Hexameric Clusters Research Articles

Integrated Monomer Synthesis and Framework Assembly: Achieving Isoreticular Modulation of Hydrogen‐Bonded Organic Frameworks

Systematic construction of isoreticular hydrogen‐bonded organic frameworks (HOFs) promises tailored material properties crucial for diverse applications, yet is challenging due to the weak, flexible, and non‐directional nature of hydrogen bonds. Herein, we develop an “integrated monomer synthesis‐framework assembly” (ISA) methodology for constructing a series of isoreticular HOFs. Unlike traditional methods where monomers are first synthesized and then assembled into HOFs, the ISA system employs dicyandiamide rigid hydrogen‐bonded hexameric clusters as connecting nodes to covalently react with planarized C3‐symmetric cyano‐precursors (C3‐CPs) to generate diaminotriazine (DAT) monomers, while simultaneously inducing the directional assembly into isoreticular (6,3)‐net hcb topological DAT‐C6‐HOFs. The pore sizes and microenvironments of the resulting DAT‐C6‐HOFs can be precisely tuned by varying the structural modulation (length and steric hindrance) of the π‐bridge on C3‐CPs, enabling highly selective sensing towards perfluorooctanoic acid over other homologous molecules, that are difficult to be separated and detected by chromatography. Overall, the ISA methodology facilitates the scalable creation of families of isostructural HOFs and provides a customized structural platform for investigating factors beyond topology that impact the capturing, releasing, and responding to guest molecules.

Integrated Monomer Synthesis and Framework Assembly: Achieving Isoreticular Modulation of Hydrogen-Bonded Organic Frameworks.

Systematic construction of isoreticular hydrogen-bonded organic frameworks (HOFs) promises tailored material properties crucial for diverse applications, yet is challenging due to the weak, flexible, and non-directional nature of hydrogen bonds. Herein, we develop an "integrated monomer synthesis-framework assembly" (ISA) methodology for constructing a series of isoreticular HOFs. Unlike traditional methods where monomers are first synthesized and then assembled into HOFs, the ISA system employs dicyandiamide rigid hydrogen-bonded hexameric clusters as connecting nodes to covalently react with planarized C3-symmetric cyano-precursors (C3-CPs) to generate diaminotriazine (DAT) monomers, while simultaneously inducing the directional assembly into isoreticular (6,3)-net hcb topological DAT-C6-HOFs. The pore sizes and microenvironments of the resulting DAT-C6-HOFs can be precisely tuned by varying the structural modulation (length and steric hindrance) of the π-bridge on C3-CPs, enabling highly selective sensing towards perfluorooctanoic acid over other homologous molecules, that are difficult to be separated and detected by chromatography. Overall, the ISA methodology facilitates the scalable creation of families of isostructural HOFs and provides a customized structural platform for investigating factors beyond topology that impact the capturing, releasing, and responding to guest molecules.

Synthesis and Crystal Structure Analysis of Some Aromatic Imines of Syringaldehyde

A series of syringaldehyde imines with para-substituted anilines have been synthesized in a good yield, and their crystal structures have been analyzed. The orientation of the syringaldehyde hydroxyl group plays in important role in the intermolecular hydrogen-bonding pattern of the molecules. The O–H…N hydrogen bonding interactions primarily determine the three-dimensional packing of the molecules, even though they make up a relatively small percentage of intermolecular interactions in the molecules. The three structures with the p-hydroxy group cis to the imine group give hydrogen-bonded zigzag chains in the monoclinic crystals, while the structure with a trans hydroxy group crystallize in a hexagonal space group (R3¯) and form hydrogen-bonded hexamers. The hexagonal structure also displays Br…Br interactions, forming additional hexameric clusters. The analysis of published p-hydroxyphenyl imine crystal structures from the Cambridge Crystallographic Database revealed patterns in the length of the hydrogen bonding interactions based on steric congestion around the hydroxyl group.

Synthesis and Characterization of Cerium-Oxo Clusters Capped by Acetylacetonate.

