Dodecahedral Clusters Research Articles

High-Nuclearity Ln210Al140 Clusters: Neonates of Open Hollow Dodecahedral Cage Families.

Open hollow dodecahedral cage clusters have long been a coveted target in synthetic chemistry, yet their creation poses immense challenges. Here we report two open hollow dodecahedral lanthanide-aluminum (Ln-Al) heterometallic cage clusters, namely, [Ln210Al140(μ2-OH)210(μ3-OH)540(OAc)180(H2O)156](ClO4)120·(MeCN)x·(H2O)y, (Ln = Dy and x = 27, y = 300 for 1; Ln = Y and x = 28, y = 420 for 2). Remarkably, the 350 metal atoms in 1 and 2 display a Keplerate-type four-shell structure of truncated icosidodecahedron@dodecahedron@dodecahedron@icosidodecahedron. The diameter of the cationic cluster in 1 is approximately 5.0 nm, with an inner cavity diameter of about 2.8 nm and a window diameter of roughly 0.66 nm. The cluster in 1 boasts an accessible inner void volume of up to 15,000 Å3. Notably, these cage clusters maintain stability in water, and the truncated icosidodecahedrons in 1 and 2 are the first of their kind synthesized to date. Given that the open hollow dodecahedral Ln-Al cage cluster has never been reported before, this work represents a member in the family of hollow open dodecahedral cages.

Statistical Equivalence of Quantum Chemical Methods for Energy Distribution in Water Clusters.

Methods of quantum chemistry are instrumental in understanding molecular structures and properties. However, the results demonstrate significant variability, which is difficult to predict and rationalize. The fundamental question is whether some molecular systems exhibit properties invariant with respect to the computational method. The idea explored here is that collective properties of statistical ensembles should be more robust than characteristics of individual molecules and their arbitrary sets. This effect is demonstrated for the complete set of hydrogen-bond topologies of the dodecahedral water cluster (H2 O)20 . Non-Gaussian energy distributions produced by various methods have the same functional form despite strong differences in mean values and standard deviations. The conclusion is tested on methods of different complexity and origin employing a number of criteria. A linear mapping between the energies produced by different methods is discussed. The significance of the results is in establishing a collective equivalence property of quantum chemical methods.

Energy Scale Deformation on Regular Polyhedra

A variant of energy scale deformation is considered for the S = 1/2 antiferromagnetic Heisenberg model on polyhedra. The deformation is induced by the perturbations to the uniform Hamiltonian, whose coefficients are determined by the bond coordinates. On the tetrahedral, octahedral, and cubic clusters, the perturbative terms do not affect the ground state of the uniform Hamiltonian when they are sufficiently small. On the other hand, for the icosahedral and dodecahedral clusters, it is numerically confirmed that the ground state of the uniform Hamiltonian is almost insensitive to the perturbations unless they lead to a discontinuous change in the ground state. The obtained results suggest the existence of a generalization of sine-square deformation in higher dimensions.

Intermetallic Compounds KnMm (М = Ag, Au, As, Sb, Bi, Ge, Sn, Pb): Geometrical and Topological Analysis, Cluster Precursors, and Self-Assembly of Crystal Structures

A geometrical and topological analysis and simulation of the self-assembly of the crystal structures of intermetallic compounds formed in the K–M (M = Ag, Au, As, Sb, Bi, Ge, Sn, Pb) systems have been performed using computation methods (the ToposPro software). The precursor metal clusters of KnMm crystal structures are determined based on the algorithms of structure-graph decomposition in cluster structures and construction of the basic net of structure in the form of a graph with nodes corresponding to cluster centers. Tetrahedral metal clusters, forming packings in the K3Bi-cF16, K3Bi-hP8, K2As2-oP16, K2Sb2-mP16, and K2Sb2-mP32 crystal structures; tetrahedral metal clusters and spacers for the K(K2As2)2-mC18, K4(Pb4)-tI64, and K2(Au4)-hP12 structures; polyhedral metal clusters KK4Pb12 and spacers for the Pb12K(K4Pb12)-cI58 structure; and dodecahedral metal clusters KGe20 and spacers for the K3Ge3(KGe20)-cP54 structure have been found. The symmetry and topology code of the self-assembly of crystal structures of intermetallic compounds KnMm has been reconstructed from precursors $$S_{3}^{0}$$ in the following form: primary chain $$S_{3}^{1}$$ → microlayer $$S_{3}^{2}$$ → microframework $$S_{3}^{3}$$ .

