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.     

Prediction of molecular solvation free energy based on the optimization of atomic solvation parameters with genetic algorithm

We propose an improved solvent contact model to estimate the solvation free energy of an organic molecule from individual atomic contributions. The modification of the solvation model involves the optimization of three kinds of parameters in the solvation free energy function: atomic fragmental volume, maximum atomic occupancy, and atomic solvation parameters. All of these atomic parameters for 24 atom types are developed by the operation of a standard genetic algorithm in such a way as to minimize the difference between experimental and calculated solvation free energies. The data set for experimental solvation free energies is divided into a training set of 131 compounds and a test set of 24 compounds. Linear regressions with the optimized atomic parameters yield fits with the squared correlation coefficients (r2) of 0.89 and 0.86 for the training set and for the test set, respectively. Overall, the results indicate that the improved solvent contact model with the newly developed atomic parameters would be a useful tool for rapid calculation of molecular solvation free energies in aqueous solution.     

Aggregation of alkyllithiums in tetrahydrofuran

Density functional theory was used to examine the solvation number and aggregation state of several alkyllithium compounds in clusters with tetrahydrofuran molecules coordinated to each lithium atom. We then made the microsolvation approximation and approximated the bulk free energy of solvation by the free energy of clustering with solvent molecules in the gas phase. The trends in the computed results are in reasonable agreement with the available experimental data.     

Computational molecular characterization of the flavonoid rutin

In this work, we make use of a model chemistry within Density Functional Theory (DFT) recently presented, which is called M05-2X, to calculate the molecular structure of the flavonoid Rutin, as well as to predict the infrared (IR) and ultraviolet (UV-Vis) spectra, the dipole moment and polarizability, the free energy of solvation in different solvents as an indication of solubility, the HOMO and LUMO orbitals, and the chemical reactivity parameters that arise from Conceptual DFT. The calculated values are compared with the available experimental data for this molecule as a means of validation of the used model chemistry.     

The treatment of solvation by a generalized Born model and a self-consistent charge-density functional theory-based tight-binding method

We present a model to calculate the free energies of solvation of small organic compounds as well as large biomolecules. This model is based on a generalized Born (GB) model and a self-consistent charge-density functional theory-based tight-binding (SCC-DFTB) method with the nonelectrostatic contributions to the free energy of solvation modeled in terms of solvent-accessible surface areas (SA). The parametrization of the SCC-DFTB/GBSA model has been based on 60 neutral and six ionic molecules composed of H, C, N, O, and S, and spanning a wide range of chemical groups. Effective atomic radii as parameters have been obtained through Monte Carlo Simulated Annealing optimization in the parameter space to minimize the differences between the calculated and experimental free energies of solvation. The standard error in the free energies of solvation calculated by the final model is 1.11 kcal mol(-1). We also calculated the free energies of solvation for these molecules using a conductor-like screening model (COSMO) in combination with different levels of theory (AM1, SCC-DFTB, and B3LYP/6-31G*) and compared the results with SCC-DFTB/GBSA. To assess the efficiency of our model for large biomolecules, we calculated the free energy of solvation for a HIV protease-inhibitor complex containing 3,204 atoms using the SCC-DFTB/GBSA and the SCC-DFTB/COSMO models, separately. The computed relative free energies of solvation are comparable, while the SCC-DFTB/GBSA model is three to four times more efficient, in terms of computational cost.     

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.     

一组和AMBER力场配合的普适波恩模型参数

提出了一套和AMBER力场相匹配的普适波恩模型参数.新的参数集包含21种原子类型的初始半径和屏蔽因子.参数通过遗传算法拟合359个小分子水合自由能的实验值得到.采用新的参数，预测了44个小分子的水合自由能，预测值和实验值能很好地吻合，而且大大优于采用Jayaram参数得到的结果.此外，采用新的参数，还预测了15个蛋白质的水合自由能，预测值和PB/SA预测得到的结果能很好地吻合.     

Anisotropic solvent model of the lipid bilayer. 1. Parameterization of long-range electrostatics and first solvation shell effects

A new implicit solvation model was developed for calculating free energies of transfer of molecules from water to any solvent with defined bulk properties. The transfer energy was calculated as a sum of the first solvation shell energy and the long-range electrostatic contribution. The first term was proportional to solvent accessible surface area and solvation parameters (σ(i)) for different atom types. The electrostatic term was computed as a product of group dipole moments and dipolar solvation parameter (η) for neutral molecules or using a modified Born equation for ions. The regression coefficients in linear dependencies of solvation parameters σ(i) and η on dielectric constant, solvatochromic polarizability parameter π*, and hydrogen-bonding donor and acceptor capacities of solvents were optimized using 1269 experimental transfer energies from 19 organic solvents to water. The root-mean-square errors for neutral compounds and ions were 0.82 and 1.61 kcal/mol, respectively. Quantification of energy components demonstrates the dominant roles of hydrophobic effect for nonpolar atoms and of hydrogen-bonding for polar atoms. The estimated first solvation shell energy outweighs the long-range electrostatics for most compounds including ions. The simplicity and computational efficiency of the model allows its application for modeling of macromolecules in anisotropic environments, such as biological membranes.     

