Understanding and Tracking the Excess Proton in Ab Initio Simulations; Insights from IR Spectra

Data-driven molecular dynamics simulation of water isotope separation using a catalytically active ultrathin membrane

Water isotope separation, specifically separating heavy from light water, is a technologically important problem due to the usage of heavy water in applications such as nuclear magnetic resonance, nuclear power, and spectroscopy. Separation of heavy water from light water is difficult due to very similar physical and chemical properties between the isotopes. We show that a catalytically active ultrathin membrane (e.g., a nanopore in MoS2) can enable chemical exchange processes and physicochemical mechanisms that lead to efficient separation of deuterium from hydrogen. The separation process is inherently multiscale in nature with the shorter times representing chemical exchange processes and the longer timescales representing the transport phenomena. To bridge the timescales, we employ a deep learning methodology which uses short time scale ab initio molecular dynamics data for training and extends the timescales to the classical molecular dynamics regime to demonstrate isotope separation and reveal the underlying complex physicochemical processes.

Reshaping the QM Region On-the-Fly: Adaptive-Shape QM/MM Dynamic Simulations of a Hydrated Proton in Bulk Water

Adaptive quantum mechanics/molecular mechanics (QM/MM) reclassifies on-the-fly a molecule or molecular fragment as QM or MM during dynamics simulations without abrupt changes in the energy or forces. Notably, the permuted adaptive-partitioning (PAP) algorithms have been applied to simulate a hydrated proton, with a mobile QM zone anchored at a pseudoatom called a proton indicator. The position of the proton indicator approximates the location of the delocalized excess proton, yielding a smooth trajectory of the proton diffusing via the Grotthuss mechanism in aqueous solutions. The mobile QM zone, which has been taken to be a sphere with a preset radius, follows the proton wherever it goes. Although the simulations are successful, the use of a spherical QM zone has one disadvantage: A large preset radius must be utilized to minimize the chance of missing water molecules that are important to proton translocation. A large radius leads to a large QM zone, which is computationally expensive. In this work, we report a new way to set up the QM zone, where one includes only the water molecules important to proton transfer. The importance of a given water molecule is quantified by its "weight" that depends on its relation to the reaction path of proton transfer. The weight varies smoothly, ensuring that a water molecule gradually appears in or disappears from the QM zone without abrupt changes, as required by the PAP method. Consequently, the shape of the QM zone evolves on-the-fly, keeping the QM zone as small as possible and as large as necessary. Test simulations demonstrate that the new algorithm significantly improves the computation efficiency while maintaining the proper descriptions of proton transfer in bulk water.

In Silico Demonstration of Fast Anhydrous Proton Conduction on Graphanol

Development of new materials capable of conducting protons in the absence of water is crucial for improving the performance, reducing the cost, and extending the operating conditions for proton exchange membrane fuel cells. We present detailed atomistic simulations showing that graphanol (hydroxylated graphane) will conduct protons anhydrously with very low diffusion barriers. We developed a deep learning potential (DP) for graphanol that has near-density functional theory accuracy but requires a very small fraction of the computational cost. We used our DP to calculate proton self-diffusion coefficients as a function of temperature, to estimate the overall barrier to proton diffusion, and to characterize the impact of thermal fluctuations as a function of system size. We propose and test a detailed mechanism for proton conduction on the surface of graphanol. We show that protons can rapidly hop along Grotthuss chains containing several hydroxyl groups aligned such that hydrogen bonds allow for conduction of protons forward and backward along the chain without hydroxyl group rotation. Long-range proton transport only takes place as new Grotthuss chains are formed by rotation of one or more hydroxyl groups in the chain. Thus, the overall diffusion barrier consists of a convolution of the intrinsic proton hopping barrier and the intrinsic hydroxyl rotation barrier. Our results provide a set of design rules for developing new anhydrous proton conducting membranes with even lower diffusion barriers.

Highly Altered State of Proton Transport in Acid Pools in Charged Reverse Micelles

Transport mechanisms of solvated protons of 1 M HCl acid pools, confined within reverse micelles (RMs) containing the negatively charged surfactant sodium bis(2-ethylhexyl) sulfosuccinate (NaAOT) or the positively charged cetyltrimethylammonium bromide (CTABr), are analyzed with reactive force field simulations to interpret dynamical signatures from TeraHertz absorption and dielectric relaxation spectroscopy. We find that the forward proton hopping events for NaAOT are further suppressed compared to a nonionic RM, while the Grotthuss mechanism ceases altogether for CTABr. We attribute the sluggish proton dynamics for both charged RMs as due to headgroup and counterion charges that expel hydronium and chloride ions from the interface and into the bulk interior, thereby increasing the pH of the acid pools relative to the nonionic RM. For charged NaAOT and CTABr RMs, the localization of hydronium near a counterion or conjugate base reduces the Eigen and Zundel configurations that enable forward hopping. Thus, localized oscillatory hopping dominates, an effect that is most extreme for CTABr in which the proton residence time increases dramatically such that even oscillatory hopping is slow.

