Incorporation of reaction field effects into density functional calculations for molecules of arbitrary shape in solution (original) (raw)
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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.
Physical Review E, 2002
In the density functional theory formulation of molecular solvents, the solvation free energy of a solute can be obtained directly by minimization of a functional, instead of the thermodynamic integration scheme necessary when using atomistic simulations. In the homogeneous reference fluid approximation, the expression of the free-energy functional relies on the direct correlation function of the pure solvent. To obtain that function as exactly as possible for a given atomistic solvent model, we propose the following approach: first to perform molecular simulations of the homogeneous solvent and compute the position and angle-dependent two-body distribution functions, and then to invert the Ornstein-Zernike relation using a finite rotational invariant basis set to get the corresponding direct correlation function. This rather natural scheme is proved, for the first time to our knowledge, to be valuable for a dipolar solvent involving long range interactions. The resulting solvent free-energy functional can then be minimized on a three-dimensional grid around a solute to get the solvent particle and polarization density profiles and solvation free energies. The viability of this approach is proven in a comparison with ''exact'' molecular dynamics calculations for the simple test case of spherical ions in a dipolar solvent.
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.
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 .
Multipole electrostatics in hydration free energy calculations
Journal of Computational Chemistry, 2011
Hydration free energy (HFE) is generally used for evaluating molecular solubility, which is an important property for pharmaceutical and chemical engineering processes. Accurately predicting HFE is also recognized as one fundamental capability of molecular mechanics force field. Here, we present a systematic investigation on HFE calculations with AMOEBA polarizable force field at various parameterization and simulation conditions. The HFEs of seven small organic molecules have been obtained alchemically using the Bennett Acceptance Ratio method. We have compared two approaches to derive the atomic multipoles from quantum mechanical calculations: one directly from the new distributed multipole analysis and the other involving fitting to the electrostatic potential around the molecules. Wave functions solved at the MP2 level with four basis sets (6-311G*, 6-31111G(2d,2p), cc-pVTZ, and aug-cc-pVTZ) are used to derive the atomic multipoles. HFEs from all four basis sets show a reasonable agreement with experimental data (root mean square error 0.63 kcal/mol for aug-cc-pVTZ). We conclude that aug-cc-pVTZ gives the best performance when used with AMOEBA, and 6-31111G(2d,2p) is comparable but more efficient for larger systems. The results suggest that the inclusion of diffuse basis functions is important for capturing intermolecular interactions. The effect of long-range correction to van der Waals interaction on the hydration free energies is about 0.1 kcal/mol when the cutoff is 12Å , and increases linearly with the number of atoms in the solute/ligand. In addition, we also discussed the results from a hybrid approach that combines polarizable solute with fixed-charge water in the HFE calculation. q 2010 Wiley Periodicals, Inc. J Comput Chem 32: 967-977, 2011
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.
The Journal of Chemical Physics, 2020
The capability of molecular density functional theory in its lowest, second-order approximation, equivalent to the hypernetted chain approximation in integral equations, to predict accurately the hydration free-energies and microscopic structure of molecular solutes is explored for a variety of systems: spherical hydrophobic solutes, ions, water as a solute, and the Mobley's dataset of organic molecules. The successes and the caveats of the approach are carefully pinpointed. Compared to molecular simulations with the same force field and the same fixed solute geometries, the theory describes accurately the solvation of cations, less so that of anions or generally H-bond acceptors. Overall, the electrostatic contribution to solvation free-energies of neutral molecules is correctly reproduced. On the other hand the cavity contribution is poorly described but can be corrected using scaledparticle theory ideas. Addition of a physically-motivated, one-parameter cavity correction accounting for both pressure and surface effects in the nonpolar solvation contribution yields a precision of 0.8 kcal/mol for the overall hydration free energies of the whole Mobley's dataset. Inclusion of another one-parameter cavity correction for the electrostatics brings it to 0.6 kcal/mol, that is k B T. This is accomplished with a three-orders of magnitude numerical speed-up with respect to molecular simulations.
Journal of the American Chemical Society, 1994
In this paper, we combine high-level ab initio quantum chemical calculations with a continuum description of the solvent to obtain accurate solvation free energies of organic solutes in water. By using correlated wave functions at the generalized valence bondperfect pairing (GVB-PP) level, we are able to efficiently produce accurate gas-phase charge distributions. These are then used to obtain solvation energies in a self-consistent formalism which cycles through quantum chemical calculations in the solvent reaction field and continuum electrostatic calculations utilizing polarized solute charges. An average error of 0.6 kcal/mol for solvation energies is obtained for 29 molecules. A systematic discrepancy between theory and experiment is obtained for the difference in solvation free energy between several methylated and unmethylated primary amines and amides. This poses a major puzzle in theoretical modeling of solvation effects.
Theoretical Basis for the Treatment of Solvent Effects in the Context of Density Functional Theory
Understanding Chemical Reactivity, 2002
This chapter reviews the theoretical background for continuum models of solvation, recent advances in their implementation, and illustrative examples of their use. Continuum models are the most efficient way to include condensed-phase effects into quantum mechanical calculations, and this is typically accomplished by the using self-consistent reaction field (SCRF) approach for the electrostatic component. This approach does not automatically include the non-electrostatic component of solvation, and we review various approaches for including that aspect. The performance of various models is compared for a number of applications, with emphasis on heterocyclic tautomeric equilibria because they have been the subject of the widest variety of studies. For nonequilibrium applications, e.g., dynamics and spectroscopy, one must consider the various time scales of the solvation process and the dynamical process under consideration, and the final section of the review discusses these issues.