A general treatment of solubility. 2. QSPR prediction of free energies of solvation of specified solutes in ranges of solvents

As part of our general QSPR treatment of solubility (started in the preceding paper), we now present quantitative relationships between solvent structures and the solvation free energies of individual solutes. Solvation free energies of 80 diverse organic solutes are each modeled in a range from 15 to 82 solvents using our CODESSA PRO software. Significant correlations (in terms of squared correlation coefficient) are found for all the 80 solutes: the best fit is obtained for n-propylamine (R(2) = 0.996); the lowest R(2) corresponds to toluene (0.604).     

Treating entropy and conformational changes in implicit solvent simulations of small molecules

Implicit solvent models are increasingly popular for estimating aqueous solvation (hydration) free energies in molecular simulations and other applications. In many cases, parameters for these models are derived to reproduce experimental values for small molecule hydration free energies. Often, these hydration free energies are computed for a single solute conformation, neglecting solute conformational changes upon solvation. Here, we incorporate these effects using alchemical free energy methods. We find significant errors when hydration free energies are estimated using only a single solute conformation, even for relatively small, simple, rigid solutes. For example, we find conformational entropy (TDeltaS) changes of up to 2.3 kcal/mol upon hydration. Interestingly, these changes in conformational entropy correlate poorly (R2 = 0.03) with the number of rotatable bonds. The present study illustrates that implicit solvent modeling can be improved by eliminating the approximation that solutes are rigid.     

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

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

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.     

Free energy calculation methods: A theoretical and empirical comparison of numerical errors and a new method qualitative estimates of free energy changes

We present a comparison of four free energy calculation methods: thermodynamic integration (TI); traditional free energy perturbation (FEP); Bennett's acceptance ratio method (IPS); and a method that is related to an implementation of the WHAM method (CRS). The theoretical bases of the methods are first described, then calculations of the solvation free energies of methane and ethane are performed to determine the magnitude of the errors for the different methods. We find that the methods give similar errors when many intermediate states (windows) are used, but the IPS and CRS methods give smaller errors than the TI and FEP methods when no intermediate states are used. We also present a new procedure (based on the CRS method) that uses coordinates from simulations of a set of solutes to calculate the salvation free energies of additional solutes for which no simulations were performed. Solvation free energies for nine solutes (methanol, dimethylether, methylamine, methylammonium, dimethylamine, fluoromethane, difluoromethane, trifluoromethane, and tetrafluoromethane) are estimated based only on simulations of set of small hydrophobic solutes (including methane, ethane, and propane). These estimates can be surprisingly accurate and appear to be useful for making rapid estimates of solvation free energies. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 902–919, 1997     

A molecular dynamics computer simulation study of room-temperature ionic liquids. I. Equilibrium solvation structure and free energetics

Solvation in 1-ethyl-3-methylmidazolium chloride and in 1-ethyl-3-methylimidazolium hexafluorophosphate near equilibrium is investigated via molecular dynamics computer simulations with diatomic and benzenelike molecules employed as probe solutes. It is found that electrostriction plays an important role in both solvation structure and free energetics. The angular and radial distributions of cations and anions become more structured and their densities near the solute become enhanced as the solute charge separation grows. Due to the enhancement in structural rigidity induced by electrostriction, the force constant associated with solvent configuration fluctuations relevant to charge shift and transfer processes is also found to increase. The effective polarity and reorganization free energies of these ionic liquids are analyzed and compared with those of highly polar acetonitrile. Their screening behavior of electric charges is also investigated.     

Solvation of coumarin 153 in supercritical fluoroform

We present a study of local density augmentation around an attractive solute (i.e., giving rise to more attractive interaction with the solvent than solvent-solvent interactions) in supercritical fluoroform. This work is based on molecular dynamics simulations of coumarin 153 in supercritical fluoroform at densities both above and below the critical density, ranging from dilute gas-like to liquid-like, at a reduced temperature (T/T(c)) of 1.03. We focused on studying the structure of the solvation shell and the variation of the solute electronic absorption and emission shifts with density. Quantum calculations at the density functional theory (DFT) level were run on the solute in the ground state, and time-dependent DFT calculations were performed in the solute excited state in order to determine the solute-solvent potential parameters. The results obtained for the Stokes shift are in agreement with the experimental measurements. To evaluate local density augmentation from simulations, we used two different definitions, one based on the solvation number and the other derived from solvatochromic shifts. In the former case, the agreement with experimental results is good, while, in the latter case, better agreement is achieved by perturbatively including the induced-dipole contribution to the solvation energy.     

