Hybrid supermolecule-polarizable continuum approach to solvation: Application to the mechanism of the Stevens rearrangement

Semiempirical molecular orbital theory has been used to study the effects of solvation by acetonitrile on the Stevens rearrangement of methylammonium formylmethylide to 2-aminopropanal. Three methods of solvation have been used to investigate both the electrostatic and specific solvent–solute effects of solvation: a supermolecule calculation involving the complete geometry optimization of up to six solvent molecules about the solute, the conductor-like screening model (COSMO) polarizable continuum method which allows for geometry optimization of the solute in a solvent defined by its dielectric constant, and a hybrid method in which up to five solvent molecules are incorporated inside the solute cavity and complete geometry optimization of the complex is carried out within the polarizable continuum. A comparison of the calculated geometries, rearrangement activation energies, and enthalpies of solvation from these approaches is presented, and the explicit versus bulk solvation effects are discussed. The overall effect of all methods for incorporating solvation effects is that the radical pair pathway is perferred over the concerted mechanism. © 1996 by John Wiley & Sons, Inc.     

Free energy of solvation from molecular dynamics simulation applying Voronoi-Delaunay triangulation to the cavity creation

The free energy of solvation for a large number of representative solutes in various solvents has been calculated from the polarizable continuum model coupled to molecular dynamics computer simulation. A new algorithm based on the Voronoi-Delaunay triangulation of atom-atom contact points between the solute and the solvent molecules is presented for the estimation of the solvent-accessible surface surrounding the solute. The volume of the inscribed cavity is used to rescale the cavitational contribution to the solvation free energy for each atom of the solute atom within scaled particle theory. The computation of the electrostatic free energy of solvation is performed using the Voronoi-Delaunay surface around the solute as the boundary for the polarizable continuum model. Additional short-range contributions to the solvation free energy are included directly from the solute-solvent force field for the van der Waals-type interactions. Calculated solvation free energies for neutral molecules dissolved in benzene, water, CCl4, and octanol are compared with experimental data. We found an excellent correlation between the experimental and computed free energies of solvation for all the solvents. In addition, the employed algorithm for the cavity creation by Voronoi-Delaunay triangulation is compared with the GEPOL algorithm and is shown to predict more accurate free energies of solvation, especially in solvents composed by molecules with nonspherical molecular shapes.     

Predictions of solvation and vaporization enthalpies. 1.n-alkane +n-alkane solutions

A simple method for the calculation of the enthalpy of solvation is presented and demonstrated for 35 n-alkane + n-alkane solutions at 25°C. There is a good agreement between the predicted and experimental values. The calculation was based on the separation of the solvation enthalpy into the cavity formation and solute-solvent interaction contributions. The former term was determined from the activation enthalpy of the solvent viscous flow and solute molar volume while the latter on the basis of the dispersion energy using van der Waals diameters for n-propyl group. The procedure was also successful in prediction of the vaporization enthalpy of C₅–C₁₇ n-alkanes.     

Efficient and accurate solvation energy calculation from polarizable continuum models

A new approach is proposed to enhance the efficiency and accuracy for calculation of the long-range electrostatic interaction from implicit solvation models, i.e., the polarizable continuum model (PCM) and its variants, conductorlike PCM/conductorlike screening model and integral equation formalism PCM. In these methods the solvent electrostatics effects are represented by a set of discrete apparent charges distributed on tesserae of the molecular cavity surface embedding the solute. In principle, the accuracy of these methods is improved if the cavity surface is tessellated to finer tesserae; however, the computational time is increased rapidly. We show that such undesired dependency between accuracy and efficiency is a result of the inaccurate treatment of the apparent charge self-contribution to the potential and/or electric field. By taking into account the full effects due to the size and curvature of the segment occupied by each apparent charge, the error in calculated electrostatic solvation free energy is essentially zero for ions (point charge at the center of a sphere) regardless of the degree of tessellation used. For molecules where gradient of apparent charge density is nonzero at the cavity surface, we propose a multiple-sampling technique which significantly lowers the calculated error compared to the original PCM methods, especially when very few numbers of tesserae are used.     

