With a view to a better understanding of the influence of atomic quantum delocalisation effects on the phase behaviour of water, path integral simulations have been undertaken for almost all of the known ice phases using the TIP4P/2005 model, in conjunction with the rigid rotor propagator proposed by Müser and Berne [Phys. Rev. Lett. 77, 2638]. The quantum contributions then being known, a new empirical model of water is developed (TIP4PQ/2005) which reproduces, to a good degree, a number of the physical properties of the ice phases, for example densities, structure and relative stabilities.

In this note we present results for the heat capacity at constant pressure for the TIP4PQ/2005 model, as obtained from path integral simulations. The model does a rather good job of describing both the heat capacity of ice I h and of liquid water. Classical simulations using the TIP4P/2005, TIP3P, TIP4P, TIP4P-Ew, SPC/E and TIP5P models are unable to reproduce the heat capacity of water. Given that classical simulations do not satisfy the third law of thermodynamics, one would expect such a failure at low temperatures. However, it seems that for water, nuclear quantum effects influence the heat capacities all the way up to room temperature. The failure of classical simulations to reproduce C p points to the the necessity of incorporating nuclear quantum effects to describe this property accurately.

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Path integral simulations have been performed to determine the temperature of the maximum in density of water of the rigid, nonpolarizable TIP4PQ/2005 model treating long range Coulombic forces with the reaction field method. A maximum in density is found at 280 K, just 3 K above the experimental value. In tritiated water the maximum occurs at a temperature about 12 K higher than in water, in reasonable agreement with the experimental result. Contrary to the usual assumption that the maximum in classical water is about 14 K above that in water, we found that for TIP4PQ/2005 this maximum is about 30 K above. For rigid water models the internal energy and the temperature of maximum density do not follow a linear behavior when plotted as a function of the inverse of the hydrogen mass. In addition, it is shown that, when used with Ewald sums, the TIP4PQ/2005 reproduces quite nicely not only the maximum in density of water, but also the liquid densities, the structure of liquid water and the vaporization enthalpy. It was shown in a previous work that it also reproduces reasonably well the density and relative stabilities of ices. Therefore the TIP4PQ/2005 model, while still simple, allows one to analyze the interplay between quantum effects related to atomic masses and intermolecular forces in water.

Quantum path-integral simulations of the hydrate solid structures have been performed using the recently proposed TIP4PQ/2005 model. By also performing classical simulations using this model, the impact of the nuclear quantum effects on the hydrates is highlighted; nuclear quantum effects significantly modify the structure, densities, and energies of the hydrates, leading to the conclusion that nuclear quantum effects are important not only when studying the solid phases of water but also when studying the hydrates. To analyze the validity of a classical description of hydrates, a comparison of the results of the TIP4P/2005 model (optimized for classical simulations) with those of TIP4PQ/2005 (optimized for path-integral simulations) was undertaken. A classical description of hydrates is able to correctly predict the densities at temperatures above 150 K and the relative stabilities between the hydrates and ice I(h). The inclusion of nuclear quantum effects does not significantly modify the sequence of phases found in the phase diagram of water at negative pressures, namely, I(h)-->sII-->sH. In fact the transition pressures are little affected by the inclusion of nuclear quantum effects; the phase diagram predictions for hydrates can be performed with reasonable accuracy using classical simulations. However, for a reliable calculation of the densities below 150 K, the sublimation energies, the constant pressure heat capacity, and the radial distribution functions, the incorporation of nuclear quantum effects is indeed required.

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The properties of quantum fluids in Fourier space, as the system response functions to weak external fields, are analyzed taking the quantum hard-sphere fluid as a probe. This serves to clarify the physical meaning of the different radial correlation functions that can be defined in a path-integral quantum fluid, since these functions are the r-space counterparts of the response functions. The basic feature of the external field relevant to this discussion is connected with its localizing/nonlocalizing effect on the quantum particles composing the fluid (i.e., a localizing field causes the collapse of the particle thermal packet). Fields that localize the quantum particles reveal the so-called instantaneous quantities (e.g., the conventional static structure factor), which are related with the diagonal elements of the density matrix. Fields that do not localize the quantum particles show the so-called linear response quantities, which are related to the diagonal and the off-diagonal density matrix elements. To perform this study the path-integral formalism is considered from the functional analysis approach. Given that the Gaussian Feynman–Hibbs effective potential picture is known to represent well many structural features of the quantum hard-sphere fluid, the parallel study of the response functions within this picture is also presented. In particular, the latter picture provides an accurate Ornstein–Zernike scheme that can be used for numerical calculations of response functions over a wide range of conditions, and also gives fine estimates for quantities difficult to compute with the path integral. Results for the quantum hard-sphere fluid obtained within the latter scheme are reported, tests of consistency are given, and the possibility of approximating the instantaneous response function by means of the coherent part of the linear response function is assessed.