D. Asthagiri

Absolute hydration free energies of ions, ion–water clusters, and quasichemical theory

Experimental studies of ion–water clusters have provided insights into the microscopic aspects of hydration phenomena. One common view is that extending those experimental studies to larger cluster sizes would give the single-ion absolute hydration free energies not obtainable by classical thermodynamic methods. This issue is reanalyzed in the context of recent computations and molecular theories of ion hydration, particularly considering the hydration of H+, Li+, Na+, and HO− ions, and thence the hydration of neutral ion pairs. The hydration free energies of neutral pairs computed here are in good agreement with experimental results, whereas the calculated absolute hydration free energies and the excess chemical potentials deviate consistently from some recently tabulated hydration free energies based on ion–water cluster data. We show how the single-ion absolute hydration free energies are not separated from the potential of the phase in recent analyses of ion–water cluster data, even in the limit of la...

Free energy of liquid water on the basis of quasichemical theory and ab initio molecular dynamics

We use ab initio molecular dynamics as a basis for quasichemical theory evaluation of the free energy of water near conventional liquid thermodynamic states. The Perdew-Wang-91 (PW91), Perdew-Burke-Ernzerhof (PBE), and revised PBE (rPBE) functionals are employed. The oxygen radial density distribution using the rPBE functional is in reasonable agreement with current experiments, whereas the PW91 and PBE functionals predict a more structured oxygen radial density distribution. The diffusion coefficient with the rPBE functional is in reasonable accord with experiments. Using a maximum entropy procedure, we obtain x0 from the coordination number distribution xn for oxygen atoms having n neighbors. Likewise, we obtain p0 from pn, the probability of observing cavities of specified radius containing n water molecules. The probability x0 is a measure of the local chemical interactions and is central to the quasichemical theory of solutions. The probability p0, central to the theory of liquids, is a measure of the free energy required to open cavities of defined sizes in the solvent. Using these values and a reasonable model for electrostatic and dispersion effects, the hydration free energy of water in water at 314 K is calculated to be -5.1 kcal/mole with the rPBE functional, in encouraging agreement with the experimental value of -6.1 kcal/mole.

Inner shell definition and absolute hydration free energy of K+(aq) on the basis of quasi-chemical theory and ab initio molecular dynamics

The K+(aq) ion is an integral component of many cellular processes, amongst which the most important, perhaps, is its role in transmitting electrical impulses along the nerve. Understanding its hydration structure and thermodynamics is crucial in dissecting its role in such processes. Here we address these questions using both the statistical mechanical quasi-chemical theory of solutions and ab initio molecular dynamics simulations. Simulations predict an interesting hydration structure for K+(aq): the population of about six (6) water molecules within the initial minimum of the observed gKO(r) at infinite dilution involves four (4) innermost molecules that the quasi-chemical theory suggests should be taken as the theoretical inner shell. The contribution of the fifth and sixth closest water molecules is observable as a distinct shoulder on the principal maximum of the gKO(r). The quasi-chemical estimate of solvation free energy for the neutral pair KOH is also in good agreement with experiments.

Quasi-chemical study of Be2+(aq) speciation

Abstract Be 2+ (aq) hydrolysis can to lead to the formation of multi-beryllium clusters, but the thermodynamics of this process has not been resolved theoretically. We study the hydration state of an isolated Be 2+ ion using both the quasi-chemical theory of solutions and ab initio molecular dynamics. These studies confirm that Be 2+ (aq) is tetra-hydrated. The quasi-chemical approach is then applied to then the deprotonation of Be(H 2 O) 4 2+ to give BeOH(H 2 O) 3 + . The calculated p K a of 3.8 is in good agreement with the experimentally suggested value around 3.5. The calculated energetics for the formation of [Be·OH·Be] 3+ are then obtained in fair agreement with experiments.

