Protonated Water Clusters Research Articles

Electron-electron-ion triple-coincidence experiment of electron-initiated valence ionization of small water clusters

The ionization and fragmentation of small water clusters induced by electron impact (80 eV) is investigated. Using a multiparticle coincidence spectrometer (reaction microscope), all three charged final state particles—two outgoing electrons and one fragment ion—are detected. Nonprotonated (H2O)2+ and protonated water clusters H3O+, [H2O]2H+, [H2O]4H+, and [H2O]5H+ are identified in the measured ion spectrum. The ionization channels for formation of these species are investigated by measuring the kinetic energy distributions and the electronic states of the ions. Only a single state can lead to (H2O)2+, which is identified as ionization of water dimer with a 1b1 hole at the hydrogen bonding donor molecule, while for the protonated water species three major electronic states corresponding to the ionization of 1b1, 3a1, and 1b2 type orbitals are observed. Published by the American Physical Society 2024

Impact of Nuclear Quantum Effects on the Structural Properties of Protonated Water Clusters.

Nuclear quantum effects (NQEs) play a crucial role in hydrogen-bonded systems due to quantum tunneling and proton fluctuation. Our understanding of how NQEs affect microstructures mainly focuses on bulk phases of liquids and solids but remains deficient for water clusters, including their hydrogen nuclei, hydrogen-bonded configurations, and temperature dependence. Here, we conducted ab initio molecular dynamics (MD) and path integral MD simulations to investigate the influence of NQEs on the structural properties of protonated water clusters H+(H2O)n (n = 3, 6, 9, 12). The results reveal that the NQEs become less evident as the cluster size increases due to the competition between NQEs and electrostatic interactions. Simulations of several H+(H2O)6 isomers at different temperatures indicate that the effect of elevated temperature on proton transfer is related to the initial structure. Interestingly, the process of proton transfer also involves the interconversion between Zundel-type and Eigen-type isomers. These findings significantly deepen our understanding of ion-water and water-water interactions, opening new avenues for the study of hydrated ion clusters and related systems.

Correlations between the Structures and Spectra of Protonated Water Clusters.

Badger's rule-like correlations between OH stretching frequencies and intensities and the OH bond length are used to develop a spectral mapping procedure for studies of pure and protonated water clusters. This approach utilizes the vibrationally averaged OH bond lengths, which were obtained from diffusion Monte Carlo simulations that were performed using the general potential developed by Yu and Bowman. Good agreement is achieved between the spectra obtained using this approach and previously reported spectra for H+(H2O)n clusters, with n = 3, 4, and 5, as well as their perdeuterated analogues. The analysis of the spectra obtained by this spectral mapping approach supports previous work that assigned the spectrum of H+(H2O)6 to a mixture of Eigen and Zundel-like structures. Analysis of the calculated spectra also suggests a reassignment of the frequency of one of the transitions that involves the OH stretching vibration of the OH bonds in the hydronium core in the Eigen-like structure of H+(H2O)6 from 1917 cm-1 to roughly 2100 cm-1. For D+(D2O)6, comparison of the measured spectrum to those obtained by using the spectral mapping approach suggests that the carrier of the measured spectrum is one or more of the isomers of D+(D2O)6 that contain a four-membered ring and two flanking water molecules. While there are several candidate structures, the two flanking water molecules most likely form a chain that is bound to the hydronium core.

Threshold collision induced dissociation of protonated water clusters.

We report threshold collision induced dissociation experiments on protonated water clusters thermalized at low temperature for sizes n = 19-23. Fragmentation cross sections are recorded as a function of the collision energy and analyzed with a statistical model. This model allows us to account for dissociation cascades and provides values for the dissociation energies of each cluster. These values, averaging around 0.47eV, are in good agreement with theoretical predictions at various levels of theory. Furthermore, the dissociation energies show a trend for the n = 21 magic and n = 22 anti-magic numbers relative to their neighbours, which is also in agreement with theory. These results provide further evidence to resolve the disagreement between previously published experimental values. A careful quantitative treatment of cascade dissociation in this model introduces interdependence between the dissociation energies of neighboring sizes, which reduces the number of free fitting parameters and improves both reliability and uncertainties on absolute dissociation energies deduced from experiments.

