Search for Low Energy Structures of Water Clusters (H2O)n, n = 20−22, 48, 123, and 293

Revisiting the IR Spectra of H2S in an Argon Matrix: Identification of (H2S)n (n ≤ 4) Clusters via the Spectral Assignment of νS-H Transitions

Small-molecular clusters of H2S up to tetramer have been experimentally identified in a cold and solid argon matrix by the spectral assignment of νS-H fundamental transitions for different H2S:argon mixing ratios. Normal-mode frequency calculations at the MP2-CP/aug-cc-pV(Q + d)Z level have been used to support the spectral assignments. In addition, modulations in relative populations of different clusters due to the annealing of the deposited matrix and the preheating of the H2S-argon gas mixture before deposition reinforced the spectral assignments. Variations in mixing ratio, annealing of the matrix, and preheating of the gas mixture have also been used, in a combined manner, to unambiguously identify the ν1 and ν3 bands of the H2S monomer, which has been a matter of dispute for a long period. The two bands have been identified at 2634.4 and 2648.0 cm-1, respectively, while three bands at 2581.5, 2568.4, and 2547.6 cm-1 have been assigned to H-bonded dimers, cyclic trimers, and cyclic tetramers, respectively. Multiple bands within 2550-2580 cm-1 have been assigned to caged tetramers. The cooperative strengthening of S-H···S H bonds in cyclic H2S clusters was evident from the linear increment in νS-H spectral shifts with cluster size.

Analysis of two overlapping fragmentation approaches in density matrix construction: GMBE-DM vs. ADMA

In this study, we conduct a comparative analysis of two density matrix construction methods: the generalized many-body expansion for building density matrices (GMBE-DM) based on the set-theoretical principle of inclusion/exclusion and the adjustable density matrix assembler (ADMA) based on the Mulliken-Mezey ansatz. We apply these methods to various noncovalent clusters, including water clusters, ion-water clusters, and ion-pair clusters, using both small 6-31G(d) and large def2-TZVPPD basis sets. Our findings reveal that the GMBE-DM method, particularly when combined with the purification scheme and truncation at the one-body level [GMBE(1)-DM-P], exhibits superior performance across all test systems and basis sets. In contrast, all ADMA set of methods show reasonable results only with small and compact basis sets. For example, GMBE(1)-DM-P outperforms the best ADMA method by at least 4 and 16 times with small and large basis sets, respectively, in the case of (H2O)N=6-55. This highlights the significance of the basis set choice for ADMA, which is even more critical than the fragmentation scheme, such as the size of subsystems, while GMBE-DM consistently produces accurate results irrespective of the chosen basis set. Consequently, the efficient and robust GMBE(1)-DM-P approach is recommended as a fragmentation method for generating accurate absolute and relative energies across different binding patterns and basis sets for noncovalent clusters.

Accurate prediction of global-density-dependent range-separation parameters based on machine learning

In this work, we develop an accurate and efficient XGBoost machine learning model for predicting the global-density-dependent range-separation parameter, ωGDD, for long-range corrected functional (LRC)-ωPBE. This ωGDDML model has been built using a wide range of systems (11 466 complexes, ten different elements, and up to 139 heavy atoms) with fingerprints for the local atomic environment and histograms of distances for the long-range atomic correlation for mapping the quantum mechanical range-separation values. The promising performance on the testing set with 7046 complexes shows a mean absolute error of 0.001 117 a0-1 and only five systems (0.07%) with an absolute error larger than 0.01 a0-1, which indicates the good transferability of our ωGDDML model. In addition, the only required input to obtain ωGDDML is the Cartesian coordinates without electronic structure calculations, thereby enabling rapid predictions. LRC-ωPBE(ωGDDML) is used to predict polarizabilities for a series of oligomers, where polarizabilities are sensitive to the asymptotic density decay and are crucial in a variety of applications, including the calculations of dispersion corrections and refractive index, and surpasses the performance of all other popular density functionals except for the non-tuned LRC-ωPBE. Finally, LRC-ωPBE (ωGDDML) combined with (extended) symmetry-adapted perturbation theory is used in calculating noncovalent interactions to further show that the traditional ab initio system-specific tuning procedure can be bypassed. The present study not only provides an accurate and efficient way to determine the range-separation parameter for LRC-ωPBE but also shows the synergistic benefits of fusing the power of physically inspired density functional LRC-ωPBE and the data-driven ωGDDML model.

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.

