Cluster Symmetry Research Articles

The benefits of alternation and alkylation: large amplitude hydrogen bond librational modes of alcohol trimers and tetramers

Intermolecular hydrogen bond librational modes in cyclic trimers and tetramers of methanol and t-butyl alcohol isolated at low temperature in pulsed supersonic jet expansions are observed by direct absorption spectroscopy in the far-infrared region. The large amplitude librational modes probe the strength and directionality of the intermolecular hydrogen bonds. In addition, their frequency and intensity is very sensitive to the angle which the alkyl groups form with the hydrogen bonded ring. Theoretical predictions which fail to describe the trends in cluster size, alkylation and symmetry splitting reported in this work are likely to miss important ingredients of the underlying intermolecular interaction. Analysis of the vibrational correlation diagram between planar and puckered tetramer structures circumvents some deficiencies of approximate treatments.

Unitary symmetry and classification of the states of n-spin clusters. Magnetic and thermodynamic parameters

The unitary symmetry and classification of spin clusters by spin momenta S are considered on the basis of reduction of the full linear group to unitary groups U2s + 1 and orthogonal rotation group R3. Reduction of the permutation group Pn of n spins to the point group of the cluster is applied to the classification of the spatial states of a spin cluster with the use of permutation quantum numbers introduced in this work and the Young diagrams of the permutation group Pn. Examples of the classification of spin systems with spins s = 1/2, 1, 3/2, 2, and 5/2 with U2s + 1 × Pn groups (n = 5–15) are reported. This classification is common for all spin clusters and is the same for both cyclic clusters and 3D clusters with symmetry groups of a crystal. On the basis of this classification, the magnetic and thermodynamic parameters of a spin system are calculated as a function of the number of spins and temperature. For s = 1/2 clusters, the analytical formulas are derived for magnetic susceptibility, internal energy, heat capacity, and entropy as a function of quantum numbers for a cluster with any number of spins, and their dependences on temperature and the number of atoms are considered.

Controlled perturbation-induced switching in pulse-coupled oscillator networks

Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may in principle support switching processes in these networks and enable novel kinds of neural computations. For small networks of coupled oscillators, we here investigate under which conditions and how system symmetry enforces or forbids certain switching transitions that may be induced by perturbations. For networks of five oscillators, we derive explicit transition rules that for two cluster symmetries deviate from those known from oscillators coupled continuously in time. A third symmetry yields heteroclinic networks that consist of sets of all unstable attractors with that symmetry and the connections between them. Our results indicate that pulse-coupled systems can reliably generate well-defined sets of complex spatiotemporal patterns that conform to specific transition rules. We briefly discuss possible implications for computation with spiking neural systems.

A density-functional study of aluminium, iron, zirconium and cerium microclusters

The geometries and electronic structural properties of AB and ABC (A, B, C = Al, Fe, Zr, Ce) microclusters have been systematically investigated by using a hybrid density-functional method (B3LYP) approach. The spectroscopic constants of ground-state AB and ABC (A, B, C = Al, Fe, Zr, Ce) are obtained, and are found to be in agreement with other available experimental and theoretical results. The calculated gaps between highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) are clearly changed when X is doped into the AB dimers (X = Al, Fe, Zr, Ce). The calculated results indicate that a triangular form with D3h, C2v or Cs symmetry is the most stable for the corresponding ABC trimers, and, in addition, the possible isomers (linear structure) with D∞h or C∞v symmetry of three-atom clusters were found to be of higher energies. We conclude that AlFe and Al2Fe have the highest chemical stability of all the AB dimers and ABC trimers, respectively, due to the high HOMO-LUMO gap. We also find that the binding energy of Ce3 is the largest in magnitude among all ABC (A, B, C = Al, Fe, Zr, Ce) trimers, as is the case with Ce2 among all AB (A, B, C = Al, Fe, Zr, Ce) dimers. The most stable geometry, charge transfer and possible dissociation channels are also discussed.