Calculation of the free energy of solvation for neutral analogs of amino acid side chains

The ability of the GROMOS96 force field to reproduce partition constants between water and two less polar solvents (cyclohexane and chloroform) for analogs of 18 of the 20 naturally occurring amino acids has been investigated. The estimations of the solvation free energies in water, in cyclohexane solution, and chloroform solution are based on thermodynamic integration free energy calculations using molecular dynamics simulations. The calculations show that while the force field reproduces the experimental solvation free energies of nonpolar analogs with reasonable accuracy the solvation free energies of polar analogs in water are systematically overestimated (too positive). The dependence of the calculated free energies on the atomic partial charges was also studied.     

A Continuum Reaction Field Theory of Polarizable, Nondipolar, Quadrupolar Solvents: Ab Initio Study of Equilibrium Solvation in Benzene

A continuum theory to describe solvation in nondipolar quadrupolar solvents is developed by accounting for electronic polarizability. A general Hamiltonian for a solute–solvent system in an arbitrary nonequilibrium configuration is obtained in terms of two field variables—densities of the solvent quadrupole and induced dipole moments. Equilibrium solvation is studied by optimizing this Hamiltonian with account of cavity boundaries. As an application, electronic structures and free energies of small molecules in benzene are examined with ab initio methods. Solvation stabilization due to solvent quadrupole moments is found to be substantial; for the solutes considered here, it is comparable to and often in excess of that arising from solvent-induced dipole moments.     

Comparison of two simulation methods to compute solvation free energies and partition coefficients

The thermodynamic integration (TI) and expanded ensemble (EE) methods are used here to calculate the hydration free energy in water, the solvation free energy in 1‐octanol, and the octanol‐water partition coefficient for a six compounds of varying functionality using the optimized potentials for liquid simulations (OPLS) all‐atom (AA) force field parameters and atomic charges. Both methods use the molecular dynamics algorithm as a primary component of the simulation protocol, and both have found wide applications in fields such as the calculation of activity coefficients, phase behavior, and partition coefficients. Both methods result in solvation free energies and 1‐octanol/water partition coefficients with average absolute deviations (AAD) from experimental data to within 4 kJ/mol and 0.5 log units, respectively. Here, we find that in simulations the OPLS‐AA force field parameters (with fixed charges) can reproduce solvation free energies of solutes in 1‐octanol with AAD of about half that for the solute hydration free energies using a extended simple point charge (SPC/E) model of water. The computational efficiency of the two simulation methods are compared based on the time (in nanoseconds) required to obtain similar standard deviations in the solvation free energies and 1‐octanol/water partition coefficients. By this analysis, the EE method is found to be a factor of nine more efficient than the TI algorithm. For both methods, solvation free energy calculations in 1‐octanol consume roughly an order of magnitude more CPU hours than the hydration free energy calculations. © 2012 Wiley Periodicals, Inc.     

Evaluation of solvation free energies for small molecules with the AMOEBA polarizable force field

The effects of electronic polarization in biomolecular interactions will differ depending on the local dielectric constant of the environment, such as in solvent, DNA, proteins, and membranes. Here the performance of the AMOEBA polarizable force field is evaluated under nonaqueous conditions by calculating the solvation free energies of small molecules in four common organic solvents. Results are compared with experimental data and equivalent simulations performed with the GAFF pairwise‐additive force field. Although AMOEBA results give mean errors close to “chemical accuracy,” GAFF performs surprisingly well, with statistically significantly more accurate results than AMOEBA in some solvents. However, for both models, free energies calculated in chloroform show worst agreement to experiment and individual solutes are consistently poor performers, suggesting non‐potential‐specific errors also contribute to inaccuracy. Scope for the improvement of both potentials remains limited by the lack of high quality experimental data across multiple solvents, particularly those of high dielectric constant. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

A new set of atomic radii for accurate estimation of solvation free energy by Poisson–Boltzmann solvent model

