Molecular density functional theory of solvation: from polar solvents to water

A classical density functional theory approach to solvation in molecular solvent is presented. The solvation properties of an arbitrary solute in a given solvent, both described by a molecular force field, can be obtained by minimization of a position and orientation-dependent free-energy density functional. In the homogeneous reference fluid approximation, limited to two-body correlations, the unknown excess term of the functional approximated by the angular-dependent direct correlation function of the pure solvent. We show that this function can be extracted from a preliminary MD simulation of the pure solvent by computing the angular-dependent pair distribution function and solving subsequently the molecular Ornstein-Zernike equation using a discrete angular representation. The corresponding functional can then be minimized in the presence of an arbitrary solute on a three-dimensional cubic grid for positions and Gauss-Legendre angular grid for orientations to provide the solvation structure and free-energy. This two-step procedure is proved to be much more efficient than direct molecular dynamics simulations combined to thermodynamic integration schemes. The approach is shown to be relevant and accurate for prototype polar solvents such as the Stockmayer solvent or acetonitrile. For water, although correct for neutral or moderately charged solute, it tends to underestimate the tetrahedral solvation structure around H-bonded solutes, such as spherical ions. This can be corrected by introducing suitable three-body correlation terms that restore both an accurate hydration structure and a satisfactory energetics.     

Molecular solvation in water-methanol and water-sorbitol mixtures: the roles of preferential hydration, hydrophobicity, and the equation of state

Molecular dynamics simulations of aqueous mixtures of methanol and sorbitol were performed over a wide range of binary composition, density (pressure), and temperature to study the equation of state and solvation of small apolar solutes. Experimentally, methanol is a canonical solubilizing agent for apolar solutes and a protein denaturant in mixed-aqueous solvents; sorbitol represents a canonical "salting-out" or protein-stabilizing cosolvent. The results reported here show increasing sorbitol concentration under isothermal, isobaric conditions results in monotonic increases in apolar solute excess chemical potential (mu2ex) over the range of experimentally relevant temperatures. For methanol at elevated temperatures, increasing cosolvent composition results in monotonically decreasing mu2ex. However, at lower temperatures mu2ex exhibits a maximum versus cosolvent concentration, as seen experimentally for Ar in ethanol-water solutions. Both density anomalies and hydrophobic effects--characterized by temperatures of density maxima and apolar solute solubility minima, respectively--are suppressed upon addition of either sorbitol or methanol at all temperatures and compositions simulated here. Thus, the contrasting effects of sorbitol and methanol on solute chemical potential cannot be explained by qualitative differences in their ability to enhance or suppress hydrophobic effects. Rather, we find mu2ex values across a broad range of temperatures and cosolvent composition can be quantitatively explained in terms of isobaric changes in solvent density--i.e., the equation of state--along with the corresponding packing fraction of the solvent. Analysis in terms of truncated preferential interaction parameters highlights that care must be taken in interpreting cosolvent effects on solvation in terms of local preferential hydration.     

Thermodynamic studies of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol at 25°C

The osmotic coefficients of binary methanol and ethanol solutions of 1-dodecanol and 1-tetradecanol wer measured at 25°C up to 8 mol-kg^–1 in methanol and 5.5 mol-kg^–1 in ethanol. The activity coefficients of the solute were calculated from Bjerrum's relation. From the osmotic and activity coeficients the excess Gibbs energies of solution as well as the respective partial molar functions of solute and solvent and the virial pair interaction coefficients for the excess Gibbs energies were calculated. In addition, the difference in the Gibbs energy of solvation for the solvent in solution relative to the pure solvent was calculated, as well as the partial molar volumes and excess partial molar volumes of solutes at infinite dilution, and the coefficients of pairwise contributions to the excess volume were determined. The thermodynamic parameters obtained are discussed on the basis of solute-solvent and solute-solute interactions.     

