A solvation‐free‐energy functional: A reference‐modified density functional formulation

The three‐dimensional reference interaction site model (3D‐RISM) theory, which is one of the most applicable integral equation theories for molecular liquids, overestimates the absolute values of solvation‐free‐energy (SFE) for large solute molecules in water. To improve the free‐energy density functional for the SFE of solute molecules, we propose a reference‐modified density functional theory (RMDFT) that is a general theoretical approach to construct the free‐energy density functional systematically. In the RMDFT formulation, hard‐sphere (HS) fluids are introduced as the reference system instead of an ideal polyatomic molecular gas, which has been regarded as the appropriate reference system of the interaction‐site‐model density functional theory for polyatomic molecular fluids. We show that using RMDFT with a reference HS system can significantly improve the absolute values of the SFE for a set of neutral amino acid side‐chain analogues as well as for 504 small organic molecules. © 2015 Wiley Periodicals, Inc.     

On the choice of a reference state for one‐step perturbation calculations between polar and nonpolar molecules in a polar environment

One‐step perturbation is an efficient method to estimate free energy differences in molecular dynamics (MD) simulations, but its accuracy depends critically on the choice of an appropriate, possibly unphysical, reference state that optimizes the sampling of the physical end states. In particular, the perturbation from a polar moiety to a nonpolar one and vice versa in a polar environment such as water poses a challenge which is of importance when estimating free energy differences that involve entropy changes and the hydrophobic effect. In this work, we systematically study the performance of the one‐step perturbation method in the calculation of the free enthalpy difference between a polar water solute and a nonpolar “water” solute molecule solvated in a box of 999 polar water molecules. Both these polar and nonpolar physical reference states fail to predict the free enthalpy difference as obtained by thermodynamic integration, but the result is worse using the nonpolar physical reference state, because both a properly sized cavity and a favorable orientation of the polar solute in a polar environment are rarely, if ever, sampled in a simulation of the nonpolar solute in such an environment. Use of nonphysical soft‐core reference states helps to sample properly sized cavities, and post‐MD simulation rotational and translational sampling of the solute to be perturbed leads to much improved free enthalpy estimates from one‐step perturbation. © 2012 Wiley Periodicals, Inc.     

Analysis of retrograde behavior and the cross-over effect in supercritical fluids

In this paper, results based upon thermodynamic stability theory are developed which lead to a set of both necessary and sufficient conditions for the existence of retrograde behavior in a multicomponent solute system dissolved in a pure supercritical fluid. While experimental evidence of retrograde behavior in single solute systems has been known for some time, recently data have been obtained showing the retrograde effect in binary solute systems dissolved in a pure supercritical fluid.In such systems, cross-over regions may be defined. These are pressure—temperature regions where the solubility of one solute increases while that of the other decreases with a change in temperature at constant pressure. The existence of cross-over regions in multicomponent mixtures can have implications for a new separation technique using pure supercritical fluids. In conjunction with an equation of state, the results derived here allow cross-over regions to be predicted, thus enabling one to identify candidate systems and thermodynamic conditions for the cross-over process. For this work a variation of a perturbed hard sphere model equation of state was used for the calculations.     

Modeling simple amphiphilic solutes in a Jagla solvent

Methanol is an amphiphilic solute whose aqueous solutions exhibit distinctive physical properties. The volume change upon mixing, for example, is negative across the entire composition range, indicating strong association. We explore the corresponding behavior of a Jagla solvent, which has been previously shown to exhibit many of the anomalous properties of water. We consider two models of an amphiphilic solute: (i) a "dimer" model, which consists of one hydrophobic hard sphere linked to a Jagla particle with a permanent bond, and (ii) a "monomer" model, which is a limiting case of the dimer, formed by concentrically overlapping a hard sphere and a Jagla particle. Using discrete molecular dynamics, we calculate the thermodynamic properties of the resulting solutions. We systematically vary the set of parameters of the dimer and monomer models and find that one can readily reproduce the experimental behavior of the excess volume of the methanol-water system as a function of methanol volume fraction. We compare the pressure and temperature dependence of the excess volume and the excess enthalpy of both models with experimental data on methanol-water solutions and find qualitative agreement in most cases. We also investigate the solute effect on the temperature of maximum density and find that the effect of concentration is orders of magnitude stronger than measured experimentally.     

