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.     

Predicting hydrophobic solvation by molecular simulation: 1. Testing united‐atom alkane models

We present a systematic test of the performance of three popular united‐atom force fields—OPLS‐UA, GROMOS and TraPPE—at predicting hydrophobic solvation, more precisely at describing the solvation of alkanes in alkanes. Gibbs free energies of solvation were calculated for 52 solute/solvent pairs from Molecular Dynamics simulations and thermodynamic integration making use of the IBERCIVIS volunteer computing platform. Our results show that all force fields yield good predictions when both solute and solvent are small linear or branched alkanes (up to pentane). However, as the size of the alkanes increases, all models tend to increasingly deviate from experimental data in a systematic fashion. Furthermore, our results confirm that specific interaction parameters for cyclic alkanes in the united‐atom representation are required to account for the additional excluded volume within the ring. Overall, the TraPPE model performs best for all alkanes, but systematically underpredicts the magnitude of solvation free energies by about 6% (RMSD of 1.2 kJ/mol). Conversely, both GROMOS and OPLS‐UA systematically overpredict solvation free energies (by ∼13% and 15%, respectively). The systematic trends suggest that all models can be improved by a slight adjustment of their Lennard‐Jones parameters. © 2016 Wiley Periodicals, Inc.     

Simple physics-based analytical formulas for the potentials of mean force for the interaction of amino acid side chains in water. 1. Approximate expression for the free energy of hydrophobic association based on a Gaussian-overlap model

A physics-based model is proposed to derive approximate analytical expressions for the cavity component of the free energy of hydrophobic association of spherical and spheroidal solutes in water. The model is based on the difference between the number and context of the water molecules in the hydration sphere of a hydrophobic dimer and of two isolated hydrophobic solutes. It is assumed that the water molecules touching the convex part of the molecular surface of the dimer and those in the hydration spheres of the monomers contribute equally to the free energy of solvation, and those touching the saddle part of the molecular surface of the dimer result in a more pronounced increase in free energy because of their more restricted mobility (entropy loss) and fewer favorable electrostatic interactions with other water molecules. The density of water in the hydration sphere around a single solute particle is approximated by the derivative of a Gaussian centered on the solute molecule with respect to its standard deviation. On the basis of this approximation, the number of water molecules in different parts of the hydration sphere of the dimer is expressed in terms of the first and the second mixed derivatives of the two Gaussians centered on the first and second solute molecules, respectively, with respect to the standard deviations of these Gaussians, and plausible analytical expressions for the cavity component of the hydrophobic-association energy of spherical and spheroidal solutes are introduced. As opposed to earlier hydration-shell models, our expressions reproduce the desolvation maxima in the potentials of mean force of pairs of nonpolar solutes in water, and their advantage over the models based on molecular-surface area is that they have continuous gradients in the coordinates of solute centers.     

A semiempirical free energy force field with charge-based desolvation

The authors describe the development and testing of a semiempirical free energy force field for use in AutoDock4 and similar grid-based docking methods. The force field is based on a comprehensive thermodynamic model that allows incorporation of intramolecular energies into the predicted free energy of binding. It also incorporates a charge-based method for evaluation of desolvation designed to use a typical set of atom types. The method has been calibrated on a set of 188 diverse protein-ligand complexes of known structure and binding energy, and tested on a set of 100 complexes of ligands with retroviral proteases. The force field shows improvement in redocking simulations over the previous AutoDock3 force field.     

Sorption of small molecules in various polycarbonates and Kapton-H

Pressure-composition isotherms were determined at 20°C for CO₂ in Kapton and various substituted polycarbonates and for H₂O, Ar, N₂, CH₄, and acetone in bisphenol-A-polycarbonate. The isotherms are described by two parameters an average free energy of sorption and a width of a Gaussian distribution of free sorption energies. Within the framework of a recent model these parameters can be calculated assuming an elastic distortion of the polymer caused by the incorporation of solute atoms in preexisting holes. By comparing experimental values with predictions of the model the experimental width of the free energy distribution is only 30% smaller than the theoretical one. Functional relationships are obeyed between the sorption parameters on the one hand and glass transition temperature, average hole volume, and molecular volume of the solute on the other hand. Deviations occur for larger molecules like acetone and ethylene which are attributed to a viscoelastic distortion of the polymer. Comparing free energies of solution for the rubbery and glassy state of the polymer reveals more negative values for the glassy polymers despite their extra elastic distortion energy. This discrepancy is overcome by taking into account that the occupied volume has to be re-formed in the case of the rubbery or liquid polymer. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 483–494, 1998     

Predicting hydration free energies with chemical accuracy: the SAMPL4 challenge

An implicit solvent model described by a non-simple dielectric medium is used for the prediction of hydration free energies on the dataset of 47 molecules in the SAMPL4 challenge. The solute is represented by a minimal parameter set model based on a new all atom force-field, named the liquid simulation force-field. The importance of a first solvation shell correction to the hydration free energy prediction is discussed and two different approaches are introduced to address it: either with an empirical correction to a few functional groups (alcohol, ether, ester, amines and aromatic nitrogen), or an ab initio correction based on the formation of a solute/explicit water complex. Both approaches give equally good predictions with an average unsigned error <1 kcal/mol. Chemical accuracy is obtained.     

