Single Ion Solvation Free Energies Research Articles

Phenol alkylation under phase transfer catalysis conditions: Insights on the mechanism and kinetics from computations

• Additional phenol improves the partition equilibrium. • The RN4+PhO−(PhOH) complex reacts in the organic phase. • Higher aggregates may be involved for Et4N + and Pr4N+. Experiments reported in the literature involving alkylation of the phenol under phase transfer catalysis conditions support the formation of the RN 4 + PhO ― (PhOH) complex in the organic phase. This complex could be directly involved in the transition state. In the present theoretical study, the phase transfer catalyzed alkylation of phenol was investigated using M06-2X calculations and solvent effect using the SMD model combined with reliable experimental single-ion solvation free energy data in aqueous solution. The analysis was done for tetraethylammonium, tetrapropylammonium and tetrabutylammonium phase transfer catalysts. In the case of tetrabutylammonium ion, the calculations have predicted a reaction kinetics compatible with experimental data. In addition, the BuN 4 + PhO ― (PhOH) complex is calculated to be the active species in the catalysis. For the tetraethylammonium and tetrapropylammonium cations, both the RN 4 + PhO ― and RN 4 + PhO ― (PhOH) complexes are not able to explain the catalysis, suggesting that another more complex aggregate can be involved in the process.

Single-ion solvation free energy: A new cluster–continuum approach based on the cluster expansion method

A new hybrid discrete–continuum solvation approach for ions that does not require the use of thermodynamic cycles.

Balancing the structural, vibrational and dielectric properties of an advanced flexible water model

The extensive re-parametrisation of the flexible SPC-mTR water potential resulted in more suitable ensemble averages for the intramolecular geometry of ambient water along with improved vibrational properties and an adequate relative static permittivity. The optimisation strategy followed the example of the successful three-point water models OPC3 and H2O-DC in which overpolarised partial charges and modified intramolecular geometries were employed. The improved structural, vibrational and dielectric properties of the new SPC-mTR2 parametrisation are expected to provide a superior performance in QM/MM-type simulations aimed at the determination of single-ion solvation free energies.

Consistent description of ion-specificity in bulk and at interfaces by solvent implicit simulations and mean-field theory.

Solvent-implicit Monte Carlo (MC) simulations and mean-field theory are used to predict activity coefficients and excess interfacial tensions for NaF, NaCl, NaI, KF, KCl, and KI solutions in good agreement with experimental data over the entire experimentally available concentration range. The effective ionic diameters of the solvent-implicit simulation model are obtained by fits to experimental activity coefficient data. The experimental activity coefficients at high salt concentrations are only reproduced if the ion-specific concentration-dependent decrement of the dielectric constant is included. The dielectric-constant dependent contribution of the single-ion solvation free energy to the activity coefficient is significant and is included. To account for the ion-specific excess interfacial tension of salt solutions, in addition to non-ideal solution effects and the salt-concentration-dependent dielectric decrement, an ion-specific ion-interface interaction must be included. This ion-interface interaction, which acts in addition to the dielectric image-charge repulsion, is modeled as a box potential, is considerably more long-ranged than the ion radius, and is repulsive for all ions considered except iodide, in agreement with previous findings and arguments. By comparing different models that include or exclude bulk non-ideal solution behavior, dielectric decrement effects, and ion-interface interaction potentials, we demonstrate how bulk and interfacial ion-specific effects couple and partially compensate each other. Our MC simulations, which correctly include ionic correlations and interfacial dielectric image-charge repulsion, are used to determine effective ion-surface interaction potentials that can be used in a modified Poisson-Boltzmann theory.

Machine Learning-Guided Approach for Studying Solvation Environments.

Molecular-level understanding and characterization of solvation environments are often needed across chemistry, biology, and engineering. Toward practical modeling of local solvation effects of any solute in any solvent, we report a static and all-quantum mechanics-based cluster-continuum approach for calculating single-ion solvation free energies. This approach uses a global optimization procedure to identify low-energy molecular clusters with different numbers of explicit solvent molecules and then employs the smooth overlap for atomic positions learning kernel to quantify the similarity between different low-energy solute environments. From these data, we use sketch maps, a nonlinear dimensionality reduction algorithm, to obtain a two-dimensional visual representation of the similarity between solute environments in differently sized microsolvated clusters. After testing this approach on different ions having charges 2+, 1+, 1-, and 2-, we find that the solvation environment around each ion can be seen to usually become more similar in hand with its calculated single-ion solvation free energy. Without needing either dynamics simulations or an a priori knowledge of local solvation structure of the ions, this approach can be used to calculate solvation free energies within 5% of experimental measurements for most cases, and it should be transferable for the study of other systems where dynamics simulations are not easily carried out.

