Free energy of liquid water from a computer simulation via cell theory

A method to calculate the free energy of water from computer simulation is presented. Based on cell theory, it approximates the potential energy surface sampled in the simulation by an anisotropic six-dimensional harmonic potential to model the three hindered translations and three hindered rotations of a single rigid water molecule. The potential is parametrized from the magnitude of the forces and torques measured in the simulation. The entropy of these six harmonic oscillators is calculated and summed with a conformational term to give the total entropy. Combining this with the simulation enthalpy yields the free energy. The six water models examined are TIP3P, SPC, TIP4P, SPC/E, TIP5P, and TIP4P-Ew. The results reproduce experiment well: free energies for all models are within 1.6 kJ mol(-1) and entropies are within 3.6 J K(-1) mol(-1). Approximately two-thirds of the entropy comes from translation, a third from rotation, and 5% from conformation. Vibrational frequencies match those in the experimental infrared spectrum and assist in their assignment. Intermolecular quantum effects are found to be small, with free energies for the classical oscillator lying 0.5-0.7 kJ mol(-1) higher than in the quantum case. Molecular displacements and vibrational and zero point energies are also calculated. Altogether, these results validate the harmonic oscillator as a quantitative model for the liquid state.     

Heat capacity of tetrahydrofuran clathrate hydrate and of its components, and the clathrate formation from supercooled melt

We report a thermodynamic study of the formation of tetrahydrofuran clathrate hydrate by explosive crystallization of water-deficient, near stoichiometric, and water-rich solutions, as well as of the heat capacity, C(p), of (i) supercooled tetrahydrofuran-H2O solutions and of the clathrate hydrate, (ii) tetrathydrofuran (THF) liquid, and (iii) supercooled water and the ice formed on its explosive crystallization. In explosive freezing of supercooled solutions at a temperature below 257 K, THF clathrate hydrate formed first. The nucleation temperature depends on the cooling rate, and excess water freezes on further cooling. The clathrate hydrate melts reversibly at 277 K and C(p) increases by 770 J/mol K on melting. The enthalpy of melting is 99.5 kJ/mol and entropy is 358 J/mol K. Molar C(p) of the empty host lattice is less than that of the ice, which is inconsistent with the known lower phonon frequency of H2O in the clathrate lattice. Analysis shows that C(p) of THF and ice are not additive in the clathrate. C(p) of the supercooled THF-H2O solutions is the same as that of water at 247 K, but less at lower temperatures and more at higher temperatures. The difference tends to become constant at 283 K. The results are discussed in terms of the hydrogen-bonding changes between THF and H2O.     

Quasi-harmonic approximation of thermodynamic properties of ice Ih, II, and III

Several thermodynamic properties of ice Ih, II, and III are studied by a quasi-harmonic approximation and compared to results of quantum path integral and classical simulations. This approximation allows to obtain thermodynamic information at a fraction of the computational cost of standard simulation methods, and at the same time permits studying quantum effects related to zero-point vibrations of the atoms. Specifically, we have studied the crystal volume, bulk modulus, kinetic energy, enthalpy, and heat capacity of the three ice phases as a function of temperature and pressure. The flexible q-TIP4P/F model of water was employed for this study, although the results concerning the capability of the quasi-harmonic approximation are expected to be valid independently of the employed water model. The quasi-harmonic approximation reproduces with reasonable accuracy the results of quantum and classical simulations showing an improved agreement at low temperatures (T< 100 K). This agreement does not deteriorate as a function of pressure as long as it is not too close to the limit of mechanical stability of the ice phases.     