Cerium-oxo clusters have applications in fields ranging from catalysis to electronics and also hold the potential to inform on aspects of actinide chemistry. Toward this end, a cerium-acetylacetonate (acac1-) monomeric molecule, Ce(acac)4 (Ce-1), and two acac1--decorated cerium-oxo clusters, [Ce10O8(acac)14(CH3O)6(CH3OH)2]·10.5MeOH (Ce-10) and [Ce12O12(OH)4(acac)16(CH3COO)2]·6(CH3CN) (Ce-12), were prepared and structurally characterized. The Ce(acac)4 monomer contains CeIV. Crystallographic data and bond valence summation values for the Ce-10 and Ce-12 clusters are consistent with both clusters having a mixture of CeIII and CeIV cations. Ce L3-edge X-ray absorption spectroscopy, performed on Ce-10, showed contributions from both CeIII and CeIV. The Ce-10 cluster is built from a hexameric cluster, with six CeIV sites, that is capped by two dimeric CeIII units. By comparison, Ce-12, which formed upon dissolution of Ce-10 in acetonitrile, consists of a central decamer built from edge sharing CeIV hexameric units, and two monomeric CeIII sites that are bound on the outer corners of the inner Ce10 core. Electrospray ionization mass spectrometry data for solutions prepared by dissolving Ce-10 in acetonitrile showed that the major ions could be attributed to Ce10 clusters that differed primarily in the number of acac1-, OH1-, MeO1-, and O2- ligands. Small angle X-ray scattering measurements for Ce-10 dissolved in acetonitrile showed structural units slightly larger than either Ce10 or Ce12 in solution, likely due to aggregation. Taken together, these results suggest that the acetylacetonate supported clusters can support diverse solution-phase speciation in organic solutions that could lead to stabilization of higher order cerium containing clusters, such as cluster sizes that are greater than the Ce10 and Ce12 reported herein.

A fitting program for structural determination of molecular clusters from rotational spectroscopy

The characterization of the structures of molecular clusters, which serve as building blocks for bulk substances, provides crucial insight into the interactions between constituent units. Chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy, combined with state-of-the-art quantum chemical calculations, is a powerful tool for characterizing the structures of molecular clusters, as the rotational spectra are directly related to the mass distribution of a molecule or cluster. However, determining the structures of large or complex clusters from experimental rotational spectra remains challenging due to their structural flexibility. Ab initio and density functional theory calculations for searching their stable structures could be significantly time-consuming and method-dependent. To address these challenges, we have developed an approach that relies on the experimental rotational constants to search for potential molecular structures without quantum chemical optimization. Our approach involves creating an initial set of conformers through either a semi-empirical sampling program or the quasi-Monte Carlo method. After-ward, the trust region reflective algorithm is utilized for structure fitting. This procedure enables us to quickly generate potential conformers and gain access to precise structural information. We apply our fitting program to water hexamer and benzaldehyde-water clusters, and the resulting topological structures align extremely well with the experimental results.

Nanoscale mapping of shifts in dark plasmon modes in sub 10 nm aluminum nanoantennas

In this work, we report the fabrication and spectroscopic characterization of subwavelength aluminum nanocavities—consisting of hexamer or tetramer clusters of sub 10 nm width Al nanorods—with tunable localized surface plasmon resonance (LSPR) energies on suspended SiN x membranes. Here the volume plasmon (VP) and LSPR modes of lithographically-fabricated Al nanocavities are revealed by low-loss electron energy-loss spectroscopy (EELS) in an aberration corrected scanning transmission electron microscope (STEM). We show that the existence of grain boundaries (GBs) in these nanocavities results in shifts in the VP energy and a reduction in the VP lifetime. We map the VP energy and lifetime across GBs and we observe a decrease in VP energy and lifetime at GBs that is consistent with a reduction in free carrier density and increased plasmon scattering at these locations. Dipolar LSPR modes resonant in the UV and blue regions of the electromagnetic spectrum as well as higher-energy optically dark quadrupolar and hexapolar LSPR modes are also observed and mapped by STEM and EELS. All LSPR modes are confirmed via electromagnetic simulations based on the boundary element method. Both tetramer and hexamer structures support the excitation of dipolar bright and dipolar dark modes. Finally, we find that asymmetries in fabricated nanorod hexamer and tetramer nanocavities result in a mode mixing leading to a shift in dipolar dark LSPR modes.

Characterization of a Hexanuclear Plutonium(IV) Nanostructure in an Acetate Solution via Visible-Near Infrared Absorption Spectroscopy, Extended X-ray Absorption Fine Structure Spectroscopy, and Density Functional Theory.

