Site-specific vibrational spectral signatures of water molecules in the magic H3O+ (H2O)20 and Cs+ (H2O)20 clusters

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.

ZundEig: The Structure of the Proton in Liquid Water from Unsupervised Learning

The structure of the excess proton in liquid water has been the subject of lively debate on both experimental and theoretical fronts for the last century. Fluctuations of the proton are typically interpreted in terms of limiting states referred to as the Eigen and Zundel species. Here, we put these ideas under the microscope, taking advantage of recent advances in unsupervised learning that use local atomic descriptors to characterize environments of acidic water combined with advanced clustering techniques. Our agnostic approach leads to the observation of only one charged cluster and two neutral ones. We demonstrate that the charged cluster involving the excess proton is best seen as an ionic topological defect in water's hydrogen bond network, forming a single local minimum on the global free-energy landscape. This charged defect is a highly fluxional moiety, where the idealized Eigen and Zundel species are neither limiting configurations nor distinct thermodynamic states. Instead, the ionic defect enhances the presence of neutral water defects through strong interactions with the network. We dub the combination of the charged and neutral defect clusters as ZundEig, demonstrating that the fluctuations between these local environments provide a general framework for rationalizing more descriptive notions of the proton in the existing literature.

Exploring the Origins of the Intensity of the OH Stretch-HOH Bend Combination Band in Water

While the intensity of the OH stretching fundamental transition is strongly correlated to hydrogen-bond strength, the intensity of the corresponding transition to the state with one quantum of excitation in both the OH stretching and HOH bending vibrations in the same water molecule shows a much weaker sensitivity to the hydrogen-bonding environment. The origins of this difference are explored through analyses of the contributions of terms in the expansion of the dipole moment to the calculated intensity. It is found that the leading contribution to the stretch-bend intensity involves the second derivative of the dipole moment with respect to the OH bond length and HOH angle. While this is not surprising, the insensitivity of this derivative to the hydrogen-bonding environment is unexpected. Possible contributions of mode mixing are also explored. While mode mixing leads to splittings of the energies of nearly degenerate excited states, it does not result in significant changes in the sum of the intensities of these transitions. Analysis of changes in the partial charges on the hydrogen atoms upon displacement of the HOH angles shows that these charges generally increase with increasing HOH angle. This effect is partially canceled by a decrease in the charge of the hydrogen atom when a hydrogen bond is broken. The extent of this cancellation increases with the hydrogen bond strength, which is reflected in the observed insensitivity of the intensity of the stretch-bend transition to hydrogen-bond strength.

Surface Confinement of Finite-Size Water Droplets for SO3 Hydrolysis Reaction Revealed by Molecular Dynamics Simulations Based on a Machine Learning Force Field

As an important source for sulfuric acid in the atmosphere, hydrolysis of sulfur trioxide (SO₃) takes place with water clusters of sizes from several molecules to several nanometers, resulting in various final products, including neutral (H₂SO₄)-(H₂O) clusters and ionic (HSO₄)^--(H₃O)⁺ clusters. The diverse products may be due to the ability of proton transfer and the formation of hydrated ions for water cluster of finite sizes, especially the sub-micrometer ones. However, the detailed molecular-level mechanism is still unclear due to the lack of available characterization and simulations tools. Here, we developed a quantum chemistry-level machine learning (ML) model to simulate the hydrolysis of SO₃ with water clusters of sizes up to nanometers. The simulation results demonstrate diverse reaction paths taking place between SO₃ and water clusters of different sizes. Generally, neutral (H₂SO₄)-(H₂O) clusters are preferred by water clusters of ultra-small size, and a loop structure-mediated mechanism with SO₃(H₂O)_n≤4 structures and a non-loop structure-mediated mechanism with structure relaxation are observed. As the water cluster size increases to (H₂O)₈, a (HSO₄)^--(H₃O)⁺ ion-pair product emerges; and the Eigen-Zundel ion conversion-like proton transfer mechanism takes place and stabilizes the ion pairs. As the water cluster sizes further increase beyond several nanometers ((H₂O)_n≥32), the (SO₄)^2-[(H₃O)⁺]₂ ion-pair product appears. The reason could be that the surface of these water clusters is large enough to screen Coulomb repulsion between two tri-coordinated ion-pair complexes. These findings would provide new perspectives for understanding SO₃ hydrolysis in the real atmosphere and sulfuric acid chemistry in atmospheric aerosols.

Character of the OH Bend-Stretch Combination Band in the Vibrational Spectra of the "Magic" Number H3O+(H2O)20 and D3O+(D2O)20 Cluster Ions

The fundamental transitions that contribute to the diffuse OH stretching spectrum of water are known to increase in width and intensity with increasing red shift from the free OH frequency. In contrast, the profile of the higher-energy combination band involving the OH stretching and the intramolecular HOH bending modes displays a qualitatively different spectral shape with a much faster falloff on the lower-energy side. We elucidate the molecular origin of this difference by analyzing the shapes of the combination bands in the IR spectra of cryogenically cooled H₃O⁺(H₂O)₂₀ and D₃O⁺(D₂O)₂₀ clusters. The difference in the shapes of the bands is traced to differences in the dependence of their transition dipole matrix elements on the hydrogen-bonding environment. The fact that individual transitions across the combination band envelope have similar intensities makes it a useful way to determine the participation of various sites in extended H-bonding networks.