Tracking the Delocalized Proton in Concerted Proton Transfer in Bulk Water

A solvated proton in water is often characterized as a charge or structural defect, and it is important to track its evolution on-the-fly in certain dynamics simulations. Previously, we introduced the proton indicator, a pseudo-atom, whose position approximates the location of the excess proton modeled as a structural defect. The proton indicator generally yields a smooth trajectory of a hydrated proton diffusing in aqueous solutions, including in the events of stepwise proton transfer via the Grotthuss mechanism; however, the proton indicator did not perform well in the events of concerted proton transfer, for which it occasionally yielded large position displacements between two successive time steps. To overcome this hurdle, we develop a new algorithm of a proton indicator with greatly enhanced performance for concerted proton transfer in bulk water. A protocol is proposed to exhaustively explore the hydrogen-bonding network of the water wires over which the excess proton is delocalized and to properly account for the contributions of the water molecules in this network as the geometry evolves. The new proton indicator (called Indicator 2.0) is assessed in dynamics simulations of an excess proton in bulk water and in specially constructed model systems of more complex architectures. The results demonstrate that the new indicator yields a smooth trajectory in both stepwise and concerted proton transfers.

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.

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.

Improved Indicator Algorithms for Tracking a Hydrated Proton as A Local Structural Defect in Grotthuss Diffusion in Aqueous Solutions

Keeping track of a hydrated proton in dynamics simulations is important and nontrivial. Here, we report two revised algorithms for the proton indicator, a pseudo-atom whose position approximates the location of an excess proton diffusing via the Grotthuss mechanism in aqueous solution. The new methods describe the delocalized proton as a structural defect. Encouragingly, in test simulations of a hydrated proton in bulk water, the new algorithms substantially outperform the original scheme by significantly reducing large displacements in the indicator positions upon donor switch, yielding smoother trajectories that effectively track the movement of the solvated proton.

Chemistrees: Data-Driven Identification of Reaction Pathways via Machine Learning

We propose to analyze molecular dynamics (MD) output via a supervised machine learning (ML) algorithm, the decision tree. The approach aims to identify the predominant geometric features which correlate with trajectories that transition between two arbitrarily defined states. The data-driven algorithm aims to identify these features without the bias of human “chemical intuition”. We demonstrate the method by analyzing the proton exchange reactions in formic acid solvated in small water clusters. The simulations were performed with ab initio MD combined with a method to efficiently sample the rare event, path sampling. Our ML analysis identified relevant geometric variables involved in the proton transfer reaction and how they may change as the number of solvating water molecules changes.

Using Constrained Density Functional Theory to Track Proton Transfers and to Sample Their Associated Free Energy Surface

Ab initio molecular dynamics (AIMD) and quantum mechanics/molecular mechanics (QM/MM) methods are powerful tools for studying proton solvation, transfer, and transport processes in various environments. However, due to the high computational cost of such methods, achieving sufficient sampling of rare events involving excess proton motion-especially when Grotthuss proton shuttling is involved-usually requires enhanced free energy sampling methods to obtain informative results. Moreover, an appropriate collective variable (CV) that describes the effective position of the net positive charge defect associated with an excess proton is essential both for tracking the trajectory of the defect and for the free energy sampling of the processes associated with the resulting proton transfer and transport. In this work, such a CV is derived from first principles using constrained density functional theory (CDFT). This CV is applicable to a broad array of proton transport and transfer processes as studied via AIMD and QM/MM simulations.

Proton Traffic Jam: Effect of Nanoconfinement and Acid Concentration on Proton Hopping Mechanism

The properties of the water network in concentrated HCl acid pools in nanometer-sized reverse non-ionic micelles were probed with TeraHertz absorption, dielectric relaxation spectroscopy, and reactive force field simulations capable of describing proton hopping mechanisms. We identify that only at a critical micelle size of W0=9 do solvated proton complexes form in the water pool, accompanied by a change in mechanism from Grotthuss forward shuttling to one that favors local oscillatory hopping. This is due to a preference for H+ and Cl- ions to adsorb to the micelle interface, together with an acid concentration effect that causes a "traffic jam" in which the short-circuiting of the hydrogen-bonding motif of the hydronium ion decreases the forward hopping rate throughout the water interior even as the micelle size increases. These findings have implications for atmospheric chemistry, biochemical and biophysical environments, and energy materials, as transport of protons vital to these processes can be suppressed due to confinement, aggregation, and/or concentration.