Water clusters and density fluctuations in liquid water based on extended hierarchical clustering methods

The microscopic structures of liquid water at ambient temperatures remain a hot debate, which relates with structural and density fluctuations in the hydrogen bond network. Here, we use molecular dynamics simulations of liquid water to study the properties of three-dimensional cage-like water clusters, which we investigate using extended graph-based hierarchical clustering methods. The water clusters can cover over 95% of hydrogen bond network, among which some clusters maximally encompass thousands of molecules extending beyond 3.0 nm. The clusters imply fractal behaviors forming percolating networks and the morphologies of small and large clusters show different scaling rules. The local favored clusters and the preferred connections between adjacent clusters correspond to lower energy and conformational entropy depending on cluster topologies. Temperature can destroy large clusters into small ones. We show further that the interior of clusters favors high-density patches. The water molecules in the small clusters, inside which are the void regarded as hydrophobic objects, have a preference for being more tetrahedral. Our results highlight the properties and changes of water clusters as the fundamental building blocks of hydrogen bond networks. In addition, the water clusters can elucidate structural and density fluctuations on different length scales in liquid water.

Hierarchical clustering analysis of hydrogen bond networks in aqueous solutions

To understand the relation between the macroscopic properties and microscopic structure of hydrogen bond networks in solutions, we introduced a hierarchical clustering method to analyze the typical configurations of water clusters in this type of network. Regarding hydrogen bonds as frames, the rings, fragments and clusters are defined and analyzed to provide a comprehensive perspective for the distributional and dynamic characteristics of the hydrogen-bonding network in NaCl solution at different concentrations. The properties of the radial distribution function and hydrogen bonds are first analyzed. Destruction and shorter lifetimes of hydrogen bonds are observed in solutions. In further analysis of the two-dimensional configuration, i.e., ring, and three-dimensional configuration, i.e., fragment, the average number, size and lifetime of these structures consistently decrease as the concentration increases. Ionic effects on disrupting rings and fragments are significant in the first hydration shell, especially with sodium cations, and these effects weaken beyond the first hydration shell. Regarding the clusters obtained using the Louvain algorithm, our results indicate that clusters break and become smaller as the NaCl concentration increases. The presence of ions also leads to the isolation of clusters and therefore the inhibition of changes. The lifetime of clusters increases with NaCl concentration, indicating the slowed breakage and reformation of clusters in NaCl solutions. This method can be further applied to quantitatively characterize hydrogen bond networks to elucidate more properties of aqueous solutions.

A hierarchical clustering method of hydrogen bond networks in liquid water undergoing shear flow

Many properties of water, such as turbulent flow, are closely related to water clusters, whereas how water clusters form and transform in bulk water remains unclear. A hierarchical clustering method is introduced to search out water clusters in hydrogen bonded network based on modified Louvain algorithm of graph community. Hydrogen bonds, rings and fragments are considered as 1st-, 2nd-, and 3rd-level structures, respectively. The distribution, dynamics and structural characteristics of 4th- and 5th-level clusters undergoing non-shear- and shear-driven flow are also analyzed at various temperatures. At low temperatures, nearly 50% of water molecules are included in clusters. Over 60% of clusters remain unchanged between neighboring configurations. Obvious collective translational motion of clusters is observed. The topological difference for clusters is elucidated between the inner layer, which favors 6-membered rings, and the external surface layer, which contains more 5-membered rings. Temperature and shearing can not only accelerate the transformation or destruction of clusters at all levels but also change cluster structures. The assembly of large clusters can be used to discretize continuous liquid water to elucidate the properties of liquid water.

Structures, relative stability and binding energies of neutral water clusters, (H2O)2–30

We have revised the structures of neutral water clusters, (H₂O)_n=2–30, with the affordable M06-2X functional, presenting up to 25 isomers for each cluster size.

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.

Gauging the performance of some density functionals including dispersion and nonlocal corrections for relative energies of water 20-mers

Currently, development of density functional theory approximations and their benchmarking for accurately modeling different types of molecular interactions become a very active field of research. In this report, performance of the dispersion (D3) and nonlocal (NL) corrected density functionals has been compared with generalized energy-based fragmentation approach at the complete basis set limit for predicting the relative energies of 10 low-energy isomers of water nanoclusters (H₂O)₂₀ as an illustrative example of hydrogen bonded systems. Considering a variety of exchange-correlation density functionals in combination with D3 and NL corrections we find that the D3 based approximations outperform the functionals incorporating NL correction. It is also shown that the LC-ωPBE-D3 and rPW86PBE-NL functionals have the best trend from the viewpoint of the order of stabilities in water nanoclusters under study.