Molecular vibrational spectral simulation connects theoretical cluster structure identification and vibrational spectral evidence

Structure identification of molecular clusters has long been a fundamental and challenging issue for cluster science. The traditional theoretical optimization on the potential energy surface heavily depends on the levels of theory and sometimes diverse identifications were reported. A solution to these disputations is to reinspect the theoretical results with the experimental data such as vibrational predissociation spectra with high sensitivity to the molecular cluster structures. Herein, the combination of global low-lying structure search and vibrational predissociation spectral simulation is proposed as an accurate and reliable approach for cluster structure identification, by which the assignments can be validated using experimental measurements. The qualitative agreement between simulated and measured vibrational spectra lends solid experimental evidence to the assignment of the cluster structures. Taking NH₄⁺(H₂O)_n (n = 2-4) as an example, we have unambiguously identified their structures and directly demonstrated the coexistence of two NH₄⁺(H₂O)₄ isomers (with 3 and 4 water molecules directly linked to NH₄⁺, respectively), which were debatable in previous studies. The developed methods would pave the way to the structure determination of the molecular clusters.

Vibrational Signatures of HNO3 Acidity When Complexed with Microhydrated Alkali Metal Ions, M+·(HNO3)(H2O)n=5 (M = Li, K, Na, Rb, Cs), at 20 K

The speciation of strong acids like HNO₃ under conditions of restricted hydration is an important factor in the rates of chemical reactions at the air-water interface. Here, we explore the trade-offs at play when HNO₃ is attached to alkali ions (Li⁺-Cs⁺) with four water molecules in their primary hydration shells. This is achieved by analyzing the vibrational spectra of the M⁺·(HNO₃)(H₂O)₅ clusters cooled to about 20 K in a cryogenic photofragmentation mass spectrometer. The local acidity of the acidic OH group is estimated by the extent of the red shift in its stretching frequency when attached to a single water molecule. The persistence of this local structural motif (HNO₃-H₂O) in all of these alkali metal clusters enables us to determine the competition between the effect of the direct complexation of the acid with the cation, which acts to enhance acidity, and the role of the water network in the first hydration shell around the ions, which acts to counter (screen) the intrinsic effect of the ion. Analysis of the vibrational features associated with the acid molecule, as well as those of the water network, reveals how cooperative interactions in the microhydration regime conspire to effectively offset the intrinsic enhancement of HNO₃ acidity afforded by attachment to the smaller cations.

Some opinions on MD-based vibrational spectroscopy of gas phase molecules and their assembly: An overview of what has been achieved and where to go

We hereby review molecular dynamics simulations for anharmonic gas phase spectroscopy and provide some of our opinions of where the field is heading. With these new directions, the theoretical IR/Raman spectroscopy of large (bio)-molecular systems will be more easily achievable over longer time-scale MD trajectories for an increase in accuracy of the MD-IR and MD-Raman calculated spectra. With the new directions presented here, the high throughput 'decoding' of experimental IR/Raman spectra into 3D-structures should thus be possible, hence advancing e.g. the field of MS-IR for structural characterization by spectroscopy. We also review the assignment of vibrational spectra in terms of anharmonic molecular modes from the MD trajectories, and especially introduce our recent developments based on Graph Theory algorithms. Graph Theory algorithmic is also introduced in this review for the identification of the molecular 3D-structures sampled over MD trajectories.

Manifolds of low energy structures for a magic number of hydrated sulfate: SO42-(H2O)24

Low energy structures of SO₄^2-(H₂O)₂₄ have been obtained using a combination of classical molecular dynamics simulations and refinement of structures and energies by quantum chemical calculations. Extensive exploration of the potential energy surface led to a number of low-energy structures, confirmed by accurate calibration calculations. An overall analysis of this large set was made after devising appropriate structural descriptors such as the numbers of cycles and their combinations. Low energy structures bear common motifs, the most prominent being fused cycles involving alternatively four and six water molecules. The latter adopt specific conformations which ensure the appropriate surface curvature to form a closed cage without dangling O-H bonds and at the same time provide 12-coordination of the sulfate ion. A prominent feature to take into account is isomerism via inversion of hydrogen bond orientations along cycles. This generates large families of ca. 100 isomers for this cluster size, spanning energy windows of 10-30 kJ mol^-1. This relatively ignored isomerism must be taken into account to identify reliably the lowest energy minima. The overall picture is that the magic number cluster SO₄^2-(H₂O)₂₄ does not correspond to formation of a single, remarkable structure, but rather to a manifold of structural families with similar stabilities. Extensive calculations on isomerization mechanisms within a family indicate that large barriers are associated to direct inversion of hydrogen bond networks. Possible implications of these results for magic number clusters of other anions are discussed.

Towards complete assignment of the infrared spectrum of the protonated water cluster H+(H2O)21

The spectroscopic features of protonated water species in dilute acid solutions have been long sought after for understanding the microscopic behavior of the proton in water with gas-phase water clusters H⁺(H₂O)_n extensively studied as bottom-up model systems. We present a new protocol for the calculation of the infrared (IR) spectra of complex systems, which combines the fragment-based Coupled Cluster method and anharmonic vibrational quasi-degenerate perturbation theory, and demonstrate its accuracy towards the complete and accurate assignment of the IR spectrum of the H⁺(H₂O)₂₁ cluster. The site-specific IR spectral signatures reveal two distinct structures for the internal and surface four-coordinated water molecules, which are ice-like and liquid-like, respectively. The effect of inter-molecular interaction between water molecules is addressed, and the vibrational resonance is found between the O-H stretching fundamental and the bending overtone of the nearest neighboring water molecule. The revelation of the spectral signature of the excess proton offers deeper insight into the nature of charge accommodation in the extended hydrogen-bonding network underpinning this aqueous cluster.