Hydrogen-bonded network of hydration water around model solutes

Clustering of water molecules in the hydration shells of spherical structureless solutes was studied in dependence on thermodynamic state, solute radius R(sp) and strength U(0) of water-solute interaction. Two qualitatively different clustering states of hydration water have been found: an "ordered" state with a hydrogen-bonded (H-bonded) network, which includes most of the hydration water, and a "disordered" state with small H-bonded clusters of hydration water. The transition from the ordered to disordered state occurs upon increasing temperature and decreasing pressure. This percolation transition is rounded due to the finite solute size and occurs in some temperature (pressure) interval. A finite-size scaling was applied to determine the transition temperature T(∞) in the limit R(sp)→∞. Strengthening of the water-solute interaction strongly enhances the stability of the ordered state: the transition temperature increases by about 35 °C, when U(0) decreases by 1 kcal mol(-1). At T > T(∞) and fixed U(0), the stability of the H-bonded water network increases upon decreasing solute size.     

Generalized phase behavior of small molecules and nanoparticles

Prediction and understanding of the thermodynamic properties and kinetics of phase transitions in molecular systems depends on tuning intermolecular interactions such that the desired structures are assembled. These interactions can depend on the solvent temperature and composition and are difficult to determine in an a priori manner. This is especially true for large and complex molecules and nanoparticles with functionalized surfaces. Here, we demonstrate the use of the pair contribution of the long-time self-diffusivity determined by pulsed-field gradient spin-echo nuclear magnetic resonance as a probe of these interactions. Materials with high solubilities have scaled long-time self-diffusivity, D2, values that are close to hard sphere values and decrease as the solubility decreases. We find a remarkable correlation between solubility and D2 for a wide range of hydrogen-bonding solutes that crystallize upon quenching solutions from high temperature. This generalized phase behavior can be understood in terms of the solutes' interacting with attractive forces that have an extent that is only a small fraction of their diameters.     

Distinct Diffusion in Macromolecule‐Solvent Mixtures

Summary: The specificity of interactions between pairs of molecules cannot be explicitly given by experimental transport coefficients such as intra‐ or mutual diffusion coefficients. But a microscopic interpretation of the transport properties exists, where distinct diffusion coefficients (DDCs) are related to preferential, correlated motion among distinct molecules. Since in general the DDCs do not play the role of an indicator for molecular self‐association phenomena if not compared with some appropriate standard, here we propose DDCs of hard spheres at the second order of volume fraction as new standard coefficients. The analysis based on these novel DDCs is designed to study intermolecular interaction between macromolecule and solvent. Comparisons of the novel non‐ideal with previous ideal reference states were done, and their combined use is shown to reinforce information conveyed by the usual velocity correlation analysis. The comparison of novel hard sphere standards with real DDCs, corresponding to an homologous chemical series of poly(ethylene glycol)‐water mixtures, provides a look at this polymer‐solvent mixture in a dilute and semi‐dilute regime.

Comparison between real (calculated by using Equation (5)–(7) and experimental data) and hard‐sphere based distinct diffusion coefficients for PEG 200 (1: Dequation/tex2gif-stack-1.gif; 2: Dequation/tex2gif-stack-2.gif and 3: Dequation/tex2gif-stack-3.gif).     

How hydrophobic buckminsterfullerene affects surrounding water structure

The hydrophobic hydration of fullerenes in water is of significant interest as the most common Buckminsterfullerene (C60) is a mesoscale sphere; C60 also has potential in pharmaceutical and nanomaterial applications. We use an all-atom molecular dynamics simulation lasting hundreds of nanoseconds to determine the behavior of a single molecule of C60 in a periodic box of water, and compare this to methane. A C60 molecule does not induce drying at the surface; however, unlike a hard sphere methane, a hard sphere C60 solute does. This is due to a larger number of attractive Lennard-Jones interactions between the carbon atom centers in C60 and the surrounding waters. In these simulations, water is not uniformly arranged but rather adopts a range of orientations in the first hydration shell despite the spherical symmetry of both solutes. There is a clear effect of solute size on the orientation of the first hydration shell waters. There is a large increase in hydrogen-bonding contacts between waters in the C60 first hydration shell. There is also a disruption of hydrogen bonds between waters in the first and second hydration shells. Water molecules in the first hydration shell preferentially create triangular structures that minimize the net water dipole near the surface near both the methane and C60 surface, reducing the total energy of the system. Additionally, in the first and second hydration shells, the water dipoles are ordered to a distance of 8 A from the solute surface. We conclude that, with a diameter of approximately 1 nm, C60 behaves as a large hydrophobic solute.     