Accessibility of Lithium Cations in VSH‐2 Zeotype: Structural Effects and Formation of Protonated Water Clusters

AbstractThe accessibility of lithium cations in microporous vanadosilicate VSH‐2Cs of composition Cs2(VO)(Si6O14) ⋅ 3H2O was investigated by Single Crystal X‐ray Diffraction, Attenuated Total Reflection Fourier Transformed Infrared Spectroscopy and Density Functional Theory calculations. The topological symmetry of VSH‐2Cs is described in space group Cmca. After Li‐ion exchange, the structure of VSH‐2Li adopted monoclinic symmetry (space group C2/c) with a=17.011(2) Å, b=8.8533(11) Å, c=12.4934(16) Å, β=91.677(4)°, V=1880.7(4) Å3. The strong interactions between Li ions and oxygen‐framework atoms drive the main deformation mechanism, which is based on cooperative rotation of SiO4 and VO5 units around their oxygen atoms that behave as hinges. Exchange of Cs+ by Li+ is incomplete and accompanied by the formation of protonated species to counterbalance the electrostatic charge. The incorporation of protons is mediated by the presence of water dimers in the structural channels. H2O molecules in VSH‐2Li account not only as “space‐fillers” after the removal of large Cs ions but also mediate proton transfer to compensate the negative charge of the host vanadosilicate framework.

Internal Proton Transfer in the Activation of Heliorhodopsin

Heliorhodopsin (HeR), a recently discovered new rhodopsin family, contains a single counterion of the protonated Schiff base, E108 in HeR from Thermoplasmatales archaeon SG8-52-1 (TaHeR). Upon light absorption, the M and O intermediates form in HeRs, as well as type-1 microbial rhodopsins, indicating that the proton transfer from the Schiff base leads to the activation of HeRs. The present flash photolysis study of TaHeR in the presence of a pH-sensitive dye showed that TaHeR contains a proton-accepting group (PAG) inside protein. Comprehensive mutation study of TaHeR found the E108D mutant abolishing the M formation, which is not only at pH 8, but also at pH 9 and 10. The lack of M observation does not originate from the short lifetime of the M intermediate in E108D, as FTIR spectroscopy revealed that a red-shifted K-like intermediate is long lived in E108D. It is likely that the K-like intermediate returns to the unphotolyzed state without internal proton transfer in E108D. E108 and D108 are the Schiff base counterions of the wild-type and E108D mutant TaHeR, respectively, whereas small difference in length of side chains determine internal proton transfer reaction from the Schiff base. Based on the present finding, we propose that the internal water cluster (four water molecules) constitutes PAG in the M intermediate of TaHeR. In the wild type TaHeR, a protonated water cluster is stabilized by forming a salt bridge with E108. In contrast, slightly shortened counterion (D108) cannot stabilize the protonated water cluster in E108D, and thus impairs internal proton transfer from the Schiff base.

Nuclear Motion Is Classical: Spectrum of a Magic Protonated Water Cluster.

The assumption that nuclear motion is classical explains many phenomena. The problems of Schrödinger's cat and the EPR paradoxon do not exist in a perfectly deterministic theory. All it needs is to describe nuclear motion classically right from the beginning. To establish this simple idea, it must be tested for as many examples as possible. In the present paper, we use ab initio molecular dynamics to investigate the infrared spectrum of a 'magic' protonated water cluster H3O+(H2O)20 which exhibits some features that were believed to afford a quantum treatment of nuclear motion. The role of the temperature in contrast to a quantum mechanical description is discussed.

Magic Numbers and Stabilities of Photoionized Water Clusters: Computational and Experimental Characterization of the Nanosolvated Hydronium Ion.

