Atlas of putative minima and low-lying energy networks of water clusters n = 3-25

Edge-sharing water prisms

Regular-shaped water clusters and nanostructures can be of particular interest for the self-assembly of complex structures and functional materials involving water molecules. Polyhedral water clusters are the most well studied. The low-energy structures of water hexamer, octamer and decamer are shaped like right prisms. The cavities of gas hydrates also have a polyhedral shape. Ice nanotubes are of no less interest both as configurations of global energy minima and in terms of possible applications. This article presents the results of the first systematic study of the structure and properties of a special class of water clusters. It reveals different combinations of three right prisms sharing an edge. According to modern calculations, the configurations of global energy minima of water clusters with the number of molecules being eighteen and twenty have this structure precisely. The topological characteristics of the edge-sharing water prisms are studied and the formulas for estimating the residual entropy are obtained. For these clusters (3-prisms), the usefulness of using a discrete model of intermolecular interaction [strong-weak-effective-bond model], previously developed for polyhedral water clusters, is shown. Calculations of the binding energy were performed using the non-additive Amoeba potential. To understand the relative stability of 3-prisms among other cluster forms, we use the structures recently reported in a published database containing over 3 × 106 unique water cluster networks (H2O)N of size N = 3-25 [Rakshit et al., J. Chem. Phys., 2019, 151(21), 214307, DOI: 10.1063/1.5128378].

Cluster-in-Cluster Approach for Computing MP2-Level Vibrational Infrared Spectra of Large Molecular Clusters

Constructing the Hessian matrix (HM) for large molecules demands huge computational resources. Here, we report a cluster-in-cluster (CIC) procedure for efficiently evaluating HM and dipole derivatives for large molecular clusters by employing the second-order Møller-Plesset perturbation (MP2) theory. The highlight of the proposal is the separation of the estimations of Hartree-Fock (HF) and post-HF components. The parent cluster with n molecules is divided (virtually) into n subclusters centering each monomer and accommodating its near neighbors decided by a distance cutoff. The HF-level HM is obtained by doing full calculation (FC), while the correlation part is approximated by the respective subclusters. A software automating the procedure [followed by calculating infrared (IR) frequencies and intensities] is applied to deduce the IR spectrum for a variety of molecular clusters, particularly water clusters of various sizes, containing up to ∼2000 basis functions. The accuracy of the IR spectrum constructed using CIC is remarkable, with a substantial time advantage (with respect to its FC counterpart). The reduced computational resources and the tractability of the computations are other major benefits of the procedure.

Spectroscopic and Theoretical Identifications of Two Structural Motifs of (H2O)10 Cluster

Precise characterization of archetypal systems of aqueous hydrogen-bonding networks is essential for developing accurate potential functions and universal models of water. The structures of water clusters (H2O)n (n = 2-9) have been verified recently through size-specific infrared spectroscopy with a vacuum ultraviolet free electron laser (VUV-FEL) and quantum chemical studies. For (H2O)10, the pentagonal prism and butterfly motifs were proposed to be important building blocks and were observed in previous experiments. Here we report the size-specific infrared spectra of (H2O)10 via a joint experimental and theoretical study. Well-resolved spectra provide a unique signature for the coexistence of pentagonal prism and butterfly motifs. These (H2O)10 motifs develop from the dominant structures of (H2O)n (n = 8, 9) clusters. This work provides an intriguing prelude to the diverse structure of liquid water and opens avenues for size-dependent measurement of larger systems to understand the stepwise formation mechanism of hydrogen-bonding networks.

Acceleration of Graph Neural Network-Based Prediction Models in Chemistry via Co-Design Optimization on Intelligence Processing Units

Atomic structure prediction and associated property calculations are the bedrock of chemical physics. Since high-fidelity ab initio modeling techniques for computing the structure and properties can be prohibitively expensive, this motivates the development of machine-learning (ML) models that make these predictions more efficiently. Training graph neural networks over large atomistic databases introduces unique computational challenges, such as the need to process millions of small graphs with variable size and support communication patterns that are distinct from learning over large graphs, such as social networks. We demonstrate a novel hardware-software codesign approach to scale up the training of atomistic graph neural networks (GNN) for structure and property prediction. First, to eliminate redundant computation and memory associated with alternative padding techniques and to improve throughput via minimizing communication, we formulate the effective coalescing of the batches of variable-size atomistic graphs as the bin packing problem and introduce a hardware-agnostic algorithm to pack these batches. In addition, we propose hardware-specific optimizations, including a planner and vectorization for the gather-scatter operations targeted for Graphcore's Intelligence Processing Unit (IPU), as well as model-specific optimizations such as merged communication collectives and optimized softplus. Putting these all together, we demonstrate the effectiveness of the proposed codesign approach by providing an implementation of a well-established atomistic GNN on the Graphcore IPUs. We evaluate the training performance on multiple atomistic graph databases with varying degrees of graph counts, sizes, and sparsity. We demonstrate that such a codesign approach can reduce the training time of atomistic GNNs and can improve their performance by up to 1.5× compared to the baseline implementation of the model on the IPUs. Additionally, we compare our IPU implementation with a Nvidia GPU-based implementation and show that our atomistic GNN implementation on the IPUs can run 1.8× faster on average compared to the execution time on the GPUs.