Selenium hydride atomization,fate of free atoms and spectroscopic temperature in miniature diffusion flame atomizer studied by atomic absorption spectrometry

The mechanism of hydride atomization and the fate of free atoms was investigated in the miniature diffusion flame. Selenium hydride was used as a model for the other hydrides. Mercury vapor was employed as an analyte to study physical processes, such as macroscopic movements and free atom diffusion, controlling the distribution of free analyte atoms in the observation volume, separately from chemical reactions of the free atoms. Free atoms were detected by atomic absorption spectrometry. Spectroscopic temperature measurements based on atomic absorption at 196.1 and 204.0 nm Se lines were used to determine the temperature distribution. The spatial temperature distribution was highly inhomogeneous ranging from 150°C to 1300°C. The whole flame volume is actually a cloud of hydrogen radicals maintaining analyte in the free atom state since hydrogen radicals formed in outer zone of the flame diffuse to its cooler inner parts.     

MST continuum study of the hydration free energies of monovalent ionic species

In this study, we revisit the protocol previously proposed within the framework of the Miertus-Scrocco-Tomasi (MST) continuum model to define the cavity between the solute and solvent for predicting hydration free energies of univalent ions. The protocol relies on the use of a reduced cavity (around 10-15% smaller than the cavity used for neutral compounds) around the atom(s) bearing the formal charge. The suitability of this approach is examined here for a series of 47 univalent ions for which accurate experimental hydration free energies are available. Attention is also paid to the effect of the charge renormalization protocol used to correct uncertainties arising from the electron density located outside the solute cavity. The method presented here provides, with a minimum number of fitted parameters, reasonable estimates within the experimental error of the hydration free energy of ions (average relative error of 4.7%) and is able to reproduce solvation in water of both small and large ions.     

On the molecular origins of volumetric data

We use a statistical thermodynamic approach and a simple thermodynamic model of hydration to examine the molecular origins of the volumetric properties of solutes. In this model, solute-solvent interactions are treated as a binding reaction. The free energy of hydration of the noninteracting solute species coincides with the free energy of cavity formation, while the free energy of solute-solvent interactions is given by the binding polynomial. By differentiating the relationship for the free energy of hydration with respect to temperature and pressure, one obtains the complete set of equations describing the thermodynamic profile of hydration, including enthalpy, entropy, volume, compressibility, expansibility, and so forth. The model enables one to rigorously define in thermodynamic terms the hydration number and the related concept of hydration shell, which are both widely used as operational definitions in experimental studies. Hydration number, nh, is the effective number of water molecules solvating the solute and represents the derivative of the free energy of hydration with respect to the logarithm of water activity. One traditional way of studying hydration relies on the use of volumetric measurements. However, microscopic interpretation of macroscopic volumetric data is complicated and currently relies on empirical models that are not backed by theory. We use our derived model to link the microscopic determinants of the volumetric properties of a solute and its statistical thermodynamic parameters. In this treatment, the partial molar volume, V degrees, of a solute depends on the cavity volume, hydration number, and the properties of waters of hydration. In contrast, the partial molar isothermal compressibility, K degrees T, and expansibility, E degrees, observables, in addition to the intrinsic compressibility and expansibility of the cavity enclosing the solute, hydration number, and the properties of waters of hydration, contain previously unappreciated relaxation terms that originate from pressure- and temperature-induced perturbation of the equilibrium between the solvated solute species. If significant, the relaxation terms may bring about a new level of nonadditivity to compressibility and expansibility group contributions that goes beyond the overlap of the hydration shells of adjacent groups. We apply our theoretical results to numerical analyses of the volume and compressibility responses to changes in the distribution of solvated species of polar compounds.     

Partial molar volume of small molecules in glassy polymers

The sorption of atoms or molecules in glassy polymers is assumed to occur within a variety of sites belonging to the intermolecular volume and providing different space for the dissolved molecules. If the size of the small molecule is larger than the size of the site, the glassy polymer is elastically distorted during sorption of the solute molecules. Minimizing the total free energy yields the result that large sites are occupied first, giving rise to small volume changes only. By increasing the solute concentration, smaller sites have to be occupied as well and the corresponding volume changes are larger. Thus the molecules can be considered to act as probes for the intermolecular space. A quantitative analysis and comparison with experimental results provides information on the intermolecular space in a glassy polymer. Compared to the dual-sorption model, the model of this study is able to explain the nonlinear relationship between volume change of the polymer and the partial pressure of the solute. At large solute concentrations, swelling of the glassy polymer or its transformation into the rubbery state occurs, which gives rise to structural changes after desorption. © 1993 John Wiley & Sons, Inc.     