Protonated water species have been the subject of numerous experimental and computational studies. Here the authors provide a nearly complete assignment of the experimental IR spectrum of the H⁺(H₂O)₂₁ water cluster based on high-level wavefunction theory and anharmonic vibrational quasi-degenerate perturbation theory.

Coupled Local-Mode Approach for the Calculation of Vibrational Spectra: Application to Protonated Water Clusters

Spectroscopic studies of protonated water clusters (PWCs) have yielded enormous insights into the fundamental nature of the hydrated proton. Here, we introduce a new coupled local-mode (CLM) approach to calculate PWC OH stretch vibrational spectra. The CLM method combines a sampling of representative configurations from density functional theory (DFT)-based ab initio molecular dynamics (AIMD) simulations with DFT calculations of local-mode vibrational frequencies and couplings. Calculations of inhomogeneous OH stretch vibrational spectra for H⁺(H₂O)₄ and H⁺(H₂O)₂₁ agree well with experiment and higher-level calculations, and decompositions of the calculated spectra in terms of the coupled modes aids in the interpretation of the spectra. This observation is consistent with the idea that capturing anharmonicity and coupling is as important to accuracy as the underlying level of electronic structure theory. The CLM calculations can easily discern the configuration that dominates the experimental measurement for H⁺(H₂O)₅, which can adopt several low-energy conformations.

Identification of Isomeric Lipids by UV Spectroscopy of Noncovalent Complexes with Aromatic Molecules

The tremendous structural and isomeric diversity of lipids enables a wide range of their functions in nature but makes the identification of these biomolecules challenging. We distinguish and quantify isomeric lipids using cold ion UV fragmentation spectroscopy of their noncovalent complexes with aromatic amino acids and dipeptides. On the basis of structural simulations, specific isomer-sensitive aromatic "sensors" have been preselected for lipids of each studied class. Tyrosine appeared to be a good "sensor" to distinguish steroids and prostaglandins, which are rich in functional groups, while diphenylalanine is a better choice for sensing largely hydrophobic phospholipids. With this sensor, the relative concentrations of two isomeric glycerophospholipids mixed in solution have been determined with 3.3% accuracy, which should degrade only to 3.7% for a 14 s express measurement.

Isomer-Specific Vibrational Spectroscopy of Microhydrated Lithium Dichloride Anions: Spectral Fingerprint of Solvent-Shared Ion Pairs

The vibrational spectroscopy of lithium dichloride anions microhydrated with one to three water molecules, [LiCl2 (H2 O)1-3 ]- , is studied in the OH stretching region (3800-2800 cm-1 ) using isomer-specific IR/IR double-resonance population labelling experiments. The spectroscopic fingerprints of individual isomers can only be unambiguously assigned after anharmonic effects are considered, but then yield molecular level insight into the onset of salt dissolution in these gas phase model systems. Based on the extent of the observed frequency shifts ΔνOH of the hydrogen-bonded OH stretching oscillators solvent-shared ion pair motifs (<3200 cm-1 ) can be distinguished from intact-core structures (>3200 cm-1 ). The characteristic fingerprint of a water molecule trapped directly in-between two ions of opposite charge provides an alternative route to evaluate the extent of ion pairing in aqueous electrolyte solutions.

Weighted-Graph-Theoretic Methods for Many-Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms

We present a weighted-graph-theoretic approach to adaptively compute contributions from many-body approximations for smooth and accurate post-Hartree-Fock (pHF) ab initio molecular dynamics (AIMD) of highly fluxional chemical systems. This approach is ONIOM-like, where the full system is treated at a computationally feasible quality of treatment (density functional theory (DFT) for the size of systems considered in this publication), which is then improved through a perturbative correction that captures local many-body interactions up to a certain order within a higher level of theory (post-Hartree-Fock in this publication) described through graph-theoretic techniques. Due to the fluxional and dynamical nature of the systems studied here, these graphical representations evolve during dynamics. As a result, energetic "hops" appear as the graphical representation deforms with the evolution of the chemical and physical properties of the system. In this paper, we introduce dynamically weighted, linear combinations of graphs, where the transition between graphical representations is smoothly achieved by considering a range of neighboring graphical representations at a given instant during dynamics. We compare these trajectories with those obtained from a set of trajectories where the range of local many-body interactions considered is increased, sometimes to the maximum available limit, which yields conservative trajectories as the order of interactions is increased. The weighted-graph approach presents improved dynamics trajectories while only using lower-order many-body interaction terms. The methods are compared by computing dynamical properties through time-correlation functions and structural distribution functions. In all cases, the weighted-graph approach provides accurate results at a lower cost.

Demystifying the Diffuse Vibrational Spectrum of Aqueous Protons Through Cold Cluster Spectroscopy

The ease with which the pH is routinely determined for aqueous solutions masks the fact that the cationic product of Arrhenius acid dissolution, the hydrated proton, or H⁺(aq), is a remarkably complex species. Here, we review how results obtained over the past 30 years in the study of H⁺⋅(H₂O)_n cluster ions isolated in the gas phase shed light on the chemical nature of H⁺(aq). This effort has also revealed molecular-level aspects of the Grotthuss relay mechanism for positive-charge translocation in water. Recently developed methods involving cryogenic cooling in radiofrequency ion traps and the application of two-color, infrared-infrared (IR-IR) double-resonance spectroscopy have established a clear picture of how local hydrogen-bond topology drives the diverse spectral signatures of the excess proton. This information now enables a new generation of cluster studies designed to unravel the microscopic mechanics underlying the ultrafast relaxation dynamics displayed by H⁺(aq).

How many water molecules are needed to solvate one?