Confined Water Cluster Formation in Water Harvesting by Metal-Organic Frameworks: CAU-10-H versus CAU-10-CH3

Several metal-organic frameworks (MOFs) excel in harvesting water from the air or as heat pumps as they show a steep increase in water uptake at 10-30 % relative humidity (RH%). A precise understanding of which structural characteristics govern such behavior is lacking. Herein, CAU-10-H and CAU-10-CH3 are studied with H, CH3 corresponding to the functions grafted to the organic linker. CAU-10-H shows a steep water uptake ≈18 RH% of interest for water harvesting, yet the subtle replacement of H by CH3 in the organic linker drastically changes the water adsorption behavior to less steep water uptake at much higher humidity values. The materials' structural deformation and water ordering during adsorption with in situ sum-frequency generation, in situ X-ray diffraction, and molecular simulations are unraveled. In CAU-10-H, an energetically favorable water cluster is formed in the hydrophobic pore, tethered via H-bonds to the framework μOH groups, while for CAU-10-CH3, such a favorable cluster cannot form. By relating the findings to the features of water adsorption isotherms of a series of MOFs, it is concluded that favorable water adsorption occurs when sites of intermediate hydrophilicity are present in a hydrophobic structure, and the formation of energetically favorable water clusters is possible.

Descriptors of water aggregation

We rely on a total of 23 (cluster size, 8 structural, and 14 connectivity) descriptors to investigate structural patterns and connectivity motifs associated with water cluster aggregation. In addition to the cluster size n (number of molecules), the 8 structural descriptors can be further categorized into (i) one-body (intramolecular): covalent OH bond length (rOH) and HOH bond angle (θHOH), (ii) two-body: OO distance (rOO), OHO angle (θOHO), and HOOX dihedral angle (ϕHOOX), where X lies on the bisector of the HOH angle, (iii) three-body: OOO angle (θOOO), and (iv) many-body: modified tetrahedral order parameter (q) to account for two-, three-, four-, five-coordinated molecules (qm, m = 2, 3, 4, 5) and radius of gyration (Rg). The 14 connectivity descriptors are all many-body in nature and consist of the AD, AAD, ADD, AADD, AAAD, AAADD adjacencies [number of hydrogen bonds accepted (A) and donated (D) by each water molecule], Wiener index, Average Shortest Path Length, hydrogen bond saturation (% HB), and number of non-short-circuited three-membered cycles, four-membered cycles, five-membered cycles, six-membered cycles, and seven-membered cycles. We mined a previously reported database of 4 948 959 water cluster minima for (H2O)n, n = 3-25 to analyze the evolution and correlation of these descriptors for the clusters within 5 kcal/mol of the putative minima. It was found that rOH and % HB correlated strongly with cluster size n, which was identified as the strongest predictor of energetic stability. Marked changes in the adjacencies and cycle count were observed, lending insight into changes in the hydrogen bond network upon aggregation. A Principal Component Analysis (PCA) was employed to identify descriptor dependencies and group clusters into specific structural patterns across different cluster sizes. The results of this study inform our understanding of how water clusters evolve in size and what appropriate descriptors of their structural and connectivity patterns are with respect to system size, stability, and similarity. The approach described in this study is general and can be easily extended to other hydrogen-bonded systems.

The Back Door to the Surface Hydrated Electron

We use a Mg+ metal to extend the size regime of aqueous clusters to extrapolate to the bulk limit of the vertical detachment energy (VDE) of the solvated electron to >3,200, a value between 1 to over 2 orders of magnitude larger than the one previously measured experimentally or computed theoretically. We relate the VDE to the energy difference between the Mg+(H2O)n and Mg2+(H2O)n systems and the metal's second ionization potential. The extrapolated bulk VDEs of the localized surface electron, which moves away from the metal as n increases, are 1.89 ± 0.01 eV for semiempirical (n ∼ 3,200; PM6-D3H4) and 1.73 ± 0.03 eV (n ∼ 150; HF) and 1.83 ± 0.02 eV (n ∼ 150; MP2) for ab initio, in excellent agreement with the 1.6-1.8 eV range of experimental results. The VDEs converge from above (larger values) to the bulk limit, in a manner that is qualitatively opposite from previous studies and experiments lacking a charged metal, a fact justifying the "back door" approach to the solvated electron.

