Classical and quantum gibbs free energies and phase behavior of water using simulation and cell theory

A method to calculate the classical and quantum free energy of a liquid from a computer simulation by using cell theory [J. Chem. Phys. 2007, 126, 064504] is tested for liquid water and ice Ih against experiment as a function of temperature. This fast and efficient method reproduces reasonably well the experimental values of entropy, enthalpy, and free energy of a liquid across the supercooled, stable, and superheated range of temperatures considered. There are small differences between classical and quantum results of water at 298 K, necessitating a small correction term to reproduce water's enthalpy of vaporisation. Only at higher temperatures is entropy underestimated by up to 9 J K(-1) mol(-1) as verified by thermodynamic integration calculations. Satisfactory agreement for ice, however, is only obtained by using the quantum formulation. Even then, at higher temperatures, the entropies exceed experiment by up to 15 J K(-1) mol(-1). Further insight into the quantum nature of water is provided by inspecting the temperature dependence of the frequencies. The harmonic approximation is further supported by the harmonic force and torque distributions and the very similar entropies obtained from the force and torque variances. All these results suggest that the single molecule harmonic oscillator approximation for water, although not exact, provides a rapid, insightful, and useful means to evaluate the thermodynamic properties of water from a computer simulation in a way that can account for the quantization of water's energy levels.     

An accurate and simple quantum model for liquid water

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.     

Quantum effects in ice Ih

Quantum and classical simulations are carried out on ice Ih over a range of temperatures utilizing the TIP4P water model. The rigid-body centroid molecular dynamics method employed allows for the investigation of equilibrium and dynamical properties of the quantum system. The impact of quantization on the local structure, as measured by the radial and spatial distribution functions, as well as the energy is presented. The effects of quantization on the lattice vibrations, associated with the molecular translations and librations, are also reported. Comparison of quantum and classical simulation results indicates that shifts in the average potential energy are equivalent to rising the temperature about 80 K and are therefore non-negligible. The energy shifts due to quantization and the quantum mechanical uncertainties observed in ice are smaller than the values previously reported for liquid water. Additionally, we carry out a comparative study of melting in our classical and quantum simulations and show that there are significant differences between classical and quantum ice.     

A powerful computational crystallography method to study ice polymorphism

Classical molecular dynamics (MD) simulations are employed as a tool to investigate structural properties of ice crystals under several temperature and pressure conditions. All ice crystal phases are analyzed by means of a computational protocol based on a clustering approach following standard MD simulations. The MD simulations are performed by using a recently published classical interaction potential for oxygen and hydrogen in bulk water, derived from neutron scattering data, able to successfully describe complex phenomena such as proton hopping and bond formation/breaking. The present study demonstrates the ability of the interaction potential model to well describe most ice structures found in the phase diagram of water and to estimate the relative stability of 16 known phases through a cluster analysis of simulated powder diagrams of polymorphs obtained from MD simulations. The proposed computational protocol is suited for automated crystal structure identification.     

Linearized semiclassical initial value time correlation functions using the thermal Gaussian approximation: applications to condensed phase systems

The linearized approximation to the semiclassical initial value representation (LSC-IVR) has been used together with the thermal Gaussian approximation (TGA) (TGA/LSC-IVR) [J. Liu and W. H. Miller, J. Chem. Phys. 125, 224104 (2006)] to simulate quantum dynamical effects in realistic models of two condensed phase systems. This represents the first study of dynamical properties of the Ne(13) Lennard-Jones cluster in its liquid-solid phase transition region (temperature from 4 to 14 K). Calculation of the force autocorrelation function shows considerable differences from that given by classical mechanics, namely that the cluster is much more mobile (liquidlike) than in the classical case. Liquid para-hydrogen at two thermodynamic state points (25 and 14 K under nearly zero external pressure) has also been studied. The momentum autocorrelation function obtained from the TGA/LSC-IVR approach shows very good agreement with recent accurate path integral Monte Carlo results at 25 K [A. Nakayama and N. Makri, J. Chem. Phys. 125, 024503 (2006)]. The self-diffusion constants calculated by the TGA/LSC-IVR are in reasonable agreement with those from experiment and from other theoretical calculations. These applications demonstrate the TGA/LSC-IVR to be a practical and versatile method for quantum dynamics simulations of condensed phase systems.     

