Solvation Free Energy Calculations Research Articles

A hybrid solver of size modified Poisson–Boltzmann equation by domain decomposition, finite element, and finite difference

Abstract The size-modified Poisson–Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson–Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an ionic solvent. In this paper, a new SMPBE hybrid solver is developed using a solution decomposition, Schwartz’s overlapped domain decomposition, finite element, and finite difference. It is then programmed as a software package in C , Fortran , and Python based on the state-of-the-art finite element library DOLFIN from the FEniCS project. This software package is well validated on a Born ball model with analytical solution and a dipole model with known physical properties. Numerical results on six proteins with different net charges demonstrate its high performance. Finally, this new SMPBE hybrid solver is shown to be numerically stable and convergent in the calculation of electrostatic solvation free energy for 216 biomolecules and binding free energy for a DNA-drug complex.

Electrostatic solvation free energies of charged hard spheres using molecular dynamics with density functional theory interactions.

Determining the solvation free energies of single ions in water is one of the most fundamental problems in physical chemistry and yet many unresolved questions remain. In particular, the ability to decompose the solvation free energy into simple and intuitive contributions will have important implications for models of electrolyte solution. Here, we provide definitions of the various types of single ion solvation free energies based on different simulation protocols. We calculate solvation free energies of charged hard spheres using density functional theory interaction potentials with molecular dynamics simulation and isolate the effects of charge and cavitation, comparing to the Born (linear response) model. We show that using uncorrected Ewald summation leads to unphysical values for the single ion solvation free energy and that charging free energies for cations are approximately linear as a function of charge but that there is a small non-linearity for small anions. The charge hydration asymmetry for hard spheres, determined with quantum mechanics, is much larger than for the analogous real ions. This suggests that real ions, particularly anions, are significantly more complex than simple charged hard spheres, a commonly employed representation.

Using force-based adaptive resolution simulations to calculate solvation free energies of amino acid sidechain analogues.

The calculation of free energy differences is a crucial step in the characterization and understanding of the physical properties of biological molecules. In the development of efficient methods to compute these quantities, a promising strategy is that of employing a dual-resolution representation of the solvent, specifically using an accurate model in the proximity of a molecule of interest and a simplified description elsewhere. One such concurrent multi-resolution simulation method is the Adaptive Resolution Scheme (AdResS), in which particles smoothly change their resolution on-the-fly as they move between different subregions. Before using this approach in the context of free energy calculations, however, it is necessary to make sure that the dual-resolution treatment of the solvent does not cause undesired effects on the computed quantities. Here, we show how AdResS can be used to calculate solvation free energies of small polar solutes using Thermodynamic Integration (TI). We discuss how the potential-energy-based TI approach combines with the force-based AdResS methodology, in which no global Hamiltonian is defined. The AdResS free energy values agree with those calculated from fully atomistic simulations to within a fraction of kBT. This is true even for small atomistic regions whose size is on the order of the correlation length, or when the properties of the coarse-grained region are extremely different from those of the atomistic region. These accurate free energy calculations are possible because AdResS allows the sampling of solvation shell configurations which are equivalent to those of fully atomistic simulations. The results of the present work thus demonstrate the viability of the use of adaptive resolution simulation methods to perform free energy calculations and pave the way for large-scale applications where a substantial computational gain can be attained.

Structure and hydrophilicity of azo‐dye‐derived rotaxane: density functional theory approach

We investigated the most probable molecular structure, energy, and corresponding properties, including the solvation energy and binding free energy in solution, for non‐encapsulated azo dyes using quantum mechanical density functional theory (DFT). The structures of non‐encapsulated azo dyes with six conformations were optimised to find the most stable conformation with the lowest energy, but the energy differences among the conformations were within ~2.2 kcal mol−1. The LUMO–HOMO gaps were also similar, meaning that their interaction with light would be similar. The energies of alpha‐cyclodextrin (α‐CD) encircling the phenyl ring fragments were significantly higher than other conformations, because α‐CD tends preferably to encircle azo fragments to create a thermodynamically stable form. From solvation free energy calculations, the hydrophobic non‐encapsulated azo dye and hydrophilic α‐CD showed reasonable values for solvation free energy with respect to dimethyl sulphoxide (DMSO) and water: the former has more solvation in DMSO, while the latter has more solvation in water. Rotaxane formation is thermodynamically feasible in water (−3.06 kcal mol−1) but not in DMSO (25.56 kcal mol−1) according to calculation of binding free energy in solution state.

