Solute-solvent Interaction Energy Research Articles

Rapid Prediction of Solvation Free Energy. 1. An Extensive Test of Linear Interaction Energy (LIE).

The present study provides a comprehensive systematic analysis on the applicability of the linear interaction energy (LIE) approximation to the prediction of gas-to-water transfer (hydration) free energy. The study is based on molecular dynamics simulations in explicit solvent for an extensive and diverse hydration data set comprising 564 neutral compounds with measured hydration free energies, including a "traditional" data set and the more challenging drug-like SAMPL1 data set. A highly correlative LIE model was achieved without empirical scaling of the solute-solvent interaction energy terms along with a cavity term calibrated to the experiment. This model was particularly accurate for the "traditional" data set and of acceptable accuracy for the SAMPL1 data set, with mean-unsigned-errors below 1 kcal/mol and slightly above 2 kcal/mol, respectively. We have analyzed the sensitivity of the LIE model to several parameters such as continuum correction terms applied outside the explicit water shell, the impact of various charging methods, the applicability of single-conformer representation of the solute, and the inclusion of internal energy terms. The parameters with the greatest sensitivity are the charging methods used, with AM1BCC-SP (without AM1 geometry optimization) charges favored over AM1BCC-OPT and RESP charges. The inclusion of the change in intramolecular van der Waals and electrostatic energies between the solution and gas phases can also lead to improved prediction accuracies. Functional group based error analysis identified several chemical classes as minor outliers with systematic errors. A direct comparison of the LIE and free energy perturbation (FEP) approaches using the same force field and charging method shows that the LIE approximation is at least as accurate as the FEP approach with a reduction of computing time by at least 1 order of magnitude.

Nonergodic activated kinetics in polar media

A theoretical formulation is developed for the activated kinetics when some subset of nuclear modes of the thermal bath is slower than the reaction and ergodicity of the thermal bath is not maintained. Nonergodic free energy profiles along the reaction coordinate are constructed by using restricted canonical ensembles with the phase space available to the system found by solving a self-consistent kinetic equation. The resulting activation barrier incorporates not only thermodynamic parameters but also dynamical information from the time autocorrelation function of the solute-solvent interaction energy. The theory is applied to the reactions of solvolysis and charge transfer in polar media.

Orientational order of near D3h solutes in nematic liquid crystals. II. Description via Gay–Berne model with embedded quadrupoles

We perform Monte Carlo simulations of a mixture of soft ellipsoids with embedded quadrupoles as a model of various chloro- and methyl-substituted benzenes dissolved in nematic liquid crystals. We find that oblate Gay-Berne ellipsoids with multiple embedded quadrupoles qualitatively reproduce the trend in the order parameter asymmetry experimentally observed in NMR spectra. The trend is opposite to what is expected on the basis of the interaction of the solute's quadrupole with the solvent's average electric field gradient "felt" by dissolved dihydrogen molecules. We identify the specific minimum of the solute-solvent interaction energy landscape that may produce the unexpected sign of the order parameter asymmetry that is seen in the experiment and the simulation.

Free-Energy Analysis of Solvation with the Method of Energy Representation

A new theory of solutions, the method of energy representation, is introduced by adopting the solute-solvent interaction energy as the coordinate of distribution functions. The density-functional theory is formulated over the energy coordinate, and an approximate functional for the solvation free energy is given in terms of energy distribution functions in the solution and reference solvent systems. The method of energy representation greatly expands the scope of solution theory and is amenable to supercritical fluid, flexible molecules with intramolecular degrees of freedom, inhomogeneous system, and quantum-mechanical/molecular-mechanical (QM/MM) system. Through the combination with molecular simulation, the functional for the solvation free energy is demonstrated to perform well for nonpolar, polar, and ionic solutes in water over a wide range of thermodynamics conditions, with drastic reduction of the computational demand compared to the standard free-energy perturbation and thermodynamic integration methods. As an application to inhomogeneous system involving flexible species, the molecular binding into micelle and membrane is analyzed by treating micelle and membrane as a mixed solvent system consisting of water and amphiphilic molecule.

Influence of ionization on the conformational preferences of peptide models. Ramachandran surfaces of N‐formyl‐glycine amide and N‐formyl‐alanine amide radical cations

Ramachandran maps of neutral and ionized HCO-Gly-NH2 and HCO-Ala-NH2 peptide models have been built at the B3LYP/6-31++G(d,p) level of calculation. Direct optimizations using B3LYP and the recently developed MPWB1K functional have also been carried out, as well as single-point calculations at the CCSD(T) level of theory with the 6-311++G(2df,2p) basis set. Results indicate that for both peptide models ionization can cause drastic changes in the shape of the PES in such a way that highly disallowed regions in neutral PES become low-energy regions in the radical cation surface. The structures localized in such regions, epsilonL+* and epsilonD+* are highly stabilized due to the formation of 2-centre-3-electron interactions between the two carbonyl oxygens. Inclusion of solvent effects by the conductor-like polarizable continuum model (CPCM) shows that the solute-solvent interaction energy plays an important role in determining the stability order.