Solvatochromism and preferential solvation of Brooker's merocyanine in water–methanol mixtures

The excitation energy of Brooker's merocyanine in water–methanol mixtures shows nonlinear behavior with respect to the mole fraction of methanol, and it was suggested that this behavior is related to preferential solvation by methanol. We investigated the origin of this behavior and its relation to preferential solvation using the three‐dimensional reference interaction site model self‐consistent field method and time‐dependent density functional theory. The calculated excitation energies were in good agreement with the experimental behavior. Analysis of the coordination numbers revealed preferential solvation by methanol. The free energy component analysis implied that solvent reorganization and solvation entropy drive the preferential solvation by methanol, while the direct solute–solvent interaction promotes solvation by water. The difference in the preferential solvation effect on the ground and excited states causes the nonlinear excitation energy shift. © 2017 Wiley Periodicals, Inc.     

The statistical thermodynamics of solvation

Statistical mechanics provides the basis for a rigorous theory of molecules and molecular complexes in chemically inert media. It is found that the free energy of solvation may be calculated, provided the distribution function for the solvent molecules around the solute molecules is known. A relation is deduced between the volume change on dissolving, the free energy of solvation, and the isothermal compressibility of the pure solvent. The general equations are applied to a solution of solid spheres in a structureless medium. The theoretical deductions are found to be in qualitative agreement with the thermodynamic solvation parameters for oxygen and argon in inert solvents.     

Determination of the enthalpy of solute-solvent interaction from the enthalpy of solution: aqueous solutions of erythritol and L-threitol

In this work the enthalpy of the solute-solvent interaction of erythritol and L-threitol in aqueous solution was determined from the values obtained for the enthalpy of solvation. The values for this property were calculated from those determined for the enthalpies of solution and sublimation. To determine the values of the enthalpy of solute-solvent interaction, the solvation process is considered as taking place in three steps: opening a cavity in the solvent to hold the solute molecule, changing the solute conformation when it passes from the gas phase into solution, and interaction between the solute and the solvent molecules. The cavity enthalpy was calculated by the scaled particle theory and the conformational enthalpy change was estimated from the value of this function in the gas phase and in solution. Both terms were determined by DFT calculations. The solvent effect on the solute conformation in solution was estimated using the CPCM solvation model. The importance of the cavity and conformational terms in the interpretation of the enthalpy of solvation is noted. While the cavity term has been used by some authors, the conformational term is considered for the first time. The structural features in aqueous solution of erythritol and L-threitol are discussed.     

Thermodynamics of solvation and solvophobic effect in formamide

Using semi-adiabatic calorimetry, we measured the enthalpies of solution for various low-polar compounds including alkanes, aromatic hydrocarbons and their halogenated derivatives in formamide at temperature of 298 K. For the same compounds, the values of limiting activity coefficients in formamide were determined using GC headspace analysis at 298 K, and Gibbs free energies of solution and solvation were calculated. Based on these data and the available literature values of the Gibbs free energy of solvation in formamide for a number of other low-polar solutes, a study of the solvophobic effect in this solvent is performed, and its resemblance to the hydrophobic effect in aqueous solutions is demonstrated. It is shown that the contribution of the solvophobic effect into the solvation Gibbs free energy in formamide is much higher than that in aliphatic alcohols, but lower than that in water. Like in water, the magnitude of this contribution for different solutes linearly increases with the solute molecular volume. Solvophobic effect also significantly affects the enthalpies of dissolution in formamide, causing them to be more negative in the case of alkanes and more positive in the case of arenes.     

Atomic radii: Incorporation of solvation effects

Atomic radii used to define the solute cavity in continuum-based methods are determined by reproducing the solvent-accessible surface defined as the loci of minima in a potential (solvent interaction potential) between the solute and a probe. This potential includes electrostatic interaction (ion–dipole, ion–quadrupole, and ion-induced dipole) terms as well as a Lennard–Jones energy term. The method alleviates the need to distinguish solute atoms in different chemical environments. These radii, when used in the calculation of solvation free energies, are shown to be superior to fixed atom-specific radii or to radii obtained from the electron isodensity surface from quantum-mechanical calculations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1482–1493, 1998     

The H2O2+OH-->HO2+H2O reaction in aqueous solution from a charge-dependent continuum model of solvation

