Resolving Heterogeneous Dynamics of Excess Protons in Aqueous Solution with Rate Theory

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.

Fast Structural Dynamics in Concentrated HCl Solutions: From Proton Hopping to the Bulk Viscosity

Concentrated acid solutions, particularly HCl, have been studied extensively to examine the proton hopping and infrared spectral signatures of hydronium ions. Much less attention has been given to the structural dynamics of concentrated HCl solutions. Here, we apply optical heterodyne detected-optical Kerr effect (OHD-OKE) measurements to examine HCl concentration-dependent dynamics from moderate (0.8 m) to very high (15.5 m) concentrations and compare the results to the dynamics of NaCl solutions, as Na+ is similar in size to the hydronium cation. Both HCl and NaCl OHD-OKE signals decay as triexponentials at all concentrations, in contrast to pure water, which decays as a biexponential. Two remarkable features of the HCl dynamics are the following: (1) the bulk viscosity is linearly related to the slowest decay constant, t3, and (2) the concentration-dependent proton hopping times, determined by ab initio MD simulations and 2D IR chemical exchange experiments, both obtained from the literature, fall on the same line as the slowest structural dynamics relaxation time, t3, within experimental error. The structural dynamics of hydronium/chloride/water clusters, with relaxation times t3, are responsible for the concentration dependence of microscopic property of proton hopping and the macroscopic bulk viscosity. The slowest time constant (t3), which does not have a counterpart in pure water, is 3 ps at 0.8 m and increases by a factor of ∼2 by 15.5 m. The two fastest HCl decay constants, t1 and t2, are similar to those of pure water and increase mildly with the concentration.

Tracing mechanistic pathways and reaction kinetics toward equilibrium in reactive molten salts

In the dynamic environment of multi-component reactive molten salts, speciation unfolds as a complex process, involving multiple competing reaction pathways that are likely to face free energy barriers before reaching the reaction equilibria. Herein, we unravel intricate speciation in the AlCl3-KCl melt compositions with rate theory and ab initio molecular dynamics simulations. We find that the compositions with 100 and 50 mol% AlCl3 exclusively comprise neutral Al2Cl6 dimers and charged AlCl4- monomers, respectively. In intermediate AlCl3-KCl compositions, the chemical speciation proves to be a very complex process, requiring over 0.5 nanosecond to reach an equilibrium distribution of multiple species. It is a consequence of the competitive formation and dissociation of additional species, including charged Al dimers, trimers, and tetramers. Here, the species formation occurs through ion exchange events, which we explain by computing free energy landscapes and employing a Marcus-like rate theory. We show that both interspecies and intraspecies ion exchanges are probable and are dictated by the local structural reorganization reflected in the change of local coulombic fields. The species distributions are validated by comparing computed Raman spectra and neutron structure factors with the available experimental data. We find an excellent simulation-experiment agreement in both cases. Nevertheless, Raman spectroscopy turns out to be particularly advantageous for distinguishing between unique species distributions because of the distinct vibrational signatures of different species. The mechanistic insight into reaction dynamics gained in this study will be essential for the advancement of molten salts as reactive media in high-temperature energy applications.

Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer

Water is a key ingredient for life and plays a central role as solvent in many biochemical reactions. However, the intrinsically quantum nature of the hydrogen nucleus, revealing itself in a large variety of physical manifestations, including proton transfer, gives rise to unexpected phenomena whose description is still elusive. Here we study, by a combination of state-of-the-art quantum Monte Carlo methods and path-integral molecular dynamics, the structure and hydrogen-bond dynamics of the protonated water hexamer, the fundamental unit for the hydrated proton. We report a remarkably low thermal expansion of the hydrogen bond from zero temperature up to 300 K, owing to the presence of short-Zundel configurations, characterised by proton delocalisation and favoured by the synergy of nuclear quantum effects and thermal activation. The hydrogen bond strength progressively weakens above 300 K, when localised Eigen-like configurations become relevant. Our analysis, supported by the instanton statistics of shuttling protons, reveals that the near-room-temperature range from 250 K to 300 K is optimal for proton transfer in the protonated water hexamer.

Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

Ionization Difference between Weak and Strong Electrolytes as Perturbed by Conductivity Spectra Analysis

While the static structure of aqueous electrolytes has been studied for decades, their dynamic microscopic structure remains unresolved yet critical in many areas. We report a comparative study of dc and ac (1 Hz to 20 GHz) conductivity data of weak and strong electrolytes, highlighting previously missing differences and similarities. Based on these results, we introduce into consideration the intrinsic short-lived ions of water, namely, excess protons (H₃O⁺) and proton holes (OH^-). We show that the model accounting for the neutralization of these ions by the species of electrolyte explains the conductivity of aqueous solutions in the concentration range 10^-7-10 M. Based on independent experimental data, we hypothesize that the aggregation of the species in weak electrolytes may determine the main difference between the conductivity of weak and strong electrolytes. Our results push forward the understanding of the dynamic structure of aqueous electrolyte solutions and are important to nanofluidic, biological, and electrochemical systems.

Generalized Transition State Theory Treatment of Water-Assisted Proton Transport Processes in Proteins

Transition state theory (TST) is widely employed for estimating the transition rate of a reaction when combined with free energy sampling techniques. A derivation of the transition theory rate expression for a general n-dimensional case is presented in this work which specifically focuses on water-assisted proton transfer/transport reactions, especially for protein systems. Our work evaluates the TST prefactor calculated at the transition state dividing surface compared to one sampled, as an approximation, in the reactant state in four case studies of water-assisted proton transport inside membrane proteins and highlights the significant impact of the prefactor position dependence in proton transport processes.

Nucleation Rate Theory for Coordination Number: Elucidating Water-Mediated Formation of a Zigzag Na2SO4 Morphology

Predicting and controlling nanostructure formation during nucleation can pave the way to synthesizing novel energy materials via crystallization. However, such control over nucleation and crystallization remains challenging due to an inadequate understanding of critical factors that govern evolving atomistic structures and dynamics. Herein, we utilize coordination number as a reaction coordinate and rate theory to investigate how sodium sulfate, commonly known as a phase-change energy material, nucleates in a supersaturated aqueous solution. In conjunction with ab initio and force field-based molecular dynamics simulation, the rate theoretical analysis reveals that sodium sulfate from an initially dissolved metastable state transits to a heterogeneous mixture of prenucleated clusters and finally to a large cylindrical zigzag morphology. Measurements of Raman spectra and their ab initio modeling confirm that this nucleated morphology contains a few waters for every sulfate. Rate processes such as solvent exchange and desolvation exhibit high sensitivity to the evolving prenucleation/nucleation structures, providing a means to distinguish between critical nucleation precursors. Desolvation and forming the first-shell interionic coordination structure via monomer-by-monomer addition around sulfates are found to explain the formation of large nuclei. Thus, a detailed understanding of the step-by-step structure formation across scales has been achieved. This can be leveraged to predict nucleation-related structures and dynamics and potentially control the synthesis of novel phase-change materials for energy applications.

Proton-transfer spectroscopy beyond the normal-mode scenario

A stochastic theory is developed to predict the spectral signature of proton-transfer processes and is applied to infrared spectra computed from ab initio molecular-dynamics simulations of a single [Formula: see text] cation. By constraining the oxygen atoms to a fixed distance, this system serves as a tunable model for general proton-transfer processes with variable barrier height. Three spectral contributions at distinct frequencies are identified and analytically predicted: the quasi-harmonic motion around the most probable configuration, amenable to normal-mode analysis, the contribution due to transfer paths when the proton moves over the barrier, and a shoulder for low frequencies stemming from the stochastic transfer-waiting-time distribution; the latter two contributions are not captured by normal-mode analysis but exclusively reported on the proton-transfer kinetics. In accordance with reaction rate theory, the transfer-waiting-contribution frequency depends inversely exponentially on the barrier height, whereas the transfer-path-contribution frequency is rather insensitive to the barrier height.

