Polyhedral Water Clusters Research Articles

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].

Barrier-free molecular reorientations in polyhedral water clusters

The structural stability of the weakest bonded configurations of water clusters in the form of gas hydrate cavities D and T, as well as in the form of Kelvin’s polyhedron, was tested using the local geometric optimization with the polarizable force field AMOEBA. A number of different barrier-free molecular rearrangements were observed. Most of the configurations changed their shapes, forming surface defects of the same type. But the main attention is paid to the concerted molecular reorientations leading to the proton shift along hydrogen bonds. A number of statements about the topology of the hydrogen-bonded network are rigorously proved. It is concluded that the structural stability of configurations and the features of structural transformations are basically determined by the arrangement of the homodromic hydrogen-bonded water rings. The stability of the configurations, which retained their original shape during local geometric optimization, was studied by the molecular dynamics method with a gradual increase in temperature. Some interesting effects were found. This is the stabilizing locking of the most polarized configurations, as well as very intense amplitude oscillations of the free OH group at the end of two-bond flips.

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.

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.

Effects of temperatures and carbon dioxide nanobubbles on superior electric storage for anodically oxidized films of AlY10 amorphous alloy

The effects of temperature and nanometer-sized bubbles (NBs) on a superior electric storage capacitor for anodically oxidized films of AlY10 amorphous alloys were determined at temperatures ranging from 275 to 298 K in 0.4 M H2SO4 solutions with NBs of ozone, oxygen, and carbon dioxide. The AAO specimen obtained by solution with carbon dioxide NBs at 278 K showed longer discharging time. The discharging time increases with increasing charging time and then saturates after around 70 s. The increment in temperature makes the structure from simple series capacitor with large capacitance to simple parallel capacitor with lower capacitance and larger resistance. The stability of NBs in water could be explained by enclosure in protonated polyhedral water clusters. The collapse of clusters with oxygen NBs result in the formation of OH− radicals and its resulting elution of Al, while carbon oxide NBs prevent the formation of OH− radicals, promoting sluggish oxidation that is required for the formation of AlO6 clusters.

Dipole moment of polyhedral water clusters: mathematical relationships and their application

Polyhedral water clusters are characterized by exponential proton disorder and a complex molecular interaction. Nevertheless, a simple theory has been developed for these systems. It allows predicting classes of the most stable proton configurations that differ in the arrangement of hydrogen atoms (protons) in the hydrogen bonds. The stability for a particular configuration is evaluated on the basis of the analysis of local topological characteristics of the hydrogen bond network. However, the stability of water clusters is determined also by another, clearly non-topological global characteristic: the magnitude of the total dipole moment. In this article we show that the total dipole moment of polyhedral water clusters is proportional to the vector sum of polyhedron edges if their direction coincides with the direction of hydrogen bonds. This makes it possible not to take into account separately the contribution of free (dangling) hydrogen atoms when classifying proton configurations.

Electronic origin of the dependence of hydrogen bond strengths on nearest-neighbor and next-nearest-neighbor hydrogen bonds in polyhedral water clusters (H2O)n, n = 8, 20 and 24.

The influence of the nearest neighbor and next-nearest neighbor water molecules on the strength of the hydrogen (H) bonds was examined for the polyhedral clusters of cubic (H2O)8, dodecahedral (H2O)20 and tetrakaidecahedral (H2O)24 cages. The relative stability and the characteristics of the H bond networks are also studied. The charge-transfer (CT) and dispersion interaction terms of every pair of H bonds are evaluated using perturbation theory based on the locally-projected molecular orbitals (LPMO PT). Every water molecule and every H-bonded pair in these polyhedral clusters are classified by the types of the neighbor molecules and H bonds. The relative binding energies among the polyhedral clusters are grouped by these classifications. The optimized OO distances, which are strongly correlated with the calculated pairwise CT terms, are dependent on the 49 sub-groups of the H bonds determined by the type of the neighbor molecules. The electronic origin of this dependence is analyzed using Mulliken's charge-transfer theory, and employing a few assumptions, the analytical formulas for the contribution of the CT terms to the H bond energy are derived.

Classification of hydrogen bond flips in small water polyhedra applied to concerted proton tunneling.

Recently a new mechanism of proton tunneling in a prism-like water hexamer was revealed [Richardson et al., Science, 2016, 351, 1310]. The tunneling motion involves the concerted breaking of two hydrogen bonds and rotations of two nearest water molecules. Eventually, this structural transformation means flipping one of the hydrogen bonds without the creation of defects in the hydrogen bond network. On the surface of polyhedral water clusters, there are five essentially different types of hydrogen bonds, and only two of them can be changed in this manner. In this article, the topological classification of such transformations for five small water polyhedra: triangular, pentagonal, and hexagonal prisms as well as cube and polyhedron 4454, consisting of four square and four pentagonal faces, is presented. Our classification includes the enumeration of all possible one-bond-flips with consideration of the types of hydrogen bonds on the polyhedral surface. Attention is paid to the most stable proton configurations which can be studied in experiments. It was established that a number of one-bond-flip transitions between the low energy configurations are possible in clusters in the shape of triangular and pentagonal prisms.