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.

An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2-25

We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2-11, 16-17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (D_e's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2-25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83-119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (D_e's) throughout the entire cluster range (n = 2-25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ∼4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6-3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.

Water model for hydrophobic cavities: structure and energy from quantum-chemical calculations

This ab initio study aims to design a series of large water clusters having a hollow clathrate-like cage able to host hydrophobic solutes of various sizes. Starting from the (H₂O)_n (n = 18, 20, 24 and 28) hollow cages, water layers have been added in a stepwise manner in order to model the configuration of water molecules beyond the primary shell. The large (H₂O)₁₀₀, (H₂O)₁₂₀ and (H₂O)₁₄₀ clusters complete the hydrogen bonding network of the cage with optimal and regular tiling of the do-, tetra-decahedron and hexa-decahedron, respectively. This study is corroborated by an investigation of dense water clusters up to the (H₂O)₁₂₃ one, being highly consistent with experimental data on ice concerning the electronic and zero-point energies for aggregate formation at 0 K and enthalpy and entropy at 273 K. The cavity creation profoundly alters the orientation of water molecules compared with those found in dense clusters. Nevertheless, such a large reorganization is necessary to maximize the water-water attraction by making it similar to the one found in dense clusters. The cage formation is an endothermic process; however, the computed values are large compared with previous reports for hydrocarbon aqueous solutions. Larger clusters are required for a more fruitful comparison.

Many-Body Contributions in Water Nanoclusters

Many-body interactions in water are known to be important but difficult to treat in atomistic models and often are included only as a correction. Polarizable models treat them explicitly, with long-range many-body potentials, within their classical approximation. However, their calculation is computationally expensive. Here, we evaluate how relevant the contributions to the many-body interaction associated with different coordination shells are. We calculate the global energy minimum, and the corresponding configuration, for nanoclusters of up to 20 water molecules. We find that including the first coordination shell, i.e., the five-body term of the central molecule, is enough to approximate within 5% the global energy minimum and its structure. We show that this result is valid for three different polarizable models, the Dang-Chang, the MB-pol, and the Kozack-Jordan potentials. This result suggests a strategy to develop many-body potentials for water that are reliable and, at the same time, computationally efficient.

A specific MNDO parameterization for water

A modified neglect of differential overlap has been parameterized specifically for water and its oligomers with the addition of polarization functions on both hydrogen and oxygen, Feynman dispersion, and a slight modification of the treatment of the hydrogen nucleus. The results show that it is possible to easily obtain good geometries and energies for hydrogen-bonded water aggregates. Data from the Benchmark Energy and Geometry Database water-cluster database were used to parameterize the new Hamiltonian for water clusters from the dimer to the decamer using MP2/aug-cc-pVDZ optimized geometries and CCSD(T)/CBS oligomerization energies. Seventy five oligomerization and rearrangement energies derived from the parameterization data are reproduced with a root mean-square error (RMSE) of 0.79 kcal mol^-1 and the geometries of 38 oligomers with an RMSE of 0.17 Å. Interestingly, the Feynman dispersion term adopts a role different from that intended and tunes the atomic polarizability. The implications of these results in terms of future dedicated neglect of diatomic differential overlap Hamiltonians and those that use force-field-like atom types are discussed.

Spectroscopic snapshot for neutral water nonamer (H2O)9: Adding a H2O onto a hydrogen bond-unbroken edge of (H2O)8

Structural characterization of neutral water clusters is crucial to understanding the structures and properties of water, but it has been proven to be a challenging experimental target due to the difficulty in size selection. Here, we report the size-specific infrared spectra of confinement-free neutral water nonamer (H₂O)₉ based on threshold photoionization, using a tunable vacuum ultraviolet free-electron laser. Distinct OH stretch vibrational fundamentals in the 3200-3350 cm^-1 region are observed, providing unique spectral signatures for the formation of an unprecedented (H₂O)₉ structure evolved by adding a ninth water molecule onto a hydrogen bond-unbroken edge of the (H₂O)₈ octamer with D_2d symmetry. This nonamer structure coexists with the five previously identified structures that can be viewed as derived by inserting a ninth water molecule into a hydrogen bond-broken edge of the D_2d/S₄ octamer. These findings provide key microscopic information for systematic understanding of the formation and growth mechanism of dynamical hydrogen-bonding networks that are responsible for the structure and properties of condensed-phase water.

