Are there any magic numbers for water nanodroplets, (H2O)n, in the range 36 ≤n≤ 50?

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.

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.

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.

Size-guided multi-seed heuristic method for geometry optimization of clusters: Application to benzene clusters

Since searching for the global minimum on the potential energy surface of a cluster is very difficult, many geometry optimization methods have been proposed, in which initial geometries are randomly generated and subsequently improved with different algorithms. In this study, a size-guided multi-seed heuristic method is developed and applied to benzene clusters. It produces initial configurations of the cluster with n molecules from the lowest-energy configurations of the cluster with n - 1 molecules (seeds). The initial geometries are further optimized with the geometrical perturbations previously used for molecular clusters. These steps are repeated until the size n satisfies a predefined one. The method locates putative global minima of benzene clusters with up to 65 molecules. The performance of the method is discussed using the computational cost, rates to locate the global minima, and energies of initial geometries. © 2018 Wiley Periodicals, Inc.

Clusters of coarse-grained water molecules

Global optimization for molecular clusters can be significantly more difficult than for atomic clusters because of the coupling between orientational and translational degrees of freedom. A coarse-grained representation of the potential can reduce the complexity of this problem, while retaining the essential features of the intermolecular interactions. In this study, we use a basin-hopping algorithm to locate putative global minima for clusters of coarse-grained water molecules modeled using a monatomic water potential for cluster sizes 3 ≤ N ≤ 55. We characterize these structures and identify structural trends using ideas from graph theory. The agreement with atomistic results and experiment is rather patchy, which we attribute to the tetrahedral bias in the three-body potential that results in too few nearest neighbor contacts and premature emergence of bulk-like structure. In spite of this issue, the results offer further useful insight into the relationship between the structure of clusters and bulk phases, and the mathematical form of a widely used model potential.