Many efforts undertaken to study the solvation process have led to general theories that may describe mean properties, but are unable to provide a detailed understanding at the molecular level. Remarkably, the basic question of how many solvent molecules are necessary to solvate one solute molecule is still open. By exploring several water aggregates of increasing complexity, in this contribution we employ semiclassical spectroscopy to determine on quantum dynamical grounds the minimal network of surrounding water molecules to make the central one display the same vibrational features of liquid water. We find out that double-acceptor double-donor tetrahedral coordination constituting the standard picture is necessary but not sufficient, and that particular care must be reserved for the quantum description of the combination band due to the coupling of the central monomer bending mode with network librations. It is actually our ability to investigate the combination band with a quantum-derived approach that allows us to answer the titular question. The minimal structure eventually responsible for proper solvation is made of a total of 21 water molecules and includes two complete solvation shells, of which the whole first one is tetrahedrally coordinated to the central molecule.

How quantum spectroscopic simulations can explain water solvation by comparison with experimental spectra.

Isolating the Contributions of Specific Network Sites to the Diffuse Vibrational Spectrum of Interfacial Water with Isotopomer-Selective Spectroscopy of Cold Clusters

Decoding the structural information contained in the interfacial vibrational spectrum of water requires understanding how the spectral signatures of individual water molecules respond to their local hydrogen bonding environments. In this study, we isolated the contributions for the five classes of sites that differ according to the number of donor (D) and acceptor (A) hydrogen bonds that characterize each site. These patterns were measured by exploiting the unique properties of the water cluster cage structures formed in the gas phase upon hydration of a series of cations M⁺·(H₂O)_n (M = Li, Na, Cs, NH₄, CH₃NH₃, H₃O, and n = 5, 20-22). This selection of ions was chosen to systematically express the A, AD, AAD, ADD, and AADD hydrogen bonding motifs. The spectral signatures of each site were measured using two-color, IR-IR isotopomer-selective photofragmentation vibrational spectroscopy of the cryogenically cooled, mass selected cluster ions in which a single intact H₂O is introduced without isotopic scrambling, an important advantage afforded by the cluster regime. The resulting patterns provide an unprecedented picture of the intrinsic line shapes and spectral complexities associated with excitation of the individual OH groups, as well as the correlation between the frequencies of the two OH groups on the same water molecule, as a function of network site. The properties of the surrounding water network that govern this frequency map are evaluated by dissecting electronic structure calculations that explore how changes in the nearby network structures, both within and beyond the first hydration shell, affect the local frequency of an OH oscillator. The qualitative trends are recovered with a simple model that correlates the OH frequency with the network-modulated local electron density in the center of the OH bond.

Effects of Temperature on Cs+(H2O)20 Clathrate Structure

Clusters consisting of 20 water molecules and a single cesium ion are especially stable due to their clathrate structure that is composed exclusively of three-coordinate water molecules. Clathrate stability was investigated using infrared photodissociation (IRPD) spectroscopy in the free-OH stretching region (∼3600-3800 cm^-1) at ion cell temperatures between 135 and 355 K. At 275 K and colder, IRPD spectra of Cs⁺(H₂O)₂₀ have just one acceptor-acceptor-donor band. At higher temperatures, a higher-energy acceptor-donor band emerges and grows in intensity. Non-clathrate Na⁺(H₂O)₂₀ structures contain both of these bands, which do not change significantly in intensity over the temperature range. These results indicate a rapid onset in the conversion from clathrate to non-clathrate structures with temperature and suggest that some clathrate population remains even at the highest temperatures investigated. These results provide new insights into the role of entropy in clathrate stability.

Infrared spectroscopy of neutral water clusters at finite temperature: Evidence for a noncyclic pentamer

Infrared spectroscopic study of neutral water clusters is crucial to understanding of the hydrogen-bonding networks in liquid water and ice. Here we report infrared spectra of size-selected neutral water clusters, (H₂O) _n (n = 3-6), in the OH stretching vibration region, based on threshold photoionization using a tunable vacuum ultraviolet free-electron laser. Distinct OH stretch vibrational fundamentals observed in the 3,500-3,600-cm^-1 region of (H₂O)₅ provide unique spectral signatures for the formation of a noncyclic pentamer, which coexists with the global-minimum cyclic structure previously identified in the gas phase. The main features of infrared spectra of the pentamer and hexamer, (H₂O) _n (n = 5 and 6), span the entire OH stretching band of liquid water, suggesting that they start to exhibit the richness and diversity of hydrogen-bonding networks in bulk water.

Capturing intrinsic site-dependent spectral signatures and lifetimes of isolated OH oscillators in extended water networks

The extremely broad infrared spectrum of water in the OH stretching region is a manifestation of how profoundly a water molecule is distorted when embedded in its extended hydrogen-bonding network. Many effects contribute to this breadth in solution at room temperature, which raises the question as to what the spectrum of a single OH oscillator would be in the absence of thermal fluctuations and coupling to nearby OH groups. We report the intrinsic spectral responses of isolated OH oscillators embedded in two cold (~20 K), hydrogen-bonded water cages adopted by the Cs⁺·(HDO)(D₂O)₁₉ and D₃O⁺·(HDO)(D₂O)₁₉ clusters. Most OH oscillators yield single, isolated features that occur with linewidths that increase approximately linearly with their redshifts. Oscillators near 3,400 cm^-1, however, occur with a second feature, which indicates that OH stretch excitation of these molecules drives low-frequency, phonon-type motions of the cage. The excited state lifetimes inferred from the broadening are considered in the context of fluctuations in the local electric fields that are available even at low temperature.