(H2O)20 Water Clusters at Finite Temperatures

We have performed an exhaustive study of energetics of (H2O)20 clusters. Our goal is to study the role that various free-energy terms play in this popular model system and see their effects on the distribution of the (H2O)20 clusters and in the infrared spectrum at finite temperatures. In more detail, we have studied the electronic ground-state structure energy and its long-range correlation (dispersion) part, vibrational zero-point corrections, vibrational entropy, and proton configurational entropy. Our results indicate a delicate competition between the energy terms; polyhedral water clusters are destabilized by dispersion interaction, while vibrational terms (zero-point and entropic) together with proton disorder entropy favor them against compact structural motifs, such as the pentagonal edge- or face-sharing prisms. Apart from small water clusters, our results can be used to understand the influence of these energy terms in water/ice systems in general. We have also developed energy expressions as a function of both earlier proposed and novel hydrogen-bond connectivity parameters for prismatic water clusters.

The transfer-matrix and max-plus algebra method for global combinatorial optimization: Application to cyclic and polyhedral water clusters

A new method for the combinatorial optimization of quasi-one-dimensional systems is presented. This method is in close analogy with the well-known transfer-matrix method. The method allows for the calculation of the lowest energy levels of the system. However, when finding the ground and some low-lying states of large complex systems, this method is more economical when compared to the standard transfer-matrix method. The method presented here is based on max-plus algebra, which has maximization and addition as its basic arithmetic operations. For the explanation of this method we use cyclic water clusters as simple examples. The efficiency of the max-plus-algebraic method is demonstrated in the course of global combinatorial optimization of hydrogen bond arrangements in large polyhedral water clusters with fixed positions of the oxygen atoms. The energy of the clusters is estimated using approximate discrete models for the intermolecular interactions.

Identifying the most stable networks in polyhedral water clusters

We present a new discrete model to identify the most stable networks in polyhedral water clusters. The model relies on the screening of the energy of the local network based on the concept of ‘strong’/‘weak’ nearest neighbor interactions according to their ( trans/ cis) orientation and the connectivity of the respective pairs to neighbors. We apply this model to the pentagonal dodecahedron (H 2O) 20 cluster using a hierarchical description of the intermolecular interactions using classical interaction potentials and several levels of electronic structure methods. This study offers a practical and efficient approach for identifying stable networks in clathrate hydrate structures.

Energy optimization of water polyhedra. I. Predictive ability of discrete models for intermolecular interaction

The reasons of high accuracy of discrete models suggested earlier for intermolecular interaction in polyhedral water clusters are discussed. It is shown that essential positive effect on accuracy of models is provided by topological correlations imposed on the structure of polyhedral clusters by Bernal-Fowler rules.

Energy optimization of water polyhedra. II. Classification of optimal configurations in clusters from a cube up to fullerene

Using a combinatory optimization method based on discrete models of intermolecular interaction, the classes of optimal configurations in polyhedral water clusters have been calculated. By means of calculations with various pair potentials an essential advantage in energy of discretely optimized configurations is ascertained. The effect of the dipole moment of clusters on their energy is studied.

O−H Stretch Modes of Dodecahedral Water Clusters: A Statistical Ab Initio Study

Infrared frequencies calculations were carried out for 20 (H2O)20 water clusters obeying the 5(12) dodecahedral geometry, optimized at the B3LYP/6-311++G** level. Their combined spectra contained 800 O-H stretch modes, ranging from 2181 to 3867 cm(-1) (unscaled), which were treated and studied as a database. Of these, 752 modes (94%) could be assigned to a single dominant O-H stretch. These 752 were classified into five subdatabases depending on the local H-bond type of the dominant stretch. The frequency (nu) was correlated with the O-H distance (b(OH)), with H-bond length (R(OO)) where applicable, and with other variables. The parameter b(OH) alone accounted for 96-99% of the variance in nu for stretches in H-bonds. The correlation with R(OO) is substantially weaker. Normal modes were classified as "high ratio" or "low ratio" depending upon the mode's distribution of kinetic energy among the O-H bonds. High-ratio modes (389 modes, or 49% of our sample) are modeled well as a single oscillator undergoing small perturbations by weak coupling from other oscillators. Low-ratio modes involve strong coupling with at least one other O-H stretch for which b(OH2) is close to b(OH). The IR intensities of modes vary widely but can be explained in terms of a single equation giving dipole moment derivatives as a function of b(OH). For the lowest-energy (H2O)20 clusters, their IR stretch spectra contained eight distinguishable absorption bands. An explanation for eight bands in terms of the theory of polyhedral water clusters is offered.

Zero Point Energy of Polyhedral Water Clusters

Polyhedral water clusters (PWCs) are cage-like (H2O)n clusters where every O participates in exactly three H bonds. For a database of 83 PWCs, 8 < or = n < or = 20, geometry was optimized and zero point energy (ZPE) was calculated at the B3LYP/6-311++G** level. ZPE correlates negatively with electronic energy (E0): each increase of 1 kcal/mol in E0 corresponds to a decrease of about 0.11 kcal/mol in ZPE. For each n, a set of four connectivity parameters accounts for 98% or more of the variance in ZPE. Linear regression of ZPE against n and this set gives an RMS error of 0.13 kcal/mol. The contributions to ZPE from stretch modes only (ZPE(S)) and from torsional modes only (ZPE(T)) also correlate strongly with E0 and with each other.

