Predicting aqueous free energies of solvation as functions of temperature

This work introduces a model, solvation model 6 with temperature dependence (SM6T), to predict the temperature dependence of aqueous free energies of solvation for compounds containing H, C, and O in the range 273-373 K. In particular, we extend solvation model 6 (SM6), which was previously developed (Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 1133) for predicting aqueous free energies of solvation at 298 K, to predict the variation of the free energy of solvation relative to 298 K. Also, we describe the database of experimental aqueous free energies of solvation for compounds containing H, C, and O that was used to parametrize and test the new model. SM6T partitions the temperature dependence of the free energy of solvation into two components: the temperature dependence of the bulk electrostatic contribution to the free energy of solvation, which is computed using the generalized Born equation, and the temperature dependence of first-solvation-shell effects which is modeled using a parametrized solvent-exposed surface-area-dependent term. We found that SM6T predicts the temperature dependence of aqueous free energies of solvation with a mean unsigned error of 0.08 kcal/mol over our entire database, whereas using the experimental value at 298 K produces a mean unsigned error of 0.53 kcal/mol.     

Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton

Thermochemical cycles that involve pKa, gas-phase acidities, aqueous solvation free energies of neutral species, and gas-phase clustering free energies have been used with the cluster pair approximation to determine the absolute aqueous solvation free energy of the proton. The best value obtained in this work is in good agreement with the value reported by Tissandier et al. (Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787), who applied the cluster pair approximation to a less diverse and smaller data set of ions. We agree with previous workers who advocated the value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton. Considering the uncertainties associated with the experimental gas-phase free energies of ions that are required to use the cluster pair approximation as well as analyses of various subsets of data, we estimate an uncertainty for the absolute aqueous solvation free energy of the proton of no less than 2 kcal/mol. Using a value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton, we expand and update our previous compilation of absolute aqueous solvation free energies; this new data set contains conventional and absolute aqueous solvation free energies for 121 unclustered ions (not including the proton) and 147 conventional and absolute aqueous solvation free energies for 51 clustered ions containing from 1 to 6 water molecules. When tested against the same set of ions that was recently used to develop the SM6 continuum solvation model, SM6 retains its previously determined high accuracy; indeed, in most cases the mean unsigned error improves when it is tested against the more accurate reference data.     

Prediction of SAMPL2 aqueous solvation free energies and tautomeric ratios using the SM8, SM8AD,and SMD solvation models

We applied the solvation models SM8, SM8AD, and SMD in combination with the Minnesota M06-2X density functional to predict vacuum-water transfer free energies (Task 1) and tautomeric ratios in aqueous solution (Task 2) for the SAMPL2 test set. The bulk-electrostatic contribution to the free energy of solvation is treated as follows: SM8 employs the generalized Born model with the Coulomb field approximation, SM8AD employs the generalized Born approximation with asymmetric descreening, and SMD solves the nonhomogeneous Poisson equation. The non-bulk-electrostatic contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell is treated as a sum of terms that are products of geometry-dependent atomic surface tensions and solvent-accessible surface areas of the individual atoms of the solute. On average, three models tested in the present work perform similarly. In particular, we achieved mean unsigned errors of 1.3 (SM8), 2.0 (SM8AD), and 2.6 kcal/mol (SMD) for the aqueous free energies of 30 out of 31 compounds with known reference data involved in Task 1 and mean unsigned errors of 2.7 (SM8), 1.8 (SM8AD), and 2.4 kcal/mol (SMD) in the free energy differences (tautomeric ratios) for 21 tautomeric pairs in aqueous solution involved in Task 2.     

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.     

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.     

PM3-SM3: A general parameterization for including aqueous solvation effects in the PM3 molecular orbital model

Our recently proposed scheme for including aqueous solvation free energies in parameterized NDDO SCF models is extended to the Parameterized Model 3 semiempirical Hamiltonian. The solvation model takes accurate account of the hydrophobic effect for hydrocarbons, as well as electric polarization of the solvent, the free energy of cavitation, and dispersion interactions. Eight heteroatoms are included (along with H and C), and the new model is parameterized accurately for the water molecule itself, which allows meaningful treatments of specifically hydrogen bonded water molecules. The unphysical partial charges on nitrogen atoms predicted by the Parameterized Model 3 Hamiltonian limit the accuracy of the predicted solvation energies for some compounds containing nitrogen, but the model may be very useful for other systems, especially those for which PM3 is preferred over AM1 for the solute properties of the particular system under study. © 1992 by John Wiley & Sons, Inc.     

Solvation of monovalent anions in acetonitrile and N,N-dimethylformamide: Parameterization of the IEF-PCM model

The present work reports the parameterization of the polarizable continuum model for predicting the free energies of solvation for monovalent anions in acetonitrile and N,N-dimethylformamide. The parameterization of the model for acetonitrile employed the experimental free energies of solvation for a set of 12 charged solutes, containing H, C, N, O, S, F, Cl, Br, and I atoms. For the N,N-dimethylformamide solutions, experimental solvation free energies for 11 monovalent anions were used. A mean absolute error of 0.7 kcal/mol in the solvation free energies has been achieved for the 12 anions in acetonitrile, whereas the mean absolute error for the 11 anions corresponds to 0.5 kcal/mol in N,N-dimethylformamide. These results indicate that the polarizable continuum model is a suitable methodology for the study of thermodynamic effects in solutions of monovalent anions in both solvents.     

