Parameterization of the hydration free energy computations for organic solutes in the framework of the implicit solvent model with the nonuniform dielectric function (original) (raw)
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The Journal of Physical Chemistry B, 2002
ABSTRACT Prediction of solvation free energies is an important subject in fundamental natural science but also important to the pharmaceutical and food industry. A popular modeling approach is to treat the solution by an implicit solvent model. The solute molecule is rigid with a fixed effective charge distribution localized at the atomic nuclei positions. The hydration free energy is described by the van der Waals energy, the solute cavity formation energy in the water phase, and the change in electrostatic solute−solvent interaction energy. The dielectric continuum is generally assumed to be a simple medium, that is, linear, homogeneous, and isotropic. However, this approximation is quite severe and will give too hydrophilic solvation free energies. We show here that the simple medium approximation must be relaxed and nonlinearity must be taken into consideration. In strong electric fields, the solvent polarization becomes saturated and the dielectric no longer responds linearly in the applied field. This effect is well-described by the modified Langevin−Debye model. This nonlinear solvation model is used to study the hydration of 181 small organic molecules. Atomic charges and radii of the solute molecule are described by a standard classical force field. We apply the optimized potentials for liquid simulation all atom (OPLS-AA) force field, which is parametrized to reproduce both structural and thermodynamical data. This leads to a mean unsigned error of 0.6 kcal/mol, which is a 25% improvement compared to a simple medium approach. The nonlinear solvation model is further improved by introducing a few charge-scaling parameters for some functional groups that show a systematic deviation from their experimental data. This yields a mean unsigned error of 0.4 kcal/mol, which is only twice the experimental uncertainty. Hence, we conclude that nonlinear dielectric effects are indeed important to incorporate in implicit solvent models, even for neutral polar molecules.
Computation of hydration free energies of organic solutes with an implicit water model
Journal of Computational Chemistry, 2006
A new approach for computing hydration free energies ⌬G solv of organic solutes is formulated and parameterized. The method combines a conventional PCM (polarizable continuum model) computation for the electrostatic component ⌬G el of ⌬G solv and a specially detailed algorithm for treating the complementary nonelectrostatic contributions (⌬G nel ). The novel features include the following: (a) two different cavities are used for treating ⌬G el and ⌬G nel . For the latter case the cavity is larger and based on thermal atomic radii (i.e., slightly reduced van der Waals radii). (b) The cavitation component of ⌬G nel is taken to be proportional to the volume of the large cavity. (c) In the treatment of van der Waals interactions, all solute atoms are counted explicitly. The corresponding interaction energies are computed as integrals over the surface of the larger cavity; they are based on Lennard Jones (LJ) type potentials for individual solute atoms. The weighting coefficients of these LJ terms are considered as fitting parameters. Testing this method on a collection of 278 uncharged organic solutes gave satisfactory results. The average error (RMSD) between calculated and experimental free energy values varies between 0.15 and 0.5 kcal/mol for different classes of solutes. The larger deviations found for the case of oxygen compounds are probably due to a poor approximation of H-bonding in terms of LJ potentials. For the seven compounds with poorest fit to experiment, the error exceeds 1.5 kcal/mol; these outlier points were not included in the parameterization procedure. Several possible origins of these errors are discussed. Figure 3. (a) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for aromatic and nitrogen compounds. (b) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for aromatic and nitrogen compounds. ⌬G el calculated with DMol 3 . compounds: ethers and alcohols. (b) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for oxygen compounds: esters and carbonyl groups. (c) Calculated [⌬G nel (calc)] and experimental [⌬G nel (exp)] nonelectrostatic components of solvation free energies in kcal/mol for oxygen compounds: ethers and alcohols. ⌬G el calculated with DMol 3 .
The Journal of Physical Chemistry, 1996
Electrostatic solvation free energies are calculated using a self consistent reaction field (SCRF) procedure that combines a continuum dielectric model of the solvent with both Hartree-Fock (HF) and density functional theory (DFT) for the solute. Several molecules are studied in aqueous solution. They comprise three groups: nonpolar neutral, polar neutral, and ionic. The calculated values of ∆G el are sensitive to the atomic radii used to define the solute molecular surface, particularly to the value of the hydrogen radius. However, the values of ∆G el exhibit reasonable correlation with experiment when a previously determined, physically motivated set of atomic radii were used to define the van der Waals surface of the solute. The standard deviation between theory and experiment is 2.51 kcal/mol for HF and 2.21 kcal/mol for DFT for the 14 molecules examined. The errors with HF or DFT are similar. The relative difference between the calculated values of ∆G el and experiment is largest for nonpolar neutral molecules, intermediate for polar neutral molecules, and smallest for ions. This is consistent with the expected relative importance of nonelectrostatic contributions to the free energy that are omitted in the model.
