Timothy T. Duignan

A continuum model of solvation energies including electrostatic, dispersion, and cavity contributions

Physically accurate continuum solvent models that can calculate solvation energies are crucial to explain and predict the behavior of solute particles in water. Here, we present such a model applied to small spherical ions and neutral atoms. It improves upon a basic Born electrostatic model by including a standard cavity energy and adding a dispersion component, consistent with the Born electrostatic energy and using the same cavity size parameter. We show that the well-known, puzzling differences between the solvation energies of ions of the same size is attributable to the neglected dispersion contribution. This depends on dynamic polarizability as well as size. Generally, a large cancellation exists between the cavity and dispersion contributions. This explains the surprising success of the Born model. The model accurately reproduces the solvation energies of the alkali halide ions, as well as the silver(I) and copper(I) ions with an error of 12 kJ mol(-1) (±3%). The solvation energy of the noble gases is also reproduced with an error of 2.6 kJ mol(-1) (±30%). No arbitrary fitting parameters are needed to achieve this. This model significantly improves our understanding of ionic solvation and forms a solid basis for the investigation of other ion-specific effects using a continuum solvent model.

A Continuum Solvent Model of the Multipolar Dispersion Solvation Energy

The dispersion energy is an important contribution to the total solvation energies of ions and neutral molecules. Here, we present a new continuum model calculation of these energies, based on macroscopic quantum electrodynamics. The model uses the frequency dependent multipole polarizabilities of molecules in order to accurately calculate the dispersion interaction of a solute particle with surrounding water molecules. It includes the dipole, quadrupole, and octupole moment contributions. The water is modeled via a bulk dielectric susceptibility with a spherical cavity occupied by the solute. The model invokes damping functions to account for solute-solvent wave function overlap. The assumptions made are very similar to those used in the Born model. This provides consistency and additivity of electrostatic and dispersion (quantum mechanical) interactions. The energy increases in magnitude with cation size, but decreases slightly with size for the highly polarizable anions. The higher order multipole moments are essential, making up more than 50% of the dispersion solvation energy of the fluoride ion. This method provides an accurate and simple way of calculating the notoriously problematic dispersion contribution to the solvation energy. The result establishes the importance of using accurate calculations of the dispersion energy for the modeling of solvation.

Ion interactions with the air-water interface using a continuum solvent model

Explaining and predicting the distribution of ions at the air-water interface has been a central challenge of physical chemistry for nearly a century. In essence, the problem amounts to calculating the change in the solvation energy of an ion as it approaches the interface. Here, we generalize our recently developed model of ionic solvation energies to calculate this interaction. The change in the Born energy as well as the static polarization response of the ion is included by using the conductor-like screening model (COSMO), which treats the ions quantum mechanically. Approximate expressions for the dispersion repulsion, cavity attraction, and surface potential contributions are also included. This model reproduces the surface tensions of electrolyte solutions and is consistent with ab initio molecular dynamics (MD) simulation. The model provides clear physical insight into iodides adsorption. Unlike alternative models, no parameters are deliberately adjusted to reproduce surface tensions, and all of the important contributions to the interactions are included. Solving this problem has important direct implications for atmospheric chemistry and bubble properties. It also has important indirect implications for the more complex interactions of ions with protein and mineral surfaces. These play a fundamental role in a vast number of biological and industrial processes. The model is conceptually simple and has low computational demand, which facilitates its extension to these important applications.

A continuum solvent model of the partial molar volumes and entropies of ionic solvation.

Continuum solvent models of electrolyte solutions are extremely useful. However, before we can use them with confidence, it is important to test them by comparison with a range of experimental properties. Here, we have adapted our recently developed1,2 simple continuum solvent model of ionic solvation free energies to calculate the solvation entropies and partial molar volumes of a group of monovalent and monatomic ions. This procedure gives good quantitative agreement for larger ions, and reproduces key qualitative features, such as the shift to positive entropies of solvation for iodide and the shift to negative partial molar volumes for small cations. Small ions require a correction to account for dielectric saturation effects, which brings them also into good agreement with experiment. We argue that this model does not require ad hoc corrections, and uses parameters that have good external physical justification. This work therefore establishes that our continuum solvent model can provide a satisfactory understanding of ionic solvation. It can thus serve as a foundation for improved models that explain and predict more complex ion specific effects.

Mass density fluctuations in quantum and classical descriptions of liquid water

First principles molecular dynamics simulation protocol is established using revised functional of Perdew-Burke-Ernzerhof (revPBE) in conjunction with Grimmes third generation of dispersion (D3) correction to describe the properties of water at ambient conditions. This study also demonstrates the consistency of the structure of water across both isobaric (NpT) and isothermal (NVT) ensembles. Going beyond the standard structural benchmarks for liquid water, we compute properties that are connected to both local structure and mass density fluctuations that are related to concepts of solvation and hydrophobicity. We directly compare our revPBE results to the Becke-Lee-Yang-Parr (BLYP) plus Grimme dispersion corrections (D2) and both the empirical fixed charged model (SPC/E) and many body interaction potential model (MB-pol) to further our understanding of how the computed properties herein depend on the form of the interaction potential.

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.

Cation effects on haemoglobin aggregation: balance of chemisorption against physisorption of ions

A theoretical model of haemoglobin is presented to explain an anomalous cationic Hofmeister effect observed in protein aggregation. The model quantifies competing proposed mechanisms of non-electrostatic physisorption and chemisorption. Non-electrostatic physisorption is stronger for larger, more polarizable ions with a Hofmeister series Li+< K+< Cs+. Chemisorption at carboxylate groups is stronger for smaller kosmotropic ions, with the reverse series Li+ > K+ > Cs+. We assess aggregation using second virial coefficients calculated from theoretical protein–protein interaction energies. Taking Cs+ to not chemisorb, comparison with experiment yields mildly repulsive cation–carboxylate binding energies of 0.48 kBT for Li+ and 3.0 kBT for K+. Aggregation behaviour is predominantly controlled by short-range protein interactions. Overall, adsorption of the K+ ion in the middle of the Hofmeister series is stronger than ions at either extreme since it includes contributions from both physisorption and chemisorption. This results in stronger attractive forces and greater aggregation with K+, leading to the non-conventional Hofmeister series K+ > Cs+ ≈ Li+.

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.

Cavitation energies can outperform dispersion interactions

AbstractThe accurate dissection of binding energies into their microscopic components is challenging, especially in solution. Here we study the binding of noble gases (He–Xe) with the macrocyclic receptor cucurbit[5]uril in water by displacement of methane and ethane as 1H NMR probes. We dissect the hydration free energies of the noble gases into an attractive dispersive component and a repulsive one for formation of a cavity in water. This allows us to identify the contributions to host–guest binding and to conclude that the binding process is driven by differential cavitation energies rather than dispersion interactions. The free energy required to create a cavity to accept the noble gas inside the cucurbit[5]uril is much lower than that to create a similarly sized cavity in bulk water. The recovery of the latter cavitation energy drives the overall process, which has implications for the refinement of gas-storage materials and the understanding of biological receptors.Binding interactions, whether between a biological receptor and ligand or between a synthetic host and guest, are frequently stronger for larger molecules than for smaller ones. This is commonly believed to arise from increased dispersion interactions, but it has now been shown that cavitation energies—always required to dissolve molecules in solution—can be more important.