Spectral signatures of excess-proton waiting and transfer-path dynamics in aqueous hydrochloric acid solutions

The theoretical basis for linking spectral signatures of hydrated excess protons with microscopic proton-transfer mechanisms has so far relied on normal-mode analysis. We introduce trajectory-decomposition techniques to analyze the excess-proton dynamics in ab initio molecular-dynamics simulations of aqueous hydrochloric-acid solutions beyond the normal-mode scenario. We show that the actual proton transfer between two water molecules involves for relatively large water-water separations crossing of a free-energy barrier and thus is not a normal mode, rather it is characterized by two non-vibrational time scales: Firstly, the broadly distributed waiting time for transfer to occur with a mean value of 200-300 fs, which leads to a broad and weak shoulder in the absorption spectrum around 100 cm-1, consistent with our experimental THz spectra. Secondly, the mean duration of a transfer event of about 14 fs, which produces a rather well-defined spectral contribution around 1200 cm-1 and agrees in location and width with previous experimental mid-infrared spectra.

Protonation of Serine in Gas and Condensed and Microsolvated States in Aqueous Solution

Identification of molecules and elucidation of their chemical structure are ubiquitous problems in chemistry. Mass spectrometry (MS) can be used due to its sensitivity and versatility. For detection to occur, analytes must be ionized and transferred to the gas phase. Soft ionization processes such as electrospray ionization are popular; however, resulting microsolvated phases can alter the chemistry of analytes and therefore detection and identification. To understand these processes, we use computational methods to probe the ionization propensity of serine in the gas phase, aqueous microsolvated clusters, and aqueous solution. We show that the tautomeric form of serine is altered by the presence of water, as five water molecules can stabilize the zwitterionic tautomer. Inclusion of cosolutes such as ions can stabilize the zwitterion with as few as one or two water molecules present. We demonstrate that ionization propensity, as measured by gas phase bacisity, can increase by over 100 kJ/mol when placed in a small water-serine cluster, showing the sensitivity of the chemistry of microsolvated analytes. Finally, detailed analysis reveals that small droplets (less than seven water molecules) are extremely sensitive to addition of further water molecules. Beyond this limit, structural and electronic properties change little with droplet size.

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.

A Holistic Approach for Elucidating Local Structure, Dynamics, and Speciation in Molten Salts with High Structural Disorder

To examine ion solvation, exchange, and speciation for minority components in molten salts (MS) typically found as corrosion products, we propose a multimodal approach combining extended X-ray absorption fine structure (EXAFS) spectroscopy, optical spectroscopy, ab initio molecular dynamics (AIMD) simulations, and rate theory of ion exchange. Going beyond conventional EXAFS analysis, our method can accurately quantify populations of different coordination states of ions with highly disordered coordination environments via linear combination fitting of the EXAFS spectra of these coordination states computed from AIMD to the experimental EXAFS spectrum. In a case study of dilute Ni(II) dissolved in the ZnCl₂+KCl melts, our method reveals heterogeneous distributions of coordination states of Ni(II) that are sensitive to variations in temperature and melt composition. These results are fully explained by the difference in the chloride exchange dynamics at varied temperatures and melt compositions. This insight will enable a better understanding and control of ion solubility and transport in MS.

Characterizing and Contrasting Structural Proton Transport Mechanisms in Azole Hydrogen Bond Networks Using Ab Initio Molecular Dynamics

Imidazole and 1,2,3-triazole are promising hydrogen-bonded heterocycles that conduct protons via a structural mechanism and whose derivatives are present in systems ranging from biological proton channels to proton exchange membrane fuel cells. Here, we leverage multiple time-stepping to perform ab initio molecular dynamics of imidazole and 1,2,3-triazole at the nanosecond time scale. We show that despite the close structural similarities of these compounds, their proton diffusion constants vary by over an order of magnitude. Our simulations reveal the reasons for these differences in diffusion constants, which range from the degree of hydrogen-bonded chain linearity to the effect of the central nitrogen atom in 1,2,3-triazole on proton transport. In particular, we uncover evidence of two "blocking" mechanisms in 1,2,3-triazole, where covalent and hydrogen bonds formed by the central nitrogen atom limit the mobility of protons. Our simulations thus provide insights into the origins of the experimentally observed 10-fold difference in proton conductivity.

