Explicitly Representing the Solvation Shell in Continuum Solvent Calculations (original) (raw)
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The Cluster−Continuum Model for the Calculation of the Solvation Free Energy of Ionic Species
The Journal of Physical Chemistry A, 2001
A hybrid approach using a combination of explicit solvent molecules and the isodensity polarizable continuum model (IPCM) method is proposed for the calculation of the solvation thermodynamic properties of ions. This model, denominated cluster-continuum, has been applied to the calculation of the solvation free energy of 14 univalent ions, mainly organic species, and compared with the results obtained with the IPCM, polarizable continuum solvation model (PCM), and SM5.42R continuum methods. The average error in our calculated solvation free energies with respect to experimental data is 8.7 kcal mol -1 . However, the great merit of our model resides in the homogeneous treatment for different ions, resulting in a standard deviation of only 2.9 kcal mol -1 for the average error. Our results suggest that the cluster-continuum model must be superior to the IPCM, PCM, and SM5.42R methods for studying chemical reactions in the liquid phase, because these continuum methods present a standard deviation of ∼8 kcal mol -1 for the average error for the species studied in this work. The model can also be used to calculate the solvation entropy of ions. Predicted solvation entropies for five ionic species are in good agreement with available experimental data.
The Journal of Chemical Physics, 2003
The combined molecular-continuum approach developed in the preceding paper was applied for calculations of equilibrium solvation energies for a large number of polyatomic ions. The structure and charge distribution of the given ion were computed using the restricted Hartree-Fock level with the 6-31G** basis set. The standard Lennard-Jones ͑LJ͒ parameters, which were not specially calibrated to fit the solvation energies, were used in molecular dynamics simulations. Water ͑the SPC model͒ was considered as a solvent. The computations show that the new scheme works satisfactorily for nitrogen cations in the frame of a standard parametrization and can be further improved for oxygen ions by tuning solute-solvent LJ parameters. The calculated relative change of the energies in families of similar cations-i.e., ammonium-type or oxonium-type cations-fits the experimental trends. The present approach is specially addressed to separate the inertial contribution to solvation free energies, which is important in view of further applications to electron transfer reactions. Computed values of the inertial contribution to solvation energies of the ions and reorganization energies for the model two-site dumbbell system are found to be systematically lower than those obtained in terms of the standard treatments ͑using the Pekar factor or the polarizable continuum model ͑PCM͒͒.
Accurate determination of absolute solvation free energy plays a critical role in numerous areas of biomolecular modeling and drug discovery. A quantitative representation of ligand and receptor desolvation, in particular, is an essential component of current docking and scoring methods. Furthermore, the partitioning of a drug between aqueous and nonpolar solvents is one of the important factors considered in pharmacokinetics. In this study, the absolute hydration free energy for a set of 239 neutral ligands spanning diverse chemical functional groups commonly found in drugs and drug-like candidates is calculated using the molecular dynamics free energy perturbation method (FEP/MD) with explicit water molecules, and compared to experimental data as well as its counterparts obtained using implicit solvent models. The hydration free energies are calculated from explicit solvent simulations using a staged FEP procedure permitting a separation of the total free energy into polar and nonpolar contributions. The nonpolar component is further decomposed into attractive (dispersive) and repulsive (cavity) components using the Weeks-Chandler-Anderson (WCA) separation scheme. To increase the computational efficiency, all of the FEP/MD simulations are generated using a mixed explicit/implicit solvent scheme with a relatively small number of explicit TIP3P water molecules, in which the influence of the remaining bulk is incorporated via the spherical solvent boundary potential (SSBP). The performances of two fixed-charge force fields designed for small organic molecules, the General Amber force field (GAFF), and the all-atom CHARMm-MSI, are compared. Because of the crucial role of electrostatics in solvation free energy, the results from various commonly used charge generation models based on the semiempirical (AM1-BCC) and QM calculations [charge fitting using ChelpG and RESP] are compared. In addition, the solvation free energies of the test set are also calculated using Poisson-Boltzmann (PB) and Generalized Born model of solvation (GB), which are two widely used continuum electrostatic implicit solvent models. The protocol for running the absolute solvation free energy calculations used throughout is automated as much as possible, with minimum user intervention, so that it can be used in large-scale analysis and force field optimization. Figure 2. Average unsigned error [AUE] in the absolute solvation free energies. The AUE is shown in the y-axis, and the chemical functionalities in the small molecules are plotted in the x-axis. The solid bars represent the solvation free energies calculated using explicit solvent/FEP method in CHARMM. The bars with dotted line and stripes represent the solvation free energy calculated using GB and PB model in Amber9.
Calculation of Solvation Free Energies of Charged Solutes Using Mixed Cluster/Continuum Models
The Journal of Physical Chemistry B, 2008
We derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. We find that some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the standard state corrections for water molecules or water clusters present in the thermodynamic cycle. This problem can be avoided by using the same standard state for each species involved in the reaction under consideration. We analyze two different thermodynamic cycles for calculating the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water molecules as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the experimental values obtained from studies of ion-water clusters. The mean absolute errors are 0.8 kcal/mol for H + and 2.0 kcal/mol for Cu 2+ . Conversely, calculations using the monomer cycle lead to mean absolute errors that are >10 kcal/mol for H + and >30 kcal/mol for Cu 2+ . The presence of hydrogen-bonded clusters of similar size on the left-and right-hand sides of the reaction cycle results in the cancelation of the systematic errors in the calculated free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H + (6 waters) and 27 kcal/mol for Cu 2+ (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu 2+ (18 waters) and 1 kcal/mol for H + (10 waters). SCHEME 1: Thermodynamic Cycle 1 (Monomer Cycle) for the Calculation of ∆G solv * (A m( ) SCHEME 2: Thermodynamic Cycle 2 (Cluster Cycle) for the Calculation of ∆G solv * (A m( ) J. Phys. Chem. B 2008, 112, 9709-9719 4. Thermodynamic Cycles for Cluster/Continuum Models 4.1. Thermodynamic Cycles for the Determination of ∆G solv * (A m( ).
