Molecular rotation as a tool for exploring specific solute-solvent interactions.

Solute-solvent interactions play an important role in determining the physicochemical properties of liquids and solutions. As a consequence, understanding these interactions has been one of the long-standing problems in physical chemistry. This Minireview describes our approach towards attaining this goal, which is to investigate rotational relaxation of a pair of closely related, medium-sized nondipolar solutes in a set of appropriately chosen solvents. Our studies indicate that solute-solvent hydrogen bonding significantly hinders solute rotation. We have also examined the role of solvent size both in the absence and presence of specific interactions and it has been observed that the size of the solvent has a bearing on solute rotation especially in the absence of specific interactions. Our results point to the fact that only strong solute-solvent hydrogen bonds have the ability to impede the rotation of the solute molecule because, in such a scenario, hydrogen-bonding dynamics and rotational dynamics transpire on comparable time scales. This aspect has been substantiated by measuring the reorientation times of the chosen solutes in solvents such as ethanol and trifluoroethanol, which have distinct hydrogen-bond donating and accepting abilities, and correlating them with solute-solvent interaction strengths. As an alternative treatment, it has been shown that specific interactions between the solute and the solvent can be modeled as dielectric friction with the extended charge distribution model. This approach is not unrealistic considering the fact that specific as well as non-specific interactions are electrostatic by nature and the differences between them are subtle.     

Long-range electrostatic interactions in hybrid quantum and molecular mechanical dynamics using a lattice summation approach

A method based on a lattice summation technique for treating long-range electrostatic interactions in hybrid quantum mechanics/molecular mechanics simulations is presented in this article. The quantum subsystem is studied at the semiempirical level, whereas the solvent is described by a two-body potential of molecular mechanics. Molecular dynamics simulations of a (quantum) chloride ion in (classical) water have been performed to test this technique. It is observed that the application of the lattice summations to solvent-solvent interactions as well as on solute-solvent ones has a significant effect on solvation energy and diffusion coefficient. Moreover, two schemes for the computation of the long-range contribution to the electrostatic interaction energy are investigated. The first one replaces the exact charge distribution of the quantum solute by a Mulliken charge distribution. The long-range electrostatic interactions are then calculated for this charge distribution that interacts with the solvent molecule charges. The second one is more accurate and involves a modified Fock operator containing long-range electron-charge interactions. It is shown here that both schemes lead to similar results, the method using Mulliken charges for the evaluation of long-range interactions being, however, much more computationally efficient.     

Study of solvent effects by means of averaged solvent electrostatic potentials obtained from molecular dynamics data

We present the theory and implementation of a new approach for studying solvent effects. The electronic structure of the solute, calculated at the ab initio level, is obtained in the presence of the surrounding medium. We employ a mean field theory in which the solvent response is described by means of point charges chosen in such a way that they reproduce the average value of the solvent electrostatic potential calculated from molecular dynamics data. In this way, the complete solvent potential can be introduced into the solute Hamiltonian without making use of a one-center multiple expansion of the solute-solvent potential. In the proposed method, only one quantum calculation has to be performed and a great number of configurations can easily be included making the calculation statistically significant. We show that, despite the large fluctuations in the solute charge distribution induced by the solvent, the proposed mean field theory adequately reproduces the energetics and properties of formamide and water molecules in aqueous solution. © 1997 by John Wiley & Sons, Inc.     

Interactions of nitrous oxide with fluorinated liquids

The interactions of nitrous oxide with fluorinated liquids are investigated by reporting original experimental results on gas solubility and interpreting them using molecular simulation. Nitrous oxide is highly soluble in the three fluorinated liquids studied-perfluorooctane, 1-bromoperfluorooctane (perfluorooctylbromide), and perfluorohexylethane-with mole fraction solubilities on the order of 0.03 under ambient conditions. An intermolecular potential model was developed for nitrous oxide, with a functional form of the Lennard-Jones plus point charges type, adjusted to the experimental multipole moments and to vapor-liquid equilibrium properties. The solubility of nitrous oxide in perfluorocarbon liquids was calculated by molecular simulation methods, and a dissimilar interaction parameter of 0.92 in the Lennard-Jones well-depths between solute and solvent had to be introduced to reach agreement with the experimental results, similar to what is found for hydrocarbon-fluorocarbon interactions. The structure of the solutions was studied by analysis of solute-solvent radial distribution functions, showing that, although electrostatic interactions are not predominant, a small orientational effect is still present between the dipole of nitrous oxide and those of the substituted fluorinated liquids.     