Energy-entropy prediction of octanol–water logP of SAMPL7 N-acyl sulfonamide bioisosters

Partition coefficients quantify a molecule’s distribution between two immiscible liquid phases. While there are many methods to compute them, there is not yet a method based on the free energy of each system in terms of energy and entropy, where entropy depends on the probability distribution of all quantum states of the system. Here we test a method in this class called Energy Entropy Multiscale Cell Correlation (EE-MCC) for the calculation of octanol–water logP values for 22 N-acyl sulfonamides in the SAMPL7 Physical Properties Challenge (Statistical Assessment of the Modelling of Proteins and Ligands). EE-MCC logP values have a mean error of 1.8 logP units versus experiment and a standard error of the mean of 1.0 logP units for three separate calculations. These errors are primarily due to getting sufficiently converged energies to give accurate differences of large numbers, particularly for the large-molecule solvent octanol. However, this is also an issue for entropy, and approximations in the force field and MCC theory also contribute to the error. Unique to MCC is that it explains the entropy contributions over all the degrees of freedom of all molecules in the system. A gain in orientational entropy of water is the main favourable entropic contribution, supported by small gains in solute vibrational and orientational entropy but offset by unfavourable changes in the orientational entropy of octanol, the vibrational entropy of both solvents, and the positional and conformational entropy of the solute.

     

Calculation of electron affinities of polycyclic aromatic hydrocarbons and solvation energies of their radical anion

Electron affinities (EAs) and free energies for electron attachment (DeltaGo(a,298K)) have been directly calculated for 45 polynuclear aromatic hydrocarbons (PAHs) and related molecules by a variety of theoretical methods, with standard regression errors of about 0.07 eV (mean unsigned error = 0.05 eV) at the B3LYP/6-31 + G(d,p) level and larger errors with HF or MP2 methods or using Koopmans' Theorem. Comparison of gas-phase free energies with solution-phase reduction potentials provides a measure of solvation energy differences between the radical anion and neutral PAH. A simple Born-charging model approximates the solvation effects on the radical anions, leading to a good correlation with experimental solvation energy differences. This is used to estimate unknown or questionable EAs from reduction potentials. Two independent methods are used to predict DeltaGo(a,298K) values: (1) based upon DFT methods, or (2) based upon reduction potentials and the Born model. They suggest reassignments or a resolution of conflicting experimental EAs for nearly one-half (17 of 38) of the PAH molecules for which experimental EAs have been reported. For the antiaromatic molecules, 1,3,5-tri-tert-butylpentalene and the dithia-substituted cyclobutadiene 1, the reduction potentials lead to estimated EAs close to those expected from DFT calculations and provide a basis for the prediction of the EAs and reduction potentials of pentalene and cyclobutadiene. The Born model has been used to relate the electrostatic solvation energies of PAH and hydrocarbon radical anions, and spherical halide anions, alkali metal cations, and ammonium ions to effective ionic radii from DFT electron-density envelopes. The Born model used for PAHs has been successfully extended here to quantitatively explain the solvation energy of the C60 radical anion.     

单原子离子溶剂化的研究 Ⅱ. 离子溶剂化吉布斯自由能的理论计算

本文采用单层结构模型的思想, 吸取Born模型的优点, 提出一种新的处理离子与第一溶剂化层溶剂分子间相互作用的方法。所得到的离子溶剂化吉布斯自由能的计算公式考虑了离子-溶剂相互作用能、离子内能和溶剂分子间相互作用能的贡献。对水、DMF和PC中各种类型的离子的计算与实验值符合得比较好。     

Theoretical determination of standard oxidation and reduction potentials of chlorophyll-a in acetonitrile

QM/MM calculations were performed on ethyl chlorophyllide-a and its radical cation and anion, by using the density functional (DF) B3LYP method to determine the molecular characteristics, and a molecular mechanics (MM) method to simulate the solvating medium. The presence of the solvent was accounted for during the optimization of the geometry of the 85-atom chlorophyll-a system by using an ONIOM methodology. A total of 24 solvent molecules were explicitly considered during the optimization process, and these were treated by the universal force field (UFF) method. Initially, the split-valence 3-21G basis set was used for optimizing the geometry of the 85-atom species, neutral, cation and anion. Electronic energies were then determined for the optimized species by making use of the polarized 6-31G(d) basis set. The ionization energy calculated (6.0 eV) is in very good agreement with the observed one (6.1 eV). The MM+ force field was used to investigate the dynamics of the acetonitrile molecules around the neutral species as well as the radical ions of chlorophyll. The required atomic charges on all the atoms were obtained from calculations on all involved molecules at the DFT/6-31G(d) level. Randomly sampled configurations were used to determine the first solvation layer contribution to the free energy of solvation of various species. A truncated 46-atom model of ethyl chlorophyllide-a was used to evaluate the thermal energies of neutral chlorophyll molecule relative to its two radical ions in the gas phase. Born energy, Onsager energy, and the Debye-Huckel energy of the chlorophyll-solvent aggregate were added as perturbative corrections to the free energy of solvation that was initially obtained through molecular dynamics method for the same complex. These calculations yield the oxidation potential as 0.75 +/- 0.32 V and the reduction potential -1.18 +/- 0.31 V at 298.15 K. The calculated values are in good agreement with the experimental midpoint potentials of +0.76 and -1.04 V, respectively.     