Multistate Reactive Molecular Dynamics Simulations of Proton Diffusion in Water Clusters and in the Bulk

The molecular mechanics with proton transfer (MMPT) force field is combined with multistate adiabatic reactive molecular dynamics (MS-ARMD) to describe proton transport in the condensed phase. Parametrization for small protonated water clusters based on electronic structure calculations at the MP2/6-311+G(2d,2p) level of theory and refinement by comparing with infrared spectra for a protonated water tetramer yields a force field which faithfully describes the minimum energy structures of small protonated water clusters. In protonated water clusters up to (H₂O)₁₀₀H⁺, the proton hopping rate is around 100 hops/ns. This rate converges for 21 ≤ n ≤ 31, and no further speedup in bulk water is found. This indicates that bulklike behavior requires the solvation of a Zundel motif by ∼25 water molecules, which corresponds to the second solvation sphere. For smaller cluster sizes, the number of available states (i.e., the number of proton acceptors) is too small and slows down proton-transfer rates. The cluster simulations confirm that the excess proton is typically located on the surface. The free-energy surface as a function of the weights of the two lowest states and a configurational parameter suggests that the "special pair" plays a central role in rapid proton transport. The barriers between this minimum-energy structure and the Zundel and Eigen minima are sufficiently low (∼1 kcal/mol, consistent with recent experiments and commensurate with a hopping rate of ∼100/ns or 1 every 10 ps), leading to a highly dynamic environment. These findings are also consistent with recent experiments which find that Zundel-type hydration geometries are prevalent in bulk water.

Disentangling the Complex Vibrational Mechanics of the Protonated Water Trimer by Rational Control of Its Hydrogen Bonds

The vibrational spectrum of the protonated water trimer, H⁺(H₂O)₃, is surprisingly complex, with many strong features in the expected region of the fundamentals associated with two H-bonded OH groups on the H₃O⁺ core ion. Here we follow how the bands in this region of the spectrum evolve when the energies of the fundamentals in the H-bonded OH stretches are systematically increased by the attachment of increasingly strongly bound "tag" molecules (He, Ar, D₂, N₂, CO, and H₂O) to the free OH position on the hydronium core ion of H⁺(H₂O)₃, as well as by replacement of the hydrogen atom in the nonbonded OH group on hydronium with methyl and ethyl groups. This allows for the incremental transformation of the complex band pattern observed in H⁺(H₂O)₃ into that of the "Eigen" structure of the protonated water tetramer. Differences among the trajectories of the various bands provide an empirical way to disentangle features primarily due to the displacements of the OH stretches bound to the hydronium core from those arising from anharmonic coupling to states involving one or more quanta in lower frequency modes. The latter are found to be dramatically enhanced when the nominal frequencies of the intermolecular OH stretching modes approach those of the intramolecular bends of the H₃O⁺ and H₂O constituents in both H and D isotopologues.

Vibrational Relaxation Dynamics of the Core and Outer Part of Proton-Hydration Clusters

We study the ultrafast relaxation dynamics of hydrated proton clusters in acetonitrile using femtosecond mid-infrared pump-probe spectroscopy. We observe a strong dependence of transient absorption dynamics on the frequency of excitation. When we excite the OH vibrations with frequencies ≤3100 cm^–1, we observe an ultrafast energy relaxation that leads to the heating of the local environment of the proton. This response is assigned to the OH vibrations of the water molecules in the core of the hydrated proton cluster. When we excite with frequencies ≥3200 cm^–1, we observe a relatively slow vibrational relaxation with a T₁ time constant ranging from 0.22 ± 0.04 ps at ν_ex = 3200 cm^–1 to 0.37 ± 0.02 ps at ν_ex = 3520 cm^–1. We assign this response to water molecules in the outer part of the hydrated proton cluster.

Introductory lecture: advances in ion spectroscopy: from astrophysics to biology

This introduction provides a historical context for the development of ion spectroscopy over the past half century by following the evolution of experimental methods to the present state-of-the-art. Rather than attempt a comprehensive review, we focus on how early work on small ions, carried out with fluorescence, direct absorption, and photoelectron spectroscopy, evolved into powerful technologies that can now address complex chemical problems ranging from catalysis to biophysics. One of these developments is the incorporation of cooling and temperature control to enable the general application of "messenger tagging" vibrational spectroscopy, first carried out using ionized supersonic jets and then with buffer gas cooling in radiofrequency ion traps. Some key advances in the application of time-resolved pump-probe techniques to follow ultrafast dynamics are also discussed, as are significant benchmarks in the refinement of ion mobility to allow spectroscopic investigation of large biopolymers with well-defined shapes. We close with a few remarks on challenges and opportunities to explore molecular level mechanics that drive macroscopic behavior.

Deconstructing water's diffuse OH stretching vibrational spectrum with cold clusters

The diffuse vibrational envelope displayed by water precludes direct observation of how different hydrogen-bond topologies dictate the spectral response of individual hydroxy group (OH) oscillators. Using cold, isotopically labeled cluster ions, we report the spectral signatures of a single, intact water (H₂O) molecule embedded at various sites in the clathrate-like cage structure adopted by the Cs⁺·(D₂O)₂₀ ion. These patterns reveal the site-dependent correlation between the frequencies of the two OH groups on the same water molecule and establish that the bound OH companion of the free OH group exclusively accounts for bands in the lower-energy region of the spectrum. The observed multiplet structures reveal the homogeneous linewidths of the fundamentals and quantify the anharmonic contributions arising from coupling to both the intramolecular bending and intermolecular soft modes.