Molecular Dynamics Investigation of Efficient SO2 Absorption by Anion-Functionalized Ionic Liquids

Ionic liquids are appropriate candidates for the absorption of acid gases such as SO2. Six anion-functionalized ionic liquids with different basicities have been studied for SO2 absorption capacity by employing quantum chemical calculations and molecular dynamics (MD) simulations. Gas phase quantum calculations unveil that the high uptake of SO2 in these ionic liquids originates from the basicity of the anions and the consequent enhanced anion-SO2 interactions. MD simulations of SO2–IL mixtures reveal the crucial role of both cations and anions in SO2 dissolution. Multiple-site interactions of SO2 with the anions have been identified. The calculated solvation free energy substantiates these observations. The order of computed Henry’s law constant values with change in the anion is in fair agreement with experimentally determined SO2 solubility order.

Approaches for calculating solvation free energies and enthalpies demonstrated with an update of the FreeSolv database.

Solvation free energies can now be calculated precisely from molecular simulations, providing a valuable test of the energy functions underlying these simulations. Here, we briefly review "alchemical" approaches for calculating the solvation free energies of small, neutral organic molecules from molecular simulations, and illustrate by applying them to calculate aqueous solvation free energies (hydration free energies). These approaches use a non-physical pathway to compute free energy differences from a simulation or set of simulations and appear to be a particularly robust and general-purpose approach for this task. We also present an update (version 0.5) to our FreeSolv database of experimental and calculated hydration free energies of neutral compounds and provide input files in formats for several simulation packages. This revision to FreeSolv provides calculated values generated with a single protocol and software version, rather than the heterogeneous protocols used in the prior version of the database. We also further update the database to provide calculated enthalpies and entropies of hydration and some experimental enthalpies and entropies, as well as electrostatic and nonpolar components of solvation free energies.

Comparison of Implicit and Explicit Solvent Models for the Calculation of Solvation Free Energy in Organic Solvents.

2015, 55, 1192-1201) and experimental data. The comparison indicates that both PB and GB give poor agreement with explicit solvent calculations and even worse agreement with experiments (root-mean-square deviation ≈ 15 kJ/mol). The main problem seems to be the prediction of the apolar contribution, which should include the solvent entropy. The quantum mechanical-based SMD model gives significantly better agreement with experimental data than do PB or GB, but it is not as good as explicit solvent calculation results. The dielectric constant ε of the solvent is found to be a powerful predictor for the polar contribution to the free energy in implicit models; however, the Onsager relation may not hold for realistic solvent, as suggested by explicit solvent and SMD calculations. From the comparison, we also find that with an optimization of the apolar contribution, the PB model gives slightly better agreement with experiments than the SMD model, whereas the correlation between the optimized GB models and experiments remains poor. Further optimization of the apolar contribution is needed for GB models to be able to treat solvents other than water.

Equivalence of M- and P-Summation in Calculations of Ionic Solvation Free Energies.

Condensed-phase simulations commonly use periodic boundary conditions (PBCs) to represent the thermodynamic limit. For the vapor to liquid transfer of an ion, the gas/liquid boundary and its associated potential change are then missing. Furthermore, the electric potential and field at a given point are given by conditionally convergent infinite series, for which different summation schemes give different results. Nevertheless, standard simulation protocols can be used to compute experimental quantities unambiguously. In particular, using an auxiliary test particle and a multistep solvation path, we show that particle-based, Ewald, and common molecule-based summation schemes for the potential and field are all essentially equivalent. However, all methods require prior knowledge of the gas/liquid boundary potential to compute ionic solvation free energies using PBC protocols for both force-field and quantum-mechanical models.