The Poisson–Boltzmann implicit solvent (PB) is widely used to estimate the solvation free energies of biomolecules in molecular simulations. An optimized set of atomic radii (PB radii) is an important parameter for PB calculations, which determines the distribution of dielectric constants around the solute. We here present new PB radii for the AMBER protein force field to accurately reproduce the solvation free energies obtained from explicit solvent simulations. The presented PB radii were optimized using results from explicit solvent simulations of the large systems. In addition, we discriminated PB radii for N‐ and C‐terminal residues from those for nonterminal residues. The performances using our PB radii showed high accuracy for the estimation of solvation free energies at the level of the molecular fragment. The obtained PB radii are effective for the detailed analysis of the solvation effects of biomolecules. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Solvation in supercritical water

Solvation in supercritical water under equilibrium and nonequilibrium conditions is studied via molecular dynamics simulations. The influence of solute charge distributions and solvent density on the solvation structures and dynamics is examined with a diatomic probe solute molecule. It is found that the solvation structure varies dramatically with the solute dipole moment, especially in low-density water, in accord with many previous studies on ion solvation. This electrostrictive effect has important consequences for solvation dynamics. In the case of a nonequilibrium solvent relaxation, if there are sufficiently many water molecules close to the solute at the outset of the relaxation, the solvent response measured as a dynamic Stokes shift is almost completely governed by inertial rotations of these water molecules. By contrast, in the opposite case of a low local solvent density near the solute, not only rotations but also translations of water molecules play an important role in solvent relaxation dynamics. The applicability of a linear response is found to be significantly restricted at low water densities.     

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phases. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates the experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. The theory provides a quantitative framework for analyzing the steady-state and time-resolved optical spectra and makes several experimentally testable predictions. The equilibrium free energy of solvation, anisotropic in the nematic phase, is given by a quadratic function of cosine of the angle between the solute dipole and the solvent nematic director. The sign of solvation anisotropy is determined by the sign of dielectric anisotropy of the solvent: solvation anisotropy is negative in solvents with positive dielectric anisotropy and vice versa. The solvation free energy is discontinuous at the point of isotropic-nematic phase transition. The amplitude of this discontinuity is strongly affected by the size of the solute becoming less pronounced for larger solutes. The discontinuity itself and the magnitude of the splitting of the solvation free energy in the nematic phase are mostly affected by microscopic dipolar correlations in the nematic solvent. Illustrative calculations are presented for the equilibrium Stokes shift and the Stokes shift time correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl and 4,4-n-heptyl-cyanopiphenyl solvents as a function of temperature in both the nematic and isotropic phases.     

The effects of solute-solvent electrostatic interactions on solvatochromic shifts in supercritical CO2

Solvent clustering around attractive solutes is an important feature of supercritical solvation. We examine here the effects of the local density enhancement on solvatochromic shifts in electronic absorption and emission spectra in supercritical CO2. We use molecular dynamics (MD) simulation to study the spectral line shifts for model diatomic solutes that become more polar upon electronic excitation. The electronic transition is modeled as either a change from a quadrupolar to a dipolar solute charge distribution or as an increase in the magnitude of the solute dipole. Our main focus is on the density dependence of the line shifts at 320 K, which corresponds to about 1.05 times the solvent critical temperature, Tc, but results for higher temperatures are also obtained in order to determine the behavior of the line shifts in the absence of local density enhancement. We find that the extent of local density enhancement at 1.05Tc is strongly correlated with solute-solvent electrostatic attraction and that the density dependence of the emission line shifts resembles the behavior of the effective local densities, rho(eff), obtained from the first-shell coordination numbers. The differences that are seen are shown to be due to solute-solvent orientational correlations which provide an additional source of enhancement for electrostatic solvation energies and spectral line shifts.     