Understanding the structure and hydrogen bonding network of (H2O)32 and (H2O)33: an improved Monte Carlo temperature basin paving (MCTBP) method and quantum theory of atoms in molecules (QTAIM) analysis

Large water clusters are of particular interest because of their connection to liquid water and the intricate hydrogen bonding networks they possess.

Different Ways of Hydrogen Bonding in Water - Why Does Warm Water Freeze Faster than Cold Water?

The properties of liquid water are intimately related to the H-bond network among the individual water molecules. Utilizing vibrational spectroscopy and modeling water with DFT-optimized water clusters (6-mers and 50-mers), 16 out of a possible 36 different types of H-bonds are identified and ordered according to their intrinsic strength. The strongest H-bonds are obtained as a result of a concerted push-pull effect of four peripheral water molecules, which polarize the electron density in a way that supports charge transfer and partial covalent character of the targeted H-bond. For water molecules with tetra- and pentacoordinated O atoms, H-bonding is often associated with a geometrically unfavorable positioning of the acceptor lone pair and donor σ^*(OH) orbitals so that electrostatic rather than covalent interactions increasingly dominate H-bonding. There is a striking linear dependence between the intrinsic strength of H-bonding as measured by the local H-bond stretching force constant and the delocalization energy associated with charge transfer. Molecular dynamics simulations for 1000-mers reveal that with increasing temperature weak, preferentially electrostatic H-bonds are broken, whereas the number of strong H-bonds increases. An explanation for the question why warm water freezes faster than cold water is given on a molecular basis.

Are fragment-based quantum chemistry methods applicable to medium-sized water clusters?

The GEBF method is demonstrated to be more accurate than the EE-MB method for medium-sized water clusters.

Low energy isomers of (H2O)25 from a hierarchical method based on Monte Carlo temperature basin paving and molecular tailoring approaches benchmarked by MP2 calculations

We report new global minimum candidate structures for the (H2O)25 cluster that are lower in energy than the ones reported previously and correspond to hydrogen bonded networks with 42 hydrogen bonds and an interior, fully coordinated water molecule. These were obtained as a result of a hierarchical approach based on initial Monte Carlo Temperature Basin Paving sampling of the cluster's Potential Energy Surface with the Effective Fragment Potential, subsequent geometry optimization using the Molecular Tailoring Approach with the fragments treated at the second order Møller-Plesset (MP2) perturbation (MTA-MP2) and final refinement of the entire cluster at the MP2 level of theory. The MTA-MP2 optimized cluster geometries, constructed from the fragments, were found to be within <0.5 kcal/mol from the minimum geometries obtained from the MP2 optimization of the entire (H2O)25 cluster. In addition, the grafting of the MTA-MP2 energies yields electronic energies that are within <0.3 kcal/mol from the MP2 energies of the entire cluster while preserving their energy rank order. Finally, the MTA-MP2 approach was found to reproduce the MP2 harmonic vibrational frequencies, constructed from the fragments, quite accurately when compared to the MP2 ones of the entire cluster in both the HOH bending and the OH stretching regions of the spectra.

Density functional studies of fused dodecahedral and irregular-dodecahedral water cages

The fused cages of dodecahedral and irregular-dodecahedral water cages with the maximum number of t1d hydrogen bonds were studied using the dispersion corrected density functional method.

Relative energies of water nanoclusters (H2O)20: comparison of empirical and nonempirical double-hybrids with generalized energy-based fragmentation approach

The applicability of recently developed parameterized and parameter-free double-hybrids for predicting the relative energies of water nanoclusters has been examined.

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.

Facilitating Minima Search for Large Water Clusters at the MP2 Level via Molecular Tailoring

Water clusters (H2O)20 and (H2O)25 are explored at the Møller-Plesset second-order perturbation (MP2) level of theory. Geometry optimization is carried out on favorable structures, initially generated by the temperature basin paving (TBP) method, utilizing the fragment-based molecular tailoring approach (MTA). MTA-based stabilization energies at the complete basis set limit are accurately estimated by grafting the energy correction using a smaller basis set. For prototypical cases, the minima are established via MTA-based vibrational frequency calculations at the MP2/aug-cc-pVDZ level. The potential of MTA in tackling large clusters is further demonstrated by performing geometry optimization at MP2/aug-cc-pVDZ starting with the global minimum of (H2O)30 reported by Monte Carlo (MC) and molecular dynamics (MD) investigations. The present study brings out the efficacy of MTA in performing computationally expensive ab initio calculations with minimal off-the-shelf hardware without significant loss of accuracy.

Accurate predictions of water cluster formation, (H₂O)(n=2-10)

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2-10 water molecules. This approach reveals new low energy conformers for (H(2)O)(n=7,9,10). The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.