Hedgehog-like Spin Fluctuation and the Boson Peak in Zn-Mg-Tb Quasicrystals

We have discussed localized collective fluctuations of short-range ordered spin in a dodecahedral spin cluster in Zn-Mg-Tb icosahedral quasicrystal and the relation to the boson peak in the topological glasses.

Structure of the telluroketone TeC(PPh2NSiMe3)2 coordinated to an Li8O6 cluster

The reaction of Li2[C(PPh2NSiMe3)2] with elemental tellurium in THF was carried out in an attempt to generate the tellurocarbonyl dianion [TeC(PPh2NSiMe3)2]2− as the dilithium derivative. This thermally unstable tridentate ligand was characterized by 31P and 7Li NMR spectroscopy. Attempted recrystallization gave yellow crystals, which were shown by X-ray crystallography to be a neutral, centrosymmetric complex comprised of two molecules of the novel telluroketone [TeC(PPh2NSiMe3)2] stabilized by N,Te,N coordination to LiOLi units of the rhombic dodecahedral cluster [Li8(μ5-O)2(μ5-OH)4(C4H8O)4].

Global Minima of Protonated Water Clusters (H2O)20H+ Revisited

A graph-theoretical analysis is performed on the (H(2)O)(20) "edge-sharing pentagonal prism" cluster to find proton configurations that yield the lowest cluster total energies. Using the low-energy structures, we create models for protonated (H(2)O)(20)H(+) clusters that compete energetically with "cage-like" structures proposed earlier in the literature. We perform benchmarking between different theoretical methods and observe significant stabilization of compact versus polyhedral clusters due to long-range electron correlation effects, which make the comparison between different cluster morphologies difficult using density functional theory only. All methodologies that we used (up to the second level of Møller-Plesset perturbation theory (MP2)) agree that for protonated clusters, the cage-like morphology proposed in [ Chem. Phys. Lett. 2000, 324, 279-288] is the most stable one. We study in detail several (H(2)O)(20)H(+) cluster structures and suggest that the energetics in small protonated water clusters is dominated by the competition of open polyhedral structures, favored by the Eigen H(9)O(4)(+) species, against van der Waals interaction and "ice rules", which both favor compact structural motifs such as the prismatic particle. We demonstrate this tendency using ab initio calculations for prismatic, dodecahedral, and cage-like clusters, while the "magic number" cluster (H(2)O)(n)H(+), n = 21, is observed to minimize all competing energy contributions simultaneously. We emphasize the utility of the cage-like cluster as a model template for ice-related atmospheric reactions and benchmark the GPAW density functional theory code for making such calculations.

A DFT study of dodecahedral beryllium silicide cage clusters

Density functional theory calculations have been conducted on 20- and 32-atom dodecahedral and face-capped dodecahedral cage clusters of beryllium and silicon. Stable Be24Si8, Be12Si8 and Be12Si20 cages are described, as is a stuffed cluster consisting of dodecahedral Si20 with an endohedral icosahedral Be12. Especial stability is associated with clusters in which faces are capped by silicon atoms, acting as electron donors to beryllium atoms.

The first example of rhombic dodecahedral CuBr clusters in a novel mixed-valence Cu(i,ii)–benzimidazole complex

Hydrothermal reaction of CuBr2 and 1,2-di(1H-benzoimidazol-2-yl)ethane-1,2-diol leads to the formation of a new mixed-valence copper(I,II) complex [(C7H5N2)(CuICuIIBr2)], which exhibits a two-dimensional layer structure, containing the first example of a rhombic dodecahedral CuBr [4,3] polyhedral column. The synthesis, crystal structure, electronic property, thermal stability and electrochemical characterization of this complex are investigated.