Modeling molecular and ionic absolute solvation free energies with quasichemical theory bounds

A recently developed statistical mechanical quasichemical theory (QCT) has led to significant insights into solvation phenomena for both hydrophilic and hydrophobic solutes. The QCT exactly partitions solvation free energies into three components: (1) Inner-shell chemical, (2) outer-shell packing, and (3) outer-shell long-ranged contributions. In this paper, we discuss efficient methods for computing each of the three parts of the free energy. A Bayesian estimation approach is developed to compute the inner-shell chemical and outer-shell packing contributions. We derive upper and lower bounds on the outer-shell long-ranged portion of the free energy by expressing this component in two equivalent ways. Local, high-energy contacts between the solute and solvent are eliminated by spatial conditioning in this free energy piece, leading to near-Gaussian distributions of solute-solvent interaction energies. Thus, the average of the two mean-field bounds yields an accurate and efficient free energy estimate. Aqueous solvation free energy results are presented for several solutes, including methane, perfluoromethane, water, and sodium and chloride ions. The results demonstrate the accuracy and efficiency of the methods. The approach should prove useful in computing solvation free energies in inhomogeneous, restricted environments.

Basis set dependence of solute-solvent interaction energy of benzene in water: A HF/DFT study

Solute-solvent interaction energies for the benzene molecule dissolved in water are computed using Hartree-Fock and B3LYP density functional theories. Explicit solvent molecules up to 14-A away from the dissolved benzene molecule are included in the calculation of interaction energies. Both basis set dependence and basis set superposition errors are carefully examined. It is found that the use of a larger basis set for the region near the solute together with a smaller basis set for the outer region gives results very close to what would have been obtained if the larger basis set had been used for the whole system. It is also shown that a correction for the basis set superposition error is a necessary component in this kind of calculations. With this correction, results obtained with different tested basis sets converge to within 1 kcal/mol.

Application of the level-set method to the implicit solvation of nonpolar molecules

A level-set method is developed for numerically capturing the equilibrium solute-solvent interface that is defined by the recently proposed variational implicit solvent model [Dzubiella, Swanson, and McCammon, Phys. Rev. Lett. 104, 527 (2006); J. Chem. Phys. 124, 084905 (2006)]. In the level-set method, a possible solute-solvent interface is represented by the zero level set (i.e., the zero level surface) of a level-set function and is eventually evolved into the equilibrium solute-solvent interface. The evolution law is determined by minimization of a solvation free energy functional that couples both the interfacial energy and the van der Waals type solute-solvent interaction energy. The surface evolution is thus an energy minimizing process, and the equilibrium solute-solvent interface is an output of this process. The method is implemented and applied to the solvation of nonpolar molecules such as two xenon atoms, two parallel paraffin plates, helical alkane chains, and a single fullerence C(60). The level-set solutions show good agreement for the solvation energies when compared to available molecular dynamics simulations. In particular, the method captures solvent dewetting (nanobubble formation) and quantitatively describes the interaction in the strongly hydrophobic plate system.

The role of local structure on formic acid decomposition in supercritical water: A hybrid quantum mechanics/Monte Carlo study

We explored water-assisted decompositions of formic acid in supercritical water in terms of local structure near reactant. A hybrid quantum mechanics/molecular mechanics (QM/MM) simulation used in this paper includes QM part as first solvation shell members around the reactant. A present QM/MM approach can simulate supercritical water solution with a reasonable computational load while keeping the simulation preciseness because a density functional theory of B3LYP/6-31+G(d) level was iterated at every 1000 Monte Carlo solute moves. The formic acid converts mainly decarboxylation by water-assisted mechanism, and the coordinated water molecules play an important role for understanding supercritical water density dependence of the reaction. We analyzed a contour map based on the solute–solvent interaction energy along with the reaction pathway. Coordinated water molecule restricted the dehydration pathway by means of hydrogen bond with formic acid, however, the coordinated water promotes the decarboxylation pathway by means of stabilization of the transition state structure with one catalytic water molecule. The contour map of the pair interaction energy along the reaction path elucidates the role of local structure on reactions in supercritical water.