EFFECTS OF SOLVENT POLARITY ON SOLVATION FREE ENERGY, DIPOLE MOMENT, POLARIZABILITY, HYPERPOLARIZABILITY AND MOLECULAR REACTIVITY OF ASPIRIN

<p><strong>Objective: </strong>The aim of the study is to explore the effects of solvent polarity on solvation free energy, dipole moment, polarizability, first order hyperpolarizability and different molecular properties like chemical hardness and softness, chemical potential, electronegativity, electrophilicity index of aspirin which may lead to better understand the reactivity and stability of aspirin in different solvent systems.</p><p><strong>Methods: </strong>Becke, 3-parameter, Lee-Yang-Parr (B3LYP) level of theory with 6-31G(d,p) basis set was employed to conduct all type of calculations for both in the gas phase and in solution. The solvation free energy, dipole moment and molecular properties were calculated by applying the Solvation Model on Density (SMD) in four solvent systems namely water, methanol, ethanol and <em>n</em>-octanol.</p><p><strong>Results: </strong>The solvation energies steadily increased as the dielectric constant was decreased i.e. free energy increases with decreasing polarity of the solvent. The dipole moment of aspirin was found to be increased when going from non-polar to polar solvents. The dipole moment of aspirin was higher in different solvents than that of the gas phase. The polarizability and first order hyperpolarizability were also increased with the increasing dielectric constant of the solvent. Moreover, ongoing from non-polar to polar solvent the chemical potential, electronegativity and electrophilicity index were increased except in <em>n</em>-octanol. The chemical potential, electronegativity and electrophilicity index of aspirin in <em>n</em>-octanol was higher than that of ethanol. On the other hand, chemical hardness was increased with decreasing polarity of the solvent and the inverse relation was found in the case of softness.</p><p><strong>Conclusion: </strong>The calculated solvation free energy, dipole moment, polarizability, first order hyperpolarizability and molecular properties found in this study may lead to the understanding of stability and reactivity of aspirin in different solvent systems.</p>

Comparative conformational variation and flexibility analysis of binding site D-loop and its importance in designing of potential tankyrases inhibitors

The principle point of this study is to know the dynamics of D-loop affecting the inhibitory action of tankyrase inhibitors (TNKSIs). The knowledge of D-loop conformational variations, flexibility analysis and its significance in the binding of TNKSIs has not been explored earlier. This study at first focused on observing the conformational changes of D-loop in tankyrases crystal structures by overlapping of D-loop residues. To achieve this, relative residue fluctuation profile and molecular mechanics with generalised born surface area solvation (MM/GBSA) free energy calculations were performed to expose the more prominent binding strength of strong inhibitors and selectivity compared with other respective site inhibitors. Molecular dynamics simulation search revealed that residue fluctuation profile of D-loop of TNKSs affects the binding potential of inhibitors. Thus, conformational changes in the D-loop affected by inhibitors can be used to screen the potent TNKSIs. The molecular docking, D-loop flexibility analysis, molecular dynamics and MM/GBSA binding energy calculations were carried out.

Modified Poisson equations for calculating solvation free energy

The dielectric polarization (P) is the key factor in calculating the solvation free energy. P can be decomposed into the product of the electric dipole per solvent (p) and the relative solvent molecular density (g). p can be calculated from the electric field (E), and g can be calculated from the mean force (F), where the electric component of F is calculated from ∇xE. The Poisson equations were modified for E and ∇xE. Strategies to estimate the boundary conditions of E and ∇xE were proposed. The dependences of P and g on the parameters used for the numerical analysis were explored. For two charged atoms in a water cluster, the values of P and g obtained by these equations were similar to those obtained from molecular dynamics simulations. The electric potential at the solute atoms and the solvation free energy determined using these equations were similar to those obtained from molecular dynamics simulations.