A new hexanuclear plutonium cluster has been stabilized in aqueous media with acetate ligands. To probe the formation of such a complex structure, visible-near infrared (vis-NIR) absorption spectroscopy, extended X-ray absorption fine structure (EXAFS) spectroscopy, and density functional theory (DFT) were combined. The presence of Pu6O4(OH)4(CH3COO)12 species in solution was first detected by vis-NIR and EXAFS spectroscopy. To confirm unambiguously this structure, EXAFS spectra were simulated from ab initio calculations. Debye-Waller factors and structural parameters were derived from DFT calculations. A large number of 5f electrons were treated as valence or core electrons using small- and large-core relativistic effective pseudopotentials. It is possible to reproduce accurately the EXAFS spectrum of the octahedral hexamer cluster at both levels of calculations. Further DFT and EXAFS calculations were performed on clusters of lower or higher nuclearities and of different geometries using the 5f-core approximation. The result shows that trimer, tetramer, flat hexamer, and even 16-mer clusters exhibit different EXAFS patterns and confirm the very specific octahedral hexanuclear EXAFS signature.

The Chemistry of Zirconium/Carboxylate Clustering Process: Acidic Conditions to Promote Carboxylate-Unsaturated Octahedral Hexamers and Pentanuclear Species.

Clustering chemistry is a key point in the design and synthesis of the secondary building units that comprise metal-organic frameworks (MOFs) based on group IV metals. In this work, the first stages of the zirconium-carboxylate clustering process in alcohol/water mixtures are studied in detail using the monocarboxylic benzoic and hydroxybenzoic acids to avoid the polymerization. Mass spectroscopy measurements performed on the reactions revealed the presence of hexa- and pentanuclear species even at low pH values and also evidenced the acid-base nature and pH dependence of the transformation between both species. The control on the chemistry governing the equilibria between these species has allowed us to isolate six new compounds in the solid state. The single-crystal X-ray diffraction analysis revealed that they are closely related to the well-known [Zr6(O)4(OH)4(OOC)12] secondary building unit found in many MOFs by removing carboxylic ligands in the case of the hexameric species ([Zr6(O)4(OH)4(OOC)8(H2O)8]4+) or by additionally removing one of the metal centers in the case of the pentameric entities ([Zr5(O)2(OH)6(OOC)4(H2O)11(alcohol)]6+). Going in detail, the unsaturated hexameric clusters exhibit different dispositions of their eight carboxylate ligands in such a way that the remaining four carboxylate-free positions are arranged according to a square planar or tetrahedral symmetry. It should be highlighted that the pentameric complexes imply an unprecedented core nuclearity in zirconium clusters and thus their isolation provides a novel building block for the design of metal-organic materials.

Structure and nature of ice XIX

Ice is a material of fundamental importance for a wide range of scientific disciplines including physics, chemistry, and biology, as well as space and materials science. A well-known feature of its phase diagram is that high-temperature phases of ice with orientational disorder of the hydrogen-bonded water molecules undergo phase transitions to their ordered counterparts upon cooling. Here, we present an example where this trend is broken. Instead, hydrochloric-acid-doped ice VI undergoes an alternative type of phase transition upon cooling at high pressure as the orientationally disordered ice remains disordered but undergoes structural distortions. As seen with in-situ neutron diffraction, the resulting phase of ice, ice XIX, forms through a Pbcn-type distortion which includes the tilting and squishing of hexameric clusters. This type of phase transition may provide an explanation for previously observed ferroelectric signatures in dielectric spectroscopy of ice VI and could be relevant for other icy materials.

Synthesis and Characterization of Ammonium Potassium Tellurium Polyoxomolybdate: (NH4)2K2TeMo6O22·2H2O with One-Dimensional Anionic Polymeric Chain [TeMo6O22]4−

A new tellurium polyoxomolybdate hydrate (NH4)2K2TeMo6O22·2H2O was synthesized via the hydrothermal reaction method at 190 °C. The compound crystallizes in a one-dimensional tellurium polymolybdate [TeMo6O22]4− chain structure. The anionic polymeric chain is composed of Mo6O22 hexamers bridged together through sharing four corner oxygen atoms on the electron lone-paired TeO4 group. The Mo6O22 hexamer cluster is assembled from six distorted MoO6 octahedra in an edge-sharing manner. The ammonium and potassium cations distribute around the [TeMo6O22]4− chains and separate them from each other and maintain the charge balance. The thermal stability and optical properties of the compound were also investigated. The optical absorption data reveal that the compound is a wide band semiconductor with an optical band gap of 3.4 eV.

