Excess Proton In Water Research Articles

Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange.

The transport of excess protons in water is central to acid-base chemistry, biochemistry and energy production. However, elucidating its mechanism has been challenging. Recent nonlinear vibrational spectroscopy experiments could not be explained by existing models. Here we use both vibrational spectroscopy calculations and neural-network-based molecular dynamics simulations that account for nuclear quantum effects for all atoms to determine the proton transport mechanism. Our simulations reveal an equilibrium between two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Proton transport follows a three-step mechanism gated by two successive hydrogen-bond exchanges: the first reduces the proton-acceptor water coordination, leading to proton transfer, and the second, the rate-limiting step, prevents rapid back-transfer by increasing the proton-donor coordination. This sequential mechanism is consistent with experimental characterizations of proton diffusion, explaining the low activation energy and the prolonged intermediate lifetimes in vibrational spectroscopy. These results are crucial for understanding proton dynamics in biochemical and technological systems.

Comparison of classical and abinitio simulations of hydronium and aqueous proton transfer.

Proton transport in aqueous systems occurs by making and breaking covalent bonds, a process that classical force fields cannot reproduce. Various attempts have been made to remedy this deficiency, by valence bond theory or instantaneous proton transfers, but the ability of such methods to provide a realistic picture of this fundamental process has not been fully evaluated. Here we compare an abinitio molecular dynamics (AIMD) simulation of an excess proton in water to a simulation of a classical H3O+ in TIP3P water. The energy gap upon instantaneous proton transfer from H3O+ to an acceptor water molecule is much higher in the classical simulation than in the AIMD configurations evaluated with the same classical potential. The origins of this discrepancy are identified by comparing the solvent structures around the excess proton in the two systems. One major structural difference is in the tilt angle of the water molecules that accept an hydrogen bond from H3O+. The lack of lone pairs in TIP3P produces a tilt angle that is too large and generates an unfavorable geometry after instantaneous proton transfer. This problem can be alleviated by the use of TIP5P, which gives a tilt angle much closer to the AIMD result. Another important factor that raises the energy gap is the different optimal distance in water-water vs H3O+-water H-bonds. In AIMD the acceptor is gradually polarized and takes a hydronium-like configuration even before proton transfer actually happens. Ways to remedy some of these problems in classical simulations are discussed.

Comparison of classical and ab initio simulations of hydronium and aqueous proton transfer.

Proton transfer represents the simplest chemical reaction, yet it is still typically not accounted for in standard biomolecular simulations. Here we compare an ab initio molecular dynamics (MD) simulation trajectory of an excess proton in water to classical MD trajectories of hydronium in TIP3P water. We characterize the structural differences between them and correlate these with the energy gap upon instant proton transfer, which is much higher in the classical simulations. One structural difference is in the tilt angle of the waters that accept an h-bond from hydronium, which is too large in TIP3P. This can be largely alleviated by use of the TIP5P model, whose lone pairs orient the water molecule properly. Other discrepancies include a lower number of h-bonds and a less favorable second solvation shell geometry in classical MD, which is likely due to lack of polarization. The identification of these structural differences paves the way toward classical MD simulations that can more closely mimic ab initio trajectories. We also present efforts to develop a classical model for hydroxide that reproduces ab initio solvation structure and proton transfer mechanism.

Von lokalen kovalenten Bindungen zu langreichweitigen elektrischen Wechselwirkungen der Protonenhydratation

AbstractScheinbar einfache und doch überraschend schwierig ist die Untersuchung überschüssiger Protonen in Wasser, die ein komplexes Quantenobjekt mit starken Wechselwirkungen zum ausgedehnten und sich dynamischen ändernden Wasserstoffbrücken‐Netzwerk der Flüssigkeit darstellen. Die auftretende Protonenhydratation spielt eine entscheidende Rolle im Energietransport von Brennstoffzellen und bei der Signalübertragung in Transmembranproteinen. Während Geometrie und Stöchiometrie bereits umfangreich in Experimenten und in der Theorie adressiert worden sind, ist die elektronische Struktur dieser spezifischen hydratisierten Protonenkomplexe bisher Verborgenen geblieben. In dieser Studie zeigen wir, Schicht für Schicht, wie der Einsatz neuer Flachstrahltechnologie für akkurate röntgenspektroskopische Messungen in Kombination mit Infrarot‐Spektralanalyse sowie Berechnungen es uns ermöglicht, orbitalspezifische spektrale Signale zu finden, die es erlauben zwei Haupteffekte in der elektronsichen Struktur zu unterscheiden: Lokale Orbitalwechselwirkungen bestimmen kovalente Bindungen zwischen dem Proton und den benachbarten Wassermolekülen, während Verschiebungen der Orbitalenergien ein Maß für die Stärke des langreichweitigen elektrischen Feldes des Protons sind.