Scaling Atomic Partial Charges of Carbonate Solvents for Lithium Ion Solvation and Diffusion.

Lithium-ion solvation and diffusion properties in ethylene carbonate (EC) and propylene carbonate (PC) were studied by molecular simulation, experiments, and electronic structure calculations. Studies carried out in water provide a reference for interpretation. Classical molecular dynamics simulation results are compared to ab initio molecular dynamics to assess nonpolarizable force field parameters for solvation structure of the carbonate solvents. Quasi-chemical theory (QCT) was adapted to take advantage of fourfold occupancy of the near-neighbor solvation structure observed in simulations and used to calculate solvation free energies. The computed free energy for transfer of Li+ to PC from water, based on electronic structure calculations with cluster-QCT, agrees with the experimental value. The simulation-based direct-QCT results with scaled partial charges agree with the electronic structure-based QCT values. The computed Li+/PF6- transference numbers of 0.35/0.65 (EC) and 0.31/0.69 (PC) agree well with NMR experimental values of 0.31/0.69 (EC) and 0.34/0.66 (PC) and similar values obtained here with impedance spectroscopy. These combined results demonstrate that solvent partial charges can be scaled in systems dominated by strong electrostatic interactions to achieve trends in ion solvation and transport properties that are comparable to ab initio and experimental results. Thus, the results support the use of scaled partial charges in simple, nonpolarizable force fields in future studies of these electrolyte solutions.

A Seamless Grid-Based Interface for Mean-Field QM/MM Coupled with Efficient Solvation Free Energy Calculations.

Among various models that incorporate solvation effects into first-principles-based electronic structure theory such as density functional theory (DFT), the average solvent electrostatic potential/molecular dynamics (ASEP/MD) method is particularly advantageous. This method explicitly includes the nature of complicated solvent structures that is absent in implicit solvation methods. Because the ASEP/MD method treats only solvent molecule dynamics, it requires less computational cost than the conventional quantum mechanics/molecular mechanics (QM/MM) approaches. Herein, we present a real-space rectangular grid-based method to implement the mean-field QM/MM idea of ASEP/MD to plane-wave DFT, which is termed "DFT in classical explicit solvents", or DFT-CES. By employing a three-dimensional real-space grid as a communication medium, we can treat the electrostatic interactions between the DFT solute and the ASEP sampled from MD simulations in a seamless and straightforward manner. Moreover, we couple a fast and efficient free energy calculation method based on the two-phase thermodynamic (2PT) model with our DFT-CES method, which enables direct and simultaneous computation of the solvation free energies as well as the geometric and electronic responses of a solute of interest under the solvation effect. With the aid of DFT-CES/2PT, we investigate the solvation free energies and detailed solvation thermodynamics for 17 types of organic molecules, which show good agreement with the experimental data. We further compare our simulation results with previous theoretical models and assumptions made for the development of implicit solvation models. We anticipate that our proposed method, DFT-CES/2PT, will enable vast utilization of the ASEP/MD method for investigating solvation properties of materials by using periodic DFT calculations in the future.

Predicting cyclohexane/water distribution coefficients for the SAMPL5 challenge using MOSCED and the SMD solvation model

We present blind predictions using the solubility parameter based method MOSCED submitted for the SAMPL5 challenge on calculating cyclohexane/water distribution coefficients at 298K. Reference data to parameterize MOSCED was generated with knowledge only of chemical structure by performing solvation free energy calculations using electronic structure calculations in the SMD continuum solvent. To maintain simplicity and use only a single method, we approximate the distribution coefficient with the partition coefficient of the neutral species. Over the final SAMPL5 set of 53 compounds, we achieved an average unsigned error of [Formula: see text] log units (ranking 15 out of 62 entries), the correlation coefficient (R) was [Formula: see text] (ranking 35), and [Formula: see text] of the predictions had the correct sign (ranking 30). While used here to predict cyclohexane/water distribution coefficients at 298K, MOSCED is broadly applicable, allowing one to predict temperature dependent infinite dilution activity coefficients in any solvent for which parameters exist, and provides a means by which an excess Gibbs free energy model may be parameterized to predict composition dependent phase-equilibrium.