International Journal of Quantum Chemistry, 2004
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 6-311ϩϩG**). Good linear correlation has been obtained for calculated and experimental gas-phase dipole moments, with an increase by ϳ30% 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 6-311ϩϩG** 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.
The pairwise descreening approximation provides a rapid computational algorithm for the evaluation of solute shape effects on electrostatic contributions to solvation energies. In this article we show that solvation models based on this algorithm are useful for predicting free energies of solvation across a wide range of solute functionalities, and we present six new general parametrizations of aqueous free energies of solvation based on this approach. The first new model is based on SM2-type atomic surface tensions, the AM1 model for the solute, and Mulliken charges. The next two new models are based on SM5-type surface tensions, either the AM1 or the PM3 model for the solute, and Mulliken charges. The final three models are based on SM5-type atomic surface tensions and are parametrized using the AM1 or the PM3 model for the solute and CM1 charges. The parametrizations are based on experimental data for a set of 219 neutral solute molecules containing a wide range of organic functional groups and the atom types H, C, N, O, F, P, S, Cl, Br, and I and on data for 42 ions containing the same elements. The average errors relative to experiment are slightly better than previous methods, butsmore significantlysthe computational cost is reduced for large molecules, and the methods are well suited to using analytic derivatives.
Calculation of Alkane to Water Solvation Free Energies Using Continuum Solvent Models
The Journal of Physical Chemistry, 1996
The FDPB/γ method and the PARSE parameter set have been recently shown to provide a computationally efficient and accurate means of calculating hydration free energies. 1 In this paper this approach is extended to the treatment of the partitioning of various solute molecules between the gas phase, water, and alkane solvents. The FDPB/γ method treats the solute molecule as a polarizable cavity embedded in a dielectric continuum. The solute charge distribution is described in terms of point charges located at atomic nuclei. Electrostatic free energies are obtained from numerical (finite difference) solutions to the Poisson (or Poisson-Boltzmann) equation, while nonpolar contributions are treated with a surface area-dependent term proportional to a surface tension coefficient, γ. To apply the FDPB/γ method to nonaqueous phases, it is necessary to derive a continuum representation of solute-solvent interactions appropriate for such systems. It is argued in this work that solute cavities in nonpolar solvents are significantly larger than in aqueous media. The physical basis for the existence of an expanded cavity in nonpolar solvents is discussed. When an expanded cavity, described in terms of increased values for atomic radii, is incorporated into the FDPB/γ formalism, good agreement between calculated and experimental solvation free energies is obtained. A new PARSE parameter set is developed for the transfer of organic molecules between alkanes and water which yields an average absolute error in solvation free energies of 0.2 kcal/mol for the 18 small molecules for which the parameters were optimized.
The Journal of Chemical Physics, 1996
A series of different simplifications of the boundary element method (BEM) for solving the Poisson–Boltzmann equation is investigated in an effort to obtain an accurate and fast enough treatment of electrostatic effects to be incorporated in Monte-Carlo and molecular dynamics simulation methods. The tested simplifications include increasing the size of Boundary Elements, decreasing the surface dot density, and ignoring the interactions between the polarization charges. Combined with terms describing the nonelectrostatic solvation effects, the simplified BEM polarization terms were built into expressions for the solvation potential. The solvation potential is treated as empirical consistent force field equations. The intervening parameters, including atomic and probe radii, are derived by different fitting strategies of calculated vs experimental vacuum to water transfer energies of 173 charged, polar, and nonpolar small molecules. These fits are shown to yield very good correlations...