The stability and distributions of small water clusters generated in a supersonic beam expansion are interrogated by tunable vacuum ultraviolet (VUV) radiation generated at a synchrotron. Time-of-flight mass spectrometry reveals enhanced population of various protonated water clusters (H+(H2O)n) based upon ionization energy and photoionization distance from source, suggesting there are "magic" numbers below the traditional n = 21 that predominates in the literature. These intensity distributions suggest that VUV threshold photoionization (11.0-11.5 eV) of neutral water clusters close to the nozzle exit leads to a different nonequilibrium state compared to a skimmed molecular beam. This results in the appearance of a new magic number at 14. Metadynamics conformer searches coupled with modern density functional calculations are used to identify the global minimum energy structures of protonated water clusters between n = 2 and 21, as well as the manifold of low-lying metastable minima. New lowest energy structures are reported for the cases of n = 5, 6, 11, 12, 16, and 18, and special stability is identified by several measures. These theoretical results are in agreement with the experiments performed in this work in that n = 14 is shown to exhibit additional stability, based on the computed second-order stabilization energy relative to most cluster sizes, though not to the extent of the well-known n = 21 cluster. Other cluster sizes that show some additional energetic stability are n = 7, 9, 12, 17, and 19. To gain insight into the balance between ion-water and water-water interactions as a function of the cluster size, an analysis of the effective two-body interactions (which sum exactly to the total interaction energy) was performed. This analysis reveals a crossover as a function of cluster size between a water-hydronium-dominated regime for small clusters and a water-water-dominated regime for larger clusters around n = 17.

Formation of Eigen or Zundel Features at Protonated Water Cluster-Aromatic Interfaces.

Interfacial interactions of protonated water clusters adsorbed at aromatic surfaces play an important role in biology, and in atmospheric, chemical and materials sciences. Here, we investigate the interaction of protonated water clusters ((H+H2O)n (where n = 1 - 3)) with benzene (Bz), coronene (Cor) and dodecabenzocoronene (Dbc)). To study the structure, stability and spectral features of these complexes, computations are done using DFT-PBE0(+D3) and SAPT0 methods. These interactions are probed by AIM electron density topography and non-covalent index (NCI) analyses. We suggest that the excess proton plays a crucial role in the stability of these model interfaces through strong inductive effects and the formation of Eigen or Zundel features. Also, computations reveal that the extension of the π-aromatic system and the increase of the number of water molecules in the H-bounded water network lead to a strengthening of the interactions between the corresponding aromatic compound and protonated water molecules, except when a Zundel ion is formed. The present findings may serve to understand in-depth the role of proton localized at aqueous medium interacting with large aromatic surfaces such as graphene interacting with acidic liquid water. Besides, we give their IR and UV-Vis spectra , which may help for their identification.

Optimal Mode Combination in the Multiconfiguration Time-Dependent Hartree Method through Multivariate Statistics: Factor Analysis and Hierarchical Clustering.

The multiconfiguration time-dependent Hartree (MCTDH) method and its multilayer extension (ML-MCTDH) are powerful algorithms for the efficient computation of nuclear quantum dynamics in high-dimensional systems. By providing time-dependent variational orbitals and an optimal choice of layered effective degrees of freedom, one is able to reduce the computational cost to an amenable number of configurations. However, choices related to selecting properly the mode grouping and tensor tree are strongly system dependent and, thus far, subjectively based on intuition and/or experience. Therefore, herein we detail a new protocol based on multivariate statistics─more specifically, factor analysis and hierarchical clustering─for a reliable and convenient guiding in the optimal design of such complex "system-of-systems" tensor-network decompositions. The advantages of employing the new algorithm and its applicability are tested on water and two floppy protonated water clusters with large amplitude motions.

