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B: Liquids, Chemical and Dynamical Processes in Solution, Spectroscopy in Solution
Finding Order in the Disordered Hydration Shell of Rapidly Exchanging Water Molecules around the Heaviest Alkali Cs and Fr +
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Santanu Roy, and Vyacheslav S. Bryantsev J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b08414 • Publication Date (Web): 27 Nov 2018 Downloaded from http://pubs.acs.org on November 28, 2018
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Finding Order in the Disordered Hydration Shell of Rapidly Exchanging Water Molecules around the Heaviest Alkali Cs+ and Fr+ Santanu Roy∗ and Vyacheslav S. Bryantsev∗ Chemical Science Division, Oak Ridge National Laboratory, 1 Bethel Valley Rd., Oak Ridge, TN 37830 E-mail:
[email protected];
[email protected] Abstract We report the structural and dynamical characterization of the intrinsically disordered hydration shells of the heaviest alkali ions, Cs+ and Fr+ , obtained in ab initio molecular dynamics simulations. The knowledge of solvation and complexion properties of short-lived Fr+ is very limited and mostly based on extrapolations from the smaller alkali metal ions. To this end, we provide a critical insight into Fr+ solvation, demonstrating an extreme example of disordered solvation with no distinction between the ion-bound and solvent-bound states of water based on the ion-water distance. However, these two states are distinguished through distance-solvent rearrangement correlation, where either coordination number or electric field is employed to treat solvent rearrangement. Utilizing reaction rate theory, we find that the water exchange timescale for Fr+ (2.1-2.3 ps) is unexpectedly slower than for Cs+ (0.5-1.2 ps), because Fr+ experiences stronger nonequilibrium solvent effects. This study provides a new perspective on weak and hydrophobic solvation. ∗
This manuscript has been authored [in part] by UT-Battelle, LLC, under contract DE-AC05-00OR22725
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Introduction Solvation and desolvation of ions and molecules is crucial for many chemical and biological process such as ion and proton transport through membrane channels, 1,2 protein folding, 3,4 nucleation and crystal growth, 5,6 and ion diffusion in energy storage systems. 7,8 While the competition between ion-solvent and solvent-solvent interactions dictates the formation of solvation shells around ions, the distribution, structure, and exchange dynamics of solvent molecules in these shells vary widely depending on the size and charge of the ion. 9,10 For example, the small and multivalent ions form well-defined solvation shells in water with multiple interconverting coordination states due to strong ion-water interactions. 10 On the contrary, the large monovalent ions such as Cs+ and Fr+ weakly interact with water and may have solvation shells that are barely stable. Thus, probing the solvation structures and dynamics of these ions by experimental techniques remain challenging, especially for Fr+ due to its short half-life (t1/2 ≤22 minutes for the most stable isotope) and only subpicomolar 11 aqueous concentration in solution. Advances in radioanalytical chemistry allowed investigation of the chemical behavior of Fr+ , 11–14 but its solvation structure and water exchange dynamics remain to be unraveled. The experimentally determined data for Fr+ are extremely scarce and many estimates rely on extrapolations from the smaller alkali metal ions, which might vary considerably. For example, the thermodynamic radius of Fr+ obtained from liquid-liquid extraction experiments was found to be closer to the size of Cs+ than previously thought. 14 Herein, we adopt ab initio molecular dynamics (AIMD) simulations that treat ion-water and water-water interactions through Density Functional Theory (DFT) to resolve the structural ordering in the hydration shells of Cs+ and Fr+ . Furthermore, we investigate the dynamics of water exchange between the hydration shells within the framework of rate theory. 15–17 Beyond with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).
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specific implications for Cs+ removal from nuclear waste 18,19 and Fr+ separation for radiopharmaceutical applications, 20,21 this work provides a new avenue for better understanding of solvation phenomena and transport of weakly hydrated ions. Identifying a solvation shell and obtaining its structural and dynamical information rely on specific experiments. Examples include X-ray and neutron scattering measurements 22,23 that have the ability to determine the number of radially distributed water molecules in the solvation shells, which can be crosschecked through computation of radial distribution functions (RDFs) from MD simulations. 24 Dielectric relaxation experiments 25 and anisotropy decay measurements in polarization-resolved infrared spectroscopic measurements 26–28 can distinguish the first-shell solvent molecules as they exhibit slower rotational dynamics than the bulk solvent. Due to extreme sensitivity to charge and size of ions, the timescales of water exchange between solvation shells may vary from (sub)picoseconds (ps) to microseconds (µs). 9 Resolving these timescales experimentally is challenging, especially when the exchange processes are ultrafast (ps or less) and the corresponding reactants and products are structurally similar. However, the two-dimensional infrared (2DIR) spectroscopy 29,30 can probe such ultrafast exchange processes due to its ability to resolve dynamics on picosecond down to femtosecond (fs) timescales. A recent combined study of AIMD and rate theory incorporated the basic philosophy of Marcus theory of electron transfer 31–33 to study solvent exchange around an organic anion and showed that the rates and pathways of solvent exchange predicted by Marcus theory are in excellent agreement with 2DIR measurements. 17 This has inspired us to utilize Marcus theory to study solvent exchange around Cs+ and Fr+ , which can be linked to future 2DIR experiments for weakly hydrated ions. As realized by Schenter and coworkers, 16 solvent rearrangement that leads to an activated state triggering electron transfer between molecules (Marcus theory) can also be responsible for transferring an anion from the paired state with a cation to the solvent separated state. Analogously, solvent rearrangement governs the solvent exchange process between the first and second solvation shells. 17 In both cases, the activated state is either an overcoordinated
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or an undercoordinated structure serving as the transition region between the reactant and product states. Thus, the fluctuating coordination number as a direct consequence of solvent rearrangement is an excellent choice for a reaction coordinate to investigate ion-pairing and solvent exchange kinetics. 10,16,17,34 In bulk water, a water molecule can accept two hydrogen bonds and donates two hydrogen bonds, resulting in coordination number of 4. In thermal equilibrium, coordination number of water fluctuates with time and reduces to a smaller number at the interfacial environment due to interaction with ions or other molecules. 17,35–37 Therefore, the ion-bound and solventbound states of a water molecule can be unambiguously distinguished in coordination number space. According to the Marcus theory of solvent exchange, 17 the pathway that connects these states can be extracted from the surface of two-dimensional potential of mean force (2DPMF) as a function of the ion-water distance and coordination number of water by examining a chain of events: first activation in coordination number, then spontaneous ionwater separation, and finally relaxation in coordination number. Traditionally, the solvent exchange rates are determined from the PMF along the reaction coordinate, namely ion-water distance, by employing transition state theory (TST) 38–42 and by examining nonequilibrium solvent effects 40,43–45 on the reaction coordinate. When TST is exact, the trajectories going from the reactant to product states directly transit to the latter after arriving at the transition state without recrossing the barrier. However, due to strong solvent effects on the reaction coordinate barrier-recrossing may occur and only a fraction of the trajectories actually has the chance to end up at the product state. This fraction is expressed in terms of transmission coefficient (κ); 0