The Influence of Distant Boundaries on the Solvation of Charged Particles

The long-ranged nature of the Coulomb potential requires a proper accounting for the influence of even distant electrostatic boundaries in the determination of the solvation free energy of a charged solute. We introduce an exact rewriting of the free energy change upon charging a solute that explicitly isolates the contribution from these boundaries and quantifies the impact of the different boundaries on the free energy. We demonstrate the importance and advantages of appropriately referencing the electrostatic potential to that of the vacuum through the study of several simple model charge distributions, for which we can isolate an analytic contribution from the boundaries that can be readily evaluated in computer simulations of molecular systems. Finally, we highlight that the constant potential of the bulk dielectric phase - the Bethe potential - cannot contribute to the solvation thermodynamics of a single charged solute when the charge distributions of the solvent and solute do not overlap in relevant configurations. But when the charge distribution of a single solute can overlap with the intramolecular charge distribution of solvent molecules, as is the case in electron holography, for example, the Bethe potential is needed when comparing to experiment. Our work may also provide insight into the validity of "extra thermodynamic assumptions" traditionally made during the experimental determination of single ion solvation free energies.

Re-examining the tetraphenyl-arsonium/tetraphenyl-borate (TATB) hypothesis for single-ion solvation free energies

Attempts to establish an absolute single-ion hydration free energy scale have followed multiple strategies. Two central themes consist of (1) employing bulk pair thermodynamic data and an underlying interfacial-potential-free model to partition the hydration free energy into individual contributions [Marcus, Latimer, and tetraphenyl-arsonium/tetraphenyl-borate (TATB) methods] or (2) utilizing bulk thermodynamic and cluster data to estimate the free energy to insert a proton into water, including in principle an interfacial potential contribution [the cluster pair approximation (CPA)]. While the results for the hydration free energy of the proton agree remarkably well between the three approaches in the first category, the value differs from the CPA result by roughly +10 kcal/mol, implying a value for the effective electrochemical surface potential of water of -0.4 V. This paper provides a computational re-analysis of the TATB method for single-ion free energies using quasichemical theory. A previous study indicated a significant discrepancy between the free energies of hydration for the TA cation and the TB anion. We show that the main contribution to this large computed difference is an electrostatic artifact arising from modeling interactions in periodic boundaries. No attempt is made here to develop more accurate models for the local ion/solvent interactions that may lead to further small free energy differences between the TA and TB ions, but the results clarify the primary importance of interfacial potential effects for analysis of the various free energy scales. Results are also presented, related to the TATB assumption in the organic solvents dimethyl sulfoxide and 1,2-dichloroethane.

Understanding the scale of the single ion free energy: A critical test of the tetra-phenyl arsonium and tetra-phenyl borate assumption.

The tetra-phenyl arsonium and tetra-phenyl borate (TATB) assumption is a commonly used extra-thermodynamic assumption that allows single ion free energies to be split into cationic and anionic contributions. The assumption is that the values for the TATB salt can be divided equally. This is justified by arguing that these large hydrophobic ions will cause a symmetric response in water. Experimental and classical simulation work has raised potential flaws with this assumption, indicating that hydrogen bonding with the phenyl ring may favor the solvation of the TB- anion. Here, we perform ab initio molecular dynamics simulations of these ions in bulk water demonstrating that there are significant structural differences. We quantify our findings by reproducing the experimentally observed vibrational shift for the TB- anion and confirm that this is associated with hydrogen bonding with the phenyl rings. Finally, we demonstrate that this results in a substantial energetic preference of the water to solvate the anion. Our results suggest that the validity of the TATB assumption, which is still widely used today, should be reconsidered experimentally in order to properly reference single ion solvation free energy, enthalpy, and entropy.

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.

Is the Solution Activity Derivative Sufficient to Parametrize Ion-Ion Interactions? Ions for TIP5P Water.