A reference-modified density functional theory: An application to solvation free-energy calculations for a Lennard-Jones solution.

In the conventional classical density functional theory (DFT) for simple fluids, an ideal gas is usually chosen as the reference system because there is a one-to-one correspondence between the external field and the density distribution function, and the exact intrinsic free-energy functional is available for the ideal gas. In this case, the second-order density functional Taylor series expansion of the excess intrinsic free-energy functional provides the hypernetted-chain (HNC) approximation. Recently, it has been shown that the HNC approximation significantly overestimates the solvation free energy (SFE) for an infinitely dilute Lennard-Jones (LJ) solution, especially when the solute particles are several times larger than the solvent particles [T. Miyata and J. Thapa, Chem. Phys. Lett. 604, 122 (2014)]. In the present study, we propose a reference-modified density functional theory as a systematic approach to improve the SFE functional as well as the pair distribution functions. The second-order density functional Taylor series expansion for the excess part of the intrinsic free-energy functional in which a hard-sphere fluid is introduced as the reference system instead of an ideal gas is applied to the LJ pure and infinitely dilute solution systems and is proved to remarkably improve the drawbacks of the HNC approximation. Furthermore, the third-order density functional expansion approximation in which a factorization approximation is applied to the triplet direct correlation function is examined for the LJ systems. We also show that the third-order contribution can yield further refinements for both the pair distribution function and the excess chemical potential for the pure LJ liquids.

Salting-out of methane in the aqueous solutions of urea and sarcosine

Hydrophobic association and solvation of methane molecules in aqueous solutions of urea and sarcosine (sa) have been studied using MD simulations. The potentials of mean force (PMFs) between methane molecules in water, water-sa, water-urea and water-urea-sa mixtures show an enhancement of methane association on the addition of these osmolytes. These observations are well supported by calculation of equilibrium constants. Calculation of thermodynamic parameters shows that the association of methane is stabilized by entropy and favored by enthalpy. The hydrophobic solvation of methane is stabilized by enthalpy and destabilized by entropy. The calculated solvation free energies of methane in these mixtures show that methane is less soluble in the mixtures of urea and sarcosine than in water. The solubility is the least in the water-urea-sa mixture. Analysis of distributions of solvent and co-solvent around methane suggests that the local densities of both urea and sarcosine are diminished around the methane in the mixtures of these osmolytes. The selective reduction of both urea and sarcosine from methane surface suggests that both urea and sarcosine push methane molecules towards water and increase the interaction between methane molecules i.e., salting-out of methane. Solvation free energies of methane molecules and the potentials of mean force between methanes were computed using molecular dynamics simulations in mixtures of osmolytes. Both urea and sarcosine enhance the association of methane molecules (saltingout) because of the exclusion of urea and sarcosine from the methane surface.

Multigrid-Based Methodology for Implicit Solvation Models in Periodic DFT.

Continuum solvation models have become a widespread approach for the study of environmental effects in Density Functional Theory (DFT) methods. Adding solvation contributions mainly relies on the solution of the Generalized Poisson Equation (GPE) governing the behavior of the electrostatic potential of a system. Although multigrid methods are especially appropriate for the solution of partial differential equations, up to now, their use is not much extended in DFT-based codes because of their high memory requirements. In this Article, we report the implementation of an accelerated multigrid solver-based approach for the treatment of solvation effects in the Vienna ab initio Simulation Package (VASP). The stated implicit solvation model, named VASP-MGCM (VASP-Multigrid Continuum Model), uses an efficient and transferable algorithm for the product of sparse matrices that highly outperforms serial multigrid solvers. The calculated solvation free energies for a set of molecules, including neutral and ionic species, as well as adsorbed molecules on metallic surfaces, agree with experimental data and with simulation results obtained with other continuum models.