Second-Order Self-Consistent Field Algorithms: From Classical to Quantum Nuclei

This work presents a general framework for deriving exact and approximate Newton self-consistent field (SCF) orbital optimization algorithms by leveraging concepts borrowed from differential geometry. Within this framework, we extend the augmented Roothaan-Hall (ARH) algorithm to unrestricted electronic and nuclear-electronic calculations. We demonstrate that ARH yields an excellent compromise between stability and computational cost for SCF problems that are hard to converge with conventional first-order optimization strategies. In the electronic case, we show that ARH overcomes the slow convergence of orbitals in strongly correlated molecules with the example of several iron-sulfur clusters. For nuclear-electronic calculations, ARH significantly enhances the convergence already for small molecules, as demonstrated for a series of protonated water clusters.

Fragment imaging in the infrared photodissociation of the Ar-tagged protonated water clusters H3O+-Ar and H+(H2O)2-Ar.

Infrared photodissociation of protonated water clusters with an Ar atom, namely H3O+-Ar and H+(H2O)2-Ar, was investigated by an imaging technique for mass-selected ions, to reveal the intra- and intermolecular vibrational dynamics. The presented system has the advantage of achieving fragment ion images with the cluster size- and mode-selective photoexcitation of each OH stretching vibration. Translational energy distributions of photofragments were obtained from the images upon the excitation of the bound (νb) and free (νf) OH stretching vibrations. The energy fractions in the translational motion were compared between νbI and νfI in H3O+-Ar or between νbII and νfII in H+(H2O)2-Ar, where the labels "I" and "II" represent H3O+-Ar and H+(H2O)2-Ar, respectively. In H3O+-Ar, the νfI excitation exhibited a smaller translational energy than νbI. This result can be explained by the higher vibrational energy of νfI, which enabled it to produce bending (ν4) excited H3O+ fragments that should be favored according to the energy-gap model. In contrast to H3O+-Ar, the νbII excitation of an Ar-tagged H2O subunit and the νfII excitation of an untagged H2O subunit resulted in very similar translational energy distributions in H+(H2O)2-Ar. The similar energy fractions independent of the excited H2O subunits suggested that the νbII and νfII excited states relaxed into a common intermediate state, in which the vibrational energy was delocalized within the H2O-H+-H2O moiety. However, the translational energy distributions for H+(H2O)2-Ar did not agree with a statistical dissociation model, which implied another aspect of the process, that is, Ar dissociation via incomplete energy randomization in the whole H+(H2O)2-Ar cluster.

Adaptive regularized Gaussian process regression for application in the context of hydrogen adsorption on graphene sheets.

We present a Gaussian process regression (GPR) scheme with an adaptive regularization scheme applied to the QM7 and QM9 test set, several protonated water clusters and specifically to the problem of atomic hydrogen adsorption on graphene sheets. For the last system our goal is to achieve good predictive accuracy with only a few training points. Therefore, we assess for these systems a self-correcting multilayer GPR model, in which the prediction is corrected by a chain of additional GPR models. In our adaptive regularization scheme, we impose no noise on the training data, but use an approach based on the data itself to account for its impurity. The strength of this strategy is that the data points are treated differently based on their importance and that the regularization can still be controlled by a single parameter. We assess how the accuracy of the prediction depends on this parameter. We can show that the new regularization scheme as well as the multilayer approach results in more robust predictors. Furthermore, we demonstrate that the predictor can be in good agreement with the density-functional theory results.

Coupled local mode method for simulating vibrational spectroscopy.

Experimental and theoretical studies have highlighted protonated water clusters (PWCs) as important models of the excess proton in aqueous systems. A significant focus has been characterizing the spectral signatures associated with different excess proton solvation motifs. Accurate vibrational frequency calculations are crucial for connecting the measured spectra to the structure of PWCs. In this paper, we extend and characterize a coupled local mode (CLM) approach for calculating the infrared spectra of PWCs using the H+(H2O)4 cluster as a benchmark system. The CLM method is relatively low cost and incorporates the anharmonicity and coupling of OH vibrations. Here, we demonstrate the accuracy of the technique compared to experiments. We also illustrate the dependence of calculated spectral features on the underlying electronic structure theory and basis sets used in the local mode frequency and coupling calculations.

Hydrogen Bond Thermodynamics in Aqueous Acid Solutions: A Combined DFT and Classical Force-Field Approach.