Isotope effects in ice Ih: a path-integral simulation

Ice Ih has been studied by path-integral molecular dynamics simulations, using the effective q-TIP4P/F potential model for flexible water. This has allowed us to analyze finite-temperature quantum effects in this solid phase from 25 to 300 K at ambient pressure. Among these effects we find a negative thermal expansion of ice at low temperatures, which does not appear in classical molecular dynamics simulations. The compressibility derived from volume fluctuations gives results in line with experimental data. We have analyzed isotope effects in ice Ih by considering normal, heavy, and tritiated water. In particular, we studied the effect of changing the isotopic mass of hydrogen on the kinetic energy and atomic delocalization in the crystal as well as on structural properties such as interatomic distances and molar volume. For D(2)O ice Ih at 100 K we obtained a decrease in molar volume and intramolecular O-H distance of 0.6% and 0.4%, respectively, as compared to H(2)O ice.     

Characterization of the TIP4P-Ew water model: vapor pressure and boiling point

The liquid-vapor-phase equilibrium properties of the previously developed TIP4P-Ew water model have been studied using thermodynamic integration free-energy simulation techniques in the temperature range of 274-400 K. We stress that free-energy results from simulations need to be corrected in order to be compared to the experiment. This is due to the fact that the thermodynamic end states accessible through simulations correspond to fictitious substances (classical rigid liquids and classical rigid ideal gases) while experiments operate on real substances (liquids and real gases, with quantum effects). After applying analytical corrections the vapor pressure curve obtained from simulated free-energy changes is in excellent agreement with the experimental vapor pressure curve. The boiling point of TIP4P-Ew water under ambient pressure is found to be at 370.3+/-1.9 K, about 7 K higher than the boiling point of TIP4P water (363.7+/-5.1 K; from simulations that employ finite range treatment of electrostatic and Lennard-Jones interactions). This is in contrast to the approximately +15 K by which the temperature of the density maximum and the melting temperature of TIP4P-Ew are shifted relative to TIP4P, indicating that the temperature range over which the liquid phase of TIP4P-Ew is stable is narrower than that of TIP4P and resembles more that of real water. The quality of the vapor pressure results highlights the success of TIP4P-Ew in describing the energetic and entropic aspects of intermolecular interactions in liquid water.     

Ab initio rigid water: effect on water structure, ion hydration, and thermodynamics

We investigate the liquid structure, ion hydration, and some thermodynamic properties associated with the rigid geometry approximation to water by applying ab initio molecular dynamics simulations (AIMD) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional at T = 320 K. We vary the rigid water geometry in order to locate a class of practical water models that yield reasonable liquid structure and dynamics, and to examine the progression of AIMD-predicted water behavior as the OH bond length varies. Water constrained at the optimal PBE gas phase geometry yields reasonable pair correlation functions. The predicted liquid phase pressure, however, is large ( approximately 8.0 kbar). Although the O-H bond in water should elongate when transferred from gas to the condensed phase, when it is constrained to 0.02, or even just 0.01 A longer than the optimal gas phase value, liquid water is predicted to be substantially overstructured compared to experiments. Zero temperature calculations of the thermodynamic properties of cubic ice underscore the sensitivity toward small variations in the O-H bond length. We examine the hydration structures of potassium, chloride, and formate ions in one rigid PBE water model. The results are in reasonable agreement with unconstrained AIMD simulations.     

Path integral calculation of free energies: quantum effects on the melting temperature of neon

The path integral formulation has been combined with several methods to determine free energies of quantum many-body systems, such as adiabatic switching and reversible scaling. These techniques are alternatives to the standard thermodynamic integration method. A quantum Einstein crystal is used as a model to demonstrate the accuracy and reliability of these free energy methods in quantum simulations. Our main interest focuses on the calculation of the melting temperature of Ne at ambient pressure, taking into account quantum effects in the atomic dynamics. The free energy of the solid was calculated by considering a quantum Einstein crystal as reference state, while for the liquid, the reference state was defined by the classical limit of the fluid. Our findings indicate that, while quantum effects in the melting temperature of this system are small, they still amount to about 6% of the melting temperature, and are therefore not negligible. The particle density as well as the melting enthalpy and entropy of the solid and liquid phases at coexistence is compared to results obtained in the classical limit and also to available experimental data.     

Communication: Thermodynamics of water modeled using ab initio simulations

We regularize the potential distribution framework to calculate the excess free energy of liquid water simulated with the BLYP-D density functional. Assuming classical statistical mechanical simulations at 350 K model the liquid at 298 K, the calculated free energy is found in fair agreement with experiments, but the excess internal energy and hence also the excess entropy are not. The utility of thermodynamic characterization in understanding the role of high temperatures to mimic nuclear quantum effects and in evaluating ab initio simulations is noted.     