Calculations of Solvation Free Energy through Energy Reweighting from Molecular Mechanics to Quantum Mechanics.

In this work, the solvation free energies of 20 organic molecules from the 4th Statistical Assessment of the Modeling of Proteins and Ligands (SAMPL4) have been calculated. The sampling of phase space is carried out at a molecular mechanical level, and the associated free energy changes are estimated using the Bennett Acceptance Ratio (BAR). Then the quantum mechanical (QM) corrections are computed through the indirect Non-Boltzmann Bennett's acceptance ratio (NBB) or the thermodynamics perturbation (TP) method. We show that BAR+TP gives a minimum analytic variance for the calculated solvation free energy at the Gaussian limit and performs slightly better than NBB in practice. Furthermore, the expense of the QM calculations in TP is only half of that in NBB. We also show that defining the biasing potential as the difference of the solute-solvent interaction energy, instead of the total energy, can converge the calculated solvation free energies much faster but possibly to different values. Based on the experimental solvation free energies which have been published before, it is discovered in this study that BLYP yields better results than MP2 and some other later functionals such as B3LYP, M06-2X, and ωB97X-D.

Solvation free-energy pressure corrections in the three dimensional reference interaction site model.

Solvation free energies are efficiently predicted by molecular density functional theory if one corrects the overpressure introduced by the usual homogeneous reference fluid approximation. Sergiievskyi et al. [J. Phys. Chem. Lett. 5, 1935-1942 (2014)] recently derived the rigorous compensation of this excess of pressure (referred as "pressure correction" or PC) and proposed an empirical "ideal gas" supplementary correction (referred as "advanced pressure correction" or PC+) that further enhances the calculated solvation free energies. In a recent paper [M. Misin, M. V. Fedorov, and D. S. Palmer, J. Chem. Phys. 142, 091105 (2015)], those corrections were applied to solvation free energy calculations using the three-dimensional reference interaction site model (3D-RISM). As for classical DFT, PC and PC+ improve greatly the predictions of 3D-RISM, but PC+ is described as decreasing the accuracy. In this article, we derive rigorously the expression of the pressure in 3D-RISM as well as the associated PC and PC+. This provides a consistent way to correct the solvation free-energies calculated by 3D-RISM method.

Spectroscopic and theoretical studies of some 4′-substituted-phenyl 2-(ethanesulfonyl)acetates. Structure of 4′-nitrophenyl 2-(ethanesulfonyl)acetate

Abstract An analysis of carbonyl bands in the infrared spectra of some 2-ethylsulfonyl 4′-substituted phenylacetates bearing substituents NO2 (1), H (2) and OMe (3), supported by B3LYP/6-31G(d,p) and SM5.42R at PM3 level calculations, along with natural bond orbital analysis (NBO) and X-ray diffraction (for 1) was performed. Theoretical data indicated the existence of two stable gauche conformations (g 1 and g 2). The g 1 conformer is the most stable, least polar and has the lowest νCO frequency. The more intense, lower frequency carbonyl doublet component found in CCl4 solution is assigned to the g 1 conformer. As the solvent dielectric constant increases (going from CCl4 to MeCN) the higher frequency νCO doublet increases in intensity. This behaviour is reproduced by the solvation free energy calculations, supporting the conformer assignments. NBO calculations indicate that the most important orbital interaction is LPO9 → π*C7=O8 for both conformers, which corresponds to [C=O ↔ C+–O-] conjugation. This stabilises the g 1 conformer to a greater extent and is responsible for the lower νCO frequency. The sum of the selected NBO delocalisation energies for 1–3 indicates that the g 1 conformer is more stable. It is concluded that the calculated greater stability of the g 1 conformer is due to a balance of attractive electrostatic and orbital interactions along with relevant hydrogen bonds. The X-ray crystal structure analysis of 1 shows the presence of two crystallographic independent but almost superimposable molecules each which adopt a cis geometry. The molecules are consolidated into the three-dimensional crystal packing by C–H…O interactions as well as by nitro- N–O…π(phenyl) contacts.