Understanding thermodynamic properties at the molecular level: multiple temperature charge density study of ribitol and xylitol

X-ray diffraction data of high quality measured to high resolution on crystals of the two pentitol epimers ribitol (centric) and xylitol (acentric) at 101, 141, and 181 K and data on the two compounds previously recorded at 122 K have formed the basis for multipole refinements with the VALRAY system. Our analysis showed that it is possible to obtain a reliable crystal electron density for an acentric compound (xylitol) from X-ray diffraction data and that the thermal motion can be deconvoluted from the static density in this temperature range. The Bader-type topological analysis of the static electron densities revealed virtually identical intramolecular interactions as well as very similar hydrogen bond interactions of ribitol and xylitol; the only minor differences are found in the weaker intermolecular interactions. The high-level periodic DFT calculations are in accordance with the thermodynamic measurements that show that the two pentitols have identical sublimation energies. A rigid body normal coordinate analysis was performed on the atomic displacement parameters obtained at the four different temperatures. The translational and librational mean square deviations derived through this analysis were used in a quantum statistical approach to derive frequencies of the corresponding harmonic oscillators. The analysis showed a consistent vibrational model for all temperatures. The frequencies were subsequently used to calculate crystal entropies assuming an Einstein-type behavior. These calculations show that the crystal entropy of ribitol is 8 J K(-1) mol(-1) higher than the crystal entropy of xylitol, confirming that it is a difference in the entropy of the two compounds that causes the difference in their free energy. Our results presented in this Article show the potential to use X-ray diffraction data to obtain physicochemical properties of crystals.     

Conformational and thermodynamic properties of gaseous levulinic acid

Molecular modeling is used to determine low-energy conformational structures and thermodynamic properties of levulinic acid in the gas phase. Structure and IR vibrational frequencies are obtained using density functional and M?ller-Plesset perturbation theories. Electronic energies are computed using G3//B3LYP and CBS-QB3 model chemistries. Computed anharmonic frequencies are consistent with reported experimental data. Population analysis shows a boat- and a chainlike structure to be most abundant at 298 K, with increasing proportions of two other conformers at higher temperatures. Population mean distribution values for thermodynamic quantities are derived. At 298 K and 1 atm, the enthalpy of formation, entropy, and heat capacity are -613.1 ± 1.0 kJ·mol(-1), 407.4 J·mol(-1)·K(-1), and 132.3 J·mol(-1)·K(-1), respectively.     

Study of thermodynamic stabilities of polytypes of n-C36H74 by solubility measurements and incoherent inelastic neutron scattering

The thermodynamic properties of the two polytypes of n-hexatriacontane (n-C36H74), single-layered structure Mon and double-layered structure Orth II have been investigated by means of solubility measurements and incoherent inelastic neutron scattering. The solubility measurements reveal that Orth II is more stable than Mon by 1.2 kJ/mol because of the advantage of larger entropy. The neutron scattering measurements show that the vibrational modes of Orth II shift to the lower frequencies compared with those of Mon in the frequency region below 120 cm(-1). The advantage of Orth II in vibrational entropy due to the low-frequency shifts is estimated to be 9.6 J K(-1)/mol at 288 K under the harmonic approximation, which nearly agrees with the entropy difference of 6.8 J K(-1)/mol between Mon and Orth II determined by solubility measurements. These results suggest that the difference in vibrational entropy due to low-frequency modes mainly contributes to the relative thermodynamic stabilities of polytypic structures of long-chain compounds. From the frequency of methyl torsional mode, it is suggested that the cohesive force at the lamellar interface is stronger in Mon than in Orth II.     

Thermodynamic Calculation on the Formation of Titanium Hydride

A modified Miedema model, using interrelationship among the basic properties of elements Ti and H, is employed to calculate the standard enthalpy of formation of titanium hydride TiHx (1≤x≤2). Based on Debye theories of solid thermal capacity, the vibrational entropy, as well as electronic entropy, is acquired by quantum mechanics and statistic thermodynamics methods, and a new approach is presented to calculate the standard entropy of formation of TiH2. The values of standard enthalpy of formation of TiHx decrease linearly with increase of x. The calculated results of standard enthalpy, entropy, and free energy of formation of TiH2 at 298.16 K are -142.39 kJ/mol, -143.0 J/(mol?K) and -99.75 kJ/mol, respectively, which is consistent with the previously-reported data obtained by either experimental or theoretic     