Generalized Solvation Heat Capacities

The partial molar heat capacity associated with a constant-pressure solvation process is extended to define a total of six generalized solvation heat capacities, each of which contain unique physical information. These arise from all the possible cross derivatives of the reversible heat of solvation (with respect to T and N), each evaluated at either constant pressure or constant volume. The resulting quantities may be interconverted using expressions that depend on the solvent equation of state and the solute partial molar volume. Moreover, contributions to each of the solvation heat capacities arising from the temperature dependence of the solute-solvent interaction energy and the solvent-reorganization energy (at either constant pressure or constant volume) are formally identified. For the self-solvation of a molecule in its own pure fluid, the latter quantities may be extracted directly from experimental data, while for more general solvation processes additional input is required, either from computer simulation or from theoretical approximations. The results are used to experimentally quantify the generalized heat capacities pertaining to the self-solvation of xenon, difluoromethane, n-hexane, and water, as well as the hydration of xenon, cyclohexane, and three hard sphere solutes (of about the same size as water, xenon, and cyclohexane).

Comparison of three effective Hamiltonian models of increasing complexity: Triazene in water as a test case

A critical comparison of widely used solvation models is reported. It is illustrated by a study of the triazene molecule in liquid water. We consider the following approaches: (1) a continuum model based on multicentric multipole expansions of the charge distribution, (2) the averaged solvent electrostatic potential from molecular dynamics (ASEP/MD) method, and (3) molecular dynamics simulations using a combined quantum mechanics/molecular mechanics potential (QM/MM/MD). We find that the solvation induces appreciable changes in the geometry and charge distribution of triazene. These changes are only qualitatively reproduced by the dielectric continuum model, which clearly underestimates induced dipole moments and solute-solvent interaction energy. We also show that the use of effective point charges placed on solute nuclei during the classical simulations may cause significant errors in the description of the solvent structure. The addition of charges representing nitrogen atom lone pairs is compulsory to reproduce the QM/MM/MD simulation results. Moreover, our results validate the use of the mean field approximation in the study of solvent effects. A major conclusion of this study is that the ASEP/MD method constitutes a reliable alternative to the much more computationally demanding QM/MM/MD methods.

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.

Cope Elimination: Elucidation of Solvent Effects from QM/MM Simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.

Polarization and Charge-Transfer Effects in Aqueous Solution via Ab Initio QM/MM Simulations

Combined ab initio quantum mechanical and molecular mechanical (QM/MM) simulations coupled with the block-localized wave function energy decomposition (BLW-ED) method have been conducted to study the solvation of two prototypical ionic systems, acetate and methylammonium ions in aqueous solution. Calculations reveal that the electronic polarization between the targeted solutes and water is the primary many-body effect, whereas the charge-transfer term only makes a small fraction of the total solute-solvent interaction energy. In particular, the polarization effect is dominated by the solvent (water) polarization.

Theoretical Studies of the Tautomeric Equilibria for Five-Member N-Heterocycles in the Gas Phase and in Solution

Tautomeric equilibria have been studied for five-member N-heterocycles and their methyl derivatives in the gas phase and in different solvents with dielectric constants of epsilon = 4.7-78.4. The free energy changes differently for tautomers upon solvation as compared to the gas phase, resulting in a shift of the equilibrium constant in solution. Solvents with increasing dielectric constant produce more negative solute-solvent interaction energies and increasing internal energies. The methyl-substituted imidazole and pyrrazole form delicate equilibria between two tautomeric forms. Depending on the solvent, the methyl-substituted triazoles and tetrazole have one or two major tautomers in solution. When estimating the relative solvation free energies by means of an explicit solvent model and using the FEP/MC method, one observes that the preferred tautomers differ in several cases from those predicted by the continuum solvent model. The 1,2-prototropic shift, as an intramolecular tautomerization path, requires about 50 kcal/mol activation energy for imidazole in the gas phase, and this route is also disfavored in a solution. The calculated activation free energy along the intramolecular path is 48-50 kcal/mol in chloroform and water as compared to a literature value of 13.6 kcal/mol for pyrrazole in DMSO. A molecular dynamics computer experiment favors the formation of an imidazole chain in chloroform, making the 1,3-tautomerization feasible along an intermolecular path in nonprotic solvents. In aqueous solution, one strong N-H...Ow hydrogen bond is formed for each species, whereas all other nitrogens in the ring form weaker, N...HwOw type hydrogen bonds. The tetrahydrofuran solvent acts as a hydrogen bond acceptor and forms N-H... Oether bonds. Molecules of the dichloromethane solvent are in favorable dipole-dipole interactions with the solute. The results obtained are useful in the design of N-heterocyclic ligands forming specified hydrogen bonds with protein side chains.