Topology-energy relationships and lowest energy configurations for pentagonal dodecahedral (H2O)20X clusters, X=empty, H2O, NH3, H3O+: The importance of O-topology

For (H(2)O)(20)X water clusters consisting of X enclosed by the 5(12) dodecahedral cage, X = empty, H(2)O, NH(3), and H(3)O(+), databases are made consisting of 55-82 isomers optimized via B3LYP/6-311++G(**). Correlations are explored between ground state electronic energy (Ee) or electronic energy plus zero point energy (Ee+ZPE) and the clusters' topology, defined as the set of directed H-bonds. Linear regression is done to identify topological features that correlate with cluster energy. For each X, variables are found that account for 99% of the variance in Ee and predict it with a rms error under 0.2 kcal/mol. The method of analysis emphasizes the importance of an intermediate level of structure, the "O-topology," consisting of O-types and a list of O pairs that are bonded but omitting H-bond directions, as a device to organize the databases and reduce the number of structures one needs to consider. Relevant variables include three parameters, which count the number of H-bonds having particular donor and acceptor types; absolute value(M)(2), where M is the cluster's vector dipole moment; and the projection of M onto the symmetry axis of X. Scatter diagrams for Ee or Ee+ZPE versus absolute value(M) show that clusters fall naturally into "families" defined by the values of certain discrete parameters, the "major parameters," for each X. Combining "family" analysis and O-topologies, a small group of clusters is identified for each X that are candidates to be the global minimum, and the minimum is determined. For X = H(3)O(+), one cluster with central hydronium lies just 2.08 kcal/mol above the lowest isomer with surface hydronium. Implications of the methodology for dodecahedral (H(2)O)(20)(NH(4)(+)) and (H(2)O)(20)(NH(4)(+))(OH(-)) are discussed, and new lower energy isomers are found. For MP2/TZVP, the lowest-energy (H(2)O)(20)(NH(4)(+)) isomer features a trifurcated H-bond. The results suggest a much more efficient and comprehensive way of seeking low-energy water cluster geometries that may have wide applicability.

Multipole Model for the Electron Group Functions Method

Electron groups provide a natural way to introduce local concepts into quantum chemistry, and the wave functions based on the group products can be considered as a framework for constructing efficient computational methods in terms of "observable" parts of molecular systems. The elements of the group wave functions (electronic structure variables) can be optimized by requiring the number of operations proportional to the size of the molecule. This directly leads to computational methods linearly scaling for large molecular systems. In the present work we consider a particular case of such a wave function implemented for the semiempirical NDDO Hamiltonian. The electron groups are expressed in terms of optimized atomic (hybrid) orbitals with chemical bonds described by geminals and the delocalized groups described by Slater determinants (with or without spin restriction). This scheme is very fast by itself but its speed is considerably limited by the computations of the interatomic Coulomb interactions. Here we develop a consistent method based on group functions which uses the multipole scheme for interatomic interactions. The explicit usage of the atomic multipoles makes the method extremely fast, although the numerical efficiency is largely achieved due to the local character of the electron groups involved. We discuss numerical characteristics of the new method as well as its possible parametrization. We apply this method to study dodecahedral water clusters with hydrogen fluoride substitution and base the analysis on the exhaustive calculation of all symmetry-independent hydrogen-bond networks.

Phase formation and structures of quasicrystals and approximants in the Zn–Mg–(Ti, Zr, Hf) system

The compositional regions for primitive (P) and face-centered (F) icosahedral quasicrystals (iQc) have been determined to be around Zn 84Mg 9Zr 7 and Zn 75Mg 18Zr 6, respectively. A 1/1 approximant of the F-type iQc was found to have a composition around Zn 77Mg 18Zr 5. A similar tendency has been verified for the Zn–Mg–Hf system. No stable iQc was observed in the Zn–Mg–Ti system. High-resolution X-ray measurements performed with synchrotron radiation showed that the stable iQcs are highly ordered and contain less phason disorder. High-angle annular dark field (HAADF) scanning transmission electron microscopy observation of the 1/1 Zn–Mg–Hf approximant effectively revealed the Hf positions in the structure, whose local contrasts can be reasonably interpreted by a structural model where icosahedral and dodecahedral Hf clusters are mutually interpenetrated. Similar appearances of local contrasts were frequently observed in HAADF images of the F-type iQc, indicating that the iQc structure is also build up of icosahedral clusters that are almost identical to those in the 1/1 approximant.