Self-assembly, dynamics, and structure of Si magic clusters

We demonstrate the preferential formation and self-assembly of monodisperse Si magic clusters $({X}_{4})$ of size $\ensuremath{\sim}13.5\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{\AA{}}$ on $\text{Si}(111)\text{\ensuremath{-}}(7\ifmmode\times\else\texttimes\fi{}7)$ surface using scanning tunneling microscope. The growth process is observed to occur via a stepwise assembly of planarized Si tetramers $({X}_{1})$ formed from Si adatoms deposited at room temperature, leading to Si tetraclusters $({X}_{2})$ (size $\ensuremath{\sim}4.6\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{\AA{}}$) and culminating in tetracluster dimer $({X}_{3})$ and trimer $({X}_{4})$ formations as the surface is being annealed progressively to $150\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$. The respective cluster species density distribution at each annealing temperature also shows the preferential formation of ${X}_{1}\ensuremath{\rightarrow}{X}_{2}\ensuremath{\rightarrow}{X}_{3}\ensuremath{\rightarrow}{X}_{4}$ at higher temperatures, which we describe using surface reaction schemes; ${X}_{1}\ensuremath{\rightarrow}{X}_{2}$, ${X}_{2}+{X}_{2}\ensuremath{\rightarrow}{X}_{3}$, and ${X}_{2}+{X}_{3}\ensuremath{\rightarrow}{X}_{4}$. We determine the activation and formation energies for respective cluster species and elucidate the formation energetics and dynamics of tetraclusters which function unequivocally as fundamental building blocks in the self-assembly of stable Si magic clusters. Finally, we resolve the structure of the Si magic cluster to comprise three tetraclusters or $n=12$ Si atoms taking into consideration (i) cluster symmetry and alignment, (ii) close packing, and (iii) minimization of dangling bonds.

A new multiobjective clustering technique based on the concepts of stability and symmetry

Most clustering algorithms operate by optimizing (either implicitly or explicitly) a single measure of cluster solution quality. Such methods may perform well on some data sets but lack robustness with respect to variations in cluster shape, proximity, evenness and so forth. In this paper, we have proposed a multiobjective clustering technique which optimizes simultaneously two objectives, one reflecting the total cluster symmetry and the other reflecting the stability of the obtained partitions over different bootstrap samples of the data set. The proposed algorithm uses a recently developed simulated annealing-based multiobjective optimization technique, named AMOSA, as the underlying optimization strategy. Here, points are assigned to different clusters based on a newly defined point symmetry-based distance rather than the Euclidean distance. Results on several artificial and real-life data sets in comparison with another multiobjective clustering technique, MOCK, three single objective genetic algorithm-based automatic clustering techniques, VGAPS clustering, GCUK clustering and HNGA clustering, and several hybrid methods of determining the appropriate number of clusters from data sets show that the proposed technique is well suited to detect automatically the appropriate number of clusters as well as the appropriate partitioning from data sets having point symmetric clusters. The performance of AMOSA as the underlying optimization technique in the proposed clustering algorithm is also compared with PESA-II, another evolutionary multiobjective optimization technique.

DFT calculations of vibrational spectra and nonlinear optical properties for MgO nanotube clusters

The IR and Raman spectra, nonlinear optical properties of MgO nanotube clusters are studied by density-functional theory at B3LYP/6-31G(d) level. The IR spectra are match closely to those in the corresponding MgO cluster and bulk materials. The strongest peaks of the IR spectra are located in the range from 650 to 750 cm −1. The Raman spectra are very sensitive to structural variations in MgO clusters, and redshift of vibrational frequency is observed in Raman spectra as increasing cluster length. The motion of the strongest peaks in spectra is discussed. The total dipole moment and the first hyperpolarizabilities oscillate between zero and a constant when the layer is grown for the layer dependence of symmetry in MgO nanotube clusters.

Geometries, Stabilities, and Vibrational Properties of Bimetallic Mo2-Doped Gen (n = 9−15) Clusters: A Density Functional Investigation

Geometries of the bimetallic Mo2Gen (n = 9-15) clusters have been investigated systematically with the density functional approach. The relative stabilities and charge-transfer and vibrational properties of these clusters are presented and discussed. The dominant geometries of Mo2Gen (n = 9-12) clusters can be described as one Mo atom inside a Ge cage and another Mo atom on the surface at smaller sizes with n = 9-12. Interestingly, the stable geometry of Mo2Ge9 cluster has the framework which is analogous to a recent experimental observation (Goicoechea, J. M.; Sevov, S. C. J. Am Chem. Soc. 2006, 128, 4155). The calculated fragmentation energies and the obtained relative stabilities demonstrate that the remarkable Mo2-doped Ge12 is the most stable species of all different sized clusters. The critical size of Mo2-encapsulated cagelike germanium clusters appears at n = 15. The largest energy gap and strongest stability of Mo2Ge12 enable this species to be a unit of multiple metal Mo-doped germanium nanotubes. Vibrational mode analyses of Mo2Gen clusters demonstrate that the Mo-Mo stretching vibrations are sensitive to the geometries of the germanium frame, and that the point-group symmetry of germanium clusters can vary the Mo-Mo stretching vibration relative to the IR inactive vibration.

