Length scales and interfacial potentials in ion hydration (original) (raw)
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Relative Free Energies for Hydration of Monovalent Ions from QM and QM:MM Simulations
Methods directly evaluating the hydration structure and thermodynamics of physiologically relevant cations (Na + , K + , Cl − , etc.) have wide ranging applications in the fields of inorganic, physical, and biological chemistry. All-atom simulations based on accurate potential energy surfaces appear to offer a viable option for assessing the chemistry of ion solvation. Although MD and free energy simulations of ion solvation with classical force fields have proven their usefulness, a number of challenges still remain. One of them is the difficulty of force field benchmarking and validation against structural and thermodynamic data obtained for a condensed phase. Hybrid quantum mechanical/molecular mechanical (QM/MM) models combined with sampling algorithms have the potential to provide an accurate solvation model and to incorporate the effects from the surrounding, which is often missing in gas-phase ab initio computations. Herein, we report the results from QM/MM free energy simulations of Na + /K + and Cl − /Br − hydration where we simultaneously characterized the relative thermodynamics of ion solvation and changes in the solvation structure. The Flexible Inner Region Ensemble Separator (FIRES) method was used to impose a spatial separation between QM region and the outer sphere of solvent molecules treated with the CHARMM27 force field. FEP calculations based on QM/MM simulations utilizing the CHARMM/deMon2k interface were performed with different basis set combinations for K + /Na + and Cl − /Br − perturbations to establish the dependence of the computed free energies on the basis set level. The dependence of the computed relative free energies on the size of the QM and MM regions is discussed. The current methodology offers an accurate description of structural and thermodynamic aspects of the hydration of alkali and halide ions in neat solvents and can be used to obtain thermodynamic data on ion solvation in condensed phase along with underlying structural properties of the ion−solvent system. Figure 11. Oxygen−ion−oxygen ADF for Cl − and Br − simulations with polarizable force field (Drude), QM, and QM/MM systems. Journal of Chemical Theory and Computation Article dx.doi.org/10.1021/ct400296w | J. Chem. Theory Comput. 2013, 9, 4165−4175
Quasichemical theory ͑QCT͒ provides a framework that can be used to partition the influence of the solvent surrounding an ion into near and distant contributions. Within QCT, the solvation properties of the ion are expressed as a sum of configurational integrals comprising only the ion and a small number of solvent molecules. QCT adopts a particularly simple form if it is assumed that the clusters undergo only small thermal fluctuations around a well-defined energy minimum and are affected exclusively in a mean-field sense by the surrounding bulk solvent. The fluctuations can then be integrated out via a simple vibrational analysis, leading to a closed-form expression for the solvation free energy of the ion. This constitutes the primitive form of quasichemical theory ͑pQCT͒, which is an approximate mathematical formulation aimed at reproducing the results from the full many-body configurational averages of statistical mechanics. While the results from pQCT from previous applications are reasonable, the accuracy of the approach has not been fully characterized and its range of validity remains unclear. Here, a direct test of pQCT for a set of ion models is carried out by comparing with the results of free energy simulations with explicit solvent. The influence of the distant surrounding bulk on the cluster comprising the ion and the nearest solvent molecule is treated both with a continuum dielectric approximation and with free energy perturbation molecular dynamics simulations with explicit solvent. The analysis shows that pQCT can provide an accurate framework in the case of a small cation such as Li + . However, the approximation encounters increasing difficulties when applied to larger cations such as Na + , and particularly for K + . This suggests that results from pQCT should be interpreted with caution when comparing ions of different sizes.
Free energy of ion hydration: Interface susceptibility and scaling with the ion size
The Journal of Chemical Physics, 2015
Free energy of solvation of a spherical ion in a force-field water is studied by numerical simulations. The focus is on the linear solvation susceptibility connecting the linear response solvation free energy to the squared ion charge. Spherical hard-sphere solutes, hard-sphere ions, and Kihara solutes (Lennard-Jones modified hard-sphere core) are studied here. The scaling of the solvation susceptibility with the solute size significantly deviates from the Born equation. Using empirical offset corrections of the solute size (or the position of the first peak of the solute-solvent distribution function) do not improve the agreement with simulations. We advance a new perspective on the problem by deriving an exact relation for the radial susceptibility function of the interface. This function yields an effective cavity radius in the Born equation calculated from the solute-solvent radial distribution function. We find that the perspective of the local response, assuming significant al...