Adsorption free energy of phenol onto coronene: Solvent and temperature effects

Molecular modeling can considerably speed up the discovery of materials with high adsorption capacity for wastewater treatment. Despite considerable efforts in computational studies, the molecular modeling of adsorption processes has several limitations in reproducing experimental conditions. Handling the environmental effects (solvent effects) and the temperature effects are part of the important limitations in the literature. In this work, we address these two limitations using the adsorption of phenol onto coronene as case study. In the proposed model, for the solvent effects, we used a hybrid solvation model, with n explicit water molecules and implicit solvation. We increasingly used n=1 to n=12 explicit water molecules. To account for the temperature effects, we evaluated the adsorption efficiency using the adsorption free energy for temperatures varying from 200 to 400K. We generated initial configurations using classical molecular dynamics, before further optimisation at the ωB97XD/aug-cc-pVDZ level of theory. Polarisable continuum solvation model (PCM) is used for the implicit solvation. The adsorption free energy is evaluated to be -1.3kcal/mol at room temperature. It has been found that the adsorption free energy is more negative at low temperatures. Above 360K, the adsorption free energy is found to be positive.

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.

Thermal stability of water polyhedra with square faces

The ability to form numerous crystalline modifications of ice and gas hydrate frameworks is a characteristic feature of water. In fact, this structural variety is much wider due to the proton disorder. Configurations with different arrangements of hydrogen atoms (protons) in hydrogen bonds are not equivalent in their properties. Polyhedral water clusters are convenient objects for studying the effect of proton disorder on the properties of ice-like systems. It was previously established that the stability of water polyhedra is determined by the competition of two factors. The geometric factor gives preference to tetrahedrally coordinated structures with a large number of pentagonal faces. The topological factor takes into account the number of energetically most favorable types of H-bonds. This number increases with the number of square faces. It was found that tetrahedrally coordinated structures are not the most stable. However, these calculations were performed without taking thermal effects into account (Kirov M. V., J Phys Chem A, 124:4463 - 4470, 2020). The purpose of the present article is to study the structural stability of various water polyhedra at different temperatures. In the course of modeling, using the Amoeba force field, the advantage of configurations with a large number of square faces is demonstrated. The structure and energetics of surface defects are studied. Several very stable structures of unusual shape were found, including polyhedra which contain 4-coordinated molecules and polyhedra whose O-H groups are directed to the cluster center. The comparative analysis of cluster stability includes the temperature intervals of melting-like transitions.

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Nonpolar Water Clusters: Proton Nuclear Magnetic Resonance Spectroscopic Evidence for Transformation from Polar Water to Nonpolar Water Clusters in Liquid State

The hydrophilic/hydrophobic interactions of water are important in biological and chemical self-assembly phenomena. Water clusters in hydrophobic environments exhibit a unique morphology. Their process of formation and nonpolar properties have been extensively studied, but no direct experimental evidence has been available until now. This study provides spectroscopic evidence for the transformation of water to nonpolar configuration via clustering. Although individual water molecules form hydrogen bonds with the hydroxyl protons of n-hexanol when codissolved in a nonpolar solvent (toluene-d₈), the water clusters are comprised solely of hydrogen bonds between water molecules and do not form hydrogen bonds with the hydroxyl protons of n-hexanol. This behavior indicates that the water clusters are nonpolar rather than polar. This study reports the first example of nonpolar water configuration produced via a liquid-state clustering. This property is a common and important interfacial phenomenon of water in chemistry, biology, materials science, geology, and meteorology.

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.

Mapping the temperature-dependent and network site-specific onset of spectral diffusion at the surface of a water cluster cage

We explore the kinetic processes that sustain equilibrium in a microscopic, finite system. This is accomplished by monitoring the spontaneous, time-dependent frequency evolution (the frequency autocorrelation) of a single OH oscillator, embedded in a water cluster held in a temperature-controlled ion trap. The measurements are carried out by applying two-color, infrared-infrared photodissociation mass spectrometry to the D₃O⁺·(HDO)(D₂O)₁₉ isotopologue of the "magic number" protonated water cluster, H⁺·(H₂O)₂₁ The OH group can occupy any one of the five spectroscopically distinct sites in the distorted pentagonal dodecahedron cage structure. The OH frequency is observed to evolve over tens of milliseconds in the temperature range (90 to 120 K). Starting at 100 K, large "jumps" are observed between two OH frequencies separated by ∼300 cm^-1, indicating migration of the OH group from the bound OH site at 3,350 cm^-1 to the free position at 3,686 cm^-1 Increasing the temperature to 110 K leads to partial interconversion among many sites. All sites are observed to interconvert at 120 K such that the distribution of the unique OH group among them adopts the form one would expect for a canonical ensemble. The spectral dynamics displayed by the clusters thus offer an unprecedented view into the molecular-level processes that drive spectral diffusion in an extended network of water molecules.