We applied our recently developed protocol of the conductorlike continuum model of solvation to describe the title reaction in aqueous solution. The model has the unique feature of the molecular cavity being dependent on the atomic charges in the solute and can be extended naturally to transition states and reaction pathways. It was used to calculate the reaction energetics and reaction rate in solution for the title reaction. The rate of reaction calculated using canonical variational transition state theory in the context of the equilibrium solvation path approximation, and including correction for tunneling through the small curvature approximation, was found to be 3.6 x 10(6) M(-1) s(-1), significantly slower than in the gas phase in accord with experiment. These results suggest that the present protocol of the conductorlike continuum model of solvation with the charge-dependent cavity definition captures qualitatively and quantitatively the solvation effects at transition states and allows for quantitative estimates of reaction rates in solutions.     

Calculation of the solvation free energy of neutral and ionic molecules in diverse solvents

The solvation free energy density (SFED) model was modified to extend its applicability and predictability. The parametrization process was performed with a large, diverse set of solvation free energies that included highly polar and ionic molecules. The mean absolute error for 1200 solvation free energies of the 379 neutral molecules in 9 organic solvents and water was 0.40 kcal/mol, and for 90 hydration free energies of ions was 1.7 kcal/mol. Overall, the calculated solvation free energies of a wide range of solute functional groups in diverse solvents were consistent with experimental data.     

Molecular probes of solvation phenomena

The properties of the molecules present in any chemical or biological system are dependent on interactions with the environment, and a quantitative understanding of solvation phenomena remains a major challenge. Molecular recognition probes provide a new approach to quantitatively measure the properties of solvents. Traditionally, solvent polarity scales have been based on spectroscopic probes that provide insight into the nature of solvent-solute interactions. This review compares the solvent polarity parameters obtained from the wavelengths of UV/Visible absorption maxima with solute H-bond parameters obtained from the free energies of solution equilibria. The similarity of the solvent and solute H-bond scales leads to a general H-bond scale that uses the same parameters to describe both solvent and solute. The general H-bond scale provides a framework for understanding the relationship between local intermolecular interactions and the properties of the bulk medium. Intermolecular interactions are sensitive to solvation equilibria, so molecular recognition probes provide fundamentally different information from spectroscopic probes that are sensitive to the populations of different solvation states of the solute. Studies of mixed solvents demonstrate the potential of molecular recognition probes for providing new insights into solvation phenomena.     

Preferential solvation of indomethacin and naproxen in ethyl acetate + ethanol mixtures according to the IKBI method

The preferential solvation parameters of indomethacin and naproxen in ethyl acetate + ethanol mixtures are derived from their thermodynamic properties by using the inverse Kirkwood–Buff integrals method. It is found that both drugs are sensitive to solvation effects, so the preferential solvation parameter, δx_EA,D, is negative in ethanol-rich and ethyl acetate-rich mixtures but positive in compositions from 0.36 to 0.71 in mole fraction of ethyl acetate. It is conjecturable that in ethanol-rich mixtures, the acidic interaction of ethanol on basic sites of the analgesics plays a relevant role in the solvation. The more solvation by ethyl acetate in mixtures of similar co-solvent compositions could be due to polarity effects. Finally, the slight preference of these compounds for ethanol in ethyl acetate-rich mixtures could be explained as the common participation of basic sites in both solvents and the acidic site of ethanol. Nevertheless, the specific solute–solvent interactions remain unclear.     

Structural peculiarities of particle solvation inN,N-dimethylformamide

Monte Carlo computer simulation of infinitely dilute solutions of Cs⁺ and I⁻ ions and Xe atoms inN,N-dimethylformamide (DMF) was performed. Peculiarities of intermolecular interactions and structural properties of the solutions were investigated. The solvation enthalpies of cations and anions are close, but the energies of the ion-solvent and solventsolvent interactions differ appreciably. The solute particles affect the energy and structural properties of DMF only in spatially localized domains. The second solvation shell of the solute particles was not structurally allocated. Two structurally and energetically differing states of DMF molecules (with normal and anomalous orientation of the dipole moments) exist in solution of Cs⁺ cations. The anomalous orientation of DMF molecules is due to the solvation steric effect, packing, and kinematic factors. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 584–596, April, 2000.     