Calorimetric study of the relationship between molecular structure and liquid crystallinity of rod-like mesogens II. Heat capacities and phase transitions of 4-(trans-4-propylcyclohexyl)benzonitrile

The molar heat capacity of the rod-like compound 4-(trans-4-propylcyclohexyl)benzonitrile (3-CBCN), purity of 99.8mol%, has been measured with an adiabatic calorimeter at temperatures between 15 and 385K. 3-CBCN is a nematogenic mesogen, whose melting and clearing points are 316.33 and 319.09 K, respectively. The enthalpy and entropy gained at fusion are 20.4 kJmol -1 and 64.4 J K -1 mol -1, respectively; those for the nematic-to-isotropic transition are 1.1 kJmol -1 and 3.5 J K -1 mol -1 respectively. 3-CBCN exhibits a supercooled nematic phase, whose molar heat capacities have been measured from 25 K below the melting point. The molar and transition entropies of 3-CBCN are discussed in relation to those of 4-propylbiphenyl-4-carbonitrile (3-BBCN) and trans,trans-4'-propylbicyclohexyl- 4-carbonitrile (3-CCCN). There seems to exist a correlation between these values and mesophase stability. Finally, Eidenschink's theoretical model for the nematic-to-isotropic transition has been applied to 3-CBCN; the transition enthalpy estimated according to this model agrees well with the observed value.     

Thermodynamic analysis of the temperature dependence of OH adsorption on Pt(111) and Pt(100) electrodes in acidic media in the absence of specific anion adsorption

The effect of temperature on the voltammetric OH adsorption on Pt(111) and Pt(100) electrodes in perchloric acid media has been studied. From a thermodynamic analysis based on a generalized adsorption isotherm, DeltaG degrees , DeltaH degrees , and DeltaS degrees values for the adsorption of OH have been determined. On Pt(111), the adsorption enthalpy ranges between -265 and -235 kJ mol(-1), becoming less exothermic as the OH coverage increases. These values are in reasonable agreement with experimental data and calculated values for the same reaction in gas phase. The adsorption entropy for OH adsorption on Pt(111) ranges from -200 J mol(-1) K(-1) (low coverage) to -110 J mol(-1) K(-1) (high coverage). On the other hand, the enthalpy and entropy of hydroxyl adsorption on Pt(100) are less sensitive to coverage variations, with values ca. DeltaH degrees = -280 kJ mol(-1) and DeltaS degrees = -180 J mol(-1) K(-1). The different dependence of DeltaS degrees with coverage on both electrode surfaces stresses the important effect of the substrate symmetry on the mobility of adsorbed OH species within the water network directly attached to the metal surface.     

Entropy and dynamics of water in hydration layers of a bilayer

We compute the entropy and transport properties of water in the hydration layer of dipalmitoylphosphatidylcholine bilayer by using a recently developed theoretical scheme [two-phase thermodynamic model, termed as 2PT method; S.-T. Lin et al., J. Chem. Phys. 119, 11792 (2003)] based on the translational and rotational velocity autocorrelation functions and their power spectra. The weights of translational and rotational power spectra shift from higher to lower frequency as one goes from the bilayer interface to the bulk. Water molecules near the bilayer head groups have substantially lower entropy (48.36 J/mol/K) than water molecules in the intermediate region (51.36 J/mol/K), which have again lower entropy than the molecules (60.52 J/mol/K) in bulk. Thus, the entropic contribution to the free energy change (TΔS) of transferring an interface water molecule to the bulk is 3.65 kJ/mol and of transferring intermediate water to the bulk is 2.75 kJ/mol at 300 K, which is to be compared with 6.03 kJ/mol for melting of ice at 273 K. The translational diffusion of water in the vicinity of the head groups is found to be in a subdiffusive regime and the rotational diffusion constant increases going away from the interface. This behavior is supported by the slower reorientational relaxation of the dipole vector and OH bond vector of interfacial water. The ratio of reorientational relaxation time for Legendre polynomials of order 1 and 2 is approximately 2 for interface, intermediate, and bulk water, indicating the presence of jump dynamics in these water molecules.     