Solute rotation in polar liquids: microscopic basis for the Stokes-Einstein-Debye model

Here, we develop a framework for a molecular level understanding of the celebrated Stokes-Einstein-Debye (SED) formula. In particular, we explore reasons behind the surprising success of the SED model in describing dipolar solute rotation in complex polar media. Relative importance of solvent viscosity and solute-solvent dipolar interaction is quantified via a self-consistent treatment for the total friction on a rotating solute where the hydrodynamic contribution is modified by the friction arising from the longer ranged solute-solvent dipolar interaction. Although the solute-solvent dipolar coupling is obtained via the Mori-Zwanzig formalism, the inclusion of solvent structure via the wave vector dependent viscosity in the hydrodynamic contribution incorporates solvent molecularity in the present theory. This approach satisfactorily describes the experimental rotation times measured using a dipolar solute, coumarin 153 (C153), in protic and aprotic polar liquids, and more importantly, provides microscopic explanation for insignificant contribution of electrical interactions on solute rotation, in contrast to the substantial role played by the translational dielectric friction in the context of ionic mobility. It is also discussed on how the present theory can be suitably extended to study the rotation of a realistic solute in media other than dipolar solvents.     

Efficient implementation of three-dimensional reference interaction site model self-consistent-field method: application to solvatochromic shift calculations

The authors present an implementation of the three-dimensional reference interaction site model self-consistent-field (3D-RISM-SCF) method. First, they introduce a robust and efficient algorithm for solving the 3D-RISM equation. The algorithm is a hybrid of the Newton-Raphson and Picard methods. The Jacobian matrix is analytically expressed in a computationally useful form. Second, they discuss the solute-solvent electrostatic interaction. For the solute to solvent route, the electrostatic potential (ESP) map on a 3D grid is constructed directly from the electron density. The charge fitting procedure is not required to determine the ESP. For the solvent to solute route, the ESP acting on the solute molecule is derived from the solvent charge distribution obtained by solving the 3D-RISM equation. Matrix elements of the solute-solvent interaction are evaluated by the direct numerical integration. A remarkable reduction in the computational time is observed in both routes. Finally, the authors implement the first derivatives of the free energy with respect to the solute nuclear coordinates. They apply the present method to "solute" water and formaldehyde in aqueous solvent using the simple point charge model, and the results are compared with those from other methods: the six-dimensional molecular Ornstein-Zernike SCF, the one-dimensional site-site RISM-SCF, and the polarizable continuum model. The authors also calculate the solvatochromic shifts of acetone, benzonitrile, and nitrobenzene using the present method and compare them with the experimental and other theoretical results.     

Monte Carlo simulation of the influence of solvent on nucleic acid base associations

The results of Monte Carlo calculations of the association between nucleic acid bases in a nonpolar solvent (CCl4) are described. The influence of the solvent on planar and stacked associations of bases was examined by analyzing the total energy of the system, including solute-solute, solute-solvent, and solvent-solvent contributions. Good quantitative agreement with the available experimental data was obtained. Solute-solvent interactions are primarily determined by dispersion forces; consequently, solute-solvent interactions vertical to the solute plane that maximize dispersion interactions are most favored, and a rough proportionally between solute-solvent energy and the surface of the solute was observed. Analysis of solvent-solvent energy is not necessarily reduced when surface area decreases, contrary to the simple cavity concept. "Single molecule probe" calculations were performed to explain the differences in base associations in H2O and CCl4. In CCl4 dispersion forces dominate and planar complexes are stabilized by maximum exposure of molecular planes to the solvent. In H2O electrostatic forces dominate so that the most stable structures are stacked association that allow the maximum number of hydrophilic centers to be exposed to the solvent.     

Solvent effects in density functional calculations of uracil and cytosine tautomerism

The effects of the solvent on the tautomeric equilibria of cytosine and uracil are studied using Onsager's reaction field model in the framework of density functional theory. In this model, the solute molecule is placed in a spherical cavity of radius ao immersed in a continuous medium with a dielectric constant e, treating the solute-solvent electrostatic interactions at the dipole level. The cavity radius is evaluated by determining the molecular volume with a quantum mechanical approach. The solvent effect brings significant changes in the geometrical parameters of some cytosine tautomers, but only very small changes to those of the uracil tautomers. Our results are in good agreement with available experimental results and confirm that the polarization of the solute by the continuum has important effects on the absolute and relative solvation energies. Frequency shifts and intensity variations in the infrared spectra due to the presence of the solvent are also presented. © 1995 John Wiley & Sons, Inc.     

