The Nature of the Hydrated Excess Proton and Its Unusual Behavior

1. The Nature of the Hydrated Excess Proton and Its Unusual Behavior

2. Proton transport in Nafion Li-ion batteries AEM fuel cells Protons Play a Key Role in Many Processes Proton channels in proteins

3. ATP synthesis and hydrolysis • Photosynthesis • Heat production • Homeostasis ATP synthase Wikimedia Commons • Flagellar rotation Protons in Biomolecular Systems • Within a cell, moving protons across a membrane allows energy to be stored as an electrochemical gradient charge separation concentration difference • This potential energy can be used to power chemical processes, such as:

4. Studying Chemical Systems • In a molecular dynamics (MD) simulation, a set of interacting particles move according to equations of motion defined by Newtonian mechanics Newton’s second law position at later time • An MD simulation produces trajectory data, which consists of the position, velocity, and energy of each particle at every time point considered in the simulation • Applying statistical mechanics allows us to derive information on macroscopic observables from this microscopic data • A force field consists of 1) a potential energy function describing inter- and intra-molecular interactions, and 2) a set of parameters which ensure agreement with experimental results • Selection of an appropriate force field is crucial to a successful MD simulation

5. The Challenge of Proton Solvation and Transport • The excess proton is a dynamic electrical charge defect delocalized over several water molecules • Despite what is taught in many textbooks, the hydrated excess proton does not exist as the simple hydronium cation (H3O+). • It is rather an “electron hole” with one missing electron from the excess proton and it is constantly moving Y. Wu, H. Chen , F. Wang, F. Paesani , and G. A. Voth, J. Phys. Chem. B (2008) • A model for proton solvation and transport (PS&T) must be able to describe the continuously changing network of hydrogen-bonded water molecules surrounding a hydrated proton • Traditional force fields, however, are not reactive; they lack the ability to describe the formation and cleavage of chemical bonds

6. Computer Modeling of Hydrated Protons • A high-level treatment of chemical reactions requires explicitly treating the involved electrons through quantum mechanics • Due to their small size, electrons move much more quickly than atoms • This difference in time scales makes it computationally expensiveto consider electrons and atoms together • Nevertheless, traditional force field models can be extended to reactive systems through special techniques • The multiscale reactive molecular dynamics (MS-RMD) methodology relies on a linear combination of several different states to model charge delocalization and dynamic bonding environments C. Knight and G. A. Voth, Acc. Chem. Res. (2012) • Ab initio molecular dynamics (AIMD) simulations are extremely accurate because they are based on quantum mechanics • The MS-RMDmethodcan be parametrizedvia AIMD data; combining these technologies allows for the sampling of longer time and length scales than would be feasible with AIMD alone

7. E H5O2+ H9O4+ Z Z E The Hydrated Proton has Two Predominant Forms • The chemical identity of the hydrated proton is described by two predominant solvation structures: the Eigen (E) and Zundel (Z) cations • Excess proton transfer between two water molecules occurs via the Zundel cation • The Eigen cation is the most stable hydrated proton species in liquid water, as shown by the probability distribution the two largest MS-RMD amplitudes (L) and the free energy profile of the proton solvation structure in bulk water (R) J. M. J. Swanson, C. M. Maupin, H. Chen, M. K. Petersen, J. Xu, Y. Wu, and G. A. Voth, J. Phys. Chem. B, (2007)

8. Grotthuss Proton Shuttling • The Grotthuss mechanism for proton transport was first proposed in 1806 by T. Grotthuss, even though he did not know the chemical formula of water (Ann. Chim. LVIII, 54 (1806)) • According to this mechanism the excess proton hops between adjacent water molecules in the water wire through successive covalent bond formation and breaking events • Modern research suggests that Grotthuss shuttling occurs by the Eigen-Zundel-Eigen (EZE) mechanism, whereby one distorted Eigen cation is converted into another with the Zundel cation as an intermediate C. Knight and G. A. Voth, Acc. Chem. Res. (2012) • The EZE mechanism for proton transport has been statistically validated through MS-RMD simulations, AIMD simulations, and photoelectron spectroscopy

9. The Special-Pair Dance • The ‘resting’ state of the solvated proton is best described as a distorted Eigen cation • Within this structure, the central hydronium ion forms strong hydrogen bonds with the three surrounding water molecules which comprise its first solvation shell • In the special-pair (SP) dance, the length of these hydrogen bonds fluctuates rapidly over time, with any one of the three bonds being shorter than the remaining two • This dance is a preparatory stage of proton transfer, during which the central hydronium ion searches for a partner • The successful partner accepts only one hydrogen bond, whereas most water molecules accept two C. Knight and G. A. Voth, Acc. Chem. Res. (2012)

