Surface tension of quantum fluids from molecular simulations

We present the first molecular simulations of the vapor-liquid surface tension of quantum liquids. The path integral formalism of Feynman was used to account for the quantum mechanical behavior of both the liquid and the vapor. A replica-data parallel algorithm was implemented to achieve good parallel performance of the simulation code on at least 32 processors. We have computed the surface tension and the vapor-liquid phase diagram of pure hydrogen over the temperature range 18-30 K and pure deuterium from 19 to 34 K. The simulation results for surface tension and vapor-liquid orthobaric densities are in very good agreement with experimental data. We have computed the interfacial properties of hydrogen-deuterium mixtures over the entire concentration range at 20.4 and 24 K. The calculated equilibrium compositions of the mixtures are in excellent agreement with experimental data. The computed mixture surface tension shows negative deviations from ideal solution behavior, in agreement with experimental data and predictions from Prigogine's theory. The magnitude of the deviations at 20.4 K are substantially larger from simulations and from theory than from experiments. We conclude that the experimentally measured mixture surface tension values are systematically too high. Analysis of the concentration profiles in the interfacial region shows that the nonideal behavior can be described entirely by segregation of H(2) to the interface, indicating that H(2) acts as a surfactant in H(2)-D(2) mixtures.     

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.     

Re-entrant phase behavior for systems with competition between phase separation and self-assembly

In patchy particle systems where there is a competition between the self-assembly of finite clusters and liquid-vapor phase separation, re-entrant phase behavior can be observed, with the system passing from a monomeric vapor phase to a region of liquid-vapor phase coexistence and then to a vapor phase of clusters as the temperature is decreased at constant density. Here, we present a classical statistical mechanical approach to the determination of the complete phase diagram of such a system. We model the system as a van der Waals fluid, but one where the monomers can assemble into monodisperse clusters that have no attractive interactions with any of the other species. The resulting phase diagrams show a clear region of re-entrance. However, for the most physically reasonable parameter values of the model, this behavior is restricted to a certain range of density, with phase separation still persisting at high densities.     

Critical and phase-equilibrium properties of an ab initio based potential model of methanol and 1-propanol using two-phase molecular dynamics simulations

Two-phase molecular dynamics simulations employing a Monte Carlo volume sampling method were performed using an ab initio based force field model parameterized to reproduce quantum-mechanical dimer energies for methanol and 1-propanol at temperatures approaching the critical temperature. The intermolecular potential models were used to obtain the binodal vapor-liquid phase dome at temperatures to within about 10 K of the critical temperature. The efficacy of two all-atom, site-site pair potential models, developed solely from the energy landscape obtained from high-level ab initio pair interactions, was tested for the first time. The first model was regressed from the ab initio landscape without point charges using a modified Morse potential to model the complete interactions; the second model included point charges to separate Coulombic and dispersion interactions. Both models produced equivalent phase domes and critical loci. The model results for the critical temperature, density, and pressure, in addition to the sub-critical equilibrium vapor and liquid densities and vapor pressures, are compared to experimental data. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here.     

Quantum dynamics of inelastic scattering with a moving grid

The time‐dependent discrete variable representation (TDDVR) of a wave function with grid points defined by the Hermite part of the Gauss–Hermite (G‐H) basis set introduces quantum corrections to classical mechanics. The grid points in this method follow classical trajectory and the approach converges to the exact quantum formulation with sufficient trajectories (TDDVR points) but just with a single grid point; only classical mechanics performs the dynamics. This newly formulated approach (developed for handling time‐dependent molecular quantum dynamics) has been explored to calculate vibrational transitions in the inelastic scattering processes. Traditional quantum mechanical results exhibit an excellent agreement with TDDVR profiles during the entire propagation when enough grid points are included in the quantum‐classical dynamics. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Vapor-liquid equilibrium of ethanol by molecular dynamics simulation and Voronoi tessellation

Explicit atom simulations of ethanol were performed by molecular dynamics using the OPLS-AA potential. The phase densities were determined self-consistently by comparing the distribution of Voronoi volumes from two-phase and single-phase simulations. This is the first demonstration of the use of Voronoi tessellation in two-phase molecular dynamics simulation of polyatomic fluids. This technique removes all arbitrary determination of the phase diagram by using single-phase simulations to self-consistently validate the probability distribution of Voronoi volumes of the liquid and vapor phases extracted from the two-phase molecular dynamics simulations. Properties from the two phase simulations include critical temperature, critical density, critical pressure, phase diagram, surface tension, and molecule orientation at the interface. The simulations were performed from 375 to 472 K. Also investigated were the vapor pressure and hydrogen bonding along the two phase envelope. The phase envelope agrees extremely well with literature values from GEMC at lower temperatures. The combined use of two-phase molecular dynamics simulation and Voronoi tessellation allows us to extend the phase diagram toward the critical point.     

Calculation and prediction of fluid phase equilibria from an equation of state

Liquids or compressed gases consisting of light molecules show deviations from classical mechanics, which are caused by the discontinuity of energy levels. From the assumption that each molecule is confined to a cell with a size depending on the free volume, a quantum correction is derived which extends any van der Waals type equation of state to quantum gases. The correction is applied to a semiempirical equation of state developed by the author. The extended equation yields reasonable critical compressibility factors and gives a better representation of PVT data than the uncorrected equation. Furthermore high pressure phase equilibria in mixtures containing helium and hydrogen have been calculated. Again the agreement with experimental data is improved; the adjustable binary interaction parameters have values close to the Berthelot-Lorentz rules and are less temperature dependent.     

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.     

