapole moments, as well as anisotropic dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole polarizability tensors. The model contains five adjustable parameters related to the repulsive interaction and damping functions in the electrostatic and dispersion interactions. Their values are adjusted to reproduce the lowest energy isomers of small clusters, (H₂O)_n with n = 2-6, as well as measured properties of the ice Ih crystal. Subsequent calculations of the energy difference between the various isomer configurations of the clusters show that SCME/f gives good agreement with results of electronic structure calculations and represents a significant improvement over the previously presented rigid SCME potential function. Analysis of the vibrational frequencies of the clusters and structural properties of ice Ih crystal show the importance of accurately describing the variation of the quadrupole moment with molecular structures.

Calorimetric Signature of Deuterated Ice II: Turning an Endotherm to an Exotherm

Calorimetric studies on ice II reveal a surprising H2O/D2O isotope effect. While the ice II to ice Ic transition is endothermic for H2O, it is exothermic for D2O samples. The transition enthalpies are +40 and -140 J/mol, respectively, where such a sign change upon isotope substitution is unprecedented in ice research. To understand the observations we employ force field calculations using two water models known to perform well for H2O ice phases and their vibrational properties. These simulations reveal that the isotope effect can be traced back to zero-point energy. q-TIP4P/F fares better and is able to account for approximately three-fourths of the isotope effect, while MB-pol only catches approximately one-third. Phonon and configurational entropy contributions are necessary to predict reasonable transition enthalpies, but they do not have an impact on the isotope effect. We suggest to use these calorimetric isotope data as a benchmark for water models.

Time dependence of quantum correlation functions

In the past few years, the exponential expansion analysis of time autocorrelation functions has provided profound insight into the leading microscopic processes driving the atomic-scale dynamics and has made it possible to highlight the presence and the role of various relaxation channels through which the fundamental correlation functions decay with time. Here we apply this method to the determination of the full time dependence of a correlation function c(t) in a quantum system at nonzero temperature, by making explicit its relationship with its Kubo transform c_{K}(t), which in some cases can be approximately computed with the presently available quantum simulation techniques. We obtain an exact expression for c(t) in terms of the exponential modes that describe the time behavior of c_{K}(t). The relative importance of the various modes in determining the overall shape of c(t) can then be studied in detail. This work extends to the full time domain the results of a previous paper [Guarini et al., Phys. Rev. Lett. 123, 135301 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.135301], in which we employed the same method to calculate the zero time value of the velocity autocorrelation function, to obtain a microscopic description of the quantum mean kinetic energy in a fluid. In particular, we show that the decay constants and the frequencies of the dominant microscopic modes of c(t) are the same as those of c_{K}(t), but the dynamics of the quantum system also contains an additional term decaying on a time scale determined solely by temperature of the system.