Biomolecular processes involve hydrated ions, and thus molecular simulations of such processes require accurate force-field parameters for these ions. In the best force-fields, both ion-water and anion-cation interactions are explicitly parametrized. First, the ion Lennard-Jones parameters are optimized to reproduce, for example, single ion solvation free energies; then ion-pair interactions are adjusted to match experimental activity or activity derivatives. Here, we apply this approach to derive optimized parameters for concentrated NaCl, KCl, MgCl2, and CaCl2 salt solutions, to be used with the TIP5P water model. These parameters are of interest because of a number of desirable properties of the TIP5P water model, especially for the simulation of carbohydrates. The results show, that this state of the art approach is insufficient, because the activity derivative often reaches a plateau near the target experimental value, for a wide range of parameter values. The plateau emerges from the interconversion between different types of ion pairs, so parameters leading to equally good agreement with the target solution activity or activity derivative yield very different solution structures. To resolve this indetermination, a second target property, such as the experimentally determined ion-ion coordination number, is required to uniquely determine anion-cation interactions. Simulations show that combining activity derivatives and coordination number as experimental target properties to parametrize ion-ion interactions, is a powerful method for reliable ion-water force field parametrization, and gives insight into the concentration of contact or solvent shared ion pairs in a wide range of salt concentrations. For the alkali and halide ions Li+, Rb+, Cs+, F-, Br-, and I-, we present ion-water parameters appropriate at infinite dilution only.

Real single ion solvation free energies with quantum mechanical simulation.

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.

CMIRS Solvation Model for Methanol: Parametrization, Testing, and Comparison with SMD, SM8, and COSMO-RS.

The new continuum solvation model, composite method for implicit representation of solvent (CMIRS), proposed by Pomogaeva and Chipman and implemented in GAMESS was parametrized for methanol solvent, with the aim of using it for ionic reactions in solution. The model was tested for predicting single-ion solvation free energy, pKa of acids and protonated bases, and the activation free-energy barriers of SN2 and SNAr reactions in methanol. A comparison was performed with other continuum models, such as SMD, SM8, and COSMO-RS. For a prediction of pKa and free-energy barriers, the order of performance was CMIRS > COSMO-RS > SMD > SM8. In particular, the CMIRS model is much superior to the other continuum models for predicting pKa of acids (without empirical corrections) and is able to evenly describe hard ions like methoxide and charge-dispersed ions like 2,4,6-trinitrophenol. On the basis of our results, we suggest that the field-extremum contribution, present in CMIRS, should be included in continuum solvation models, which can result in substantial improvement in the modeling of ionic reactions in solution.

Cluster-continuum quasichemical theory calculation of the lithium ion solvation in water, acetonitrile and dimethyl sulfoxide: an absolute single-ion solvation free energy scale.

Absolute single-ion solvation free energy is a very useful property for understanding solution phase chemistry. The real solvation free energy of an ion depends on its interaction with the solvent molecules and on the net potential inside the solute cavity. The tetraphenyl arsonium-tetraphenyl borate (TATB) assumption as well as the cluster-continuum quasichemical theory (CC-QCT) approach for Li(+) solvation allows access to a solvation scale excluding the net potential. We have determined this free energy scale investigating the solvation of the lithium ion in water (H2O), acetonitrile (CH3CN) and dimethyl sulfoxide (DMSO) solvents via the CC-QCT approach. Our calculations at the MP2 and MP4 levels with basis sets up to the QZVPP+diff quality, and including solvation of the clusters and solvent molecules by the dielectric continuum SMD method, predict the solvation free energy of Li(+) as -116.1, -120.6 and -123.6 kcal mol(-1) in H2O, CH3CN and DMSO solvents, respectively (1 mol L(-1) standard state). These values are compatible with the solvation free energy of the proton of -253.4, -253.2 and -261.1 kcal mol(-1) in H2O, CH3CN and DMSO solvents, respectively. Deviations from the experimental TATB scale are only 1.3 kcal mol(-1) in H2O and 1.8 kcal mol(-1) in DMSO solvents. However, in the case of CH3CN, the deviation reaches a value of 9.2 kcal mol(-1). The present study suggests that the experimental TATB scale is inconsistent for CH3CN. A total of 125 values of the solvation free energy of ions in these three solvents were obtained. These new data should be useful for the development of theoretical solvation models.