35Cl NQR studies of 1‐chloro‐2,4‐dinitrobenzene and 1,2‐dichloro‐3‐nitrobenzene as a function of pressure and temperature

The temperature and pressure dependences of ³⁵Cl nuclear quadrupole resonance (NQR) frequency and spin–lattice relaxation time (T₁) were investigated for 1‐chloro‐2,4‐dinitrobenzene and 1,2‐dichloro‐3‐nitrobenzene. T₁ was measured in the temperature range 77–300 K. Furthermore, the NQR frequency (ν) and T₁ for these compounds were measured as a function of pressure up to 5.1 kbar at 300 K. Relaxation was found to be due to the torsional motion of the molecule and the reorientation motion of the nitro group. By analysing the temperature dependence of T₁, the activation energy for the reorientation motion of the nitro group was obtained. The temperature dependence of the average torsional lifetimes of the molecules and the transition probabilities W₁ and W₂ for the Δm = ±1 and Δm = ±2 transitions, were also obtained. Both compounds showed a non‐linear variation of NQR frequency with pressure. The pressure coefficients were observed to be positive. A thermodynamic analysis of the data was carried out to determine the constant‐volume temperature coefficients of the NQR frequency. The spin–lattice relaxation time T₁ for both the compounds was found to be weakly dependent on pressure, showing that the relaxation is mainly due to the torsional motions. Copyright © 2002 John Wiley & Sons, Ltd.     

Rapid approximate calculation of water binding free energies in the whole hydration domain of (bio)macromolecules

The evaluation of water binding free energies around solute molecules is important for the thermodynamic characterization of hydration or association processes. Here, a rapid approximate method to estimate water binding free energies around (bio)macromolecules from a single molecular dynamics simulation is presented. The basic idea is that endpoint free‐energy calculation methods are applied and the endpoint quantities are monitored on a three‐dimensional grid around the solute. Thus, a gridded map of water binding free energies around the solute is obtained, that is, from a single short simulation, a map of favorable and unfavorable water binding sites can be constructed. Among the employed free‐energy calculation methods, approaches involving endpoint information pertaining to actual thermodynamic integration calculations or endpoint information as exploited in the linear interaction energy method were examined. The accuracy of the approximate approaches was evaluated on the hydration of a cage‐like molecule representing either a nonpolar, polar, or charged water binding site and on α‐ and β‐cyclodextrin molecules. Among the tested approaches, the linear interaction energy method is considered the most viable approach. Applying the linear interaction energy method on the grid around the solute, a semi‐quantitative thermodynamic characterization of hydration around the whole solute is obtained. Disadvantages are the approximate nature of the method and a limited flexibility of the solute. © 2016 Wiley Periodicals, Inc.     

An Interpretation of the “Anomalous” Changes in the Low‐Wavenumber Range of the Raman Spectra of L‐Alanine Crystals

“Anomalous changes” in the temperature‐ and pressure‐ dependences of the intensities and wavenumbers of the two low‐wavenumber modes in Raman spectra of single‐crystals of L ‐alanine have been interpreted in terms of a change in relative contributions of stretching and deformational components into the intermolecular vibrational bands. The relative contributions of the two components into a lattice vibration result from a change of relative orientations of molecules linked by hydrogen bonds in a three‐dimensional network on variations of temperature or pressure.     

Placevent: An algorithm for prediction of explicit solvent atom distribution—Application to HIV‐1 protease and F‐ATP synthase

We have created a simple algorithm for automatically predicting the explicit solvent atom distribution of biomolecules. The explicit distribution is coerced from the three‐dimensional (3D) continuous distribution resulting from a 3D reference interaction site model (3D‐RISM) calculation. This procedure predicts optimal location of solvent molecules and ions given a rigid biomolecular structure and the solvent composition. We show examples of predicting water molecules near the KNI‐272 bound form of HIV‐1 protease and predicting both sodium ions and water molecules near the rotor ring of F‐adenosine triphosphate (ATP) synthase. Our results give excellent agreement with experimental structure with an average prediction error of 0.39–0.65 Å. Further, unlike experimental methods, this method does not suffer from the partial occupancy limit. Our method can be performed directly on 3D‐RISM output within minutes. It is extremely useful for examining multiple specific solvent–solute interactions, as a convenient method for generating initial solvent structures for molecular dynamics calculations, and may assist in refinement of experimental structures. © 2012 Wiley Periodicals, Inc.     