The inclusion of electrostatic and dispersion interactions into potentials of mean torque for solutes dissolved in uniaxial liquid crystal solvents

A potential of mean torque is derived for a solute at infinite dilution in a uniaxial liquid crystal solvent, which contains terms originating from the dispersion interaction, and the electrostatic interaction between quadrupole moments on both molecules. It is shown that the electrostatic term is non-zero only if the solute-solvent vectors are distributed with lower than spherical symmetry. If this distribution has cylindrical symmetry then both the electrostatic and dispersion terms in the potential of mean torque are shown to depend on order parameters for the orientational distribution of the solute-solvent vectors, as well as on the order parameters of the solvent molecules.     

Solvent density inhomogeneities and solvation free energies in supercritical diatomic fluids: a density functional approach

Density functional theory is used to explore the solvation properties of a spherical solute immersed in a supercritical diatomic fluid. The solute is modeled as a hard core Yukawa particle surrounded by a diatomic Lennard-Jones fluid represented by two fused tangent spheres using an interaction site approximation. The authors' approach is particularly suitable for thoroughly exploring the effect of different interaction parameters, such as solute-solvent interaction strength and range, solvent-solvent long-range interactions, and particle size, on the local solvent structure and the solvation free energy under supercritical conditions. Their results indicate that the behavior of the local coordination number in homonuclear diatomic fluids follows trends similar to those reported in previous studies for monatomic fluids. The local density augmentation is particularly sensitive to changes in solute size and is affected to a lesser degree by variations in the solute-solvent interaction strength and range. The associated solvation free energies exhibit a nonmonotonous behavior as a function of density for systems with weak solute-solvent interactions. The authors' results suggest that solute-solvent interaction anisotropies have a major influence on the nature and extent of local solvent density inhomogeneities and on the value of the solvation free energies in supercritical solutions of heteronuclear molecules.     

Continuous medium theory for nonequilibrium solvation: I. How to correctly evaluate solvation free energy of nonequilibrium

Considering the influences of electrostatic potential Phi upon the change of solute charge distribution deltarho and rho upon the change deltaPhi at the same time, a more reasonable integral formula of dG = (1/2) integral (V) (rhodeltaPhi + Phideltarho)dV is used to calculate the change of the electrostatic free energy in charging the solute-solvent system to a nonequilibrium state, instead of the one of dG = integral (V) PhideltarhodV used before. This modification improves the expressions of electrostatic free energy and solvation free energy, in which no quantity of the intermediate equilibrium state is explicitly involved. Detailed investigation reveals that the solvation free energy of nonequilibrium only contains the interaction energy between the field due to the solute charge in vacuum, and the dielectric polarization at the nonequilibrium state. The solvent reorganization energies of forward and backward electron transfer reactions have been redefined because the derivations lead to a remarkable feature that these quantities are direction-dependent, unlike the theoretical models developed before. The deductions are given in the electric field-displacement form. Relevant discussions on the reliability of theoretical models suggested in this work have also been presented.     

A time-dependent polarizable continuum model: theory and application

This work presents an extention of the polarizable continuum model to explicitly describe the time-dependent response of the solvent to a change in the solute charge distribution. Starting from an initial situation in which solute and solvent are in equilibrium, we are interested in modeling the time-dependent evolution of the solvent response, and consequently of the solute-solvent interaction, after a perturbation in this equilibrium situation has been switched on. The model introduces an explicit time-dependent treatment of the polarization by means of the linear-response theory. Two strategies are tested to account for this time dependence: the first one employs the Debye model for the dielectric relaxation, which assumes an exponential decay of the solvent polarization; the second one is based on a fitting of the experimental data of the solvent complex dielectric permittivity. The first approach is simpler and possibly less accurate but allows one to write an analytic expression of the equations. By contrast, the second approach is closer to the experimental evidence but it is limited to the availability of experimental data. The model is applied to the ionization process of N,N-dimethyl-aniline in both acetonitrile and water. The nonequilibrium free-energy profile is studied both as a function of the solvent relaxation coordinate and as a function of time. The solvent reorganization energy is evaluated as well.     