From Local Covalent Bonding to Extended Electric Field Interactions in Proton Hydration.

Seemingly simple yet surprisingly difficult to probe, excess protons in water constitute complex quantum objects with strong interactions with the extended and dynamically changing hydrogen-bonding network of the liquid. Proton hydration plays pivotal roles in energy transport in hydrogen fuel cells and signal transduction in transmembrane proteins. While geometries and stoichiometry have been widely addressed in both experiment and theory, the electronic structure of these specific hydrated proton complexes has remained elusive. Here we show, layer by layer, how utilizing novel flatjet technology for accurate x-ray spectroscopic measurements and combining infrared spectral analysis and calculations, we find orbital-specific markers that distinguish two main electronic-structure effects: Local orbital interactions determine covalent bonding between the proton and neigbouring water molecules, while orbital-energy shifts measure the strength of the extended electric field of the proton.

Grotthuss Molecular Dynamics Simulations for Modeling Proton Hopping in Electrosprayed Water Droplets.

Excess protons in water exhibit unique transport properties because they can rapidly hop along H-bonded water wires. Considerable progress has been made in unraveling this Grotthuss diffusion mechanism using quantum mechanical-based computational techniques. Unfortunately, high computational cost tends to restrict those techniques to small systems and short times. Molecular dynamics (MD) simulations can be applied to much larger systems and longer time windows. However, standard MD methods do not permit the dissociation/formation of covalent bonds, such that Grotthuss diffusion cannot be captured. Here, we bridge this gap by combining atomistic MD simulations (using Gromacs and TIP4P/2005 water) with proton hopping. Excess protons are modeled as hydronium ions that undergo H3O+ + H2O → H2O + H3O+ transitions. In accordance with ab initio MD data, these Grotthuss hopping events are executed in "bursts" with quasi-instantaneous hopping across one or more waters. The bursts are separated by regular MD periods during which H3O+ ions undergo Brownian diffusion. The resulting proton diffusion coefficient agrees with the literature value. We apply this Grotthuss MD technique to highly charged water droplets that are in a size regime encountered during electrospray ionization (5 nm radius, ∼17,000 H2O). The droplets undergo rapid solvent evaporation and occasional H3O+ ejection, keeping them at ca. 81% of the Rayleigh limit. The simulated behavior is consistent with phase Doppler anemometry data. The Grotthuss MD technique developed here should be useful for modeling the behavior of various proton-containing systems that are too large for high-level computational approaches. In particular, we envision future applications related to electrospray processes, where earlier simulations used metal cations while in reality excess protons dominate.

Hyper‐Raman study of hydrated excess protons in water: Measurement of concentrated HCl solution

AbstractWe report hyper‐Raman (HR) spectra of concentrated hydrochloric acid solutions for the first time. HR signals from the OH stretching region to the low‐frequency region reflect the presence of chloride anions solvated in water. By contrast, it turns out that HR spectroscopy is insensitive to the presence of excess protons in water. HR spectra of HCl solutions do not show any signature of a proton continuum and shoulders on the high/low‐frequency sides of the bending mode of H2O in stark contrast to IR spectroscopy. Moreover, we found that a sharp HR signal around 500 cm−1 appear in 532 nm excited HR spectra. A laser power dependence indicates that this signal comes from a photochemical reaction. The absence of this signal under 1064 nm HR excitation and 532 nm Raman excitation suggests that the resonance (hyper‐)Raman effect enhances the signal from the photoproduct.

Resolving the Structural Debate for the Hydrated Excess Proton in Water.

It has long been proposed that the hydrated excess proton in water (aka the solvated "hydronium" cation) likely has two limiting forms, that of the Eigen cation (H9O4+) and that of the Zundel cation (H5O2+). There has been debate over which of these two is the more dominant species and/or whether intermediate (or "distorted") structures between these two limits are the more realistic representation. Spectroscopy experiments have recently provided further results regarding the excess proton. These experiments show that the hydrated proton has an anisotropy reorientation time scale on the order of 1-2 ps. This time scale has been suggested to possibly contradict the picture of the more rapid "special pair dance" phenomenon for the hydrated excess proton, which is a signature of a distorted Eigen cation. The special pair dance was predicted from prior computational studies in which the hydrated central core hydronium structure continually switches (O-H···O)* special pair hydrogen-bond partners with the closest three water molecules, yielding on average a distorted Eigen cation with three equivalent and dynamically exchanging distortions. Through state-of-art simulations it is shown here that anisotropy reorientation time scales of the same magnitude are obtained that also include structural reorientations associated with the special pair dance, leading to a reinterpretation of the experimental results. These results and additional analyses point to a distorted and dynamic Eigen cation as the most prevalent hydrated proton species in aqueous acid solutions of dilute to moderate concentration, as opposed to a stabilized or a distorted (but not "dancing") Zundel cation.