Cavitation free energy for organic molecules having various sizes and shapes

Cavitation free energy DeltaG(cav), corresponding to the formation of an excluded volume cavity in water, is calculated for a large set of organic molecules employing the thermodynamic integration procedure, which is realized as the original two-step algorithm for growing the interaction potential between the hard cavity wall and the water molecules. A large variety of solute systems is considered. Their characteristic radii change in the range 3-7 A; spherical cavities with radii 3-6 A are also studied. The interaction between water molecules is described by the four-site nonpolarizable TIP4P model. The diversity of the trial molecular set is provided by using a specially formulated nonspherical criterion classifying the cavity shapes according to their deviation from a sphere. Molecular objects were partly taken from the data base NCI Diversity with the aid of this criterion. The so-computed free energies are approximated by the linear volume dependence DeltaG(cav)V = XiV, where V is the cavity volume. This relation works fairly well until the cavity size becomes very large (the effective radius larger than 7 A). The volume dependence valid for solutes of arbitrary shapes can be included in a calculation of the nonpolar free energy component as required in the implicit water model.     

Ab initio Predictions of Structural and Thermodynamic Properties of Zr2AlC Under High Pressure and High Temperature

The structural and thermodynamic properties of Zr₂AlC at high pressure and high temperature are investigated by first principles density functional theory method. The calculated lattice parameters of Zr₂AlC are in good agreement with the available theoretical data. The pressure dependences of the elastic constants, bulk modulus, shear modulus, Young's modulus, and Vickers hardness of Zr₂AlC are successfully obtained. The elastic anisotropy is examined through the computation of the direction dependence of Young's modulus. By using the quasiharmonic Debye model, the thermodynamic properties including the Debye temperature, heat capacity, volume thermal expansion coefficient, and Grüneisen parameter at high pressure and temperature are predicted for the first time.     

电解质模型流体的MonteCarlo分子模拟

采用正则系综Monte Carlo分子模拟方法，模拟得到了一系列状态条件下1：1 价和2：2价对称电解质模型流体的径向分布函数、构型能和压缩因子的“机器实验 数据”，这些数据对构筑电解质溶液的新参考流体具有重要意义。模拟过程中，电 解质溶液被简化为硬球离子和硬球点偶扳子的混合物，离子—离子、离子—偶极和 偶极—偶极长程位能计算采用了Ewald求和方法。最后，对离子—偶极子混合物的 结构和热力学性质与体系温度、密度和浓度的关系进行了分析和讨论。     

The temperature dependence of the hard sphere diameter

The temperature dependence of the equivalent hard sphere diameter is analyzed using statistical mechanics. The analysis shows that algebraic equations for the hard sphere diameter which were developed by previous workers are not consistent with the statistical mechanics at high temperature. An algebraic equation which is consistent with the statistical mechanics is developed.     

On the Temperature–Pressure Free‐Energy Landscape of Proteins

We studied the thermodynamic stability of a small monomeric protein, staphylococcal nuclease (Snase), as a function of both temperature and pressure, and expressed it as a 3D free‐energy surface on the p,T‐plane using a second‐order Taylor expansion of the Gibbs free‐energy change ΔG upon unfolding. We took advantage of a series of different techniques (small‐angle Xray scattering, Fourier‐transform infrared spectroscopy, differential thermal analysis, pressure perturbation calorimetry and densitometry) in the evaluation of the conformation of the protein and in evaluating the changes in the thermodynamic parameters upon unfolding, such as the heat capacity, enthalpy, entropy, volume, isothermal compressibility and expansivity. The calculated results of the free‐energy landscape of the protein are in good agreement with experimental data of the p,T‐stability diagram of the protein over a temperature range from 200 to 400 K and at pressures from ambient pressure to 4000 bar. The results demonstrate that combined temperature–pressure‐dependent studies can help delineate the free‐energy landscape of proteins and hence help elucidate which features and thermodynamic parameters are essential in determining the stability of the native conformational state of proteins. The approach presented may also be used for studying other systems with so‐called re‐entrant or Tamman loop‐shaped phase diagrams.     

Modification of the Scaled Particle Theory for Solubility of Non-Polar Gases in Water

In this work based on the modified scaled particle theory (SPT), the solubility of non-polar gases (He, Ar, N₂, H₂, O₂, CO₂ and CH₄) in water has been studied over a wide range of temperatures. Calculations of Henry’s law constant by the SPT are related to the inherent physical properties and parameters of solvent and solute, all of which are considered temperature dependent. The temperature dependence of molar volume and hard sphere diameter of solvent and polarizability of solute have the most significant effects on the solubilities of gases in water. The average relative deviation is less than 3 %. Also, the effect of different mixing rules in the application of SPT to prediction of gas solubility has been studied.