Correlation of Atomic Cluster Symmetry and Glass-Forming Ability of Metallic Glass

Local structures play a crucial role in glass formation and properties. In addition to topological short-range order, the geometric property of site symmetry is another important but less known characteristic of local structures. It is shown that the observed sharp increase of glass forming ability of Ce70-xAl10Cu20Cox upon Co addition is correlated with a dramatic increase of Al site symmetry, as reflected by decreasing quadrupole frequency measured by 27Al NMR. The result is consistent with the structure model of Al-centered icosahedral clusters as the predominant structural building blocks.

Cluster self-organization of TR-containing germanate systems: Suprapolyhedral precursors and self-assembly of the crystal structures of the LiNdGeO4 and CeGeO4 compounds

A combinatorial-topological analysis of the orthogermanates LiNdGeO4 (space group Pbcn) and CeGeO4 (space group I 41/a, the scheelite structure type), which have MT frameworks composed of polyhedral structural units in the form of M dodecahedra (NdO8 and CeO8) and T tetrahedra (GeO4), is performed using the method of coordination sequences with the TOPOS program package. It is established that the structures of both orthogermanates are characterized by equivalent crystal-forming nets 4444. The cluster precursors of the M 2 T 2 cyclic type are identified by the method of two-color decomposition. The local symmetry of four-polyhedral clusters corresponds to the point group 2. In the precursor of the LiNdGeO4 orthogermanate, the Li atom is located above the M 2 T 2 ring. The number of Li-O bonds in this precursor is 4. The cluster precursors M 2 T 2 and LiM 2 T 2 are responsible for the formation of crystal-forming clusters of a higher level according to the mechanism of matrix self-assembly. The coordination numbers of the cluster precursors in two-dimensional nets for these structures are found to be equal to 4. The equivalent bilayer TR,Ge stacks that consist of eight cluster precursors are revealed in the structures under investigation. It is demonstrated that there exist three types of translational interlayer arrangements of cluster precursors upon the formation of macrostructures of the orthogermanates.

Unexpected magnetism of small silver clusters

The ground-state electronic, structural, and magnetic properties of small silver clusters, Ag$_n$ (2$\le$n$\le$22), have been studied using a linear combination of atomic Gaussian-type orbitals within the density functional theory. The results show that the silver atoms, which are diamagnetic in bulk environment, can be magnetic when they are grouped together in clusters. The Ag$_{13}$ cluster with icosahedral symmetry has the highest magnetic moment per atom among the studied silver clusters. The cluster symmetry and the reduced coordination number specific of small clusters reveal as a fundamental factor for the onset of the magnetism.

Correlation of Atomic Cluster Symmetry and Glass-Forming Ability of Metallic Glass

Correlation of Atomic Cluster Symmetry and Glass-Forming Ability of Metallic Glass

Structure and magnetism of lanthanum clusters

The optimized structure, electronic and magnetic properties of La clusters consisting of up to 14 atoms have been investigated using ab initio theoretical methods based on density-functional theory. Structural and spin isomers have been determined. We show that increase in cluster symmetry can promote ferromagnetic instability in La clusters. A giant enhancement of magnetism in ${\mathrm{La}}_{4}$, ${\mathrm{La}}_{6}$, and ${\mathrm{La}}_{13}$ clusters is predicted. We also found that the ground states of ${\mathrm{La}}_{2}$, ${\mathrm{La}}_{3}$, ${\mathrm{La}}_{5}$, ${\mathrm{La}}_{7}$, ${\mathrm{La}}_{9}--{\mathrm{La}}_{11}$, and ${\mathrm{La}}_{14}$ clusters possess nonzero magnetic moments, that ranged from $\ensuremath{\sim}0.1{\ensuremath{\mu}}_{B}$ to $1.0{\ensuremath{\mu}}_{B}$ per atom. Strong dependence of the magnetic moment on temperature for $Tg300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ is predicted. The results obtained are compared with the available experimental data and the results of other theoretical works.