The hopping mechanism of the hydrated excess proton and its contribution to proton diffusion in water.

In this work, a series of analyses are performed on ab initio molecular dynamics simulations of a hydrated excess proton in water to quantify the relative occurrence of concerted hopping events and "rattling" events and thus to further elucidate the hopping mechanism of proton transport in water. Contrary to results reported in certain earlier papers, the new analysis finds that concerted hopping events do occur in all simulations but that the majority of events are the product of proton rattling, where the excess proton will rattle between two or more waters. The results are consistent with the proposed "special-pair dance" model of the hydrated excess proton wherein the acceptor water molecule for the proton transfer will quickly change (resonate between three equivalent special pairs) until a decisive proton hop occurs. To remove the misleading effect of simple rattling, a filter was applied to the trajectory such that hopping events that were followed by back hops to the original water are not counted. A steep reduction in the number of multiple hopping events is found when the filter is applied, suggesting that many multiple hopping events that occur in the unfiltered trajectory are largely the product of rattling, contrary to prior suggestions. Comparing the continuous correlation function of the filtered and unfiltered trajectories, we find agreement with experimental values for the proton hopping time and Eigen-Zundel interconversion time, respectively.

Assessing Many-Body Effects of Water Self-Ions. II: H3O+(H2O)n Clusters

The importance of many-body effects in the hydration of the hydronium ion (H3O+) is investigated through a systematic analysis of the many-body expansion of the interaction energy carried out at the coupled-cluster level of theory for the low-lying isomers of H3O+(H2O)n clusters with n = 1-5. This is accomplished by partitioning individual fragments extracted from the whole clusters into "groups" that are classified by both the number of H3O+ and water molecules and the hydrogen-bonding connectivity within a given fragment. Effects due to the presence of the Zundel ion, (H5O2)+, are analyzed by further partitioning fragment groups by the "context" of their parent clusters. With the aid of the absolutely localized molecular orbital energy decomposition analysis (ALMO EDA), this structure-based partitioning is found to largely correlate with the character of different many-body interactions, such as cooperative and anticooperative hydrogen bonding, within each fragment. This analysis emphasizes the importance of a many-body representation of inductive electrostatics and charge transfer in modeling the hydration of an excess proton in water. The comparison between the reference coupled-cluster many-body interaction terms with the corresponding values obtained with various exchange-correlation functionals demonstrates that many of these functionals yield an unbalanced treatment of the H3O+(H2O)n configuration space.

The solvation effect on the rattling behaviour of the hydrated excess proton in water.

The solvation effect on the kinetic rattling behaviour of the hydrated excess proton H+(aq) in water is theoretically modeled by using density functional theory (DFT) and the quantum chemical cluster model (CM). To test the solvation effects on the proton morphology and rattling kinetics, different solvation models for the proton are constructed based on the gas phase (GP) Zundel cation, which include the gas phase-polarizable continuum model (GP-PCM), the gas phase-supermolecule model (GP-SM), and the gas phase-supermolecule-polarizable continuum model (GP-SM-PCM). These solvation models consider either one or both of the short- and long-range solute-solvent interactions. Meanwhile, 1 to 6 explicit solvent water molecules (Nm' = 1-6) are added around the GP Zundel cation to test different explicit solvation environments. The calculation results show that the solvation environment has an important influence on the morphology and rattling kinetics of H+(aq). The proton rattling pathways are obtained only under the condition that both symmetrical explicit solvation environments and implicit bulk solvents are present. The zero-point contribution reduces the reaction energy barrier and enables the rattling to occur spontaneously at room temperature. The theoretical modeling results provide new insights into the microscopic kinetic behaviour of proton rattling in water at the molecular level, which are helpful in studying the proton transfer mechanism in aqueous systems.