Photoluminescence in quasi-amorphous Pb 0.8X 0.2Zr 0.53Ti 0.47O 3 (X = Ca, Sr and Ba) powders: An optical and structural study

Crystalline and quasi-amorphous PZT and PZT:X (X = Ca, Sr and Ba) powders were obtained by the polymeric precursor method. Electron paramagnetic resonance (EPR) and photoluminescence (PL) data suggest that the presence of order–disorder within the lattice network, i.e., the appearance of symmetry-breaking processes that give rise to non-ideal octahedra and networks of dodecahedral clusters, is an essential factor for the occurrence of PL. Measurements of PL indicate that the shallow defects in the band gap enhance blue light emission.

Excess electron is trapped in a large single molecular cage C60F60

A new kind of solvated electron systems, sphere-shaped e(-)@C60F60 (I(h)) and capsule-shaped e(-)@C60F60 (D6h), in contrast to the endohedral complex M@C60, is represented at the B3LYP/6-31G(d) + dBF (diffusive basis functions) density functional theory. It is proven, by examining the singly occupied molecular orbital (SOMO) and the spin density map of e(-)@C60F60, that the excess electron is indeed encapsulated inside the C60F60 cage. The shape of the electron cloud in SOMO matches with the shape of C60F60 cage. These cage-like single molecular solvated electrons have considerably large vertical electron detachment energies VDE of 4.95 (I(h)) and 4.67 eV (D6h) at B3LYP/6-31+G(3df) + dBF level compared to the VDE of 3.2 eV for an electron in bulk water (Coe et al., Int Rev Phys Chem 2001, 20, 33) and that of 3.66 eV for e(-)@C20F20 (Irikura, J Phys Chem A 2008, 112, 983), which shows their higher stability. The VDE of the sphere-shaped e(-)@C60F60 (I(h)) is greater than that of the capsule-shaped e(-)@C60F60 (D6h), indicating that the excess electron prefers to reside in the cage with the higher symmetry to form the more stable solvated electron. It is also noticed that the cage size [7.994 (I(h)), 5.714 and 9.978 A (D6h) in diameter] is much larger than that (2.826 A) of (H2O)20- dodecahedral cluster (Khan, Chem Phys Lett 2005, 401, 85).

Can the dodecahedral water cluster naturally form in methane aqueous solutions? A molecular dynamics study on the hydrate nucleation mechanisms

By performing a large scale of molecular dynamics simulations, we analyze 60 x 10(6) hydration shells of methane to examine whether the dodecahedral water cluster (DWC) can naturally form in methane aqueous solutions--a fundamental question relevant to the nucleation mechanisms of methane hydrate. The analyzing method is based on identifying the incomplete cages (ICs) from the hydration shells and quantifying their cagelike degrees (zetaC=0-1). Here, the zetaC is calculated according to the H-bond topological network of IC and reflects how the IC resembles the complete polyhedral cage. In this study, we obtain the zetaC distributions of ICs in methane solutions and find the occurrence probabilities of ICs reduce with zetaC very rapidly. The ICs with zetaC>or=0.65 are studied, which can be regarded as the acceptable cagelike structures in appearance. Both increasing the methane concentration and lowering the temperature can increase their occurrence probabilities through slowing down the water molecules. Their shapes, cage-maker numbers, and average radii are also discussed. About 13-14 of these ICs are face saturated, meaning that every edges are shared by two faces. The face-saturated ICs have the potential to act as precursors of hydrate nucleus because they can prevent the encaged methane from directly contacting other dissolved methane when an event of methane aggregation occurs. The complete cages, i.e., the ICs with zetaC=1, form only in the solutions with high methane concentration, and their occurrence probabilities are about 10(-6). Most of their shapes are different from the known hydrate cages, but we indeed observe a standard 5(12)6(2) hydrate cage. We do not find the expected DWC, and its occurrence probability is estimated to be far less than 10(-7). Additionally, the IC analysis proposed in this work is also very useful in other studies not only on the formation, dissociation, and structural transition of hydrates but also on the hydrophobic hydration of apolar solutes.