Visible-Light-Driven Methane Conversion with Oxygen Enabled by Atomically Precise Nickel Catalyst

It remains an extreme challenge to activate thermodynamically unfavorable, chemically inert methane molecules under mild conditions. Herein, we report a molecular-like nickel-thiolate hexameric clu...

The Application of HEXS and HERFD XANES for Accurate Structural Characterisation of Actinide Nanomaterials: The Case of ThO2.

The structural characterisation of actinide nanoparticles (NPs) is of primary importance and hard to achieve, especially for non‐homogeneous samples with NPs less than 3 nm. By combining high‐energy X‐ray scattering (HEXS) and high‐energy‐resolution fluorescence‐detected X‐ray absorption near‐edge structure (HERFD XANES) analysis, we have characterised for the first time both the short‐ and medium‐range order of ThO2 NPs obtained by chemical precipitation. By using this methodology, a novel insight into the structures of NPs at different stages of their formation has been achieved. The pair distribution function revealed a high concentration of ThO2 small units similar to thorium hexamer clusters mixed with 1 nm ThO2 NPs in the initial steps of formation. Drying the precipitates at around 150 °C promoted the recrystallisation of the smallest units into more thermodynamically stable ThO2 NPs. HERFD XANES analysis at the thorium M4 edge, a direct probe for f states, showed variations that we have correlated with the breakdown of the local symmetry around the thorium atoms, which most likely concerns surface atoms. Together, HEXS and HERFD XANES are a powerful methodology for investigating actinide NPs and their formation mechanism.

Clusters of Hydroxyl-Functionalized Cations Stabilized by Cooperative Hydrogen Bonds: The Role of Polarizability and Alkyl Chain Length.

We explore quantum chemical calculations for studying clusters of hydroxyl-functionalized cations kinetically stabilized by hydrogen bonding despite strongly repulsive electrostatic forces. In a comprehensive study, we calculate clusters of ammonium, piperidinium, pyrrolidinium, imidazolium, pyridinium, and imidazolium cations, which are prominent constituents of ionic liquids. All cations are decorated with hydroxy-alkyl chains allowing H-bond formation between ions of like charge. The cluster topologies comprise linear and cyclic clusters up to the size of hexamers. The ring structures exhibit cooperative hydrogen bonds opposing the repulsive Coulomb forces and leading to kinetic stability of the clusters. We discuss the importance of hydrogen bonding and dispersion forces for the stability of the differently sized clusters. We find the largest clusters when hydrogen bonding is maximized in cyclic topologies and dispersion interaction is properly taken into account. The kinetic stability of the clusters with short-chained cations is studied for the different types of cations ranging from hard to polarizable or exhibiting additional functional groups such as the acidic C(2)-H position in the imidazolium-based cation. Increasing the alkyl chain length, the cation effect diminishes and the kinetic stability is exclusively governed by the alkyl chain tether increasing the distance between the positively charged rings of the cations. With adding the counterion tetrafluoroborate (BF4−) to the cationic clusters, the binding energies immediately switch from strongly positive to strongly negative. In the neutral clusters, the OH functional groups of the cations can interact either with other cations or with the anions. The hexamer cluster with the cyclic H-bond motive and “released” anions is almost as stable as the hexamer built by H-bonded ion pairs exclusively, which is in accord with recent IR spectra of similar ionic liquids detecting both types of hydrogen bonding. For the cationic and neutral clusters, we discuss geometric and spectroscopic properties as sensitive probes of opposite- and like-charge interaction. Finally, we show that NMR proton chemical shifts and deuteron quadrupole coupling constants can be related to each other, allowing to predict properties which are not easily accessible by experiment.

Serendipitous and Targeted Synthesis of High Nuclearity Clusters—Carbonate and Oxalate Encapsulating Silver Alkynides

Silver coordination compounds of the [Ag3L2] (where L = tBu-C≡C) family having perchlorate counterions exhibit template-driven self-assembly of the common square pyramidal building block. This behavior is similar to previously described observations; however, important differences arise from counterion–silver interactions. Penta- and hexameric clusters encapsulating chloride and oxalate, respectively, were crystallographically characterized. A high nuclearity cluster [(CO3)3(H2O)⊂Ag38L20]12+ was formed upon extended exposure to an ambient atmosphere by trapping three carbonates and one water molecule.