Thermodynamics of Hydration from the Perspective of the Molecular Quasichemical Theory of Solutions
The Journal of Physical Chemistry B, 2021
The quasi-chemical organization of the potential distribution theorem-molecular quasi-chemical theory (QCT)-enables practical calculations and also provides a conceptual framework for molecular hydration phenomena. QCT can be viewed from multiple perspectives: (a) As a way to regularize an ill-conditioned statistical thermodynamic problem; (b) As an introduction of and emphasis on the neighborship characteristics of a solute of interest; (c) Or as a way to include accurate electronic structure descriptions of near-neighbor interactions in defensible statistical thermodynamics by clearly defining neighborship clusters. The theory has been applied to solutes of a wide range of chemical complexity, ranging from ions that interact with water with both long-ranged and chemically intricate short-ranged interactions, to solutes that interact with water solely through traditional van der Waals interations, and including water itself. The solutes range in variety from monoatomic ions to chemically heterogeneous macromolecules. A notable feature of QCT is that in applying the theory to this range of solutes, the theory itself provides guidance on the necessary approximations and simplifications that can facilitate the calculations. In this Perspective, we develop these ideas and document them with examples that reveal the insights that can be extracted using the QCT formulation.
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.
MST Continuum Study of the Hydration Free Energies of Monovalent Ionic Species
The Journal of Physical Chemistry B, 2005
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 Luque, F. J. Chem. Phys. 1994, 182, 237]. 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.
Using molecular dynamics free energy simulations with TIP3P explicit solvent, we compute the hydration free energies of 504 neutral small organic molecules and compare them to experiments. We find, first, good general agreement between the simulations and the experiments, with an rms error of 1.24 kcal/mol over the whole set (i.e., about 2 kT) and a correlation coefficient of 0.89. Second, we use an automated procedure to identify systematic errors for some classes of compounds and suggest some improvements to the force field. We find that alkyne hydration free energies are particularly poorly predicted due to problems with a Lennard-Jones well depth and find that an alternate choice for this well depth largely rectifies the situation. Third, we study the nonpolar component of hydration free energiessthat is, the part that is not due to electrostatics. While we find that repulsive and attractive components of the nonpolar part both scale roughly with surface area (or volume) of the solute, the total nonpolar free energy does not scale with the solute surface area or volume, because it is a small difference between large components and is dominated by the deviations from the trend. While the methods used here are not new, this is a more extensive test than previous explicit solvent studies, and the size of the test set allows identification of systematic problems with force field parameters for particular classes of compounds. We believe that the computed free energies and components will be valuable to others in the future development of force fields and solvation models.
Predictions of Hydration Free Energies from All-Atom Molecular Dynamics Simulations †
The Journal of Physical Chemistry B, 2009
Here, we computed the aqueous solvation (hydration) free energies of 52 small drug-like molecules using an all-atom force field in explicit water. This differs from previous studies in that: (1) this was a blind test (in an event called SAMPL sponsored by OpenEye Software), and (2) the test compounds were considerably more challenging than have been used in the past in typical solvation tests of allatom models. Overall, we found good correlations with experimental values which were subsequently made available, but the variances are large compared to in previous tests. We tested several different charge models, and found that several standard charge models performed relatively well. We found that hypervalent sulfur and phosphorous compounds are not well handled using current force field parameters, and suggest several other possible systematic errors. Overall, blind tests like these appear to provide significant opportunities for improving force fields and solvent models.
Free energies and structures of hydrated cations, based on effective pair potentials
Chemical Physics, 1995
We present a method, based on a continuum representation of the solvent, to compute ab initio effective interaction potentials for solvated pairs. Such potentials take into account many-body effects, thus overcoming the non-additivity errors affecting uncorrected pair potentials. We apply the method to cation-water interactions, for a variety of cations: Li +, Be 2+, Mg 2+, Ca 2., Ni 2+, Zn 2+ and A13+. The potentials thus obtained are suitable for simulations of ionic solutions or clusters of water molecules surrounding a cation. We exploit them to compute hydration free energies AGhyd of cations, with the constraint that the first solvation shell contains a given number of water molecules. This enables us to find the thermodynamically most stable solvation number. The effective potential results compare well with experimental values of AGhyd and with full ab initio calculations on the [M(H20)n] q+ complexes.
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.