Structural Characterization of Protonated Water Clusters Confined in HZSM-5 Zeolites

A molecular description of the structure and behavior of water confined in aluminosilicate zeolite pores is a crucial component for understanding zeolite acid chemistry under hydrous conditions. In this study, we use a combination of ultrafast two-dimensional infrared (2D IR) spectroscopy and ab initio molecular dynamics (AIMD) to study H₂O confined in the pores of highly hydrated zeolite HZSM-5 (∼13 and ∼6 equivalents of H₂O per Al atom). The 2D IR spectrum reveals correlations between the vibrations of both terminal and H-bonded O-H groups and the continuum absorption of the excess proton. These data are used to characterize the hydrogen-bonding network within the cluster by quantifying single-, double-, and non-hydrogen-bond donor water molecules. These results are found to be in good agreement with the statistics calculated from an AIMD simulation of an H⁺(H₂O)₈ cluster in HZSM-5. Furthermore, IR spectral assignments to local O-H environments are validated with DFT calculations on clusters drawn from AIMD simulations. The simulations reveal that the excess charge is detached from the zeolite and resides near the more highly coordinated water molecules in the cluster. When they are taken together, these results unambiguously assign the complex IR spectrum of highly hydrated HZSM-5, providing quantitative information on the molecular environments and hydrogen-bonding topology of protonated water clusters under extreme confinement.

Key computational findings reveal proton transfer as driving the functional cycle in the phosphate transporter PiPT

Phosphate is an indispensable metabolite in a wide variety of cells and is involved in nucleotide and lipid synthesis, signaling, and chemical energy storage. Proton-coupled phosphate transporters within the major facilitator family are crucial for phosphate uptake in plants and fungi. Similar proton-coupled phosphate transporters have been found in different protozoan parasites that cause human diseases, in breast cancer cells with elevated phosphate demand, in osteoclast-like cells during bone reabsorption, and in human intestinal Caco2BBE cells for phosphate homeostasis. However, the mechanism of proton-driven phosphate transport remains unclear. Here, we demonstrate in a eukaryotic, high-affinity phosphate transporter from Piriformospora indica (PiPT) that deprotonation of aspartate 324 (D324) triggers phosphate release. Quantum mechanics/molecular mechanics molecular dynamics simulations combined with free energy sampling have been employed here to identify the proton transport pathways from D324 upon the transition from the occluded structure to the inward open structure and phosphate release. The computational insights so gained are then corroborated by studies of D45N and D45E amino acid substitutions via mutagenesis experiments. Our findings confirm the function of the structurally predicted cytosolic proton exit tunnel and suggest insights into the role of the titratable phosphate substrate.

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.

Actual Symmetry of Symmetric Molecular Adducts in the Gas Phase, Solution and in the Solid State

This review discusses molecular adducts, whose composition allows a symmetric structure. Such adducts are popular model systems, as they are useful for analyzing the effect of structure on the property selected for study since they allow one to reduce the number of parameters. The main objectives of this discussion are to evaluate the influence of the surroundings on the symmetry of these adducts, steric hindrances within the adducts, competition between different noncovalent interactions responsible for stabilizing the adducts, and experimental methods that can be used to study the symmetry at different time scales. This review considers the following central binding units: hydrogen (proton), halogen (anion), metal (cation), water (hydrogen peroxide).

Molecular Conformation and Hydrogen Bond Formation in Liquid Ethylene Glycol

The ethylene glycol (EG) molecule, HOCH₂CH₂OH, adopts a conformation where the central OCCO dihedral is exclusively gauche in the gaseous and crystalline states, but in the liquid state, for close to 20% of the molecules, the central OCCO adopts the energetically unfavorable trans conformation. Here we report calculations, based on ab initio molecular dynamics simulations, on the thermodynamics associated with hydrogen bond formation in the liquid state of EG between donor-acceptor pairs with different molecular conformations. We establish an operational, geometric definition of hydrogen bonds in liquid EG from an analysis of the proton NMR data and show that the key feature, irrespective of the conformation, is marked directionality with almost linear ∠HO···O angles. The free energy for hydrogen bond formation estimated as the potential of mean force for the reversible work associated with the passage from a hypothetical state where hydrogen bonding is absent and donor-acceptor pairs are randomly oriented to the hydrogen-bonded state where the pairs are oriented showed comparable magnitudes irrespective of the molecular conformation of either the donor or acceptor. The results suggest that the presence of the trans conformer in liquid EG would require an understanding of its role in the extended hydrogen-bonded network of the liquid.

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.