Hydrated Excess Proton Raman Spectral Densities Probed in Floating Water Bridges

Excess proton structures in water remain unclear. The motion and nature of excess protons in water were probed using a supported water bridge structure in electric field (E) with an intensity of ∼106 V/m. The experimental setup generated protons that exhibit a long lifetime. The effect of excess protons in water induced a ∼3% variation in the pH for a 300 V overvoltage at the cathode. The current versus voltage curves show a current space-charge-limited operation. By measuring the space-charge distribution in both the cathode and anode and by adjusting the Mott–Gurney law to the measured excess hydrated proton current and the voltage drop in the cationic space-charge region, the protonic mobility was determined to be ∼200 × 10–8 m2/(V·s) (E ≈ 4 × 106 V/m). This measured mobility, which is typically five times larger than the reported mobility for protons in water, is in agreement with the mechanism outlined by Grotthuss in 1805. The measured mid-Raman spectrum covering 1000–3800 cm–1 range indicates the species character. The hydrated excess proton spectral response through the mid-Raman at 1760 and 3200 cm–1 was attributed to the Zundel complex and the region at ∼2000 to ∼2600 cm–1 response is attributed to the Eigen complex, indicating a core structure simultaneously with a Eigen-like and Zundel-like character, suggesting a rapid fluctuation between these two structures or a new specie.

Reactive molecular dynamics models from ab initio molecular dynamics data using relative entropy minimization

We present two new multiscale molecular dynamics (MS-RMD) models for the hydrated excess proton in water developed directly from ab initio molecular dynamics (AIMD) simulation data of the same system. The potential of mean force along the proton transfer reaction coordinate and radial distribution functions for the MS-RMD models are shown to faithfully reproduce those of AIMD. The models are developed using an algorithm based on relative entropy minimization, thus demonstrating the ability of the method to rapidly generate accurate and highly efficient reactive MD force fields.

IR spectral assignments for the hydrated excess proton in liquid water

The local environmental sensitivity of infrared (IR) spectroscopy to a hydrogen-bonding structure makes it a powerful tool for investigating the structure and dynamics of excess protons in water. Although of significant interest, the line broadening that results from the ultrafast evolution of different solvated proton-water structures makes the assignment of liquid-phase IR spectra a challenging task. In this work, we apply a normal mode analysis using density functional theory of thousands of proton-water clusters taken from reactive molecular dynamics trajectories of the latest generation multistate empirical valence bond proton model (MS-EVB 3.2). These calculations are used to obtain a vibrational density of states and IR spectral density, which are decomposed on the basis of solvated proton structure and the frequency dependent mode character. Decompositions are presented on the basis of the proton sharing parameter δ, often used to distinguish Eigen and Zundel species, the stretch and bend character of the modes, the mode delocalization, and the vibrational mode symmetry. We find there is a wide distribution of vibrational frequencies spanning 1200-3000 cm-1 for every local proton configuration, with the region 2000-2600 cm-1 being mostly governed by the distorted Eigen-like configuration. We find a continuous red shift of the special-pair O⋯H+⋯O stretching frequency, and an increase in the flanking water bending intensity with decreasing δ. Also, we find that the flanking water stretch mode of the Zundel-like species is strongly mixed with the flanking water bend, and the special pair proton oscillation band is strongly coupled with the bend modes of the central H5O2+moiety.

Communication: Improved ab initio molecular dynamics by minimally biasing with experimental data.

Accounting for electrons and nuclei simultaneously is a powerful capability of ab initio molecular dynamics (AIMD). However, AIMD is often unable to accurately reproduce properties of systems such as water due to inaccuracies in the underlying electronic density functionals. This shortcoming is often addressed by added empirical corrections and/or increasing the simulation temperature. We present here a maximum-entropy approach to directly incorporate limited experimental data via a minimal bias. Biased AIMD simulations of water and an excess proton in water are shown to give significantly improved properties both for observables which were biased to match experimental data and for unbiased observables. This approach also yields new physical insight into inaccuracies in the underlying density functional theory as utilized in the unbiased AIMD.

Molecular modeling and assignment of IR spectra of the hydrated excess proton in isotopically dilute water.