Femtosecond spectroscopic study of the solvation of amphiphilic molecules by water

We use polarization-resolved mid-infrared pump-probe spectroscopy to study the aqueous solvation of proline and N-methylacetamide. These molecules serve as models to study the solvation of proteins. We monitor the orientational dynamics of partly deuterated water molecules (HDO) that are present at a low concentration in the water. We find that the OD vibration of HDO relaxes via an intermediate level, that is characterized by a hydrogen-bond that is stronger than in the ground state. With increasing concentration the lifetime of the excited state increases from 1.8 ps to 2.4 ps and the lifetime of the intermediate level from 0.6 ps to 1.0 ps. Regarding the orientational dynamics we observe biexponential behavior, which finds its origin in the presence of two classes of water molecules. There is a fraction of water molecules that has bulk-like orientational dynamics (τ_rot = 2.5 ps) and a fraction of immobilized water molecules (τ_rot > 10 ps). The relative abundance of the two fractions is determined by the nature and concentration of the solute. We find that the hydrophobic solute groups are responsible for the immobilization of water molecules. Every methyl group causes the immobilization of approximately 4 water OH groups. The hydrophilic solute groups, on the other hand, do not hinder the reorientation and the water molecules solvating them reorient with the same rate as in the bulk liquid.     

Solvatons. II. Aqueous dissociation of hydrides in the MINDOS approximation

A simple electrostatic model of solvation is presented which allows the interaction with solvent to be included systematically within semiempirical SCF calculations. Solvent effects are incorporated into the Hamiltonian for a solute molecule through a series of imaginary particles, solvatons, which represent the oriented solvent distribution around the solute.The proposed model is based on an algorithm for approximating the enthalpy of solvation of each atomic center from its charge in the molecular system and the experimental hydration enthalpies of its various ions. The calculated atomic solvation energy of one center is then modified to include the interaction with other charged atomic centers in the molecule. The method, developed here for the MINDO/3 approximation, has been applied to the calculation of the aqueous dissociation of a series of hydrides. In general, it leads to fairly accurate solvation enthalpies andpK _a values when applied to systems with fixed molecular geometries. A general discussion of the problems associated with the development of a solvation model within a semiempirical framework is also presented.     

Enthalpies of solution and solvation of amides in N,N-dimethylformamide: Application of the random contact point approach

Calorimetrically determined molar enthalpies of solution at infinite dilution in N,N-dimethylformamide and densities of several amides at 25°C are reported. Some of the enthalpies are combined with literature data for enthalpies of vaporization to obtain molar enthalpies of solvation. Relations are found between the enthalpies of solution and the size, and between these enthalpies and the enthalpic pair interaction coefficients of the solute molecules. These relations are quantified by an extension of the random contact point approach. This additivity scheme is also applied to enthalpies of solvation, vaporization and cavity formation. With this approach thermodynamic quantities of solution, solvation, vaporization, and pair interaction of different solutes and solvents are correlated with a single consistent set of group interaction parameters. In addition, the random contact point model provides a simple method to calculate thermodynamics of cavity formation which appear to be as reliable as those of the much more complicated scaled particle theory.     

A new quantum method for electrostatic solvation energy of protein

A new method that incorporates the conductorlike polarizable continuum model (CPCM) with the recently developed molecular fractionation with conjugate caps (MFCC) approach is developed for ab initio calculation of electrostatic solvation energy of protein. The application of the MFCC method makes it practical to apply CPCM to calculate electrostatic solvation energy of protein or other macromolecules in solution. In this MFCC-CPCM method, calculation of protein solvation is divided into calculations of individual solvation energies of fragments (residues) embedded in a common cavity defined with respect to the entire protein. Besides computational efficiency, the current approach also provides additional information about contribution to protein solvation from specific fragments. Numerical studies are carried out to calculate solvation energies for a variety of peptides including alpha helices and beta sheets. Excellent agreement between the MFCC-CPCM result and those from the standard full system CPCM calculation is obtained. Finally, the MFCC-CPCM calculation is applied to several real proteins and the results are compared to classical molecular mechanics Poisson-Boltzmann (MM/PB) and quantum Divid-and-Conque Poisson-Boltzmann (D&C-PB) calculations. Large wave function distortion energy (solute polarization energy) is obtained from the quantum calculation which is missing in the classical calculation. The present study demonstrates that the MFCC-CPCM method is readily applicable to studying solvation of proteins.