On the strength of hydrogen bonding within water clusters on the coordination limit

Hydrogen bonds (HB) are arguably the most important noncovalent interactions in chemistry. We study herein how differences in connectivity alter the strength of HBs within water clusters of different sizes. We used for this purpose the interacting quantum atoms energy partition, which allows for the quantification of HB formation energies within a molecular cluster. We could expand our previously reported hierarchy of HB strength in these systems (Phys. Chem. Chem. Phys., 2016, 18, 19557) to include tetracoordinated monomers. Surprisingly, the HBs between tetracoordinated water molecules are not the strongest HBs despite the widespread occurrence of these motifs (e.g., in ice I_h ). The strongest HBs within H₂ O clusters involve tricoordinated monomers. Nonetheless, HB tetracoordination is preferred in large water clusters because (a) it reduces HB anticooperativity associated with double HB donors and acceptors and (b) it results in a larger number of favorable interactions in the system. Finally, we also discuss (a) the importance of exchange-correlation to discriminate among the different examined types of HBs within H₂ O clusters, (b) the use of the above-mentioned scale to quickly assess the relative stability of different isomers of a given water cluster, and (c) how the findings of this research can be exploited to indagate about the formation of polymorphs in crystallography. Overall, we expect that this investigation will provide valuable insights into the subtle interplay of tri- and tetracoordination in HB donors and acceptors as well as the ensuing interaction energies within H₂ O clusters.

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.

Energetics of Water Polyhedra with Square Faces

In ice and other icelike systems, the structural variety of tetrahedrally coordinated systems increases strongly due to proton disorder. Configurations that differ from each other only by the arrangement of hydrogen atoms (protons) in hydrogen bonds are nonequivalent. Polyhedral water clusters are interesting objects of study since the analysis of the energetics of these tetrahedrally coordinated systems reveals very simple regularities. For water polyhedra of the most regular shape, the simplified physical model of strong and weak effective H bonds (the SWEB model) has been developed. This model allows predicting the classes of the most stable proton configurations. The number of H bonds that are more preferable from the point of view of Coulomb interaction is the only classification criterion for this model. For water polyhedra with square faces, this model becomes less accurate. However, for such clusters, there is another essential topological indicator: the number of molecules that are completely located in the planes of square faces. The results of numerous calculations show that these two topological indices largely determine the energetics of a huge number of proton configurations in water polyhedra with square faces.

Finite Systems under Pressure: Assessing Volume Definition Models from Parallel-Tempering Monte Carlo Simulations

We have investigated different approaches to handling parallel-tempering Monte Carlo (PTMC) simulations in the isothermal-isobaric ensemble of molecular cluster/nanoparticle systems for predicting structural phase diagram transitions. We have implemented various methodologies that consist of treating pressure implicitly through its effect on the volume. Thus, the main problem in the simulations under nonzero pressure becomes the volume definition of the finite nonperiodic system, and we considered approaches based on the particles' coordinates. Various volume models, namely container-volume, particle-volume, average-volume, ellipsoids-volume, and convex hull-volume, were employed, and the required corrections for each of them in the Monte Carlo computations were introduced. Finally, we explored the effects of volume/pressure changes for all models on structural phase transitions of a test system, such as the small "icelike" (H₂O)₁₂ water cluster. The temperature and pressure dependence of the cluster's heat capacity and energy-volume Pearson correlation coefficient were studied, phase diagrams were constructed using a multiple-histogram method, and attempts were made to identify phase transitions to particular cluster structures. Our results show significant differences between the employed volume models, and we discuss all pressure-induced, such as solid-solid-, solid-liquid-, and liquid-gas-like, phase transformations in the present study.

Synthetic access to calix[3]pyrroles via meso-expansion: hosts with diverse guest chemistry

The bridging units between the two α-positions of the tripyrrane moiety helped in manipulating the guest binding ability of calix[3]pyrroles.