Absolute Single-Ion Solvation Free Energy Scale in Methanol Determined by the Lithium Cluster-Continuum Approach

Absolute solvation free energy of the lithium cation in methanol was calculated by the cluster-continuum quasichemical theory of solvation. Clusters with up to five methanol molecules were investigated using X3LYP, MP2, and MP4 methods with DZVP, 6-311+G(2df,2p), TZVPP+diff, and QZVPP+diff basis sets and including the cluster solvation through the PCM and SMD continuum models. Our calculations have determined a value of -118.1 kcal mol(-1) for the solvation free energy of the lithium, in close agreement with a value of -116.6 kcal mol(-1) consistent with the TATB assumption. Using data of solvation and transfer free energy of a pair of ions, electrode potentials and pKa, we have obtained the solvation free energy of 25 ions in methanol. Our analysis leads to a value of -253.6 kcal mol(-1) for the solvation free energy of the proton, which can be compared with the value of -263.5 kcal mol(-1) obtained by Kelly et al. using the cluster pair approximation. Considering that this difference is due to the methanol surface potential, we have estimated that it corresponds to -0.429 V.

Ionic force field optimization based on single-ion and ion-pair solvation properties: Going beyond standard mixing rules

Using molecular dynamics (MD) simulations in conjunction with the SPC/E water model, we optimize ionic force-field parameters for seven different halide and alkali ions, considering a total of eight ion-pairs. Our strategy is based on simultaneous optimizing single-ion and ion-pair properties, i.e., we first fix ion-water parameters based on single-ion solvation free energies, and in a second step determine the cation-anion interaction parameters (traditionally given by mixing or combination rules) based on the Kirkwood-Buff theory without modification of the ion-water interaction parameters. In doing so, we have introduced scaling factors for the cation-anion Lennard-Jones (LJ) interaction that quantify deviations from the standard mixing rules. For the rather size-symmetric salt solutions involving bromide and chloride ions, the standard mixing rules work fine. On the other hand, for the iodide and fluoride solutions, corresponding to the largest and smallest anion considered in this work, a rescaling of the mixing rules was necessary. For iodide, the experimental activities suggest more tightly bound ion pairing than given by the standard mixing rules, which is achieved in simulations by reducing the scaling factor of the cation-anion LJ energy. For fluoride, the situation is different and the simulations show too large attraction between fluoride and cations when compared with experimental data. For NaF, the situation can be rectified by increasing the cation-anion LJ energy. For KF, it proves necessary to increase the effective cation-anion Lennard-Jones diameter. The optimization strategy outlined in this work can be easily adapted to different kinds of ions.

Computation of methodology-independent single-ion solvation properties from molecular simulations. III. Correction terms for the solvation free energies, enthalpies, entropies, heat capacities, volumes, compressibilities, and expansivities of solvated ions

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions (finite or periodic system, system or box size) and treatment of electrostatic interactions (Coulombic, lattice-sum, or cutoff-based) used during these simulations. However, as shown by Kastenholz and Hünenberger [J. Chem. Phys. 124, 224501 (2006)], correction terms can be derived for the effects of: (A) an incorrect solvent polarization around the ion and an incomplete or/and inexact interaction of the ion with the polarized solvent due to the use of an approximate (not strictly Coulombic) electrostatic scheme; (B) the finite-size or artificial periodicity of the simulated system; (C) an improper summation scheme to evaluate the potential at the ion site, and the possible presence of a polarized air-liquid interface or of a constraint of vanishing average electrostatic potential in the simulated system; and (D) an inaccurate dielectric permittivity of the employed solvent model. Comparison with standard experimental data also requires the inclusion of appropriate cavity-formation and standard-state correction terms. In the present study, this correction scheme is extended by: (i) providing simple approximate analytical expressions (empirically-fitted) for the correction terms that were evaluated numerically in the above scheme (continuum-electrostatics calculations); (ii) providing correction terms for derivative thermodynamic single-ion solvation properties (and corresponding partial molar variables in solution), namely, the enthalpy, entropy, isobaric heat capacity, volume, isothermal compressibility, and isobaric expansivity (including appropriate standard-state correction terms). The ability of the correction scheme to produce methodology-independent single-ion solvation free energies based on atomistic simulations is tested in the case of Na(+) hydration, and the nature and magnitude of the correction terms for derivative thermodynamic properties is assessed numerically.