The thermodynamics of hydrogen bonds in aqueous and acidic solutions significantly impacts the kinetics and thermodynamics of acid reaction chemistry. We utilize in this work a multiscale approach, combining density functional theory (DFT) with classical molecular dynamics (MD) to model hydrogen bond thermodynamics in an acidic solution. Using thermodynamic cycles, we split the solution phase free energy into its gas phase counterpart plus solvation free energies. We validate this DFT/MD approach by calculating the aqueous phase hydrogen bond free energy between two water molecules (H2O-···-H2O), the free energy to transform an H3O+ cation into an H5O2+ cation, and the hydrogen bond free energy of protonated water clusters (H3O+-···-H2O and H5O2+-···-H2O). The computed equilibrium hydrogen bond free energy of H2O-···-H2O is remarkably accurate, especially considering the large individual contributions to the thermodynamic cycle. Turning to cations, we find the ion to be more stable than H3O+ by roughly 1-2 kBT. This small free energy difference allows for thermal fluctuation between the two idealized motifs, consistent with spectroscopic and simulation studies. Lastly, hydrogen bonding free energies between either H+ cation and H2O in solution were found to be stronger than between two H2O, though much less so than in vacuum because of dielectric screening in solution. Altogether, our results suggest the DFT/MD approach is promising for application in modeling hydrogen bonding and proton transfer thermodynamics in condensed phases.

Path integral Brownian chain molecular dynamics: A simple approximation of quantum vibrational dynamics.

An approximate approach to quantum vibrational dynamics, "Brownian chain molecular dynamics (BCMD)," is proposed to alleviate the chain resonance and curvature problems in the imaginary time-based path integral (PI) simulation. Here the non-centroid velocity is randomized at each step when solving the equation of motion of path integral molecular dynamics. This leads to a combination of the Newton equation and the overdamped Langevin equation for the centroid and non-centroid variables, respectively. BCMD shares the basic properties of other PI approaches such as centroid and ring polymer molecular dynamics: It gives the correct Kubo-transformed correlation function at short times, conserves the time symmetry, has the correct high-temperature/classical limits, gives exactly the position and velocity autocorrelations of harmonic oscillator systems, and does not have the zero-point leakage problem. Numerical tests were done on simple molecular models and liquid water. On-the-fly ab initio BCMD simulations were performed for the protonated water cluster, , and its isotopologue, .

Infrared Spectra at Coupled Cluster Accuracy from Neural Network Representations.

Infrared spectroscopy is key to elucidating molecular structures, monitoring reactions, and observing conformational changes, while providing information on both structural and dynamical properties. This makes the accurate prediction of infrared spectra based on first-principle theories a highly desirable pursuit. Molecular dynamics simulations have proven to be a particularly powerful approach for this task, albeit requiring the computation of energies, forces and dipole moments for a large number of molecular configurations as a function of time. This explains why highly accurate first-principles methods, such as coupled cluster theory, have so far been inapplicable for the prediction of fully anharmonic vibrational spectra of large systems at finite temperatures. Here, we push cutting-edge machine learning techniques forward by using neural network representations of energies, forces, and in particular dipoles to predict such infrared spectra fully at "gold standard" coupled cluster accuracy as demonstrated for protonated water clusters as large as the protonated water hexamer, in its extended Zundel configuration. Furthermore, we show that this methodology can be used beyond the scope of the data considered during the development of the neural network models, allowing for the computation of finite-temperature infrared spectra of large systems inaccessible to explicit coupled cluster calculations. This substantially expands the hitherto existing limits of accuracy, speed, and system size for theoretical spectroscopy and opens up a multitude of avenues for the prediction of vibrational spectra and the understanding of complex intra- and intermolecular couplings.

Multicomponent Orbital-Optimized Perturbation Theory with Density Fitting: Anharmonic Zero-Point Energies in Protonated Water Clusters.