Influence of Inter- and Intramolecular Hydrogen Bonding on Kemp Decarboxylations from QM/MM Simulations

The Kemp decarboxylation reaction for benzisoxazole-3-carboxylic acid derivatives has been investigated using QM/MM calculations in protic and dipolar aprotic solvents. Aprotic solvents have been shown to accelerate the rates of reaction by 7-8 orders of magnitude over water; however, the inclusion of an internal hydrogen bond effectively inhibits the reaction with near solvent independence. The effects of solvation and intramolecular hydrogen bonding on the reactants, transition structures, and the rate of reaction are elucidated using two-dimensional potentials of mean force (PMF) derived from free energy perturbation calculations in Monte Carlo simulations (MC/FEP). Free energies of activation in six solvents have been computed to be in close agreement with experiment. Solute-solvent interaction energies show that poorer solvation of the reactant anion in the dipolar aprotic solvents is primarily responsible for the observed rate enhancements over protic media. In addition, a discrepancy for the experimental rate in chloroform has been studied in detail with the conclusion that ion-pairing between the reactant anion and tetramethylguanidinium counterion is responsible for the anomalously slow reaction rate. The overall quantitative success of the computations supports the present QM/MM/MC approach, which features PDDG/PM3 as the QM method.

From Hydrophobic to Hydrophilic Solvation: An Application to Hydration of Benzene.

We report a computer simulation study on the hydration of benzene, which, despite being hydrophobic, is a weak hydrogen bond acceptor. The effect of benzene-water hydrogen bonding on the hydration free energy has been analyzed in terms of solute-solvent energies and entropies. Our calculations show that benzene-water hydrogen bonding restricts the number of arrangements possible for the water molecules resulting in a more unfavorable (negative) solute-solvent entropy change than observed for a 'nonpolar benzene' not capable of accepting water hydrogen bonds. More favorable hydration free energies of aromatic hydrocarbons in comparison with aliphatic hydrocarbons observed experimentally as well as in our calculations must therefore be a result of more favorable solute-solvent interaction energies. This result supports the view that lower aqueous solubilities of nonpolar molecules compared to polar molecules are due to a lack of favorable electrostatic interactions with water molecules. The calculated hydration free energy, enthalpy, entropy, and hydration heat capacity of benzene are in good agreement with experimentally reported values.

An approach to the solvation free energy in terms of the distribution functions of the solute–solvent interaction energy

The energy representation of the molecular configuration in a dilute solution is introduced to express the solvent distribution around the solute over a one-dimensional coordinate specifying the solute–solvent interaction energy. On the basis of the energy representation, an approximate functional for the solvation free energy of a solute in solution is constructed by adopting the Percus-Yevick-type approximation in the unfavorable region of the solute–solvent interaction and the hypernetted-chain-type approximation in the favorable region. The solvation free energy is then given exactly to second order with respect to the solvent density and to the solute–solvent interaction. It is demonstrated that the solvation free energies of nonpolar, polar, and ionic solutes in water are evaluated accurately and efficiently from the single functional over a wide range of thermodynamic conditions. The extension to a flexible solute molecule is straightforward. The applicability of the method is illustrated for solute molecules with a stretching or torsional degree of freedom.

Prediction of the Solubility, Activity Coefficient and Liquid/Liquid Partition Coefficient of Organic Compounds

AbstractSolvation models, based on fundamental chemical structure theory, were developed in the SPARC mechanistic tool box to predict a large array of physical properties of organic compounds in water and in non‐aqueous solvents strictly from molecular structure. The SPARC self‐interaction solvation models that describe the intermolecular interaction between like molecules (solute‐solute or solvent‐solvent) were extended to quantify solute‐solvent interaction energy in order to estimate the activity coefficient in almost any solvent. Solvation models that include dispersion, induction, dipole‐dipole and hydrogen bonding interactions are used to describe the intermolecular interaction upon placing an organic solute molecule in any single or mixed solvent system. In addition to estimation of the activity coefficient for 2674 organic compounds, these solvation models were validated on solubility and liquid/liquid distribution coefficient in more than 163 solvents including water. The RMS deviations of the calculated versus observed activity coefficients, solubilities and liquid/liquid distribution coefficients were 0.272 log mole fraction, 0.487 log mole fraction and 0.44 log units, respectively.

On the nonpolar hydration free energy of proteins: surface area and continuum solvent models for the solute-solvent interaction energy.

Implicit solvent hydration free energy models are an important component of most modern computational methods aimed at protein structure prediction, binding affinity prediction, and modeling of conformational equilibria. The nonpolar component of the hydration free energy, consisting of a repulsive cavity term and an attractive van der Waals solute-solvent interaction term, is often modeled using estimators based on the solvent exposed solute surface area. In this paper, we analyze the accuracy of linear surface area models for predicting the van der Waals solute-solvent interaction energies of native and non-native protein conformations, peptides and small molecules, and the desolvation penalty of protein-protein and protein-ligand binding complexes. The target values are obtained from explicit solvent simulations and from a continuum solvent van der Waals interaction energy model. The results indicate that the standard surface area model, while useful on a coarse-grained scale, may not be accurate or transferable enough for high resolution modeling studies of protein folding and binding. The continuum model constructed in the course of this study provides one path for the development of a computationally efficient implicit solvent nonpolar hydration free energy estimator suitable for high-resolution structural and thermodynamic modeling of biological macromolecules.