Mechanistic insight into the activity of tyrosinase from variable-temperature studies in an aqueous/organic solvent

The activity of mushroom tyrosinase towards a representative series of phenolic and diphenolic substrates structurally related to tyrosine has been investigated in a mixed solvent of 34.4% methanol-glycerol (7:1, v/v) and 65.6% (v/v) aqueous 50 mM Hepes buffer at pH 6.8 at various temperatures. The kinetic activation parameters controlling the enzymatic reactions and the thermodynamic parameters associated with the process of substrate binding to the enzyme active species have been deduced from the temperature variation of the kcat and KM parameters. The activation free energy is dominated by the enthalpic term, the value of which lies in the relatively narrow range of 61+/-9 kJ mol(-1) irrespective of substrate or reaction type (monophenolase or diphenolase). The activation entropies are small and generally negative and contribute no more than 10% to the activation free energy. The substrate binding parameters are characterized by large and negative enthalpy and entropy contributions, which are typically dictated by polar protein-substrate interactions. The substrate 4-hydroxyphenylpropionic acid exhibits a strikingly anomalous temperature dependence of the enzymatic oxidation rate, with deltaH(double dagger) approximately = 150 kJ mol(-1) and deltaS(double dagger) approximately = 280 J K(-1) mol(-1), due to the fact that it can competitively bind to the enzyme through the phenol group, like the other substrates, or the carboxylate group, like carboxylic acid inhibitors. A kinetic model that takes into account the dual substrate/inhibitor nature of this compound enables rationalization of this anomalous behavior.     

Standard absolute entropy, S degrees 298 values from volume or density. 1. Inorganic materials

Standard absolute entropies of many inorganic materials are unknown; this precludes a full understanding of their thermodynamic stabilities. It is shown here that formula unit volume, V(m)(), can be employed for the general estimation of standard entropy, S degrees 298 values for inorganic materials of varying stoichiometry (including minerals), through a simple linear correlation between entropy and molar volume. V(m)() can be obtained from a number of possible sources, or alternatively density, rho, may be used as the source of data. The approach can also be extended to estimate entropies for hypothesized materials. The regression lines pass close to the origin, with the following formulas: For inorganic ionic salts, S degrees 298 /J K(-)(1) mol(-)(1) = 1360 (V(m)()/nm(3) formula unit(-)(1)) + 15 or = 2.258 [M/(rho/g cm(-)(3))] + 15. For ionic hydrates, S degrees 298 /J K(-)(1) mol(-)(1) = 1579 (V(m)()/nm(3) formula unit(-)(1)) + 6 or = 2.621 [M/(rho/g cm(-)(3))] + 6. For minerals, S degrees 298 /J K(-)(1) mol(-)(1) = 1262 (V(m)()/nm(3) formula unit(-)(1)) + 13 or = 2.095 [M/(rho/g cm(-)(3))] + 13. Coupled with our published procedures, which relate volume to other thermodynamic properties via lattice energy, the correlation reported here complements our development of a predictive approach to thermodynamics and ultimately permits the estimation of Gibbs energy data. Our procedures are simple, robust, and reliable and can be used by specialists and nonspecialists alike.     

Experimental thermodynamics of free glycine conformations: the first Raman experiment after twenty years of calculations

Low-frequency, gas-phase vibrational (Raman) spectroscopy was used in conjunction with a jet-cooled technique and ab initio calculations to study the intrinsic thermodynamic properties of the free (gas-phase) amino acid--glycine (Gly, H(2)NCHRCOOH). The first experimental evaluation of the enthalpy differences between the Gly conformations in the vapor phase is presented. The enthalpy values were determined to be 0.33 ± 0.05 and 1.15 ± 0.07 kcal mol(-1) for the ccc and gtt rotamers, respectively; the corresponding relative entropy values were -2.86 ± 0.12 and -0.12 ± 0.16 cal mol(-1) K(-1), respectively. It was proven that the low-frequency Raman and infrared spectroscopy is capable of estimating intrinsic thermodynamic parameters of protein building blocks, such as intermolecular hydrogen bonds (ccc conformer) and rotation around one of the bonds (N-C, gtt conformer). The inaccuracy of the RRHO approximation to Gly conformers was experimentally confirmed. Benchmark data for quantum theory and molecular dynamics were provided.     