Partial molar volume and solvation structure of naphthalene in supercritical carbon dioxide: a Monte Carlo simulation study

Monte Carlo simulations were used to investigate the solvation of naphthalene in supercritical carbon dioxide at a temperature of 308.38 K just above the solvent's critical temperature and at pressures of 74.6, 79.7, 87.8, and 310.2 bar covering a range from just below to far above the solvent's critical pressure and at a slightly elevated temperature of 318.15 K and a pressure of 93.0 bar. The Monte Carlo simulations were carried out in the isobaric-isothermal ensemble and employed the transferable potentials for phase equilibria (TraPPE) force field. Systems containing 2000 carbon dioxide molecules and from 0 to 4 solute molecules were used for all five state points, and additional simulations with 16 000 solvent molecules were carried out at the lower temperature and p = 79.7 bar. In agreement with experiment, the simulations yield large, negative partial molar volumes of naphthalene near the critical pressure at 79.7 bar, with values of -4340 +/- 750 and -3400 +/- 620 cm(3) mol(-1) for the 2000 and 16 000 molecule systems, respectively. Structural analysis through radial distribution functions and the corresponding number integrals yields good agreement with neutron diffraction data and shows evidence for a long-range density enhancement around solutes but lacking any specific solute-solvent clustering. Solvatochromic shifts estimated from the local solvent structure correlate well with the experimental data over the entire pressure range.     

The effects of solute-solvent electrostatic interactions on solvation dynamics in supercritical CO2

We present here the results of molecular-dynamics simulation of solvation dynamics in supercritical CO(2) at a temperature of about 1.05T(c), where T(c) is the critical temperature, and at a series of densities ranging from 0.4 to 2.0 of the critical density rho(c). We focus on electrostatic solvation dynamics, representing the electronic excitation of the chromophore as a change in its charge distribution from a quadrupolar-symmetry ground state to a dipolar excited state. Two perturbations are considered, corresponding to different magnitudes of solute excited-state dipoles, denoted as d5 and d8. The d8 solute is more attractive, leading to a larger enhancement in CO(2) clustering upon solute electronic excitation. This has a large impact on solvation dynamics, especially at densities below rho(c). At these densities, solvation dynamics is much slower for the d8 than for the d5 solute. For both solutes, solvation dynamics becomes faster at densities above rho(c) at which solvent clustering diminishes. We show that the slowest solvation time scale is associated with solvent clustering and we relate it to solute-solvent mutual translational diffusion and the extent of change in effective local density resulting from solute electronic excitation.     

Communication: On the locality of hydrogen bond networks at hydrophobic interfaces

The formation of structured hydrogen bond networks in the solvation shells immediate to hydrophobic solutes is crucial for a large number of water mediated processes. A long lasting debate in this context regards the mutual influence of the hydrophobic solute into the bulk water and the role of the hydrogen bond network of the bulk in supporting the solvation structure around a hydrophobic molecule. In this context we present a molecular dynamics study of the solvation of various hydrophobic molecules where the effect of different regions around the solvent can be analyzed by employing an adaptive resolution method, which can systematically separate local and nonlocal factors in the structure of water around a hydrophobic molecule. A number of hydrophobic solutes of different sizes and two different model potential interactions between the water and the solute are investigated.     

Treating entropy and conformational changes in implicit solvent simulations of small molecules

Implicit solvent models are increasingly popular for estimating aqueous solvation (hydration) free energies in molecular simulations and other applications. In many cases, parameters for these models are derived to reproduce experimental values for small molecule hydration free energies. Often, these hydration free energies are computed for a single solute conformation, neglecting solute conformational changes upon solvation. Here, we incorporate these effects using alchemical free energy methods. We find significant errors when hydration free energies are estimated using only a single solute conformation, even for relatively small, simple, rigid solutes. For example, we find conformational entropy (TDeltaS) changes of up to 2.3 kcal/mol upon hydration. Interestingly, these changes in conformational entropy correlate poorly (R2 = 0.03) with the number of rotatable bonds. The present study illustrates that implicit solvent modeling can be improved by eliminating the approximation that solutes are rigid.     