Quantum effects in liquid water and ice: model dependence

This paper explores the influence of choice of potential model on the quantum effects observed in liquid water and ice. This study utilizes standard rigid models and a more formal context for the rigid-body centroid molecular dynamics methodology used to perform the quantum simulations is provided. Quantum and classical molecular dynamics simulations are carried out for liquid water and ice Ih at 298 and 220 K, respectively, with the simple point charge/extended and TIP4P-Ew water models. The results obtained for equilibrium and dynamical properties are compared with those recently reported on TIP4P [L. Hernandez de la Pena and P. G. Kusalik, J. Chem. Phys. 121, 5992 (2004); L. Hernandez de la Pena et al., J. Chem. Phys 123, 144506 (2005)]. For the liquid, an energy shift of about 8% and an average molecular uncertainty of about 11 degrees were found independently of the water model. The self-diffusion coefficient consistently increases by more than 50% when going from the classical to the quantum system and quantum dynamics are found to reproduce the experimental isotopic shifts with the models examined. The ice results compare remarkably well with those previously reported for the TIP4P water model; they confirm that quantum effects are considerable and that the quantum mechanical uncertainty and the energy shifts due to quantization are smaller in ice than in liquid water. The relevance of these findings in the context of the construction of water models is briefly discussed.     

The structure,thermodynamic properties and infrared spectra of liquid water and ice

Monte Carlo simulations are used, together with models of the intramolecular and intermolecular potential surfaces, to model liquid water and several phases of ice. Intramolecular relaxation makes important contributions to both thermodynamic and structural properties. A quantum local mode analysis of the Monte Carlo configurations is used to predict the density of states and infrared absorption intensities for the intramolecular bending and stretching vibrations. The large shifts from the gas phase OH stretch frequencies observed experimentally in the liquid and solid phases are due to anharmonic terms in the intramolecular surface rather than to harmonic intermolecular coupling. A significant contribution to observed changes in IR intensity on condensation arises from the large molecular polarisability.     

Formation of high density amorphous ice by decompression of ice VII and ice VIII at 135 K

Monte Carlo computer simulations of ice VII and ice VIII phases have been undertaken using the four-point transferable intermolecular potential model of water. By following thermodynamic paths similar to those used experimentally, ice is decompressed resulting in an amorphous phase. These phases are compared to the high density amorphous phase formed upon compression of ice Ih and are found to have very similar structures. By cooling liquid water along the water/Ih melting line a high density amorphous phase was also generated.     

Theoretical investigation on the structural and thermodynamic properties of FeSe at high pressure and high temperature

A theoretical investigation on structural and thermodynamic properties of 11-type iron-based superconductor FeSe at high pressure and high temperature was performed by employing the first-principles method based on the density functional theory. Some structural parameters of FeSe in both tetragonal and hexagonal phases are reported. According to the fourth-order Birch-Murnaghan equation of states, the transition pressure P(t) of FeSe from the PbO-type phase to the NiAs-type phase was determined. The calculated results are found to be in good agreement with the available experimental data. Based on the quasi-harmonic Debye model, the pressure and temperature dependence of the thermodynamic properties for hexagonal phase FeSe were investigated. Our theoretical calculations suggest that the pressure and temperature have significant effects on the heat capacity, vibrational internal energy, vibrational entropy, vibrational Helmholtz free energy, thermal expansion coefficient and Debye temperature. Even though few theoretical reports on the structural properties of FeSe are found in the current literature, to our knowledge, this is a novel theoretical investigation on the structural and thermodynamic properties of FeSe at high temperature. We hope that the theoretical results reported here can give more insight into the structural and thermodynamic properties of other iron-based superconductors at high temperature.     

Development of transferable interaction potentials for water. V. Extension of the flexible, polarizable, Thole-type model potential (TTM3-F, v. 3.0) to describe the vibrational spectra of water clusters and liquid water

We present a new parametrization of the flexible, polarizable Thole-type model for water [J. Chem. Phys. 116, 5115 (2002); J. Phys. Chem. A 110, 4100 (2006)], with emphasis in describing the vibrational spectra of both water clusters and liquid water. The new model is able to produce results of similar quality with the previous versions for the structures and energetics of water clusters as well as structural and thermodynamic properties of liquid water evaluated with classical and converged quantum statistical mechanical atomistic simulations. At the same time it yields accurate redshifts for the OH vibrational stretches of both water clusters and liquid water.     