Hydrogen bond strength and network structure effects on hydration of non-polar molecules

We measure the solvation free energy, Δμ*, for hard spheres and Lennard-Jones particles in a number of artificial liquids made from modified water models. These liquids have reduced hydrogen bond strengths or altered bond angles. By measuring Δμ* for a number of state points at P = 1 bar and different temperatures, we obtain solvation entropies and enthalpies, which are related to the temperature dependence of the solubilities. By resolving the solvation entropy into the sum of the direct solute-solvent interaction and a term depending on the solvent reorganisation enthalpy we show that, although the hydrophobic effect in water at 300 K arises mainly from the small molecular size, its temperature dependence is anomalously low because the reorganisation enthalpy of liquid water is unusually small. We attribute this to the strong tetrahedral network which results from both the molecular geometry and the hydrogen bond strength.     

Confusing cause and effect: energy-entropy compensation in the preferential solvation of a nonpolar solute in dimethyl sulfoxide/water mixtures

We performed molecular simulations to analyze the thermodynamics of methane solvation in dimethyl sulfoxide (DMSO)/water mixtures (298 K, 1 atm). Two contributions to the interaction thermodynamics are studied separately: (i) the introduction of solute-solvent interactions (primary contribution) and (ii) the solute-induced disruption of cohesive solvent-solvent interactions (secondary contribution). The energy and entropy changes of the secondary contribution always exactly cancel in the free energy (energy-entropy compensation), hence only the primary contribution is important for understanding changes of the free energy. We analyze the physical significance of the solute-solvent energy and solute-solvent entropy associated with the primary contribution and discuss how to obtain these quantities from experiments combining solvation thermodynamic and solvent equation of state data. We show that the secondary contribution dominates changes in the methane solvation entropy and enthalpy: below 30 mol % DMSO in the mixture, methane, because of more favorable dispersion interactions with DMSO molecules, preferentially attracts DMSO molecules, which, in response, release water molecules into the bulk, causing an increase in the entropy. This large energy-entropy compensating process easily causes a confusion in the cause for and the effect of preferred methane-DMSO interactions. Methane-DMSO dispersion interactions are the cause, and the entropy change is the effect. Procedures that infer thermodynamic driving forces from analyses of the solvation entropies and enthalpies should therefore be used with caution.     

The design, synthesis and evaluation of high affinity macrocyclic carbohydrate inhibitors

Carbohydrate-protein interactions have been investigated for a model system of a monoclonal antibody, SYA/J6, which binds a trisaccharide epitope of the O-polysaccharide of the Shigella flexneri variant Y lipopolysaccharide. The thermodynamics of binding for the methyl glycoside of the native trisaccharide epitope, Rha-Rha-GlcNAc () to SYA/J6 over a range of temperatures exhibits strong, linear enthalpy-entropy compensation and a negative heat capacity change (DeltaC(p)=-152 cal mol(-1) degree(-1)). At 293 K the free energy of association is the sum of favourable enthalpy and entropy contributions (DeltaH=-3.9 kcal mol(-1) and -TDeltaS=-2.9 kcal mol(-1)). Crystal structures for SYA/J6 Fab detailed the position of the native trisaccharide epitope, Rha-Rha-GlcNAc, and facilitated a strategy to design a tighter binding, low molecular weight ligand. This involved pre-organization of the native trisaccharide in its bound conformation by addition of intramolecular constraints (a beta-alanyl or glycinyl tether). ELISA measurements indicated that the glycinyl tethered trisaccharide was not an optimal candidate for further analysis, while microcalorimetry provided data showing that the beta-alanyl tethered trisaccharide displayed a 15-fold increase in affinity for SYA/J6. Tethering resulted in a favourable entropic contribution to binding, relative to the native trisaccharide (-TDeltaDeltaS=-1.2 kcal mol(-1)). Potential energy and dynamics calculations using the AMBER Plus force fields indicated that trisaccharide adopted a rigid conformation similar to that of the bound conformation of the native trisaccharide epitope. While this strategy resulted in modest free energy gains by minimizing losses due to conformational entropy, thermodynamic data are consistent with significant contributions from solvent reorganization.     