Charge-dependent cavity radii for an accurate dielectric continuum model of solvation with emphasis on ions: aqueous solutes with oxo, hydroxo, amino, methyl, chloro, bromo, and fluoro functionalities

Dielectric continuum solvation models are widely used because they are a computationally efficacious way to simulate equilibrium properties of solutes. With advances that allow for molecular-shaped cavities, they have reached a high level of accuracy, in particular for neutral solutes. However, benchmark tests show that existing schemes for defining cavities are unable to consistently predict accurately the effects of solvation on ions, especially anions. This work involves the further development of a protocol put forth earlier for defining the cavities of aqueous solutes, with resulting advances that are most striking for anions. Molecular cavities are defined as interlocked spheres around atoms or groups of atoms in the solute, but the sphere radii are determined by simple empirically based expressions involving the effective atomic charges of the solute atoms (derived from molecular electrostatic potential) and base radii. Both of these terms are optimized for the different types of atoms or functional groups in a training set of neutral and charged solutes. Parameters in these expressions for radii were fitted by minimizing residuals between calculated and measured standard free energies of solvation (DeltaG(s)*), weighted by the uncertainty in the measured value. The calculations were performed using density functional theory with the B3LYP functional and the 6-311+G** basis set and the COnductor-like Screening MOdel (COSMO). The optimized radii definitions reproduce DeltaG(s)* of neutral solutes and singly charged ions in the training set to within experimental uncertainty and, more importantly, accurately predict DeltaG(s)* of compounds outside the training set, in particular anions (J. Phys. Chem. A 2003, 107, 5778). Inherent to this approach, the cavity definitions reflect the strength of specific solute-water interactions. We surmise that this feature underlies the success of the model, referred to as the CD-COSMO model for Charge-Dependent (also Camaioni-Dupuis) COSMO model. These findings offer encouragement that we can keep extending this scheme to other functional groups and obtain better accuracy in using continuum solvation models to predict equilibrium properties of aqueous ionic solutes. The approach is illustrated for a number of test cases, including the determination of acidities of an amine base, a study of the tautomerization equilibrium of a zwitterionic molecule (glycine), and calculating solvation energies of transition states toward a full characterization of reaction pathways in aqueous phase, here in S(N)2 exchange reactions. The calculated reaction barriers in aqueous solution are in excellent agreement with experimental values.     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

Volumetric Properties of Dilute Solutions of Water in Acetone between 288.15 and 318.15 K

Densities of dilute solutions of water in acetone, with solute mole fractions ranging up to 0.03, have been measured with an error of 8 ×10⁻⁶ g⋅cm⁻³, at 288.15, 298.15, 308.15 and 318.15 K, using a precision vibrating-tube densimeter. The partial molar volumes of the solute water (down to infinite dilution) and solvent acetone, as well as the excess molar volumes of the specified mixtures, have been calculated. The effects of the solute concentration and temperature on the volume packing changes, caused by solvation of water in acetone, have been considered.     

Simulations of solvation free energies and solubilities in supercritical solvents

Computer simulations are used to study solvation free energies and solubilities in supercritical solvents. Solvation free energies are calculated using the particle insertion method. The equilibrium solvent configurations required for these calculations are based on molecular dynamics simulations employing model solvent potentials previously tuned to reproduce liquid-vapor coexistence properties of the fluids Xe, C(2)H(6), CO(2), and CHF(3). Solutes are represented by all-atom potentials based on ab initio calculations and the OPLS-AA parameter set. Without any tuning of the intermolecular potentials, such calculations are found to reproduce the solvation free energies of a variety of typical solid solutes with an average accuracy of +/-2 kJmol. Further calculations on simple model solutes are also used to explore general aspects of solvation free energies in supercritical solvents. Comparisons of solutes in Lennard-Jones and hard-sphere representations of Xe show that solvation free energies and thus solubilities are not significantly influenced by solvent density fluctuations near the critical point. The solvation enthalpy and entropy do couple to these fluctuations and diverge similarly to solute partial molar volumes. Solvation free energies are also found to be little affected by the local density augmentation characteristic of the compressible regime. In contrast to solute-solvent interaction energies, which often provide a direct measure of local solvent densities, solvation free energies are remarkably insensitive to the presence of local density augmentation.     