The effect of aqueous solvation upon alpha-helix formation for polyalanines

The incremental free energies of aqueous solution for acetyl(ala)NNH2 in its extended unfolded and alpha-helical conformations are compared using the SM5.2 solvation method of Cramer and Truhlar. A combination of density functional theory (DFT) at the B3LYP/D95(d,p) and AM1 has been employed using the ONIOM method. The incremental solvation energies of alpha-helical structures are very similar for both ONIOM and AM1 optimized structures as these structures do not significantly change upon solution. However, the conformations of the unfolded peptides change from extended beta-strand to polyproline II conformations upon aqueous solution. The incremental solvation free energy per residue of the polyproline II structure is about 2 kcal/mol/residue greater than that for the alpha-helix, representing an upper limit for the difference between the solvation energies. However, most of this difference disappears when the energy required to distort the optimized gas-phase extended beta-strand structure to the optimized polyproline II solution structure is included in the analysis, leaving an estimated difference in incremental solvation free energy of 0.3-0.5 kcal/mol favoring the unfolded structure. The solution structure sacrifices the stability derived from the intramolecular C5 H-bonds for more favorable interactions with the aqueous solvent.     

Quantum chemical characterization of the reactions of guanine with the phenylnitrenium ion.

Density functional calculations at the B3LYP/6-311+G(2d,p)//pBP/DN level predict all cationic adducts combining guanine, at either its N2, O6, N7, or C8 positions, with phenylnitrenium ion, at either its N, 2, or 4 positions, to be lower in energy than the separated reactants. This relative stability of all adducts is preserved after addition of aqueous solvation free energies computed at the SM2 level, although some leveling of the adduct relative energies one to another is predicted. Cations having the lowest relative energies in solution correspond structurally to those adducts most commonly found when guanine reacts with larger, biologically relevant nitrenium ions in vitro and in vivo. One of these, the N-C8 adduct, is stabilized both by a rearomatized phenyl ring and by the operation of an anomeric effect not found in any of the others. On the basis of energetic analysis, direct conversion of an N-N7 cation to an N-C8 cation according to a previously proposed mechanism is unlikely; however, an alternative rearrangement converting a 2-N7 cation to an N-C8 cation via the intermediacy of a five-membered ring may be operative in nitrenium ions with aromatic frameworks better able than phenyl to stabilize endocyclic cationic charge.     

Comparison of methods to estimate the free energy of solvation:Importance in the modulation of the affinity of 3-benzazepines for the D1receptor

We computed the free energy of solvation for a series of ions and neutral molecules using two different continuum approaches. First, we used the AM1–SM1 technique, where the AM1 Fock matrix is modified to include a generalized Born contribution. Second, we applied the DelPhi approach, where the electrostatic component of the free energy of solvation is evaluated by resolving the Poisson–Boltzman equation by a finite difference method. Both methods appear equally reliable for ionic systems. For neutral compounds, AM1–SM1 performs better than DelPhi; however, the differences become less pronounced for compounds with larger free energies of solvation. In parallel, both methods were applied to study the influence of the solvation process in the overall drug receptor interaction for a series of closely related ligands for the D₁ dopamine receptor. An inverse linear relationship was found between the free energy of solvation and the logarithm of the affinity of the ligands; nevertheless, electrostatic properties are likely to modulate affinity as well. © 1993 John Wiley & Sons, Inc.     

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.     

The SAMPL3 blind prediction challenge: transfer energy overview

Prediction of the free energy of solvation of a small molecule, or its transfer energy, is a necessary step along the path towards calculating the interactions between molecules that occur in an aqueous environment. A set of these transfer energies were gathered from the literature for series of chlorinated molecules with varying numbers of chlorines based on ethane, biphenyl, and dibenzo-p-dioxin. This focused set of molecules were then provided as a blinded challenge to assess the ability of current computational solvation methods to accurately model the interactions between water and increasingly chlorinated compounds. This was presented as part of the SAMPL3 challenge, which represented the fourth iterative blind prediction challenge involving transfer energies. The results of this exercise demonstrate that the field in general has difficulty predicting the transfer energies of more highly chlorinated compounds, and that methods seem to be erring in the same direction.     