Predicting water uptake in poly(perfluorosulfonic acids) using force field simulation methods

Free energy perturbation methods were applied to predict water contents in hydrated poly(perfluorosulfonic acids) (PPFSA). The simulations were based on the TEAM force field which was derived from quantum mechanical data calculated for small molecules using density functional theory (DFT) and thermodynamic data of molecular liquids and crystal. The equilibrium water contents in three PPFSA polymers (Nafion-117, Nafion-115 and Hyflon) were predicted by evaluating excess chemical potentials of water in hydrated polymers and in pure water. High level of precision measured by average uncertainty of ca. 0.1 kcal mol(-1), and accuracy in terms of deviation from experimental data by ca. 0.2 kcal mol(-1) were obtained in the predicted excess chemical potentials. The predicted amounts of water uptake agree well with experimental values. In addition, the equilibrium and dynamic properties of hydrated Nafion-117 were calculated and the results agree well with the existing experimental and computational data. The entropy and enthalpy contributions in the calculated excess chemical potentials are analyzed and the results are consistent with intuition. A linear correlation between the entropies and enthalpies is identified for the systems studied, which indicates that just increasing the interaction energies between water and host materials does not guarantee enhancement of the water uptake.     

Orientation polarization from faster motions in the ultraviscous and glassy diethyl phthalate and its entropy

Dielectric spectra of the beta relaxation in glassy and ultraviscous liquid diethyl phthalate show that its relaxation strength Delta epsilon(beta), the distribution of times, and the relaxation rate are more sensitive to temperature T in the ultraviscous liquid than in the glassy state. The Delta epsilon(beta) against temperature plot has an elbow-shaped break near T(g) of approximately 181 K, which is remarkably similar to that observed in the entropy, enthalpy, and volume against temperature plots, and in the plot of Delta epsilon(beta) against the liquid's entropy minus its 0 K value. The ratio of Delta epsilon(beta) to diethyl phthalate's entropy, after subtracting the 0 K value, is 1.08 x 10(-3) mol K/J in the glassy state at 120.4 K, which decreases slowly to 0.81 x 10(-3) mol K/J at 176 K near T(g) and thereafter rapidly increases to 1.57 x 10(-3) mol K/J at 190 K. Variation in Delta epsilon(beta) parallels the variation of the entropy. A change in the activation energy of the beta process at T>T(g) indicates that its rate is also determined by the structure of the ultraviscous liquid. Features of beta relaxation are consistent with localized motions of molecules and may not involve small-angle motions of all molecules.     

纳米硫化钴与明胶蛋白质的原位键合作用研究

利用紫外-可见吸收光谱(UV-Vis)和傅里叶变换红外光谱(FT-IR),研究了pH值11.00时,不同温度下CoS纳米粒子与明胶蛋白质的键合作用.根据吸光度与CoS浓度的关系,由Lineweave-Burk方程计算了不同温度下CoS纳米粒子与明胶蛋白作用的键合常数K(温度为293 K时键合常数K为3.01×10³L/mol;温度为301 K时键合常数K为2.12×10³L/mol;温度为313 K时键合常数K为1.85×10³L/mol)以及对应温度下反应的热力学参数(ΔrH_m=-17.93 kJ/mol;ΔrS_m=4.93 J/(K.mol);ΔrG_m=-19.37/-19.41/-19.47kJ/mol).CoS纳米粒子与明胶蛋白之间主要靠静电力结合.研究结果为初步探索纳米颗粒与纤维状蛋白质之间相互作用的化学机制提供了必要的信息.     

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.