Nuclear quantum effects such as zero-point energy are important in a wide range of chemical and biological processes. The nuclear-electronic orbital (NEO) framework intrinsically includes such effects by treating electrons and specified nuclei quantum mechanically on the same level. Herein, we implement the NEO scaled-opposite-spin orbital-optimized second-order Møller-Plesset perturbation theory with electron-proton correlation scaling (NEO-SOS'-OOMP2) using density fitting. This efficient implementation allows applications to larger systems with multiple quantum protons. Both the NEO-SOS'-OOMP2 method and its counterpart without orbital optimization predict proton affinities to within experimental precision and relative energies of protonated water tetramer isomers in agreement with previous NEO coupled cluster calculations. Applications to protonated water hexamers and heptamers illustrate that anharmonicity is critical for computing accurate relative energies. The NEO-SOS'-OOMP2 approach captures anharmonic zero-point energies at any geometry in a computationally efficient manner and hence will be useful for investigating reaction paths and dynamics in chemical systems.

Energy Dispersion in Pyridinium-Water Nanodroplets upon Irradiation.

Postirradiation dissociation of molecular clusters has been mainly studied assuming energy redistribution in the entire cluster prior to the dissociation. Here, the evaporation of water molecules from out-of-equilibrium pyridinium–water cluster ions was investigated using the recently developed correlated ion and neutral time-of-flight (COINTOF) mass spectrometry technique in combination with a velocity-map imaging (VMI) device. This special setup enables the measurement of velocity distributions of the evaporated molecules upon high-velocity collisions with an argon atom. The distributions measured for pyridinium–water cluster ions are found to have two distinct components. Besides a low-velocity contribution, which corresponds to the statistical evaporation of water molecules after nearly complete redistribution of the excitation energy within the clusters, a high-velocity contribution is also found in which the molecules are evaporated before the energy redistribution is complete. These two different evaporation modes were previously observed and described for protonated water cluster ions. However, unlike in the case of pure water clusters, the low-velocity part of the distributions for pyridinium-doped water clusters is itself composed of two distinct Maxwell–Boltzmann distributions, indicating that evaporated molecules originate in this case from out-of-equilibrium processes. Statistical molecular dynamics simulations were performed to (i) understand the effects caused in the ensuing evaporation process by the various excitation modes at different initial cluster constituents and to (ii) simulate the distributions resulting from sequential evaporations. The presence of a hydrophobic impurity in water clusters is shown to impact water molecule evaporation due to the energy storage in the internal degrees of freedom of the impurity.

Exploring the Origins of Spectral Signatures of Strong Hydrogen Bonding in Protonated Water Clusters.

The effects of anharmonicity on the spectral features of strong ionic hydrogen bonds are explored through reduced dimensional studies of the couplings between the hydrogen bonding OH and the donor-acceptor OO stretching vibrations in protonated water clusters with 2-4 water molecules. Specifically, this study focuses on how the anharmonicities and couplings in these ions are reflected in the vibrational spectra by exploring the intensities of the transitions to states with excitation in both the OH and the OO stretching vibrations and changes in the frequency of the OO stretching vibration when the OH stretching vibration is excited. These questions are addressed through the application of several approximate treatments that are based on an adiabatic separation of the high-frequency OH and low-frequency OO stretching vibrations as well as low-order expansions of the potential and dipole surfaces. While an adiabatic approximation captures most of the trends found in the spectra and from an analysis of the two-dimensional model, a vibrational Franck-Condon approach fails to capture the intensities of these transitions. Of the terms in the expansion of the dipole moment function, those that are proportional to ΔrOH and ΔrOH2 are found to provide the largest contributions to the calculated intensities of the transitions involving excitation of both the OH and the OO stretches. This leads to the conclusion that the intensities of these transitions encode information about the frequency and anharmonicity of the OH stretching vibration and how they are affected by changes in the OO distance. The anharmonicity of the potential also leads to changes in the OO stretching frequency with excitation of the OH stretching vibration. The direction of this change in frequency encodes additional information about the strength of the ionic hydrogen bond.