Thermodynamic integration from classical to quantum mechanics

We present a new method for calculating quantum mechanical corrections to classical free energies, based on thermodynamic integration from classical to quantum mechanics. In contrast to previous methods, our method is numerically stable even in the presence of strong quantum delocalization. We first illustrate the method and its relationship to a well-established method with an analysis of a one-dimensional harmonic oscillator. We then show that our method can be used to calculate the quantum mechanical contributions to the free energies of ice and water for a flexible water model, a problem for which the established method is unstable.     

The structural,electronic, elastic,vibration and thermodynamic properties of GdMg

We have investigated the structural, elastic, electronic, vibration and thermodynamic properties of GdMg alloy using the methods of density functional theory within the generalized gradient approximation (GGA) for the exchange-correlation functional. We have presented the results on the basic physical parameters, such as the lattice constant, bulk modulus, pressure derivative of bulk modulus with and without spin-polarization (SP), second-order elastic constants, Zener anisotropy factor, Poisson's ratio, Young's modulus, and isotropic shear modulus. The thermodynamic properties of the considered compound are obtained through the quasi-harmonic Debye model. In order to obtain further information, we have also studied the pressure and temperature-dependent behavior of the volume, bulk modulus, thermal expansion coefficient, heat capacity, and Debye temperature in a wide temperature range of 0–1200 K. We have also calculated phonon frequencies and one-phonon density of states for B2 structure of GdMg compound. The temperature-dependent behavior of heat capacity and entropy obtained from phonon density of states for GdMg compound in B2 phase is also presented.     

DSC and PVT measurements

The dissociation of gas and model hydrates was studied using a classical thermodynamic method and a calorimetric method, in various aqueous media including pure water, high concentration calcium chloride solutions and water-in-oil emulsions. Methane hydrate dissociation temperatures vs. pressure curves were determined using pressure vs. temperature measurements in a constant volume cell (PVT), and high pressure differential scanning calorimetry (DSC), at 5 to 10 MPa gas pressure and at temperatures ranging from -10 to +12°C. PVT and DSC results are in good agreement, and concordant with data available in literature. From a thermodynamic point of view, there are no measurable differences between bulk solutions and emulsions. From a kinetic point of view, due to the considerable surface of interface between the two phases, emulsions allow the formation of much greater amounts of hydrate than solutions, without any agitation. Model hydrate of trichlorofluoromethane was studied in 9 to 27 mass% calcium chloride solutions in emulsion in oil, using DSC under atmospheric pressure, at temperatures ranging from -20 to +5°C. A diagram of dissociation temperature vs. salt concentration is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

氮化锗多形体的四方、单斜和正交畸变的理论研究

采用量子化学从头算方法,对Ge_3N_4的四方、单斜和正交结构同质异相体的微结构、态密度和声子谱进行了研究.形成焓为负值、弹性常数满足Born稳定性准则和声子谱无虚频等结果证实在0~20 GPa范围内3种相都能保持结构稳定.温度变化影响到晶胞体积,从而使体模量发生改变.3种Ge_3N_4都属于半导体,Ge原子和N原子之间存在明显的s-p杂化现象.当压强增大时诱发了离域电子,从而使体系的带隙减小.本文还采用准谐近似对Ge_3N_4的热力学性质进行了研究,结果表明,温度和压强对热膨胀系数、熵、热容、德拜温度和格林爱森参数产生了明显影响.m-Ge_3N_4和t-Ge_3N_4的热膨胀系数分别为o-Ge_3N_4的3倍和2倍.t-Ge_3N_4和o-Ge_3N_4的晶格谐振频率基本不受温度的影响.     

Computer simulation of the 13 crystalline phases of ice

As a reference for follow-up studies toward more accurate model parametrizations, we performed molecular-dynamics and Monte Carlo simulations for all known crystalline phases of ice, as described by the simple point-charge/extended and TIP4P water models. We started from the measured structures, densities, and temperatures, and carried out classical canonical simulations for all these arrangements. All simulated samples were cooled down close to 0 K to facilitate the comparison with theoretical estimates. We determined configurational internal energies as well as pressures, and monitored how accurately the measured configurations were preserved during the simulations. While these two models predicted very similar thermophysical and structural properties for water at ambient conditions, the predicted features for the corresponding ice polymorphs may differ significantly.