Terahertz Spectra of Microsolvated Ions: Do They Reveal Bulk Solvation Properties?

Complementing mid-infrared (mid-IR) spectroscopy mainly in the OH stretching region, liquid-state far-IR spectroscopy is successful in elucidating the properties of aqueous solutions by providing direct access to the hallmark of H-bonding at terahertz (THz) frequencies, namely, the H-bond network peak of water at roughly 200 cm^-1 and its modifications in the hydration shells around solutes. Here, the idea is scrutinized whether ion hydration can be understood by studying the THz regime of "small" ion-water clusters in the gas phase as a function of size with subsequent extrapolation to the bulk limit. Our ab initio simulations of Na⁺(H₂O) _n clusters followed by rigorous decomposition of their THz response demonstrate that the 200 cm^-1 network peak is suppressed even at n = 20 in the gas phase, yet it emerges when transferring ion-water complexes as small as n = 7 out of the liquid into vacuum. The underlying physical reason is not missing electronic polarization or charge-transfer effects in the gas phase, but rather the distinctly different structural dynamics of finite ion-water clusters in the gas phase compared to ion-water complexes of the same size in the liquid phase.

Conformational assignment of gas phase peptides and their H-bonded complexes using far-IR/THz: IR-UV ion dip experiment, DFT-MD spectroscopy, and graph theory for mode assignment

Graph theory based vibrational modes as new entities for vibrational THz spectroscopy.

Long distance ion-water interactions in aqueous sulfate nanodrops persist to ambient temperatures in the upper atmosphere

The effect of temperature on the patterning of water molecules located remotely from a single SO₄^2- ion in aqueous nanodrops was investigated for nanodrops containing between 30 and 55 water molecules using instrument temperatures between 135 and 360 K. Magic number clusters with 24, 36 and 39 water molecules persist at all temperatures. Infrared photodissociation spectroscopy between 3000 and 3800 cm^-1 was used to measure the appearance of water molecules that have a free O-H stretch at the nanodroplet surface and to infer information about the hydrogen bonding network of water in the nanodroplet. These data suggest that the hydrogen bonding network of water in nanodrops with 45 water molecules is highly ordered at 135 K and gradually becomes more amorphous with increasing temperature. An SO₄^2- dianion clearly affects the hydrogen bonding network of water to at least ∼0.71 nm at 135 K and ∼0.60 nm at 340 K, consistent with an entropic drive for reorientation of water molecules at the surface of warmer nanodrops. These distances represent remote interactions into at least a second solvation shell even with elevated instrumental temperatures. The results herein provide new insight into the extent to which ions can structurally perturb water molecules even at temperatures relevant to Earth's atmosphere, where remote interactions may assist in nucleation and propagation of nascent aerosols.

Deconstructing Prominent Bands in the Terahertz Spectra of H7O3+ and H9O4+: Intermolecular Modes in Eigen Clusters

We report experimental vibrational action spectra (210-2200 cm^-1) and calculated IR spectra, using recent ab initio potential energy and dipole moment surfaces, of H₇O₃⁺ and H₉O₄⁺. We focus on prominent far-IR bands, which postharmonic analyses show, arise from two types of intermolecular motions, i.e., hydrogen bond stretching and terminal water wagging modes, that are similar in both clusters. The good agreement between experiment and theory further validates the accuracy of the potential and dipole moment surfaces, which was used in a recent theoretical study that concluded that infrared photodissociation spectra of the cold clusters correspond to the Eigen isomer. The comparison between theory and experiment adds further confirmation of the need of postharmonic analysis for these clusters.

Matrix Isolation Spectroscopy: Aqueous p-Toluenesulfonic Acid Solvation

Interaction between p-toluenesulfonic acid (pTSA) and water is studied at -20 °C in a CCl₄ matrix. In CCl₄ water exists as monomers with restricted rotational motion about its symmetry axis. Additionally, CCl₄ is transparent in the hydrogen-bonded region; CCl₄ thus constitutes an excellent ambient thermal energy matrix isolation medium for diagnosing interactions with water. Introducing pTSA-nH₂O gives rise to two narrow resonances at 3642 cm^-1 and at 2835 cm^-1 plus a broad 3000-3550 cm^-1 absorption. In addition, negative monomer symmetric and asymmetric stretch features relative to nominally dry CCl₄ indicate that fewer water monomers exist in the cooled (-20 °C) acid solution than in room-temperature anhydrous CCl₄. The negative peaks along with the broad absorption band indicate that water monomers are incorporated into clusters. The 3642 cm^-1 resonance is assigned to the OH-π interaction with a cluster containing many water molecules per acid molecule. The 2835 cm^-1 resonance is assigned to the (S-)O-H stretch of pTSA-dihydrate. The coexistence of these two species provides insights into interactions in this acid-water CCl₄ system.

Strategy for Modeling the Infrared Spectra of Ion-Containing Water Drops

Hydrated ions are ubiquitous in environmental and biological media. Understanding the perturbation exerted by an ion on the water hydrogen bond network is possible in the nanodrop regime by recording vibrational spectra in the O-H bond stretching region. This has been achieved experimentally in recent years by forming gaseous ions containing tens to hundreds of water molecules and recording their infrared photodissociation spectra. In this paper, we demonstrate the capabilities of a modeling strategy based on an extension of the AMOEBA polarizable force field to implement water atomic charge fluctuations along with those of intramolecular structure along the dynamics. This supplementary flexibility of nonbonded interactions improves the description of the hydrogen bond network and, therefore, the spectroscopic response. Finite temperature IR spectra are obtained from molecular dynamics simulations by computing the Fourier transform of the dipole moment autocorrelation function. Simulations of 1-2 ns are required for extensive sampling in order to reproduce the experimental spectra. Furthermore, bands are assigned with the driven molecular dynamics approach. This method package is shown to compare successfully with experimental spectra for 11 ions in water drops containing 36-100 water molecules. In particular, band frequency shifts of the free O-H stretching modes at the cluster surface are well reproduced as a function of both ion charge and drop size.