W6S8 Inorganic Clusters with Organic TTF Derivative Ligands: in Pursuit of Multidimensional Conductive Networks

A series of new molecular cluster complexes with TTF derivative ligands attached to an inorganic W6S8 core were prepared, namely W6S8(PEt3-nTTFn)6 (n = 1, 2). By incorporating two useful structural motifs (the well-known π−π stacking geometry of TTF molecules and the high symmetry of octahedral clusters) into one network structure, we constructed multidimensional networks. Single-crystal X-ray diffraction studies revealed intercluster TTF π-contacts in one and two dimensions, for W6S8(PEt2TTF)6 and W6S8(PEtTTF2)6, respectively. The redox properties of W6S8(PEt2TTF)6 were studied by cyclic voltammetry. Mid- and far-IR and XPS (X-ray photoelectron spectroscopy) characterizations were performed on both the W6S8(PEt2TTF)6 cluster and its oxidized product, which helped to elucidate the identity of the poorly crystalline oxidized product. Four-point contact electrical conductivity measurements were performed on a pressed pellet of the oxidized powder product W6S8(PEt2TTF)6·xPF6 (x ≈ 5) with σRT ≈ 1 × 10-4 S cm-1, whereas the neutral cluster complex is insulating at room temperature.

Reflections on symmetry and formation of axial quasicrystals

Abstract Some ideas are presented on the geometrical factors governing structure and formation of axial quasicrystals with 5- and 7-fold symmetry, respectively. First, the importance of thin atomic layers is discussed for the growth of decagonal quasicrystals. They are the only long-range ordered structural units carrying information on the local non-crystallographic symmetry of the constituent clusters. Second, the consequences of local polysynthetic twinning for the formation of pentagonal and heptagonal quasicrystals are demonstrated. Third, the special relationship of the β-phase, (Co,Ni)1–xAl1+x, to the decagonal phase and its periodic average structure is discussed as well as its role as template for the formation and growth of decagonal Al—Co—Ni.

Model of rotational tunneling in quasicrystals of the Cd 6Yb parent compound

A microscopic theoretical model of rotational tunneling within the four-shell atomic clusters of the Cd 6Yb structure, representing a 1/1 periodic approximant of the Cd–Yb and Cd–Ca quasicrystals, is presented, where the Cd 4 tetrahedral core undergoes reorientations around its three-fold symmetry axes in the crystal potential due to outer icosahedral atomic shells. The form of the effective hindering potential was derived from the symmetry of the four-shell cluster and was found to exhibit 12 equivalent double-well minima. These minima appear naturally from the details of the Cd 6Yb atomic structure, providing link to the phenomenological tunneling-state model, where the existence of such double-well minima is assumed on the phenomenological grounds. The shape of the potential suggests two kinds of rotational tunneling processes, the Cd 4 reorientations for 120°, which involve tunneling through barriers between adjacent double wells, and the reorientations for 44°, which involve tunneling within the double wells. The low-temperature energy level scheme, representing the lowest rotational states of the Cd 4 tetrahedron undergoing rotational tunneling about its four three-fold symmetry axes, is obtained by a group-theoretical calculation. As the charge distribution within the Cd 6Yb clusters is not known, the rotational tunneling frequencies were estimated for some trial values of the potential parameters. The estimated frequencies are slow, in accordance with the large mass of the tunneling particle, the Cd 4 tetrahedron.

Global optimization of ionic MgnF2n (n=1–30) clusters

The global optimization basin-hopping (BH) method has been used to locate the global minima (GM) of Mg(n)F(2n) (n=1-30) clusters using a Born-Mayer-type potential. Some of the GM were particularly difficult to find, requiring more than 1.5 x 10(4) BH steps. We have found that both the binding energy per MgF2 unit and the effective volume of the GM isomers increase almost linearly with n, and that cluster symmetry decreases with cluster size. The data derived from the BH runs reveal a growing density of local minima just above the GM as n increases. Despite this, the attraction basin around each GM is relatively large, since after all their atomic coordinates are randomly displaced by values as high as 2.0 bohrs, the perturbed structures, upon reoptimization, relax back to the GM in more than 50% of the cases (except for n=10 and 11). The relative stabilities derived from energy second differences suggest that n=8,10,13,15, and 20 are probably the magic numbers for these systems. Mass spectrum experiments would be very useful to clarify this issue.