Aqueous solutions that model the cytosol: studies on polarity, chemical reactivity and enzyme kinetics

Concentrated solutions of a series of organic compounds have been prepared and the effects of these solutes on the properties of the solvent system assessed as a function of their concentration and nature. Polarity, as measured by Reichardt's E(T)(30) probe, exhibits a linear variation with both solute and water concentration for simple solutes. Non-linear behaviour was also observed and is associated with preferential solvation or binding of the E(T)(30) probe molecule by the added solute. The observed trends in polarity are mirrored in the effects of these solutes on chemical reactivity and enzyme kinetics. Environmental effects on the kinetics of hydrolysis of 4-nitrophenyl dichloroacetate, the hydronium-ion catalysed hydrolysis of 2-(4-nitrophenoxy)-tetrahydropyran, the acyl transfer reaction between 4-nitrophenyl acetate and TRIS, the Diels-Alder reaction between 1,4-naphthoquinone and cyclopentadiene and the trypsin-catalysed hydrolysis of 4-nitrophenyl acetate are reported and discussed in terms of the properties of the solutes and the mechanistic requirements of these reactions. Linear correlations were observed between the logarithms of the rate constants for the acetal hydrolysis, acyl transfer and Diels-Alder reactions with water concentration. Since the latter varies linearly with E(T)(30), this indicates a linear free energy relationship between solution polarity and chemical reactivity.     

Free-energy analysis of the molecular binding into lipid membrane with the method of energy representation

A statistical-mechanical treatment of the molecular binding into lipid membrane is presented in combination with molecular simulation. The membrane solution is viewed as an inhomogeneous, mixed solvent system, and the free energy of solvation of a solute in membrane is computed with a realistic set of potential functions by the method of energy representation. Carbon monoxide, carbon dioxide, benzene, and ethylbenzene are adopted as model solutes to analyze the binding into 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC) membrane. It is shown that the membrane inside is more favorable than bulk water and that the solute distribution is diffuse throughout the membrane inside. The membrane-water partition coefficient is then constructed with the help of the Kirkwood-Buff theory from the solvation free energy obtained separately in the hydrophobic, glycerol, headgroup, and aqueous regions. To discuss the role of repulsive and attractive interactions, the solvation free energy is partitioned into the DMPC and water contributions and the effect of water to stabilize the benzene and ethylbenzene solutes within the membrane is pointed out.     

UV-visible spectroscopic study of solvation in ternary solvent mixtures: ketocyanine dye in methanol + acetone + water and methanol + acetone + benzene

Solvation characteristics of a ketocyanine dye have been studied in completely miscible ternary solvent mixtures, namely, methanol + acetone + water and methanol + acetone + benzene, by monitoring the solvatochromic absorption band of the dye. The maximum energy of absorption (E) of the solute in a ternary solvent mixture differs significantly from the mole fraction average of the E values in the component solvents. Results in the corresponding binary solvent mixtures also show a deviation of the E value from the mole fraction averaged E values. The results have been explained in terms of preferential solvation using a two phase model of solvation. The excess or deficit over the bulk composition of a solvent component in the vicinity of the solute molecule in a ternary solvent mixture has been estimated using the knowledge of solvation in the corresponding binary mixtures.     

