Cluster Symmetry Research Articles

Origin of the Nonlinear Optical Response in Organotetrel Molecules, (Hetero)adamantane-Type Clusters with Organic Substituents, and Related Species.

The nonlinear optical response of (hetero)adamantane-type clusters and organotetrel molecules with the general formula [(RT)4E6] and [TR4] (T = group 14, R = organic substituents, E = S, CH2) is investigated from first principles. These clusters have been reported to efficiently convert infrared radiation into white light and are therefore extremely attractive functional materials for a multitude of applications. We demonstrate that the optical nonlinearities of the clusters in the range from 0 to 3 eV have their origin in electronic transitions within the substituents. The cluster core does not directly take part to the generation process; however, it strongly affects the intensity of the linear and nonlinear response. The relationships between optical properties and cluster symmetry, stoichiometry, substituent field, core composition, and further structural characteristics are investigated by systematical variation of R and T. This also demonstrates the possibility to finely tune the intensity as well as the frequency dependence of the optical response. Upon formation of cluster dimers, the intensity of the nonlinearities depends on the overall dimer geometry. In the case of heterogeneous dimers, the optical response strongly resembles that of a dominant cluster. Similarly, upon formation of cluster crystals, the compound inherits the optical characteristics of the parent molecules.

A Structural Model of Transition of Cubic α-Mn Into a Hexagonal Modification Based on Noncrystallographic Symmetry of Clusters

A Structural Model of Transition of Cubic α-Mn Into a Hexagonal Modification Based on Noncrystallographic Symmetry of Clusters

Spin Symmetry in Polynuclear Exchange-Coupled Clusters

The involvement of spin symmetry in the evaluation of zero-field energy levels in polynuclear transition metal and lanthanide complexes facilitates the division of the large-scale Hamiltonian matrix referring to isotropic exchange. This method is based on the use of an irreducible tensor approach. This allows for the fitting of the experimental data of magnetic susceptibility and magnetization in a reasonable time for relatively large clusters for any coupling path. Several examples represented by catena-[AN} and cyclo-[AN] systems were modeled. Magnetic data for 20 actually existing endohedral clusters were analyzed and interpreted.

Early-stage bifurcation of crystallization in a sphere

Bifurcations in kinetic pathways decide the evolution of a system. An example is crystallization, in which the thermodynamically stable polymorph may not form due to kinetic hindrance. Here, we use confined self-assembly to investigate the interplay of thermodynamics and kinetics in the crystallization pathways of finite clusters. We report the observation of decahedral clusters from colloidal particles in emulsion droplets and show that these decahedral clusters can be thermodynamically stable, just like icosahedral clusters. Our hard sphere simulations reveal how the development of the early nucleus shape passes through a bifurcation that decides the cluster symmetry. A geometric argument explains why decahedral clusters are kinetically hindered and why icosahedral clusters can be dominant even if they are not in the thermodynamic ground state.

SARS-CoV-2 Spike Protein Interaction Space.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a +sense single-strand RNA virus. The virus has four major surface proteins: spike (S), envelope (E), membrane (M), and nucleocapsid (N), respectively. The constitutive proteins present a high grade of symmetry. Identifying a binding site is difficult. The virion is approximately 50-200 nm in diameter. Angiotensin-converting enzyme 2 (ACE2) acts as the cell receptor for the virus. SARS-CoV-2 has an increased affinity to human ACE2 compared with the original SAR strain. Topological space, and its symmetry, is a critical component in molecular interactions. By exploring this space, a suitable ligand space can be characterized accordingly. A spike protein (S) computational model in a complex with ACE 2 was generated using silica methods. Topological spaces were probed using high computational throughput screening techniques to identify and characterize the topological space of both SARS and SARS-CoV-2 spike protein and its ligand space. In order to identify the symmetry clusters, computational analysis techniques, together with statistical analysis, were utilized. The computations are based on crystallographic protein data bank PDB-based models of constitutive proteins. Cartesian coordinates of component atoms and some cluster maps were generated and analyzed. Dihedral angles were used in order to compute a topological receptor space. This computational study uses a multimodal representation of spike protein interactions with some fragment proteins. The chemical space of the receptors (a dimensional volume) suggests the relevance of the receptor as a drug target. The spike protein S of SARS and SARS-CoV-2 is analyzed and compared. The results suggest a mirror symmetry of SARS and SARS-CoV-2 spike proteins. The results show thatSARS-CoV-2 space is variable and has a distinct topology. In conclusion, surface proteins grant virion variability and symmetry in interactions with a potential complementary target (protein, antibody, ligand). The mirror symmetry of dihedral angle clusters determines a high specificity of the receptor space.