Journal of Chemical Theory and Computation, 2005
Abstract: A new charge model, called Charge Model 4 (CM4), and a new continuum solvent model, called Solvation Model 6 (SM6), are presented. Using a database of aqueous solvation free energies for 273 neutrals, 112 ions, and 31 ion-water clusters, parameter sets for the mPW0 hybrid density functional of Adamo and Barone (Adamo, C.; Barone, V. J. Chem. Phys. 1998,
A continuum solvent model: the DISOLV program-algorithms, implementation, and validation
Arxiv preprint arXiv: …, 2011
Several implicit (continuum) solvent models are considered: the Polarized Continuum Model (PCM), the Surface Generalized Born model (SGB), and the COnductor-like Screening МОdel (COSMO) as well as their implementation in the form of the DISOLV program. The methods for solving the corresponding equations and for computing the analytic gradients are described. The analytic gradients are used for the fast local energy optimization of molecules in a solvent. An algorithm for the original smooth triangulated molecular surface construction is shortly discussed. The procedure for matching the model parameters and the results of the program application to proteins and ligands with the employment of the MMFF94 force field are described. The validation results show the capability of the program to reach a good accuracy (about several tenth of kcal/mol) in the case of the solvation energy calculation for 2 reasonable time periods at arbitrary shifts of the triangulated grid in use for such large molecules as proteins. A good agreement between the calculated and experimentally measured solvation energies in water is obtained with a root-mean-square deviation about 0.8 kcal/mol for several hundreds of molecules. This study was performed as a part of the works of the Moscow State University on post-genome researches and technologies and the works on the program "Supercomputer Technologies for Solving the Problems of Processing, Storage, Transfer, and Protection of Information" (state contract no. 02.740.11.0388) and also supported in part by the Russian Foundation for Basic Research (projects nos. 09-01-12097_ofi-m and 10-07-00595-a).
The Journal of Physical Chemistry, 1992
The electrostatic contributions to free energies of solvation of several small molecules have been calculated, treating the solvent as a statistical continuum. The computational method is based on solving the linearized Poisson-Boltzmann equation for the electrostatic potentials using the finite-difference scheme. A careful study of convergence indicates the importance of a fine grid spacing, as well as the short comings of rotational averaging. The computed free energies of solvation are in excellent agreement with the experimental results as well as the free energy perturbation calculations. The free energies of hydration of the natural nucleic acid bases are calculated and shown to be somewhat sensitive to charge model.
Molecular density functional theory (MDFT) offers an efficient implicit-solvent method to estimate molecule solvation free-energies, whereas conserving a fully molecular representation of the solvent. Even within a second-order approximation for the free-energy functional, the so-called homogeneous reference fluid approximation, we show that the hydration free-energies computed for a data set of 500 organic compounds are of similar quality as those obtained from molecular dynamics free-energy perturbation simulations, with a computer cost reduced by 2−3 orders of magnitude. This requires to introduce the proper partial volume correction to transform the results from the grand canonical to the isobaric-isotherm ensemble that is pertinent to experiments. We show that this correction can be extended to 3D-RISM calculations, giving a sound theoretical justification to empirical partial molar volume corrections that have been proposed recently. SECTION: Molecular Structure, Quantum Chemistry, and General Theory S olvation free energy (SFE) is one of the main physical quantities in solution chemistry. Many important characteristics, such as dissociation constants, partition coefficient (log P), which are necessary for describing most of the processes in physical chemistry and biochemistry are expressed through the SFE. Despite the importance of that physical quantity, determination of SFE is often problematic. Experimental determination of SFE is often complicated. It can require essential time and resources, especially if SFE is calculated for low soluble and low volatile substances. 1,2 This increases the importance of the numerical SFE calculations. SFE calculation methods can be separated into two classes: (i) explicit solvent methods (simulations), 3,4 and (ii) implicit solvent methods. 5 As for the advantages of the simulation methods we can name their relatively high accuracy (however, one should remember that accuracy of the simulations greatly depend on the forcefield and partial charges determination). 4,6,7 One of the disadvantages of the explicit solvent methods is their high demands to the computational resources, which make them inapplicable in some practical applications where the speed is critical.
Journal of Computational Chemistry, 1991
We report a systematic comparison of the dispersion and repulsion contributions to the free energy of solvation determined using quantum mechanical self-consistent reaction field (QM-SCRF) and classical methods. In particular, QM-SCRF computations have been performed using the dispersion and repulsion expressions developed in the framework of the integral equation formalism of the polarizable continuum model, whereas classical methods involve both empirical pairwise potential and surface-dependent approaches. Calculations have been performed for a series of aliphatic and aromatic compounds containing prototypical functional groups in four solvents: water, octanol, chloroform, and carbon tetrachloride. The analysis is focused on the dependence of the dispersion and repulsion components on the level of theory used in QM-SCRF computations, the contribution of those terms in different solvents, and the magnitude of the coupling between electrostatic and dispersion-repulsion components. Finally, comparison is made between the dispersion-repulsion contributions obtained from QM-SCRF calculations and the results determined from classical approaches.
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.