Breaking the polar‐nonpolar division in solvation free energy prediction

Implicit solvent models divide solvation free energies into polar and nonpolar additive contributions, whereas polar and nonpolar interactions are inseparable and nonadditive. We present a feature functional theory (FFT) framework to break this ad hoc division. The essential ideas of FFT are as follows: (i) representability assumption: there exists a microscopic feature vector that can uniquely characterize and distinguish one molecule from another; (ii) feature‐function relationship assumption: the macroscopic features, including solvation free energy, of a molecule is a functional of microscopic feature vectors; and (iii) similarity assumption: molecules with similar microscopic features have similar macroscopic properties, such as solvation free energies. Based on these assumptions, solvation free energy prediction is carried out in the following protocol. First, we construct a molecular microscopic feature vector that is efficient in characterizing the solvation process using quantum mechanics and Poisson–Boltzmann theory. Microscopic feature vectors are combined with macroscopic features, that is, physical observable, to form extended feature vectors. Additionally, we partition a solvation dataset into queries according to molecular compositions. Moreover, for each target molecule, we adopt a machine learning algorithm for its nearest neighbor search, based on the selected microscopic feature vectors. Finally, from the extended feature vectors of obtained nearest neighbors, we construct a functional of solvation free energy, which is employed to predict the solvation free energy of the target molecule. The proposed FFT model has been extensively validated via a large dataset of 668 molecules. The leave‐one‐out test gives an optimal root‐mean‐square error (RMSE) of 1.05 kcal/mol. FFT predictions of SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 challenge sets deliver the RMSEs of 0.61, 1.86, 1.64, 0.86, and 1.14 kcal/mol, respectively. Using a test set of 94 molecules and its associated training set, the present approach was carefully compared with a classic solvation model based on weighted solvent accessible surface area. © 2017 Wiley Periodicals, Inc.     

A classical point charge model study of system size dependence of oxidation and reorganization free energies in aqueous solution

The response of water to a change of charge of a solvated ion is, to a good approximation, linear for the type of iron-like ions frequently used as a model system in classical force field studies of electron transfer. Free energies for such systems can be directly calculated from average vertical energy gaps. Exploiting this feature, we have computed the free energy and the reorganization energy of the M2+/M3+ and M1+/M2+ oxidations in a series of model systems all containing a single Mn+ ion and an increasing number of simple point charge water molecules. Long-range interactions are taken into account by Ewald summation methods. Our calculations confirm the observation made by Hummer, Pratt, and Garcia (J. Phys. Chem. 1996, 100, 1206) that the finite size correction to the estimate of solvation energy (and hence oxidation free energy) in such a setup is effectively proportional to the inverse third power (1/L3) of the length L of the periodic cell. The finite size correction to the reorganization energy is found to scale with 1/L. These simulation results are analyzed using a periodic generalization of the Born cavity model for solvation, yielding three different estimates of the cavity radius, namely, from the infinite system size extrapolation of oxidation free energy and reorganization energy, and from the slope of the linear dependence of oxidation free energy on 1/L3. The cavity radius for the reorganization energy is found to be significantly larger compared to the radius for the oxidation (solvation) free energy. The radius controlling the 1/L3 dependence of oxidation free energy is found to be comparable to the radius for reorganization. The implication of these results for density functional theory-based ab initio molecular dynamics calculation of redox potentials is discussed.     

Theoretical studies on the effects of methods and parameterization on the calculated free energy of hydration for small molecules

Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In‐solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree–Fock levels with two basis sets (6‐31G* and 6‐311++G**). Good linear correlation has been obtained for calculated and experimental gas‐phase dipole moments, with an increase by ～30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6‐31G* and 6‐311++G** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas‐phase and in‐solution molecular electrostatic potentials at in‐solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all‐atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6‐31G* level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

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.     

Adsorption and solvation of ethanol at the water liquid-vapor interface: a molecular dynamics study

The free energy profiles of methanol and ethanol at the water liquid-vapor interface at 310K were calculated using molecular dynamics computer simulations. Both alcohols exhibit a pronounced free energy minimum at the interface and, therefore, have positive adsorption at this interface. The surface excess was computed from the Gibbs adsorption isotherm and was found to be in good agreement with experimental results. Neither compound exhibits a free energy barrier between the bulk and the surface adsorbed state. Scattering calculations of ethanol molecules from a gas phase thermal distribution indicate that the mass accommodation coefficient is 0.98, and the molecules become thermalized within 10 ps of striking the interface. It was determined that the formation of the solvation structure around the ethanol molecule at the interface is not the rate-determining step in its uptake into water droplets. The motion of an ethanol molecule in a water lamella was followed for 30 ns. The time evolution of the probability distribution of finding an ethanol molecule that was initially located at the interface is very well described by the diffusion equation on the free energy surface.     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999