Heredity of clusters in liquid Ta rapid solidification process and its correlation with local symmetry

Metallic glass (MG) has received intensive attention in the fields of amorphous physics and materials science, owing to its excellent mechanical properties, good corrosion resistance, and large elastic deformation limit. Comparing with traditional oxide glass, the limited glass-forming ability (GFA) seriously restricts the application of MG in engineering. Therefore, the GFA has been a hot scientific issue in the field of amorphous material research. Recently, scientists have fully realized that GFA is closely related to the local atomic structure in liquid as well as its evolution features. Since the MG is called the “freezing” liquid, exploring the correlation of local atomic structures between liquid phase and solid phase under rapid solidification conditions is helpful in understanding the microstructural mechanism of GFA. Therefore, the rapid solidification process of liquid Ta is investigated via molecular dynamics simulation. The pair correlation function (PDF), the largest standard cluster (LSC), and the reverse atomic trajectory tracking methods are used to characterize and analyze the microstructure and its evolution during the rapid solicitation of liquid Ta. The results show that the local atomic configurations of the rapidly solidified Ta are various Kasper clusters as well as their distorted configurations, among of which [1/444, 10/555, 2/666] deformed icosahedron (or Z13 cluster) accounts for the highest proportion. The trend of hereditary ability of clusters revealed by the onset temperature of continuous heredity is consistent well with that by the fraction of staged heredity. The geometric symmetry of clusters can be quantitatively characterized by using the local symmetry parameter (LSP). The hereditary ability of clusters is closely related to their LSP. The local five-fold symmetry is beneficial to enhancing hereditary ability, while local four- and six-fold symmetry are disadvantageous for that. The probability of clusters with the same LSC index emerging in the energy range follows the Gaussian distribution, and the expected average atomic potential energy <inline-formula><tex-math id="M3">\begin{document}$ {E}_{\rm exp}^{j} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231153_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231153_M3.png"/></alternatives></inline-formula> is almost linearly related to the LSP, and <inline-formula><tex-math id="M4">\begin{document}$ {E}_{\rm exp}^{j} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231153_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="24-20231153_M4.png"/></alternatives></inline-formula> decreases with the increase of LSP<sub>5</sub>. The high local five-fold symmetry reduces the average atomic potential energy of LSC, thereby enhancing its configurational heredity. These findings have guiding significance in improving GFA through regulating the local symmetry of liquid monatomic metals or alloys.

Co-evolution mechanism of the atomic/nano scale structural heterogeneity of Fe-based metallic glasses during relaxation and the effect on magnetic properties

Metallic glasses are structurally heterogeneous on the atomic and nano scales. However, few investigations have been conducted on how the structural heterogeneities in these two scales co-evolve during annealing. In this work, the atomic and nanoscale structural heterogeneity evolution accompanying the magnetic softness is systematically discussed based on the literature and our previous synchrotron X-ray diffraction and atomic force microscopy results. We revealed the co-evolution mechanism of structural heterogeneities on the atomic and nano scales during annealing via the insight of percolation theory from the point of view of the local five-fold symmetry of the clusters. The results indicate that the reduction of atomic-scale structural heterogeneity during annealing is accompanied by an increase in the degree of local five-fold symmetry of the clusters and an alteration in their connection patterns. As the local five-fold symmetry of clusters in Fe-based metallic glasses reaches the percolation threshold, the nanoscale liquid-like regions tend to transform into solid-like regions. The great degree of percolation causes the pronounced weakening of the nanoscale structural heterogeneity accompanying changes in the shape and number of the liquid-like regions. The reduction of the number of liquid-like regions causes a reduction in vertical anisotropy and magnetic softening due to a more uniform and less free volume within the sub-circular shaped liquid-like region.

Self-gravitating clusters of Fermi-Dirac gas with planar, cylindrical, or spherical symmetry: Evolution of density profiles with temperature.

We calculate density profiles for self-gravitating clusters of an ideal Fermi-Dirac gas with nonrelativistic energy-momentum relation and macroscopic mass at thermal equilibrium. Our study includes clusters with planar symmetry in dimensions D=1,2,3, clusters with cylindrical symmetry in D=2,3, and clusters with spherical symmetry in D=3. Wall confinement is imposed where needed for stability against escape. The length scale and energy scale in use render all results independent of total mass and prove adequate at all temperatures. We present exact analytic expressions for (fully degenerate) T=0 density profiles in four of the six combinations of symmetry and dimensionality. Our numerical results for T>0 describe the emergence, upon quasistatic cooling, of a core with incipient degeneracy surrounded by a more dilute halo. The equilibrium macrostates are found to depend more strongly on the cluster symmetry than on the space dimensionality. We demonstrate the mechanical and thermal stability of spherical clusters with coexisting phases.