Combinatorial structure optimization of polyhedral water clusters based on discrete models of intermolecular interaction

Energetically most favorable configurations of polyhedral water clusters were calculated using a new discrete model allowing for electrostatic interactions between molecules being the second and third neighbors in a hydrogen-bond network. Calculation results are presented with pair-additive potentials ST2, TIP4P, and TIP5P and compared with the results of recent quantum-chemical calculations. Energetically most favorable structures of cyclic water clusters and extended gas hydrate frameworks are discussed.

Application of database methods to the prediction of B3LYP-optimized polyhedral water cluster geometries and electronic energies

A method is described for a rapid prediction of B3LYP-optimized geometries for polyhedral water clusters (PWCs). Starting with a database of 121 B3LYP-optimized PWCs containing 2277 H-bonds, linear regressions yield formulas correlating O–O distances, O–O–O angles, and H–O–H orientation parameters, with local and global cluster descriptors. The formulas predict O–O distances with a rms error of 0.85 pm to 1.29 pm and predict O–O–O angles with a rms error of 0.6° to 2.2°. An algorithm is given which uses the O–O and O–O–O formulas to determine coordinates for the oxygen nuclei of a PWC. The H–O–H formulas then determine positions for two H’s at each O. For 15 test clusters, the gap between the electronic energy of the predicted geometry and the true B3LYP optimum ranges from 0.11 to 0.54 kcal/mol or 4 to 18 cal/mol per H-bond. Linear regression also identifies 14 parameters that strongly correlate with PWC electronic energy. These descriptors include the number of H-bonds in which both oxygens carry a non-H-bonding H, the number of quadrilateral faces, the number of symmetric angles in 5- and in 6-sided faces, and the square of the cluster’s estimated dipole moment.

Ab initio molecular-orbital calculations for dodecahedral water clusters including rare-gas atoms

Dodecahedral water clusters including rare-gas atoms and molecules are considered to play an important role in the beginning of the formation of gas hydrates in solutions. To investigate their stability, ab initio molecular-orbital calculations were performed at the MP2/6-311G(d,p)//HF/6-311G(d,p) level. In He, Ne, Ar, and Kr, the cohesive energies of the 12-hedral water clusters including each rare-gas atom were negative, whereas in Xe they were positive. Neon in the dodecahedral cluster was almost as stable as Ar and Kr in the dodecahedral clusters; the latter two are known as clathrate-forming gases. This suggests the probability of the existence of Ne clathrate hydrate, which is generally considered to be impossible. The chemical shifts of Xe incorporated in polyhedral water clusters were computed for the first time. The computed values qualitatively agree with the experimental results. PACS Nos.: 31.15Ar, 31.15Md, 31.15Ne, 36.40Cg, 36.40Mr

Polyhedral water clusters, I: Formal consequences of the ice rules

Polyhedral water clusters (PWCs) are (H 2O) n clusters in which every oxygen is 3-coordinated. An analog of the Bernal–Fowler ice rules, when combined with graph-theoretic facts about polyhedra, leads to a rich variety of mathematical relationships regarding structural descriptors of PWCs. These relationships are developed and rigorously proved. The emphasis is on relationships involving four structural parameters which are correlated with the electronic energy of PWCs. Principal results are the recognition of the importance of three levels of information in the H-bonding pattern of a PWC; the definition and classification of the ‘F-components’ and ‘L-components’ of a PWC; a method for generating all PWCs obeying the ice rules for a given polyhedral pattern; and a method based on the four-color theorem for producing low energy PWCs that have a property called ‘contiguity two’.

Polyhedral water clusters, II: correlations of connectivity parameters with electronic energy and hydrogen bond lengths

Polyhedral water clusters (PWCs) are (H 2O) n clusters in which every oxygen is three-coordinated. Four polyhedral geometries on which water clusters can be based are the cube ( n=8), pentagonal prism ( n=10), hexagonal prism ( n=12), and 4 45 4 octahedron ( n=12). For each of these geometries, a database was obtained of PWCs optimized at the B3LYP/6-311++G ∗∗ level. The total database contained 1311 hydrogen bonds in 82 optimized PWCs. Using linear regression, correlations were sought linking aspects of the clusters' H-bonding pattern with their electronic energies and with the lengths of their H-bonds. Excluding six very high-energy clusters whose H-bonding pattern included a motif called a cyclic component, 98.9% or more of the variance in clusters' electronic energy could be accounted for by just three connectivity parameters, for each of the geometries. Five families of H-bonds were distinguished based on the presence or absence of a pendent H on the acceptor and donor O and on the layout of adjacent H's. Within each family, the presence or absence of pendent H's on first and second neighbor O's accounted for 86–95% of the variance in H-bond length, and could be used to predict H-bond length with an RMS error≤2.4 pm.