Sizes of atoms and ions and covalency of bonding in molecules and crystals

A new system of atomic radii for the elements up to barium inclusive is constructed. Values of the radii are chosen so as the dependence between the dissociation energy of diatomic homonuclear molecules and a depth of atom overlapping is monotonous, and the scatter of data is minimal. The depth of overlapping is calculated as a difference between the sum of atomic radii and an experimental interatomic distance. Conclusions are made that: the radii of free atoms and ions are determined by the value of the electron density equal to 0.01 au; they considerably change in molecules and crystals only as a result of the charge transfer from cation to anion; covalent bonding is well described by the overlapping of free atoms (ions), confined by the surface of the given radius, and its energy depends upon the depth of overlapping of valence electron densities of atoms. A method of overlapping atoms is proposed for the approximate estimation of ionic sizes and charges in bound systems.     

Dual-mode free volume model for diffusion of gas molecules in glassy polymers

The development of a new model for the diffusion of gas molecules in glassy polymers is presented which utilizes concepts from free volume theory and relies on a dual-mode interpretation of sorptive dilation in glassy polymers. Three assumptions are made in the development of the model. First, the free volume available for molecular transport processes is taken as constant below the glass transition temperature. Second, two populations of gas molecules are assumed to exist—one which contributes to the maintenance of an iso-free volume state upon sorptive dilation and one which does not contribute owing to sorption into regions of unrelaxed volume. Third, the former population is assumed to be mobile while the latter is not. The resulting model predicts, at constant temperature, a diffusion coefficient that is independent of solute volume fraction. This is in contrast to the widely used dual-mode sorption model with partial immobilization for gas transport in glassy polymers which leads to a diffusion coefficient that is dependent on solute mole fraction through the molar gas concentration. The new model is used to interpret gas transport data from permeation experiments for carbon dioxide, methane, and ethylene in three polycarbonates. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1737–1746, 1997     

Effect of the Solute Cavity on the Solvation Energy and its Derivatives within the Framework of the Gaussian Charge Scheme

The treatment of the solvation charges using Gaussian functions in the polarizable continuum model results in a smooth potential energy surface. These charges are placed on top of the surface of the solute cavity. In this article, we study the effect of the solute cavity (van der Waals-type or solvent-excluded surface-type) using the Gaussian charge scheme within the framework of the conductor-like polarizable continuum model on (a) the accuracy and computational cost of the self-consistent field (SCF) energy and its gradient and on (b) the calculation of free energies of solvation. For that purpose, we have considered a large set of systems ranging from few atoms to more than 200 atoms in different solvents. Our results at the DFT level using the B3LYP functional and the def2-TZVP basis set show that the choice of the solute cavity does neither affect the accuracy nor the cost of calculations for small systems (< 100 atoms). For larger systems, the use of a vdW-type cavity is recommended, as it prevents small oscillations in the gradient (present when using a SES-type cavity), which affect the convergence of the SCF energy gradient. Regarding the free energies of solvation, we consider a solvent-dependent probe sphere to construct the solvent-accessible surface area required to calculate the nonelectrostatic contribution to the free energy of solvation. For this part, our results for a large set of organic molecules in different solvents agree with available experimental data with an accuracy lower than 1 kcal/mol for both polar and nonpolar solvents.     

Solvation of hydrophobes in water and simple liquids

The solvation of nonpolar molecules in water and that in simple liquids are compared and contrasted. First, solvation thermodynamics is reviewed in a way that focuses on how the enthalpy and entropy of solvation depend on the choice of microscopic volume change v in the solvation process--including special choices v being zero (fixed-volume condition) and v being the partial molecular volume of a solute molecule (fixed-pressure condition)--and how the solvation quantities are related with temperature derivatives of the solvation free energy. Second, the solvation free energy and the solvation enthalpy of a Lennard-Jones (LJ) atom in model water are calculated in the parameter space representing the solute size and the strength of the solute-solvent interaction, and the results are compared with those for an LJ atom in the LJ solvent. The solvation diagrams showing domains of different types of solvation in the parameter space are obtained both for the constant-volume condition and for the constant-pressure condition. Similarities between water and the simple liquid are found when the constant-volume solvation is considered while a significant difference manifests itself in the fixed-pressure solvation. The domain of solvation of hydrophobic character in the parameter space is large in the constant-volume solvation both for water and for the simple liquid. When switched to the constant-pressure condition accompanying a microscopic volume change, the hydrophobic domain remains large in water but it becomes significantly small in the simple liquid. The contrasting results are due to the smallness of the thermal pressure coefficient of water at low temperatures.     

Effect of available volumes on radial distribution functions

The traditional method of analyzing solution structuring properties of solutes using atom–atom radial distribution functions (rdfs) can give rise to misleading interpretations when the volume occupied by the solute is ignored. It is shown by using the examples of O(4) in α- and β-D-allose that a more reliable interpretation of rdfs can be obtained by normalising the rdf using the available volume, rather than the traditional volume of a spherical shell. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 363–367, 1998     

The impact of surface area,volume, curvature,and Lennard–Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard–Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent–solute interfaces, and define a generalized Poisson–Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature‐based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.