Ab initio procedure for aqueous-phase pKa calculation: the acidity of nitrous acid

We present an ab initio procedure for accurately calculating aqueous-phase pKa values and apply it to study the acidity of nitrous acid (HNO2, or HONO). The aqueous-phase pK(a) of nitrous acid was obtained from calculated gas-phase acidities and solvation free energies via a thermodynamic cycle and the solvation model chemistry of Barone et al. (J. Chem. Phys. 1997, 107, 3210). Solvation free energies were calculated at the HF/6-31G(d) level using the dielectric-polarizable continuum and the integral equation formalism-polarizable continuum solvent models (D-PCM and IEF-PCM, respectively), with the D-PCM model yielding the most accurate pKa values. For HF free energies of solvation, significant improvements in accuracy could be made by moving to the larger 6-311++G(3df,3pd) and aug-cc-pVQZ basis sets. Solvation free energies were also calculated using the density functional theory (DFT) methods B3LYP, TPSS, PBE0, B1B95, VSXC, B98 and O3LYP, with the most accurate methods being TPSS and VSXC, which provided average errors of less than 0.11 pKa units. Solvation free energies calculated with the different DFT methods were relatively insensitive to the basis set used. Our theoretical calculations are compared with experimental results obtained using stopped flow spectrophotometry. The pKa of nitrous acid was measured as 3.16 at 25 degrees C, and the enthalpy and entropy of nitrous acid dissociation were calculated from measurements as 6.7 kJ mol(-1) and -38.4 J mol(-1) K(-1), respectively, between 25 and 45 degrees C. The UV/visible absorption spectra of the nitrite ion and nitrous acid were also examined, and molar extinction coefficients were obtained for each.     

Implicit solvent models: Combining an analytical formulation of continuum electrostatics with simple models of the hydrophobic effect

The recent development of approximate analytical formulations of continuum electrostatics opens the possibility of efficient and accurate implicit solvent models for biomolecular simulations. One such formulation (ACE, Schaefer & Karplus, J. Phys. Chem., 1996, 100:1578) is used to compute the electrostatic contribution to solvation and conformational free energies of a set of small solutes and three proteins. Results are compared to finite-difference solutions of the Poisson equation (FDPB) and explicit solvent simulations and experimental data where available. Small molecule solvation free energies agree with FDPB within 1–1.5 kcal/mol, which is comparable to differences in FDPB due to different surface treatments or different force field parameterizations. Side chain conformation free energies of aspartate and asparagine are in qualitative agreement with explicit solvent simulations, while 74 conformations of a surface loop in the protein Ras are accurately ranked compared to FDPB. Preliminary results for solvation free energies of small alkane and polar solutes suggest that a recent Gaussian model could be used in combination with analytical continuum electrostatics to treat nonpolar interactions. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 322–335, 1999     

Ion solvation thermodynamics from simulation with a polarizable force field

Thermodynamic measurements of the solvation of salts and electrolytes are relatively straightforward, but it is not possible to separate total solvation free energies into distinct cation and anion contributions without reference to an additional extrathermodynamic assumption. The present work attempts to resolve this difficulty using molecular dynamics simulations with the AMOEBA polarizable force field and perturbation techniques to directly compute absolute solvation free energies for potassium, sodium, and chloride ions in liquid water and formamide. Corresponding calculations are also performed with two widely used nonpolarizable force fields. The simulations with the polarizable force field accurately reproduce in vacuo quantum mechanical results, experimental ion-cluster solvation enthalpies, and experimental solvation free energies for whole salts, while the other force fields do not. The results indicate that calculations with a polarizable force field can capture the thermodynamics of ion solvation and that the solvation free energies of the individual ions differ by several kilocalories from commonly cited values.     

Continuum solvation models in the linear interaction energy method

The linear interaction energy (LIE) method in combination with two different continuum solvent models has been applied to calculate protein-ligand binding free energies for a set of inhibitors against the malarial aspartic protease plasmepsin II. Ligand-water interaction energies are calculated from both Poisson-Boltzmann (PB) and Generalized Born (GB) continuum models using snapshots from explicit solvent simulations of the ligand and protein-ligand complex. These are compared to explicit solvent calculations, and we find close agreement between the explicit water and PB solvation models. The GB model overestimates the change in solvation energy, and this is caused by consistent underestimation of the effective Born radii in the protein-ligand complex. The explicit solvent LIE calculations and LIE-PB, with our standard parametrization, reproduce absolute experimental binding free energies with an average unsigned error of 0.5 and 0.7 kcal/mol, respectively. The LIE-GB method, however, requires a constant offset to approach the same level of accuracy.