Toward robust computational electrochemical predicting the environmental fate of organic pollutants

A number of density functionals was utilized for the calculation of electron attachment free energy for nitrocompounds, quinones and azacyclic compounds. Different solvation models have been tested on the calculation of difference in free energies of solvation of oxidized and reduced forms of nitrocompounds in aqueous solution, quinones in acetonitrile, and azacyclic compounds in dimethylformamide. Gas‐phase free energies evaluated at the mPWB1K/tzvp level and solvation energies obtained using SMD model to compute solvation energies of neutral oxidized forms and PCM(Pauling) to compute solvation energies of anion‐radical reduced forms provide reasonable accuracy of the prediction of electron attachment free energy, difference in free solvation energies of oxidized and reduced forms, and as consequence yield reduction potentials in good agreement with experimental data (mean absolute deviation is 0.15 V). It was also found that SMD/M05‐2X/tzvp method provides reduction potentials with deviation of 0.12 V from the experimental values but in cases of nitrocompounds and quinones this accuracy is achieved due to the cancelation of errors. To predict reduction ability of naturally occurred iron containing species with respect to organic pollutants we exploited experimental data within the framework of Pourbaix (E_h ? pH) diagrams. We conclude that surface‐bound Fe(II) as well as certain forms of aqueous Fe(II)_aq are capable of reducing a variety of nitroaromatic compounds, quinones and novel high energy materials under basic conditions (pH > 8). At the same time, zero‐valent iron is expected to be active under neutral and acidic conditions. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Analysis of SM8 and Zap TK calculations and their geometric sensitivity

A prospective study of aqueous solvation energies was done using the SM8 and Zap TK models for a variety of geometries. CM4M charges calculated with M06 and M06-2X were found to yield similar results for the SM8 model. Zap TK calculations were primarily done with AM1BCC charges but limited attempts to use charges derived from DFT showed promise. The OMEGA application quickly generated conformations that performed well with both solvation models, while the use of computationally expensive DFT optimized geometries yielded increased RMSE and MSE. It is shown that increasing levels of gas phase geometry optimization yield increasingly unfavorable solvation energy for single conformer models.     

High-throughput prediction of blood-brain partitioning: a thermodynamic approach

A high-throughput in silico screening tool for potentially CNS active compounds was developed on the basis of the correlation of solvation free energies and blood-brain partitioning (log(cbrain/cblood) = log BB) data available from experimental sources. Utilizing a thermodynamic approach, solvation free energies were calculated by the fast and efficient generalized Born/surface area continuum solvation model, which enabled us to evaluate more than 10 compounds/min. Our training set involved a structurally diverse set of 55 compounds and yielded a function of log BB = 0.035Gsolv + 0.2592 (r = 0.85, standard error 0.37). Calculation of solvation free energies for 8700 CNS active compounds (CIPSLINE database) revealed that Gsolv is higher than -50 kJ/mol for the 96% of these compounds which can be used as suitable criteria for the identification of compounds preferable for CNS penetration.     

Single-ion solvation free energies and the normal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide

The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.     

The solvation, partitioning, hydrogen bonding, and dimerization of nucleotide bases: a multifaceted challenge for quantum chemistry

We present M06-2X density functional calculations of the chloroform/water partition coefficients of cytosine, thymine, uracil, adenine, and guanine and calculations of the free energies of association of selected unsubstituted and alkylated nucleotide base pairs in chloroform and water. Both hydrogen bonding and π-π stacking interactions are considered. Solvation effects are treated using the continuum solvent models SM8, SM8AD, and SMD, including geometry optimization in solution. Comparison of theoretical results with available experimental data indicates that all three of these solvation models predict the chloroform-water partition coefficients for the studied nucleobases qualitatively well, with mean unsigned errors in the range of 0.4-1.3 log units. All three models correctly predict the preference for hydrogen bonding over stacking for nucleobase pairs solvated in chloroform, and SM8, SM8AD, and SMD show similar accuracy in predicting the corresponding free energies of association. The agreement between theory and experiment for the association free energies of the dimers in water is more difficult to assess, as the relevant experimental data are indirect. Theory predicts that the stacking interaction of nucleobases in water is more favorable than hydrogen bonding for only two out of three tested hetero-dimers.     

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.     

Quantum chemical calculations of reduction potentials of AnO2(2+)/AnO2+ (An = U, Np, Pu, Am) and Fe3+/Fe2+ couples

The reduction potentials of the AnO(2)(H(2)O)(5)(2+)/AnO(2)(H(2)O)(5)(+) couple (An = U, Np, Pu, and Am) and Fe(H(2)O)(6)(3+) to Fe(H(2)O)(6)(2+) in aqueous solution were calculated at MP2, CASPT2, and CCSD(T) levels of theory. Spin-orbit effects for all species were estimated at the CASSCF level. Solvation of the hydrated metal cations was modeled both by polarizable conductor model (PCM) calculation and by solvating the solutes with over one thousand TIP3P water molecules in the QM/MM framework. The redox reaction energy calculated by QM/MM method agreed well with the PCM method after corrections using the classical Born formula for the contribution from the rest of the solvation sphere and correction for dynamic response of solvent polarization in the MM region. Calculated reduction potentials inclusive of spin-orbit effect, zero-point energy, thermal corrections, entropy effect, and PCM solvation energy were found to be comparable with experimental data. The difference between CASPT2 calculated and experimental reduction energies were less than 35 kJ/mol in all cases, which ensures that CASPT2 (and CCSD(T)) calculations provide reasonable estimates of the thermochemistry of these reactions.