Infrared (IR) spectroscopy of the water O-H stretch has been widely used to probe both the local hydrogen-bonding structure and dynamics of aqueous systems. Although of significant interest, the IR spectroscopy of excess protons in water remains difficult to assign as a result of extensive and strong intermolecular interactions in hydrated proton complexes. As an alternate approach, we develop a mixed quantum-classical model for the vibrational spectroscopy of the excess proton in isotopically dilute water that draws on frozen proton-water clusters taken from reactive molecular dynamics trajectories of the latest generation multi-state empirical valence bond proton model (MS-EVB 3.2). A semi-empirical single oscillator spectroscopic map for the instantaneous transition frequency and transition dipole moment is constructed using potential energy surfaces for the O-H stretch coordinate of the excess proton using electronic structure calculations. Calculated spectra are compared with experimental spectra of dilute H+ in D2O obtained from double-difference FTIR to demonstrate the validity of the map. The model is also used to decompose IR spectra into contributions from different aqueous proton configurations. We find that the O-H transition frequency continuously decreases as the oxygen-oxygen length for a special pair proton decreases, shifting from Eigen- to Zundel-like configurations. The same shift is accompanied by a shift of the flanking water stretches of the Zundel complex to higher frequency than the hydronium O-H vibrations.

Potentials of mean force in acidic proton transfer reactions in constrained geometries

Free energy barriers associated with the transfer of an excess proton in water and related to the potentials of mean force in proton transfer episodes have been computed in a wide range of thermodynamic states, from low-density amorphous ices to high-temperature liquids under the critical point for unconstrained and constrained systems. The latter were represented by set-ups placed inside hydrophobic graphene slabs at the nanometric scale allocating a few water layers, namely one or two in the narrowest case. Water–proton and carbon–proton forces were modelled with a Multi-State Empirical Valence Bond method. As a general trend, a competition between the effects of confinement and temperature is observed on the local hydrogen-bonded structures around the lone proton and, consequently, on the mean force exerted by its environment on the water molecule carrying the proton. Free energy barriers estimated from the computed potentials of mean force tend to rise with the combined effect of increasing temperatures and the packing effect due to a larger extent of hydrophobic confinement. The main reason observed for such enhancement of the free energy barriers was the breaking of the second coordination shell around the lone proton.

The Hydrated Excess Proton in the Zundel Cation H5O2+: The Role of Ultrafast Solvent Fluctuations

AbstractThe nature of the excess proton in liquid water has remained elusive after decades of extensive research. In view of ultrafast structural fluctuations of bulk water scrambling the structural motifs of excess protons in water, we selectively probe prototypical protonated water solvates in acetonitrile on the femtosecond time scale. Focusing on the Zundel cation H5O2+ prepared in room‐temperature acetonitrile, we unravel the distinct character of its vibrational absorption continuum and separate it from OH stretching and bending excitations in transient pump‐probe spectra. The infrared absorption continuum originates from a strong ultrafast frequency modulation of the H+ transfer vibration and its combination and overtones. Vibrational lifetimes of H5O2+ are found to be in the sub‐100 fs range, much shorter than those of unprotonated water. Theoretical results support a picture of proton hydration where fluctuating electrical interactions with the solvent and stochastic thermal excitations of low‐frequency modes continuously modify the proton binding site while affecting its motions.

The Hydrated Excess Proton in the Zundel Cation H5 O2 (+) : The Role of Ultrafast Solvent Fluctuations.

The nature of the excess proton in liquid water has remained elusive after decades of extensive research. In view of ultrafast structural fluctuations of bulk water scrambling the structural motifs of excess protons in water, we selectively probe prototypical protonated water solvates in acetonitrile on the femtosecond time scale. Focusing on the Zundel cation H5 O2 (+) prepared in room-temperature acetonitrile, we unravel the distinct character of its vibrational absorption continuum and separate it from OH stretching and bending excitations in transient pump-probe spectra. The infrared absorption continuum originates from a strong ultrafast frequency modulation of the H(+) transfer vibration and its combination and overtones. Vibrational lifetimes of H5 O2 (+) are found to be in the sub-100 fs range, much shorter than those of unprotonated water. Theoretical results support a picture of proton hydration where fluctuating electrical interactions with the solvent and stochastic thermal excitations of low-frequency modes continuously modify the proton binding site while affecting its motions.

Ultrafast 2D IR spectroscopy of the excess proton in liquid water.

Despite decades of study, the structures adopted to accommodate an excess proton in water and the mechanism by which they interconvert remain elusive. We used ultrafast two-dimensional infrared (2D IR) spectroscopy to investigate protons in aqueous hydrochloric acid solutions. By exciting O-H stretching vibrations and detecting the spectral response throughout the mid-IR region, we observed the interaction between the stretching and bending vibrations characteristic of the flanking waters of the Zundel complex, [H(H2O)2](+), at 3200 and 1760 cm(-1), respectively. From time-dependent shifts of the stretch-bend cross peak, we determined a lower limit on the lifetime of this complex of 480 femtoseconds. These results suggest a key role for the Zundel complex in aqueous proton transfer.