Ionized water clusters , n = 2 to 6: A high‐accuracy study of structures and energetics

AbstractIonized water clusters, , have been of remarkable interest owing to their crucial roles in many chemical and biological processes. Small cationic water clusters , n = 2 to 6 serve as reasonable models for understanding the nature of the ionized water. In this study, employing high‐level ab initio quantum chemical methods, such as the density‐fitted orbital‐optimized linearized coupled‐cluster doubles (DF‐OLCCD), coupled‐cluster singles and doubles (CCSD), and coupled‐cluster singles and doubles with perturbative triples [CCSD(T)], a high‐accuracy study of structures and energetics for cationic water clusters [, n = 2‐6] is presented. In this study, 2 dimer, 8 trimer, 18 tetramer, 23 pentamer, and 25 hexamer clusters are reported. Most of the structures considered are reported for the first time. Relative, binding, and vertical attachment energies (VAEs), for the first time, are presented at the complete basis set (CBS) limit, extrapolating energies of the aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets, to provide the most accurate energetics to date. Our results demonstrate that as cluster size increases, the VAE value decreases, which indicates that large‐size clusters better compensate for the electron deficiency compared with small‐size clusters. The VAE values for pentamer and hexamer clusters are 118.5 to 165.5 and 121.9 to 153.7 kcal mol−1, respectively. Further, our binding energy results, at the CCSD(T)/CBS level, indicate strong bindings in cationic clusters due to hydrogen bond interactions. The average binding energy per water molecule varies from −16.6 to −21.8 kcal mol−1 for the clusters considered. Hence, we present the most extensive and accurate study on ionized water clusters to date. Further, our results indicate that the DF‐OLCCD method is very promising for ionic molecular clusters, and its accuracy approaches the CCSD(T) quality. The inexpensive analytic gradients of DF‐OLCCD, compared with CCSD(T), make it very helpful for high‐accuracy studies of molecular geometries.

High-Level VSCF/VCI Calculations Decode the Vibrational Spectrum of the Aqueous Proton

The hydrated excess proton is a common species in aqueous chemistry, which complexes with water in a variety of structures. The infrared spectrum of the aqueous proton is particularly sensitive to this array of structures, which manifests as continuous IR absorption from 1000 to 3000 cm-1 known as the "proton continuum". Because of the extreme breadth of the continuum and strong anharmonicity of the involved vibrational modes, this spectrum has eluded straightforward interpretation and simulation. Using protonated water hexamer clusters from reactive molecular dynamics trajectories, and focusing on their central H+(H2O)2 structures' spectral contribution, we reproduce the linear IR spectrum of the aqueous proton with a high-level local monomer quantum method and highly accurate many-body potential energy surface. The accuracy of this approach is first verified in the vibrational spectra of the two isomers of the protonated water hexamer in the gas phase. We then apply this approach to 800 H+(H2O)6 clusters, also written as [H+(H2O)2](H2O)4, drawn from multistate empirical valence bond simulations of the bulk liquid to calculate the infrared spectrum of the aqueous proton complex. Incorporation of anharmonic effects to the vibrational potential and quantum mechanical treatment of the proton produces a better agreement to the infrared spectrum compared to that of the double-harmonic approximation. We assess the correlation of the proton stretching mode with different atomistic coordinates, finding the best correlation with ⟨ROH⟩, the expectation value of the proton-oxygen distance ROH. We also decompose the IR spectrum based on normal mode vibrations and ⟨ROH⟩ to provide insight on how different frequency regions in the continuum report on different configurations, vibrational modes, and mode couplings.

2-Methyl-4-(4-nitro-phen-yl)but-3-yn-2-ol: crystal structure, Hirshfeld surface analysis and computational chemistry study.

The di-substituted acetyl-ene residue in the title compound, C11H11NO3, is capped at either end by di-methyl-hydroxy and 4-nitro-benzene groups; the nitro substituent is close to co-planar with the ring to which it is attached [dihedral angle = 9.4 (3)°]. The most prominent feature of the mol-ecular packing is the formation, via hy-droxy-O-H⋯O(hy-droxy) hydrogen bonds, of hexa-meric clusters about a site of symmetry . The aggregates are sustained by 12-membered {⋯OH}6 synthons and have the shape of a flattened chair. The clusters are connected into a three-dimensional architecture by benzene-C-H⋯O(nitro) inter-actions, involving both nitro-O atoms. The aforementioned inter-actions are readily identified in the calculated Hirshfeld surface. Computational chemistry indicates there is a significant energy, primarily electrostatic in nature, associated with the hy-droxy-O-H⋯O(hy-droxy) hydrogen bonds. Dispersion forces are more important in the other identified but, weaker inter-molecular contacts.