Investigation of Size-Selective Zr2@Sin (n = 16−24) Caged Clusters

The size-selective Zr(2)Si(n) (n = 16-24) caged clusters have been investigated by density functional approach in detail. Their geometries, relative stabilities, electronic properties and ionization potentials have been discussed. The dominant structures of bimetallic Zr(2) doped silicon caged clusters gradually transform to Zr(2) totally encapsulated structures with increase of the clustered size from 16 to 24, which is good agreement with the recent experimental result (J. Phys. Chem. A. 2007, 111, 42). Two novel isomers, i.e., naphthalene-like and dodecahedral Zr(2)Si(20) clusters, are found as low-lying conformers. Furthermore, the novel quasi-1D naphthalene-like Zr(n)Si(m) nanotubes are first reported. The second-order energy differences reveal that magic numbers of the different sized neutral Zr(2)Si(n) clusters appear at n = 18, 20 and 22, which are attributed to the fullerene-like, dodecahedral and polyhedral structures, respectively. The HOMO-LUMO gaps (>1 eV) of all the size-selective Zr(2)Si(n) clusters suggest that encapsulation of the bimetallic zirconium atoms is favorable for increasing the stabilities of silicon cages.

Tensile deformation accommodation in microscopic metallic glasses via subnanocluster reconstructions

We present results on the structure and the atomistic mechanisms for tensile deformation accommodation of the Cu46Zr54 microscopic metallic glass. At equilibrium, 23% of the atoms belong to tiny Cu-centered icosahedral clusters (Cu-ICO) and approximately 41% Zr centered slightly larger ICO-like clusters. Under deformation, the number of Cu-ICOs remains dynamically constant until yielding through a continuous cluster destruction-recreation process. Plastic deformation occurs homogeneously and is locally accommodated through the formation of rhombic dodecahedral clusters with significant (∼2%) atomic density drop. These findings explain very recent experimental results demonstrating the fundamental differences of plastic deformation mechanisms between bulk metallic and microscopic glasses.

Hydrogen peroxide and ammonia on protonated ice clusters

A temperature controlled source for protonated water clusters has been combined with high-resolution mass spectroscopy to study the stability pattern of ice clusters and compounds with ammonia and hydrogen peroxide depending on temperature. The stability pattern of pure protonated ice shows the two well known peaks at 21 and 28 molecules and also less pronounced structure up to n=55. Ammonia and hydrogen peroxide do not destroy this pattern but shift it by a number of water molecules. The additives are therefore integrated in the persisting crystalline structure of the pure protonated ice. Based on this structural information, density functional theory calculations reveal that hydrogen peroxide and ammonia occupy surface positions on a dodecahedral 21-molecule cluster and are not caged in the center.

Effect of Methane Adsorption on the Lifetime of a Dodecahedral Water Cluster Immersed in Liquid Water: A Molecular Dynamics Study on the Hydrate Nucleation Mechanisms

By performing 400 molecular dynamics simulations, we observe that the rigid dodecahedral water cluster (DWC) encaging a methane molecule has an affinity for other methane molecules diffusing freely in liquid water and can adsorb them by chance. Utilizing the affinity, we successfully prepare seven series (200 runs in each series) of DWCs adsorbing 0−12 methane molecules, and study how the adsorbed methane molecules affect the DWC lifetime. The results show that the adsorbed methane molecules can prolong the lifetime of DWC. The structures and dynamics of the DWC and its surroundings are also analyzed. We find that the adsorbed methane molecules slow down the water molecules in both the DWC and its surroundings, reduce the number of H-bonds that tend to break the DWC, and change the H-bond networks of the DWC surroundings from the liquid water structure toward the cagelike structure. On the basis of these observations, a methane aggregation mechanism caused by the DWC adsorbing dissolved methane molecules ...

Dodecahedral Clusters and Novel Cubic Allotropic Forms of Carbon, Silicon, and Germanium: Computer Simulation

A method is described for building up novel three‐dimensional periodical structures consisting of atoms C, Si or Ge. Polyhedral dodecahedral shape clusters X20 are basis of such lattices. Three‐dimensional nets with simple cubic lattices can be produced on the base of X20 clusters. Each cluster X20 has six neighboring clusters X20. Two neighboring clusters are bound by two covalent bonds. It is found that large size cavities are contained in such structures. Cubic clusters X8 can be disposed in these cavities. Each cluster X8 has eight neighboring clusters X20 and is covalently linked with one of these clusters. As a result, periodical crystalline structures [X8@(X20)8]n (or [X28]n) with simple cubic lattice can be produced. The lattice parameters of these crystals were found using DFT‐PBE optimized calculations of clusters X8 @ (X20)8 and X8 @ (X20H13)8. Structure of the [C28]n crystal was obtained more accurate by the PBE96/FLAPW method. Calculations of density of states show that the crystal is dielectric with an energy gap of 3.3 eV.