Kinetic isotope effects and how to describe them

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.

Disentangling the Complex Vibrational Spectrum of the Protonated Water Trimer, H+(H2O)3, with Two-Color IR-IR Photodissociation of the Bare Ion and Anharmonic VSCF/VCI Theory

Vibrational spectroscopy of the protonated water trimer provides a stringent constraint on the details of the potential energy surface (PES) and vibrational dynamics governing excess proton motion far from equilibrium. Here we report the linear spectrum of the cold, bare H⁺(H₂O)₃ ion using a two-color, IR-IR photofragmentation technique and follow the evolution of the bands with increasing ion trap temperature. The key low-energy features are insensitive to both D₂ tagging and internal energy. The D₂-tagged D⁺(D₂O)₃ spectrum is reported for the first time, and the isotope dependence of the band pattern is surprisingly complex. These spectra are reproduced by large-scale vibrational configuration interaction calculations based on a new full-dimensional PES, which treat the anharmonic effects arising from large amplitude motion. The results indicate such extensive mode mixing in both isotopologues that one should be cautious about assigning even the strongest features to particular motions, especially for the absorptions that occur close to the intramolecular bending mode of the water molecule.

Hidden role of intermolecular proton transfer in the anomalously diffuse vibrational spectrum of a trapped hydronium ion

We report the vibrational spectra of the hydronium and methyl-ammonium ions captured in the C_3v binding pocket of the 18-crown-6 ether ionophore. Although the NH stretching bands of the CH₃NH₃⁺ ion are consistent with harmonic expectations, the OH stretching bands of H₃O⁺ are surprisingly broad, appearing as a diffuse background absorption with little intensity modulation over 800 cm^-1 with an onset ∼400 cm^-1 below the harmonic prediction. This structure persists even when only a single OH group is present in the HD₂O⁺ isotopologue, while the OD stretching region displays a regular progression involving a soft mode at about 85 cm^-1 These results are rationalized in a vibrationally adiabatic (VA) model in which the motion of the H₃O⁺ ion in the crown pocket is strongly coupled with its OH stretches. In this picture, H₃O⁺ resides in the center of the crown in the vibrational zero-point level, while the minima in the VA potentials associated with the excited OH vibrational states are shifted away from the symmetrical configuration displayed by the ground state. Infrared excitation between these strongly H/D isotope-dependent VA potentials then accounts for most of the broadening in the OH stretching manifold. Specifically, low-frequency motions involving concerted motions of the crown scaffold and the H₃O⁺ ion are driven by a Franck-Condon-like mechanism. In essence, vibrational spectroscopy of these systems can be viewed from the perspective of photochemical interconversion between transient, isomeric forms of the complexes corresponding to the initial stage of intermolecular proton transfer.

Structural and electrostatic effects at the surfaces of size- and charge-selected aqueous nanodrops

The effects of ion charge, polarity and size on the surface morphology of size-selected aqueous nanodrops containing a single ion and up to 550 water molecules are investigated with infrared photodissociation (IRPD) spectroscopy and theory.

The effects of ion charge, polarity and size on the surface morphology of size-selected aqueous nanodrops containing a single ion and up to 550 water molecules are investigated with infrared photodissociation (IRPD) spectroscopy and theory. IRPD spectra of M(H₂O)_n where M = La³⁺, Ca²⁺, Na⁺, Li⁺, I^–, SO₄^2– and supporting molecular dynamics simulations indicate that strong interactions between multiply charged ions and water molecules can disrupt optimal hydrogen bonding (H-bonding) at the nanodrop surface. The IRPD spectra also reveal that “free” OH stretching frequencies of surface-bound water molecules are highly sensitive to the ion's identity and the OH bond's local H-bond environment. The measured frequency shifts are qualitatively reproduced by a computationally inexpensive point-charge model that shows the frequency shifts are consistent with a Stark shift from the ion's electric field. For multiply charged cations, pronounced Stark shifting is observed for clusters containing ∼100 or fewer water molecules. This is attributed to ion-induced solvent patterning that extends to the nanodrop surface, and serves as a spectroscopic signature for a cation's ability to influence the H-bond network of water located remotely from the ion. The Stark shifts measured for the larger nanodrops are extrapolated to infinite dilution to obtain the free OH stretching frequency of a surface-bound water molecule at the bulk air–water interface (3696.5–3701.0 cm^–1), well within the relatively wide range of values obtained from SFG measurements. These cluster measurements also indicate that surface curvature effects can influence the free OH stretching frequency, and that even nanodrops without an ion have a surface potential that depends on cluster size.

Mapping gas phase dipeptide motions in the far-infrared and terahertz domain

Vibrational signatures of Ac-Phe-AA-NH₂ dipeptides are recorded and analysed in the far IR/THz spectral domain (100–800 cm⁻¹, 3–24 THz), with the ‘AA’ amino acid chosen within the series ‘AA’ = Gly, Ala, Pro, Cys, Ser, Val. Phe stands for phenylalanine.

Nanometer patterning of water by tetraanionic ferrocyanide stabilized in aqueous nanodrops

Formation of the small, highly charged tetraanion ferrocyanide, Fe(CN)₆^4–, stabilized in aqueous nanodrops and its influence to the surrounding hydrogen-bonding network of water is reported.