Computation of methodology-independent single-ion solvation properties from molecular simulations. IV. Optimized Lennard-Jones interaction parameter sets for the alkali and halide ions in water

The raw single-ion solvation free energies computed from atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [M. A. Kastenholz and P. H. Hünenberger, J. Chem. Phys. 124, 224501 (2006); M. M. Reif and P. H. Hünenberger, J. Chem. Phys. 134, 144103 (2010)], the application of appropriate correction terms permits to obtain methodology-independent results. The corrected values are then exclusively characteristic of the underlying molecular model including in particular the ion-solvent van der Waals interaction parameters, determining the effective ion size and the magnitude of its dispersion interactions. In the present study, the comparison of calculated (corrected) hydration free energies with experimental data (along with the consideration of ionic polarizabilities) is used to calibrate new sets of ion-solvent van der Waals (Lennard-Jones) interaction parameters for the alkali (Li(+), Na(+), K(+), Rb(+), Cs(+)) and halide (F(-), Cl(-), Br(-), I(-)) ions along with either the SPC or the SPC/E water models. The experimental dataset is defined by conventional single-ion hydration free energies [Tissandier et al., J. Phys. Chem. A 102, 7787 (1998); Fawcett, J. Phys. Chem. B 103, 11181] along with three plausible choices for the (experimentally elusive) value of the absolute (intrinsic) hydration free energy of the proton, namely, ΔG(hyd)(⊖)[H(+)] = -1100, -1075 or -1050 kJ mol(-1), resulting in three sets L, M, and H for the SPC water model and three sets L(E), M(E), and H(E) for the SPC/E water model (alternative sets can easily be interpolated to intermediate ΔG(hyd)(⊖)[H(+)] values). The residual sensitivity of the calculated (corrected) hydration free energies on the volume-pressure boundary conditions and on the effective ionic radius entering into the calculation of the correction terms is also evaluated and found to be very limited. Ultimately, it is expected that comparison with other experimental ionic properties (e.g., derivative single-ion solvation properties, as well as data concerning ionic crystals, melts, solutions at finite concentrations, or nonaqueous solutions) will permit to validate one specific set and thus, the associated ΔG(hyd)(⊖)[H(+)] value (atomistic consistency assumption). Preliminary results (first-peak positions in the ion-water radial distribution functions, partial molar volumes of ionic salts in water, and structural properties of ionic crystals) support a value of ΔG(hyd)(⊖)[H(+)] close to -1100 kJ·mol(-1).

Ionic force field optimization based on single-ion and ion-pair solvation properties

Molecular dynamics simulations of ionic solutions depend sensitively on the force fields employed for the ions. To resolve the fine differences between ions of the same valence and roughly similar size and in particular to correctly describe ion-specific effects, it is clear that accurate force fields are necessary. In the past, optimization strategies for ionic force fields either considered single-ion properties (such as the solvation free energy at infinite dilution or the ion-water structure) or ion-pair properties (in the form of ion-ion distribution functions). In this paper we investigate strategies to optimize ionic force fields based on single-ion and ion-pair properties simultaneously. To that end, we simulate five different salt solutions, namely, CsCl, KCl, NaI, KF, and CsI, at finite ion concentration. The force fields of these ions are systematically varied under the constraint that the single-ion solvation free energy matches the experimental value, which reduces the two-dimensional {sigma,epsilon} parameter space of the Lennard-Jones interaction to a one dimensional line for each ion. From the finite-concentration simulations, the pair potential is extracted and the osmotic coefficient is calculated, which is compared to experimental data. We find a strong dependence of the osmotic coefficient on the force field, which is remarkable as the single-ion solvation free energy and the ion-water structure remain invariant under the parameter variation. Optimization of the force field is achieved for the cations Cs(+) and K(+), while for the anions I(-) and F(-) the experimental osmotic coefficient cannot be reached. This suggests that in the long run, additional parameters might have to be introduced into the modeling, for example by modified mixing rules.

Single-ion solvation free energies and the normal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide.

The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.

Application of the mean spherical approximation to the estimation of single ion thermodynamic quantities of salvation for monoatomic monovalent ions in aqueous solutions

Abstract : The expression for the Gibbs energy of solvation for simple 1-1 electrolytes within the mean spherical approximation has been fitted to data for 20 alkali metal halides in water. In performing this fit, one needs to assume a radius for each ion, the Pauling values often having been chosen in the past. The MSA parameters appear as corrections to these radii and are different for cations and anions. Two sets of ionic radii were considered, the Pauling values from crystallographic data and values based on X-ray diffraction results obtained in aqueous solutions. Excellent fits between theory and experiment were obtained, the results with the latter set of radii being preferred. This analysis provides an extrathermodynamic route to single ion solvation free energies and yields results which are very close to the real free energy of solvation measured by Randles.