Use of a solvatochromic probe for study of solvation in ternary solvent mixture

Solvation characteristics of 2,6-diphenyl-4-(2,4,6-triphenyl-1-pyridino)phenolate in completely miscible ternary solvent mixtures (viz., methanol + acetone + water, methanol + acetone + benzene, and methanol + chloroform + benzene) have been studied by using an electronic spectroscopic procedure. The transition energy (E) corresponding to the charge-transfer band maximum of the solute in a ternary solvent mixture differs significantly from the average E-values in the component solvents weighted by the mole fraction of the solvents. A two-phase model of solvation has been invoked to explain the results. The excess or deficit of solvent components in the local region of the solute molecule over that in the bulk has been estimated using the knowledge of solvation in binary solvent mixtures.     

Influence of concentration and anion size on hydration of H+ ions and water structure

Neutron diffraction experiments with hydrogen isotope substitution on aqueous solutions of HCl and HBr have been performed at concentrations ranging from 1:17 to 1:83 solute per water molecules, at ambient conditions. Data are analyzed using the empirical potential structure refinement technique in order to extract information on both the ion hydration shells and the microscopic structure of the solvent. It is found that the influence of these solutes on the water structure is less concentration dependent than that of salts or hydroxides. Moreover protons readily form a strong H-bond with a water molecule upon solvation, at all proportions. The majority of them is also bonded via a longer bond to another water molecule, giving a prepeak in the g(OwOw). At high solute concentration, the second water molecule may be substituted by the counterion. In particular at solute concentrations of the order of 1:17 or higher, all protons have an anion within a distance of 4.5 A.     

Ermod: Fast and versatile computation software for solvation free energy with approximate theory of solutions

ERmod is a software package to efficiently and approximately compute the solvation free energy using the method of energy representation. Molecular simulation is to be conducted at two condensed‐phase systems of the solution of interest and the reference solvent with test‐particle insertion of the solute. The subprogram ermod in ERmod then provides a set of energy distribution functions from the simulation trajectories, and another subprogram slvfe determines the solvation free energy from the distribution functions through an approximate functional. This article describes the design and implementation of ERmod, and illustrates its performance in solvent water for two organic solutes and two protein solutes. Actually, the free‐energy computation with ERmod is not restricted to the solvation in homogeneous medium such as fluid and polymer and can treat the binding into weakly ordered system with nano‐inhomogeneity such as micelle and lipid membrane. ERmod is available on web at http://sourceforge.net/projects/ermod . © 2014 Wiley Periodicals, Inc.     

Solute-solvent interactions between a range of solutes and trifluoropropyl siloxane stationary phases in terms of gas-liquid chromatography activity coefficients

Summary Several poly(3,3,3-methyltrifluoropropyl siloxane) stationary phases with a low percentage of trifluoropropyl have been recharacterised by means of activity coefficients at temperatures in the range 60–140°C. The temperature effect of activity coefficients was studied. Thermodynamic magnitudes: excess Gibbs energy, excess enthalpy and excess entropy for 44 solutes on these polymers were calculated, and their relationships with solutes’ molecular connectivity indexes were tested. Solute-polymer interactions were calculated at 120°C according to the solvation parameter model, and several correlations for selected solutes and polymers were investigated, mainly the effect of solutes’ structure on the non-polar interactions and the effect of the solute dipole moment on the polar interactions. In addition, the influence of polymer polarity on the different polar and non-polar interactions was investigated.     

Linear solvation energy relationship of the solubility of very polar gases: Sulfur dioxide,hydrogen chloride,hydrogen bromide,and ammonia

A linear free energy relationship was found for the log (mole fraction) of solutes in a wide variety of organic solvents with the solvatochromic parameters and the Hildebrand solubility parameter. The solutes were the highly dipolar gases sulfur dioxide, hydrogen chloride, hydrogen bromide, and ammonia at 25°C and 1 atm. partial pressure of the solute. It was found that correlations were greatly improved if solvatochromic parameters for the solvent as a monomer were used rather than the values for the bulk solvent. In solutions with these very dipolar gases, the mole ratio of solute to solvents approaches unity in many of the solutions, so a molecule of solute is interacting primarily with a particular molecule of the solvent. Therefore, the use of the solvatochromic parameters for the solvent as monomer is physically reasonable.