Liquid-vapor and liquid-liquid phase equilibria of the Brodholt-Sampoli-Vallauri polarizable water model

Liquid-vapor and liquid-liquid phase equilibria of the polarizable Brodholt-Sampoli-Vallauri water model have been investigated by Gibbs ensemble Monte Carlo computer simulations. The coexisting liquid and vapor densities and energy of vaporization of the model is found to be in a reasonable agreement with experimental data in the entire temperature range of liquid-vapor coexistence. The critical temperature and density of the model are found to be 615 K and 0.278 gcm(3), respectively, close to the experimental values of 647.1 K and 0.322 gcm(3). In the supercooled state two distinct liquid-liquid coexistence regions are observed. The existence of liquid-liquid phase separation of a polarizable water model is demonstrated for the first time.     

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.     

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.     

Classical probability matrix: Prediction of quantum-state distributions by a moment analysis of classical trajectories

A new method is presented for extracting approximate quantum mechanical state-to-state transition probabilities from the results of classical trajectory calculations. The method recognizes quantum discreteness by dealing with the quantum mechanical probability matrix, but all dynamical quantities are evaluated by classical mechanics. It is illustrated by application to the linear atom-diatom collision (vibrational excitation); it is capable of treating both classically allowed and classically forbidden processes.     

Fast quantum crystallography

Typical contemporary X-ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R-factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.     

Computational studies on thermodynamic properties, effective diameters, and free volume of argon using an ab initio potential

A quantum mechanical derived ab initio interaction potential for the argon dimer was tested in molecular simulations to reproduce the thermophysical properties of the vapor-liquid phase equilibria using the Gibbs ensemble Monte Carlo simulations as well as the liquid and supercritical equation of state using the NVT Monte Carlo simulations. The ab initio interaction potential was taken from the literature. A recently developed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was used to compute the effective diameters of argon in fluid phases and the results were subsequently applied in the generic van der Waals theory to compute the free volume of argon. The calculated densities of the coexisting phases, the vapor pressure, and the equation of state show excellent agreement with experimental values. The effective diameters and free volumes of argon are given over a wide range of densities and temperatures. An empirical formula was used to fit the effective diameters as a function of density and temperature. The computed free volume will be used in future investigations to calculate the transport properties of argon.     

Classical and quantum mechanical infrared echoes from resonantly coupled molecular vibrations

The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting variant Planck's over 2pi-->0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity.     

Contracted Schrödinger equation in quantum phase‐space

The phase space formulation of quantum mechanics is equivalent to standard quantum mechanics where averages are calculated by way of phase space integration as in the case of classical statistical mechanics. We derive the quantum hierarchy equations, often called the contracted Schrödinger equation, in the phase space representation of quantum mechanics which involves quasi‐distributions of position and momentum. We use the Wigner distribution for the phase space function and the Moyal phase space eigenvalue formulation to derive the hierarchy. We show that the hierarchy equations in the position, momentum, and position‐momentum representations are very similar in structure. © 2017 Wiley Periodicals, Inc.     

跨接VTSRK方程计算烃类的pVT性质

烃类pVT性质的精细表征对能源动力、化工等领域应用有重要价值,临界区热力性质描述是难点之一.本文建立了烷烃(C1-C20)的跨接比容平移Soave-Redlich-Kwong(SRK)(跨接VTSRK)状态方程,在SRK状态方程的基础上引入了比容平移和跨接方法,以改善饱和液相密度和近临界区域热力学性质的计算精度,方程参数被表达为物质临界参数和偏心因子的函数.比较结果表明,跨接方程对烷烃(C1-C20)饱和蒸气压、饱和气相密度、饱和液相密度的计算平均偏差分别为1.01%、1.83%和0.93%,显著优于原方程,单相区和近临界区的pVT性质计算精度也比原状态方程有较大改善.进一步将方程推广到环烷烃(环丙烷、环戊烷和环己烷)和苯、甲苯的计算,也获得了较好效果,验证了方程的预测能力.     

跨接VTSRK方程计算烃类的pVT性质

烃类pVT性质的精细表征对能源动力、化工等领域应用有重要价值,临界区热力性质描述是难点之一.本文建立了烷烃（C1-C20）的跨接比容平移Soave-Redlich-Kwong（SRK）（跨接VTSRK）状态方程,在SRK状态方程的基础上引入了比容平移和跨接方法,以改善饱和液相密度和近临界区域热力学性质的计算精度,方程参数被表达为物质临界参数和偏心因子的函数. 比较结果表明,跨接方程对烷烃（C1-C20）饱和蒸气压、饱和气相密度、饱和液相密度的计算平均偏差分别为1.01%、1.83%和0.93%,显著优于原方程,单相区和近临界区的pVT性质计算精度也比原状态方程有较大改善. 进一步将方程推广到环烷烃（环丙烷、环戊烷和环己烷）和苯、甲苯的计算,也获得了较好效果,验证了方程的预测能力.     

The use of two-phase molecular dynamics simulations to determine the phase behavior and critical point of propane molecular models

Molecular dynamics simulations were performed to determine two-phase configurations of model propane molecules below the critical point and in the near-critical, two-phase region. A postprocessor that uses a Monte Carlo method for determination of volumes attributable to each molecule was used to obtain density histograms of the particles from which the bulk coexisting equilibrium vapor and liquid densities were determined. This method of analyzing coexisting densities in a two-phase simulation is straightforward and can be easily implemented for complex, multisite models. Various degrees of internal flexibility in the propane models have little effect on the coexisting densities at temperatures 40 K or more below the critical point, but internal flexibility (angle bending and bond vibrations) does affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point.