10. The Special-Pair Dance and Proton Transfer • Once a successful partner is identified, the proton transfer event occurs between the special pair • The partner transfers significant electronic charge to the hydronium cation along the strong SP hydrogen bond • As per the EZE mechanism, the Zundel cation corresponds to the transition state of proton transfer O. Markovitch, H. Chen, S. Izvekov, F. Paesani, G.A. Voth, and N. Agmom, J. Phys. Chem. B (2008) • The SP dance demonstrates the sensitive coupling between the excess proton and its surrounding hydrogen bond network • Proton transfer, therefore, occurs via a cooperative, diffusive process rather than by simple hopping • The study of these mechanisms was accomplished by combining the efficiency of the MS-RMDmethodand the accuracy of AIMD

11. Hydrated Proton Dynamics and Charge Defect Delocalization • A “stable” resonating hydrated proton structure exists for 1-2 ps. • This structure involves a single central oxygen atom, but several transient Zundel-like structures. • This structure is best characterized as a “distorted” Eigen cation. Excess Proton Charge Defect:Center of Excess Charge (CEC) (Position shown by yellow ball) CEC The “Special Pair Dance” O. Markovitch,H. Chen,S. Izvekov, F. Paesani,G. A. Voth,and N. Agmon, “Statistical Identification of the Mechanism of Proton Mobility”, J. Phys. Chem. B 112, 9456 (2008).

12. Acid Dissociation in Water: A Complex Process • Shown at right is the so-called “potential of mean force” or free energy curve for the dissociation of the hydrated proton center of excess charge (CEC) from the aspartic acid in water along the reaction coordinate (RC) • The colored regions reflect the distribution functions from the MS-RMD simulations as a function of CEC distance from the Asp carbonyl oxygens • A vertical slice as a function of the RC gives the hydrated proton distribution function like in slide 7 Aspartic Acid pKa: 3.7 Eigen-like structures are most stable at larger values of RC Zundel-like structures occur at transitions An ion pair is evident around RC = 3

13. Amphiphilic Character of the Hydrated Proton • One might expect that two hydrated protons would repel each other because of their net positive charges • However, the interactions between hydrated protons are not so straightforward • At 0.43−0.85 M concentrations, hydronium cations are found to form unusually stable contact ion pairs by positioning the hydronium oxygen lone pair sides toward one another • This unexpected behavior can be attributed to the amphiphilic nature of the hydrated excess proton, which arises from the directionally asymmetric ability of the core hydronium entity to form hydrogen bonds with neighboring water molecules C. Knight and G. A. Voth, Acc. Chem. Res. (2012) • The three H-atoms of the hydronium form strong H-bonds within the Eigen cation, thus imparting hydrophilic character • However, the lone pair of the hydronium is a hydrophobic region, because it is energetically unfavorable for the net-positive hydronium ion to accept a hydrogen bond J. Xu, S. Izvekov, and G. A. Voth, J. Phys. Chem. B (2010)

14. Hydrated Protons at the Water-Vacuum Interface • Conventional analysis of ion solvation near the dielectric boundary at the liquid-vapor interface holds that ions should be expelled from the interface • The amphiphilic nature of the hydrated proton disrupts the hydrogen-bonding network in bulk water • As predicted by MS-RMD simulations, this results in an enhanced hydronium concentration near the water-vapor interface in acidic aqueous solution and at the surface of water clusters M. K. Petersen, S. S. Iyengar, T. J. F. Day, and G. A. Voth, J. Phys. Chem. B, (2004) Hydronium cation ‘Dangling’ O-H bond Hydronium cation ‘Dangling’ O-H bond • This unusual behavior stems from the fact that the hydrophobiclone pair at the interface can be oriented toward the vapor region to minimize its disturbance in the bulk water • These theoretical predictions were subsequently verified through agreement with experimental results

15. Hydrophobic particles (light) in salt solution Hydrophobic particles (light) in acidic solution H. Chen, J. Xu, and G. A. Voth, J. Phys. Chem. B (2009) Hydrophobic Interactions • The aggregation and dispersion of hydrophobic particles in water is principally determined by the interplay between enthalpy and entropy • Although the aggregation of hydrophobic particles is typically favored entropically, it is more complicated enthalpically since H-bonding rearrangements in the surrounding solvent must be considered • As demonstrated in MS-RMD simulations, the solubility of hydrophobic molecules is enhanced by low pH conditions • Although a hydronium cation has a similar radius to the salting-out cations K+ and NH4+, hydrophobic particles are more soluble in acidic solution than in salt solution of the same concentration • This behavior can be explained by the existence of associated hydrophobe- hydrated proton structures, which form as a result of hydronium’s unusual amphiphilic character Hydrophobic particles (light) in salt solution Hydrophobic particles (light) in acidic solution • Although a hydronium cation has a similar radius to the salting-out cations K+ and NH4+, hydrophobic soluble in acidic solution than in salt solution of the same concentration The present results taken together reveal that the enhanced solubility of hydrophobic species in acidic aqueous solutions largely originates from the existence of associated hydrophobe- hydrated proton structures.

16. Applications • PS&T in biomolecular systems has presented the most challenging and arguably important application for the MS-RMD simulation methodology to date • Computer simulations have been applied to the following systems Phospholipid membranes Aquaporin channels Cytochrome c oxidase Influenza A M2 proton channel Mutated aquaporins Carbonic anhydrase

17. Acknowledgements This research has been supported by the National Science Foundation