Ar-buffer-assisted deposition of Cu 13 on Cu(1 1 1) surfaces

In this paper, the deposition of Cu 13 onto Cu(1 1 1) surface through argon buffer layers was investigated by molecular dynamics (MD) simulations. The interactions between Cu–Cu, Cu–Ar, and Ar–Ar were described by Finnis–Sinclair (FS) tight-binding potential and L–J potential, respectively. The impact energy was chosen to be 2–6 eV/atom in order to compare with experimental results. It was observed that with Ar-buffer layers, the Cu cluster deposited on the surface may retain its free cluster symmetry (I h). Whereas, on originally bare Cu surface, the deposited Cu cluster lost its original symmetry completely and was recrystalized to have the same fcc structure as the substrate. The Ar-buffer dissipates most of the translational energy of the incident cluster. Therefore, it prevents the cluster from being overheated upon impinging. Furthermore, the interaction between Ar and Cu benefits the confinement of the cluster structure. Our study shows that with Ar-buffer layers, the lateral spread of deposited clusters is 20% smaller than that on the bare Cu surface. This is consistent with the experimental findings.

Size-dependent fivefold and icosahedral symmetry in silver clusters

Trapped ion electron diffraction measurements on silver cluster cations, $\mathrm{Ag}_{n}{}^{+}$ for sizes $n=36--46,55$ at $\ensuremath{\sim}120\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ describe an evolution in structural symmetry with increasing cluster size. Diffraction patterns characterize fivefold symmetry at smaller sizes which evolves to icosahedral symmetry at $n=55$. Low energy isomer structures were identified by statistical search methods and optimized by density-functional calculations. Comparison of diffraction data with these theoretical structures confirms the presence of local order having fivefold symmetry for sizes $n=36--39,43$ and global order having icosahedral symmetry at the closed shell size $n=55$.

Phosphorylation of Bovine Adrenodoxin by Protein Kinase CK2 Affects the Interaction with Its Redox Partner Cytochrome P450scc (CYP11A1)

Adrenodoxin (Adx), a [2Fe-2S] vertebrate-type ferredoxin, transfers electrons from the NADPH-dependent flavoprotein Adx reductase (AdR) to mitochondrial cytochrome P450 enzymes of the CYP11A and CYP11B families, which catalyze key reactions in steroid hormone biosynthesis. Adx is a known phosphoprotein, but the kinases that phosphorylate Adx have remained mostly obscure. The aim of this study was to identify previously unknown Adx phosphorylating kinases and to acquire a deeper insight into the functional consequences of such a modification. Here, we show for the first time that bovine Adx is a substrate of protein kinase CK2, whereas bovine CYP11A1, CYP11B1, and AdR are not phosphorylated by this kinase. CK2 phosphorylation of mature Adx requires the presence of both the catalytic alpha-subunit and the regulatory beta-subunit of CK2 and takes place exclusively at residue Thr-71, which is located within the redox partner interaction domain of the protein. We created two Adx mutants, Adx-T71E (imitating a phosphorylation) and Adx-T71V (which cannot be phosphorylated at this site), respectively, and investigated how these mutations affected the interaction of Adx with its redox partners. These data were supplemented with detailed spectroscopic and functional assays using the phosphorylated protein. All Adx species behaved like wild type (Adx-WT) with respect to their redox potential, iron-sulfur cluster symmetry, and overall backbone structure. Substrate conversion assays catalyzed by CYP11A1 showed an increase in product formation when Adx-T71E or CK2-phosphorylated Adx were used as electron carrier instead of Adx-WT, whereas the activity toward CYP11B1 was not altered using these Adx species. Additionally, Adx-T71E represents the only full-length Adx mutant which leads to an increase in CYP11A1 product formation. Therefore, characterizing this full-length mutant helps to improve our knowledge on the functional effects of phosphorylations on complex redox systems.