Sustained Solar H2 Evolution from a Thiazolo[5,4-d]thiazole-Bridged Covalent Organic Framework and Nickel-Thiolate Cluster in Water.

Solar hydrogen (H2) evolution from water utilizing covalent organic frameworks (COFs) as heterogeneous photosensitizers has gathered significant momentum by virtue of the COFs’ predictive structural design, long-range ordering, tunable porosity, and excellent light-harvesting ability. However, most photocatalytic systems involve rare and expensive platinum as the co-catalyst for water reduction, which appears to be the bottleneck in the development of economical and environmentally benign solar H2 production systems. Herein, we report a simple, efficient, and low-cost all-in-one photocatalytic H2 evolution system composed of a thiazolo[5,4-d]thiazole-linked COF (TpDTz) as the photoabsorber and an earth-abundant, noble-metal-free nickel-thiolate hexameric cluster co-catalyst assembled in situ in water, together with triethanolamine (TEoA) as the sacrificial electron donor. The high crystallinity, porosity, photochemical stability, and light absorption ability of the TpDTz COF enables excellent long-term H2 production over 70 h with a maximum rate of 941 μmol h–1 g–1, turnover number TONNi > 103, and total projected TONNi > 443 until complete catalyst depletion. The high H2 evolution rate and TON, coupled with long-term photocatalytic operation of this hybrid system in water, surpass those of many previously known organic dyes, carbon nitride, and COF-sensitized photocatalytic H2O reduction systems. Furthermore, we gather unique insights into the reaction mechanism, enabled by a specifically designed continuous-flow system for non-invasive, direct H2 production rate monitoring, providing higher accuracy in quantification compared to the existing batch measurement methods. Overall, the results presented here open the door toward the rational design of robust and efficient earth-abundant COF–molecular co-catalyst hybrid systems for sustainable solar H2 production in water.

Highly efficient and very robust blue-excitable yellow phosphors built on multiple-stranded one-dimensional inorganic-organic hybrid chains.

Inorganic-organic hybrid semiconductors are promising candidates for energy-related applications. Here, we have developed a unique class of multiple-stranded one-dimensional (1D) structures as very robust and efficient lighting phosphors. Following a systematic ligand design strategy, these structures are constructed by forming multiple coordination bonds between adjacent copper iodide inorganic building units Cu m I m (m = 2, 4, 6) (e.g. dimer, tetramer and hexamer clusters) and strong-binding bidentate organic ligands with low LUMO energies which give rise to infinite 1D chains of high stability and low bandgaps. The significantly enhanced thermal/photostability of these multiple-stranded chain structures is largely attributed to the multi-dentate nature and enhanced Cu-N bonding, and their excellent blue excitability is a result of using benzotriazole based ligands with low-lying LUMO energies. These facts are confirmed by Density Functional Theory (DFT) calculations. The luminescence mechanism of these compounds is studied by temperature dependent photoluminescence experiments. High internal quantum yields (IQYs) are achieved under blue excitation, marking the highest value reported so far for crystalline inorganic-organic hybrid yellow phosphors. Excellent thermal- and photo-stability, coupled with high luminescence efficiency, make this class of materials promising candidates for use as rare-earth element (REE) free phosphors in energy efficient general lighting devices.

On the Problem of Criteria for Phase Transitions in Water Clusters (A Hexamer and Octamer Example)

The study concerns the dynamics of a network of hydrogen bonds in small water clusters (on the example of hexamer and octamer clusters). The numerical experiment is carried out with the molecular dynamics method using two analytical rigid potentials TIP4P and TIP5P. According to the obtained results, the criteria of phase transitions provided by the cluster theory are not reliable enough in the case of small water clusters. This is testified by the distributions of potential energies of individual molecules in the clusters. It is shown that the appearance of several peaks in these distributions reflects the number of hydrogen bonds between the molecule and other molecules of the cluster.