Induced Fit and Mobility of Cycloalkanes within Nanometer-Sized Confinements at 5 K

Host-guest architectures provide ideal systems for investigating site-specific physical and chemical effects. Condensation events in nanometer-sized confinements are particularly interesting for the investigation of intermolecular and molecule-surface interactions. They may be accompanied by conformational adjustments representing induced fit packing patterns. Here, we report that the symmetry of small clusters formed upon condensation, their registry with the substrate, their lateral packing, and their adsorption height are characteristically modified by the packing of cycloalkanes in confinements. While cyclopentane and cycloheptane display cooperativity upon filling of the hosting pores, cyclooctane and to a lesser degree cyclohexane diffusively redistribute to more favored adsorption sites. The dynamic behavior of cyclooctane is surprising at 5 K given the cycloalkane melting point of >0 °C. The site-specific modification of the interaction and behavior of adsorbates in confinements plays a crucial role in many applications of three-dimensional porous materials as gas storage agents or catalysts/biocatalysts.

Model Selection Using K-Means Clustering Algorithm for the Symmetrical Segmentation of Remote Sensing Datasets

The importance of unsupervised clustering methods is well established in the statistics and machine learning literature. Many sophisticated unsupervised classification techniques have been made available to deal with a growing number of datasets. Due to its simplicity and efficiency in clustering a large dataset, the k-means clustering algorithm is still popular and widely used in the machine learning community. However, as with other clustering methods, it requires one to choose the balanced number of clusters in advance. This paper’s primary emphasis is to develop a novel method for finding the optimum number of clusters, k, using a data-driven approach. Taking into account the cluster symmetry property, the k-means algorithm is applied multiple times to a range of k values within which the balanced optimum k value is expected. This is based on the uniqueness and symmetrical nature among the centroid values for the clusters produced, and we chose the final k value as the one for which symmetry is observed. We evaluated the proposed algorithm’s performance on different simulated datasets with controlled parameters and also on real datasets taken from the UCI machine learning repository. We also evaluated the performance of the proposed method with the aim of remote sensing, such as in deforestation and urbanization, using satellite images of the Islamabad region in Pakistan, taken from the Sentinel-2B satellite of the United States Geological Survey. From the experimental results and real data analysis, it is concluded that the proposed algorithm has better accuracy and minimum root mean square error than the existing methods.

The first-principles study on structures, electronic and magnetic properties of the first row TM@C12N16 clusters

ABSTRACT The structures, electronic and magnetic attributes of the first row TM@C12N16 clusters have been calculated at the PBE level. The results reveal that the cage structure of C3N4 clusters can be maintained, while the symmetry of C12N16 clusters can be changed by TM encapsulated. TM encapsulated decreases the structural stability of the C12N16 clusters, and Sc@C12N16, V@C12N16, and Co@C12N16 clusters display better structural stability than other TM@C12N16 clusters. The C12N16 clusters display more chemical activity than the C3N4 sheet. TM atoms of TM@C12N16 clusters lose a few electrons (0.037–0.600 |e|), while Co, Cu and Zn atoms acquire 0.054|e|, 0.084 |e| and 0.050 |e|, respectively. Spin densities of the encapsulated TM atoms are degenerated except for Co (0.110 |e|) and Ni (0.029 |e|).

A Novel 2D Clustering Algorithm Based on Recursive Topological Data Structure

In the field of data science and data mining, the problem associated with clustering features and determining its optimum number is still under research consideration. This paper presents a new 2D clustering algorithm based on a mathematical topological theory that uses a pseudometric space and takes into account the local and global topological properties of the data to be clustered. Taking into account cluster symmetry property, from a metric and mathematical-topological point of view, the analysis was carried out only in the positive region, reducing the number of calculations in the clustering process. The new clustering theory is inspired by the thermodynamics principle of energy. Thus, both topologies are recursively taken into account. The proposed model is based on the interaction of particles defined through measuring homogeneous-energy criterion. Based on the energy concept, both general and local topologies are taken into account for clustering. The effect of the integration of a new element into the cluster on homogeneous-energy criterion is analyzed. If the new element does not alter the homogeneous-energy of a group, then it is added; otherwise, a new cluster is created. The mathematical-topological theory and the results of its application on public benchmark datasets are presented.

Chemical design of self-propelled Janus droplets

Chemical design of self-propelled Janus droplets

Common structural basis of short- and long-time relaxation dynamics in metallic glass-forming liquids

Classical molecular dynamics simulations were performed for five model metallic glass-forming liquids to investigate the structure correlation with both short-time β and long-time α relaxation dynamics. It is found that Debye-Waller factor characterizing the short-time β relaxation decreases with increasing five-fold local symmetry in atomic clusters, following a power-law behavior. It is also found that the equation of Debye-Waller factor and α-relaxation time, which is widely studied in polymer systems, is applicable in metallic glass-forming systems as well. Furthermore, a new equation is derived for the five-fold local symmetry and α-relaxation time, which describes the simulated data very well. These findings indicate that there exist a common structural basis for both the short-time β-relaxation and the long-time α-relaxation dynamics.