The Journal of Physical …, 2009
We present a new continuum solvation model based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent. The model is called SMD, where the "D" stands for "density" to denote that the full solute electron density is used without defining partial atomic charges. "Continuum" denotes that the solvent is not represented explicitly but rather as a dielectric medium with surface tension at the solute-solvent boundary. SMD is a universal solvation model, where "universal" denotes its applicability to any charged or uncharged solute in any solvent or liquid medium for which a few key descriptors are known (in particular, dielectric constant, refractive index, bulk surface tension, and acidity and basicity parameters). The model separates the observable solvation free energy into two main components. The first component is the bulk electrostatic contribution arising from a self-consistent reaction field treatment that involves the solution of the nonhomogeneous Poisson equation for electrostatics in terms of the integralequation-formalism polarizable continuum model (IEF-PCM). The cavities for the bulk electrostatic calculation are defined by superpositions of nuclear-centered spheres. The second component is called the cavity-dispersionsolvent-structure term and is the contribution arising from short-range interactions between the solute and solvent molecules in the first solvation shell. This contribution is a sum of terms that are proportional (with geometry-dependent proportionality constants called atomic surface tensions) to the solvent-accessible surface areas of the individual atoms of the solute. The SMD model has been parametrized with a training set of 2821 solvation data including 112 aqueous ionic solvation free energies, 220 solvation free energies for 166 ions in acetonitrile, methanol, and dimethyl sulfoxide, 2346 solvation free energies for 318 neutral solutes in 91 solvents (90 nonaqueous organic solvents and water), and 143 transfer free energies for 93 neutral solutes between water and 15 organic solvents. The elements present in the solutes are H, C, N, O, F, Si, P, S, Cl, and Br. The SMD model employs a single set of parameters (intrinsic atomic Coulomb radii and atomic surface tension coefficients) optimized over six electronic structure methods: M05-2X/MIDI!6D, M05-2X/ 6-31G*, M05-2X/6-31+G**, M05-2X/cc-pVTZ, B3LYP/6-31G*, and HF/6-31G*. Although the SMD model has been parametrized using the IEF-PCM protocol for bulk electrostatics, it may also be employed with other algorithms for solving the nonhomogeneous Poisson equation for continuum solvation calculations in which the solute is represented by its electron density in real space. This includes, for example, the conductorlike screening algorithm. With the 6-31G* basis set, the SMD model achieves mean unsigned errors of 0.6-1.0 kcal/mol in the solvation free energies of tested neutrals and mean unsigned errors of 4 kcal/mol on average for ions with either Gaussian03 or GAMESS.
Boundary integral methods for the Poisson equation of continuum dielectric solvation models
International Journal of Quantum Chemistry, 1997
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the algorithmic discussion lays the basis for multigrid methods of solution, methods that are likely to be necessary for similarly accurate numerical solution of these models for much larger solutes. Other aspects of the algorithmic work show how macroscopic surfaces such as solution interfaces and membranes may be incorporated and also show how these methods can be transferred directly to periodic boundary conditions. This dielectric model is found to give interesting and helpful results for the variation in solvation free energy with solute geometry. However, it typically significantly over-stabilizes classic attractive ion-pairing configurations. On the basis of the examples and algorithmic considerations, we make some observations about extension of this continuum model incrementally to reintroduce molecular detail of the solvation structure.
The Journal of Physical Chemistry A, 2005
A parametrization of the polarizable continuum model (PCM) is presented having the experimental hydration free energies of 215 neutral molecules as target. The cavitation and dispersion contributions were based on the Tuñon-Silla-Pascual-Ahuir et al. Chem. Phys. Lett. 1993, 203, 289) and Floris-Tomasi (Floris, F.; Tomasi, J. J. Comput. Chem. 1989, 10, 616) expressions, respectively. Both the polar and nonpolar contributions were evaluated on the same solvent-excluding molecular surface that used unscaled Bondi atomic radii. The parametrization was provided for the HF, XR, LSDA, B3LYP, and mPW1PW91 methods at the 6-31G(d) basis set, and the results are in fair agreement with the experimental data. For the sake of comparison, the PCM(UAHF) and our parametrization (PCM2), both at HF level, have produced ∆G PCM(UAHF) ) a∆G exp (a ) 1.02 ( 0.02, r ) 0.945, sd ) 0.987, F test ) 1778) and ∆G PCM2 ) a∆G exp (a ) 0.95 ( 0.02, r ) 0.952, sd ) 0.843, F test ) 2070), respectively. The mean absolute deviations from experimental data were 0.67 and 0.68 kcal/mol for PCM(UAHF) and PCM2, respectively.