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.

X-ray scattering reveals ion clustering of dilute chromium species in molten chloride medium

Enhancing the solar energy storage and power delivery afforded by emerging molten salt-based technologies requires a fundamental understanding of the complex interplay between structure and dynamics of the ions in the high-temperature media. Here we report results from a comprehensive study integrating synchrotron X-ray scattering experiments, ab initio molecular dynamics simulations and rate theory concepts to investigate the behavior of dilute Cr3+ metal ions in a molten KCl-MgCl2 salt. Our analysis of experimental results assisted by a hybrid transition state-Marcus theory model reveals unexpected clustering of chromium species leading to the formation of persistent octahedral Cr-Cr dimers in the high-temperature low Cr3+ concentration melt. Furthermore, our integrated approach shows that dynamical processes in the molten salt system are primarily governed by the charge density of the constituent ions, with Cr3+ exhibiting the slowest short-time dynamics. These findings challenge several assumptions regarding specific ionic interactions and transport in molten salts, where aggregation of dilute species is not statistically expected, particularly at high temperature.

Molecular Origins of the Barriers to Proton Transport in Acidic Aqueous Solutions

The self-consistent iterative multistate empirical valence bond (SCI-MS-EVB) method is used to analyze the structure, thermodynamics, and dynamics of hydrochloric acid solutions. The reorientation time scales of irreversible proton transport are elucidated by simulating 0.43, 0.85, 1.68, and 3.26 M HCl solutions at 270, 285, 300, 315, and 330 K. The results indicate increased counterion pairing with increasing concentration, which manifests itself via a reduced hydronium oxygen-chloride (O*-Cl) structuring in the radial distribution functions. Increasing ionic concentration also reduces the diffusion of the hydrated excess protons, principally by reducing the contribution of the Grotthuss proton hopping (shuttling) mechanism to the overall diffusion process. In agreement with prior experimental findings, a decrease in the activation energy of reorientation time scales was also observed, which is explicitly explained by using activated rate theory and an energy-entropy decomposition of the state-averaged radial distribution functions. These results provide atomistic verification of suggestions from recent two-dimensional infrared spectroscopy experiments that chloride anions (as opposed to hydrated excess protons) create entropic barriers to proton transport.

Decoding the 2D IR spectrum of the aqueous proton with high-level VSCF/VCI calculations

The aqueous proton is a common and long-studied species in chemistry, yet there is currently intense interest devoted to understanding its hydration structure and transport dynamics. Typically described in terms of two limiting structures observed in gas-phase clusters, the Zundel H₅O₂ ⁺ and Eigen H₉O₄ ⁺ ions, the aqueous structure is less clear due to the heterogeneity of hydrogen bonding environments and room-temperature structural fluctuations in water. The linear infrared (IR) spectrum, which reports on structural configurations, is challenging to interpret because it appears as a continuum of absorption, and the underlying vibrational modes are strongly anharmonically coupled to each other. Recent two-dimensional IR (2D IR) experiments presented strong evidence for asymmetric Zundel-like motifs in solution, but true structure-spectrum correlations are missing and complicated by the anharmonicity of the system. In this study, we employ high-level vibrational self-consistent field/virtual state configuration interaction calculations to demonstrate that the 2D IR spectrum reports on a broad distribution of geometric configurations of the aqueous proton. We find that the diagonal 2D IR spectrum around 1200 cm^-1 is dominated by the proton stretch vibrations of Zundel-like and intermediate geometries, broadened by the heterogeneity of aqueous configurations. There is a wide distribution of multidimensional potential shapes for the proton stretching vibration with varying degrees of potential asymmetry and confinement. Finally, we find specific cross peak patterns due to aqueous Zundel-like species. These studies provide clarity on highly debated spectral assignments and stringent spectroscopic benchmarks for future simulations.