Role of fluctuations in a snug-fit mechanism of KcsA channel selectivity

The thermodynamic exclusion of Na+ relative to K+ in potassium channels is examined by calculating the distribution of binding energies for Na+ and K+ in a model of the selectivity filter of the KcsA potassium channel. These distributions are observed to take a surprisingly simple form: Gaussian with a slight positive skewness that is insignificant in the present context. Complications that might be anticipated from these distributions are not problematic here. Na+ occupies the filter with a mean binding energy substantially lower than that of K+. The difference is comparable to the difference in hydration free energies of Na+ and K+ in bulk aqueous solution. Thus, the average energies of binding to the filter do not discriminate Na+ from K+ when measured from a baseline of the difference in bulk hydration free energies. The strong binding of Na+ constricts the filter, consistent with a negative partial molar volume of Na+ in water in contrast with a positive partial molar volume of K+ in water. Discrimination in favor of K+)can be attributed to the scarcity of favorable binding configurations for Na+ compared to K+. That relative scarcity is quantified as enhanced binding energy fluctuations, which reflects both the energetically stronger binding of Na+ and the constriction of the filter induced by Na+ binding.

Hydration of krypton and consideration of clathrate models of hydrophobic effects from the perspective of quasi-chemical theory.

Ab initio molecular dynamics (AIMD) results on a krypton-water liquid solution are presented and compared to recent XAFS results for the radial hydration structure for a Kr atom in liquid water solution. Though these AIMD calculations have important limitations of scale, the comparisons with the liquid solution results are satisfactory and significantly different from the radial distributions extracted from the data on the solid Kr/H(2)O clathrate hydrate phase. The calculations also produce the coordination number distribution that can be examined for metastable coordination structures suggesting possibilities for clathrate-like organization; none are seen in these results. Clathrate pictures of hydrophobic hydration are discussed, as is the quasi-chemical theory that should provide a basis for clathrate pictures. Outer shell contributions are discussed and estimated; they are positive and larger than the positive experimental hydration free energy of Kr(aq), implying that inner shell contributions must be negative and of comparable size. Clathrate-like inner shell hydration structures on a Kr atom solute are obtained for some, but not all, of the coordination number cases observed in the simulation. The structures found have a delicate stability. Inner shell coordination structures extracted from the simulation of the liquid, and then subjected to quantum chemical optimization, always decomposed. Interactions with the outer shell material are decisive in stabilizing coordination structures observed in liquid solution and in clathrate phases. The primitive quasi-chemical estimate that uses a dielectric model for the influence of the outer shell material on the inner shell equilibria gives a contribution to hydration free energy that is positive and larger than the experimental hydration free energy. The what are we to tell students question about hydrophobic hydration, often answered with structural clathrate pictures, is then considered; we propose an alternative answer that is consistent with successful molecular theories of hydrophobic effects and based upon distinctive observable properties of liquid water. Considerations of parsimony, for instance Ockhams razor, then suggest that additional structural hypotheses in response to what are we to tell students are not required at this stage.

An analysis of molecular packing and chemical association in liquid water using quasichemical theory

We calculate the hydration free energy of liquid TIP3P water at 298 K and 1 bar using a quasi-chemical theory framework in which interactions between a distinguished water molecule and the surrounding water molecules are partitioned into chemical associations with proximal (inner-shell) waters and classical electrostatic-dispersion interactions with the remaining (outer-shell) waters. The calculated free energy is found to be independent of this partitioning, as expected, and in excellent agreement with values derived from the literature. An analysis of the spatial distribution of inner-shell water molecules as a function of the inner-shell volume reveals that water molecules are preferentially excluded from the interior of large volumes as the occupancy number decreases. The driving force for water exclusion is formulated in terms of a free energy for rearranging inner-shell water molecules under the influence of the field exerted by outer-shell waters in order to accommodate one water molecule at the center. The results indicate a balance between chemical association and molecular packing in liquid water that becomes increasingly important as the inner-shell volume grows in size.