Towards a modellisation of the solvation energy in multi-component solvents. The interesting case of a charged solute imbedded in a polymer-containing electrolyte solution

In this paper we propose a mean-field theory to calculate the solvation free energy of a charged solute imbedded in a complex multi-component solvent. We considered a solvent made up of a mixture of small (electrolyte solution) and large (polymer) components. The presence of macromolecules ensures reduced mixing entropy among the different solvent components, an effect due to polymer connectivity. The reduced entropy favours strong preferential distribution of a particular solvent even in the presence of weak preferential solute–solvent interactions. In addition, two energy terms must be considered: (a) the interaction between the solute electrostatic potential and the electrolyte solution and (b) the formation of a polymer–solute interface. Because of the different dielectric permittivity of the solvent components, the electrolyte and polymer distribution functions are strongly coupled: ions, indeed, are more solvated in regions of higher local dielectric permittivity arising from the inhomogeneous mixing of solvent and polymer. We combined together the different energy terms in the framework of the de Gennes free energy functional for polymer solutions along with a generalised Poisson–Boltzmann equation developed for inhomogeneous dielectric media. Moreover, the preferential electrolyte solvation in regions of greater polarity was considered by an extension of the Born equation. Setting the polymer dielectric permittivity smaller than the solvent one and making null the specific polymer–solute interactions, we calculated enhanced electrolyte concentration and reduced polymer concentration near the solute surface on raising the solute surface charge density. The theory shows also the breakdown of the widely used separation between electrostatic and surface tension-dependent contributions to solvation energy when non-ideal mixed solvents are considered. In fact, according to the model, the surface tension of such mixed solvents strongly depends on the solute surface charge density: at high potentials the interfacial tension may increase rather than decrease on raising the polymer volume fraction. The theoretical results have been compared with experimental data on polymer+electrolyte solution surface tension and with solubility data of colloidal particles. The comparison evidences the complex behaviour of multi-component solvents going well beyond the trivial weighted average of the dielectric permittivity and surface tension of the isolated chemical components. Deviations from the simple behaviour predicted by an average picture of multi-component solvents could be understood by developing more sophisticated, but still simple, approaches like that proposed in this paper.Contribution to the Jacopo Tomasi Honorary Issue. This paper is dedicated to Jacopo Tomasi. I learned much of the difficult art of transforming complex problems into simple models after reading his early works on solvation energy.     

New approach to free energy of solvation applying continuum models to molecular dynamics simulation

A new approach to the calculation of the free energy of solvation from trajectories obtained by molecular dynamics simulation is presented. The free energy of solvation is computed as the sum of three contributions originated at the cavitation of the solute by the solvent, the solute-solvent nonpolar (repulsion and dispersion) interactions, and the electrostatic solvation of the solute. The electrostatic term is calculated based on ideas developed for the broadly used continuum models, the cavitational contribution from the excluded volume by the Claverie-Pierotti model, and the Van der Waals term directly from the molecular dynamics simulation. The proposed model is tested for diluted aqueous solutions of simple molecules containing a variety of chemically important functions: methanol, methylamine, water, methanethiol, and dichloromethane. These solutions were treated by molecular dynamics simulations using SPC/E water and the OPLS force field for the organic molecules. Obtained free energies of solvation are in very good agreement with experimental data.     

Interactions of fluorinated gases with ionic liquids: solubility of CF4, C2F6, and C3F8 in trihexyltetradecylphosphonium bis(trifluoromethylsulfonyl)amide

The interactions between ionic liquids and totally fluorinated alkanes are investigated by associating gas solubility measurements with molecular simulation calculations. Experimental values for the solubility of perfluoromethane, perfluoroethane, and perfluoropropane in one ionic liquidtrihexyltetradecylphophonium bis(trifluoromethylsulfonyl)amide [P 6,6,6,14][Ntf 2]are reported between 303 and 343 K and close to atmospheric pressure. All mole fraction solubilities decrease with increasing temperature. From the variation of Henry's law constants with temperature, the thermodynamic functions of solvation were calculated. The precision of the experimental data, considered as the average absolute deviation of the Henry's law constants from appropriate smoothing equations, is always better than +/-3%. By the analysis of the differences between the solute-solvent radial distribution functions of perfluoromethane and perfluoropropane obtained by molecular simulation, it was possible to explain why solubility increases with the size of the perfluoroalkane. The trend of solubility is explained on the basis of the location of the solute with respect to the solvent ions as well as on the differences in the solute-solvent energies of interaction.