Formation of the small, highly charged tetraanion ferrocyanide, Fe(CN)₆^4–, stabilized in aqueous nanodrops is reported. Ion–water interactions inside these nanodrops are probed using blackbody infrared radiative dissociation, infrared photodissociation (IRPD) spectroscopy, and molecular modeling in order to determine how water molecules stabilize this highly charged anion and the extent to which the tetraanion patterns the hydrogen-bonding network of water at long distance. Fe(CN)₆^4–(H₂O)₃₈ is the smallest cluster formed directly by nanoelectrospray ionization. Ejection of an electron from this ion to form Fe(CN)₆^3–(H₂O)₃₈ occurs with low-energy activation, but loss of a water molecule is favored at higher energy indicating that water molecule loss is entropically favored over loss of an electron. The second solvation shell is almost complete at this cluster size indicating that nearly two solvent shells are required to stabilize this highly charged anion. The extent of solvation necessary to stabilize these clusters with respect to electron loss is substantially lower through ion pairing with either H⁺ or K⁺ (n = 17 and 18, respectively). IRPD spectra of Fe(CN)₆^4–(H₂O)_n show the emergence of a free O–H water molecule stretch between n = 142 and 162 indicating that this ion patterns the structure of water molecules within these nanodrops to a distance of at least ∼1.05 nm from the ion. These results provide new insights into how water stabilizes highly charged ions and demonstrate that highly charged anions can have a significant effect on the hydrogen-bonding network of water molecules well beyond the second and even third solvation shells.

Computational study of inelastic neutron scattering vibrational spectra of water clusters and their relevance to hydration water in proteins

BACKGROUND

Inelastic neutron scattering (INS) vibrational spectra for hydration water in proteins can be obtained from spectral differences, but their interpretation has mainly been limited to comparisons with various forms of ice at high hydration levels without making use of available structural information from neutron protein crystallography.

METHODS

The INS vibrational spectra of free and partially constrained water clusters (up to n=17) were calculated with DFT methods using published energy-minimized structures.

RESULTS

Reference is made to neutron diffraction studies of hydrated proteins, which contain a wealth of structural information both on individual water molecules and small clusters in the inner "shell" in order to select representative clusters to serve as models for bound, rather than free clusters as they would occur in a protein.

CONCLUSIONS

INS spectra of the water librational region calculated for a combination of model bound clusters provide a qualitative account of the essentially featureless experimental spectra on water in proteins at very low hydration levels, but do indicate that the well-known rise in intensity near 500cm^-1 is connected to increasing numbers of four-coordinate water molecules in larger clusters.

GENERAL SIGNIFICANCE

The combination of structural information of hydration water from neutron protein crystallography with much more sophisticated computational methods than used herein should lead to a much more detailed picture of the hydration of proteins. This article is part of a Special Issue entitled "Science for Life" Guest Editor: Dr. Austen Angell, Dr. Salvatore Magazù and Dr. Federica Migliardo.

Characterizing the local solvation environment of OH(-) in water clusters with AIMD

In this work, we use ab initio molecular dynamics coupled with metadynamics to explore and characterize the glassy potential energy landscape of the OH(-) in a 20 and 48 water cluster. The structural, energetic, and topological properties of OH(-) are characterized for both clusters and the molecular origins of the IR signatures are examined. We find that in both the small and large clusters, the OH(-) can donate or accept a varying number of hydrogen bonds confirming that the amphiphilic character does not depend on cluster size. However, we highlight some important differences found between the energetic and topological properties of both families of clusters which may have implications on understanding the changes in the solvation structure of OH(-) between bulk and interfacial environments. By studying the IR spectra of smaller subsets of molecules within the 20 water molecule cluster, we find that the IR spectrum of the bare OH(-) as well as the water molecule donating a strong hydrogen bond to it exhibits characteristic absorption along the amphiphilic band between 1500 and 3000 cm(-1) at positions very similar to those found for the entire hydroxide cluster. The results presented here will be useful in the calibration and improvement of both ab initio and semi-empirical methods to model this complex anion.

Evidence of Polaron Excitations in Low Temperature Raman Spectra of Oxalic Acid Dihydrate

Low temperature Raman spectra of oxalic acid dihydrate (8-300 K) for both the polycrystalline and single crystal phase show strong variation with temperature in the interval from 1200 to 2000 cm(-1). Previous low temperature diffraction studies all confirmed the stability of the crystal P21/n phase with no indications of any phase transition, reporting the existence of a strong hydrogen bond between the oxalic acid and a water molecule. A new group of Raman bands in the 1200-1300 cm(-1) interval below 90 K is observed, caused by possible loss of the center of inversion. This in turn could originate either due to disorder in hydroxyl proton positions or due to proton transfer from carboxylic group to water molecule. The hypothesis of proton transfer is further supported by the emergence of new bands centered at 1600 and 1813 cm(-1), which can be explained with vibrations of H3O(+) ions. The broad band at 1600 cm(-1) looses intensity, while the band at 1813 cm(-1) gains intensity on cooling. The agreement between quantum calculations of vibrational spectra and experimentally observed Raman bands of hydronium ions in oxalic acid sesquihydrate crystal corroborates this hypothesis.

Far-infrared spectra of the tryptamine A conformer by IR-UV ion gain spectroscopy

Single-far-infrared photon excited tryptamine has structured resonance enhanced multi-photon ionization UV spectra, revealing the mode composition of the S₁-state. Upon multiple-far-infrared photon absorption, the UV spectrum broadens allowing ion gain spectroscopy to be performed.