Breaking Symmetry Relaxes Structural and Magnetic Restraints, Suppressing QTM in Enantiopure Butterfly Fe2 Dy2 SMMs*.

The {Fe2Dy2} butterfly systems can show single molecule magnet (SMM) behaviour, the nature of which depends on details of the electronic structure, as previously demonstrated for the [Fe2Dy2(μ3‐OH)2(Me‐teaH)2(O2CPh)6] compound, where the [N,N‐bis‐(2‐hydroxyethyl)‐amino]‐2‐propanol (Me‐teaH3) ligand is usually used in its racemic form. Here, we describe the consequences for the SMM properties by using enantiopure versions of this ligand and present the first homochiral 3d/4 f SMM, which could only be obtained for the S enantiomer of the ligand for [Fe2Dy2(μ3‐OH)2(Me‐teaH)2(O2CPh)6] since the R enantiomer underwent significant racemisation. To investigate this further, we prepared the [Fe2Dy2(μ3‐OH)2(Me‐teaH)2(O2CPh)4(NO3)2] version, which could be obtained as the RS‐, R‐ and S‐compounds. Remarkably, the enantiopure versions show enhanced slow relaxation of magnetisation. The use of the enantiomerically pure ligand suppresses QTM, leading to the conclusion that use of enantiopure ligands is a “gamechanger” by breaking the cluster symmetry and altering the intimate details of the coordination cluster's molecular structure.

Patchy Colloidal Clusters with Broken Symmetry.

Colloidal clusters are prepared by assembling positively charged cross-linked polystyrene (PS) particles onto negatively charged liquid cores of swollen polymer particles. PS particles at the interface of the liquid core are closely packed around the core due to interfacial wetting. Then, by evaporating solvent in the liquid cores, polymers in the cores are solidified and the clusters are cemented. As the swelling ratio of PS cores increases, cores at the center of colloidal clusters are exposed, forming patchy colloidal clusters. Finally, by density gradient centrifugation, high-purity symmetric colloidal clusters are obtained. When silica-PS core-shell particles are swollen and serve as the liquid cores, hybrid colloidal clusters are obtained in which each silica nanoparticle is relocated to the liquid core interface during the swelling-deswelling process breaking symmetry in colloidal clusters as the silica nanoparticle in the core is comparable in size with the PS particle in the shell. The configuration of colloidal clusters is determined once the number of particles around the liquid core is given, which depends on the size ratio of the liquid core and shell particle. Since hybrid clusters are heavier than PS particles, they can be purified using centrifugation.

Colloidal Particles with Triangular Patches.

Self-assembling colloidal particles into clathrate hydrates requires the particles to have tetrahedral bonds in the eclipsed conformation. It has been suggested that colloidal particles with eclipsed triangular-shaped patches can form clusters in the eclipsed conformation that leads to colloidal clathrate hydrates. However, in experiments, patches have been limited to circular shapes due to surface energy minimization. Here, we extend the particle synthesis strategy and show that colloidal particles with triangular patches can be readily fabricated by controlling the viscosity of the liquid oil droplets during a colloidal fusion process. The position, orientation, curvature, shape, and size of the patches are all exclusively determined by the intrinsic symmetry of the colloidal clusters, resulting in dipatch particles with eclipsed patches and tetrahedral patchy particles with patch vertices pointing toward each other. Patch curvature can be controlled by tuning the viscosity of the oil droplets and using different surfactants. Using strain-promoted azide-alkyne cycloaddition, single-stranded DNA can be selectively functionalized on the patches. However, after annealing these particles, dipatch particles form chains because the patches are too small to form clathrate hydrates. Under certain conditions, tetrahedral triangular patchy particles should prefer the eclipsed conformation, as it maximizes DNA hybridization. However, we observe random aggregates, which result from having triangular patches that are too big. We estimate that tetrahedral patchy particles that can crystallize need to be less than 1 μm in diameter.

Modulating Structural and Electronic Properties of Rare Archimedean and Johnson-Type Mn Cages.

High-nuclearity Mn complexes have attracted significant scientific attention due to their fascinating magnetic properties and their relevance to bioinorganic systems and catalysis. In this work, we demonstrate how the strong binding characteristics of phosphonate ligands can be coupled with sterically hindered carboxylate groups to influence the symmetry of Mn coordination clusters. We describe the structure of two high-nuclearity Mn coordination cages, {Mn12} and {Mn15}, synthesized using this approach. These cages are structurally related to the truncated tetrahedral geometry and adopt rare topological features of Archimedean and Johnson-type solids. Their structural attributes distinctively influence their magnetic properties and electrocatalytic H2O oxidation characteristics.

Building Block Symmetry Relegation Induces Mesopore and Abundant Open-Metal Sites in Metal–Organic Frameworks for Cancer Therapy

Building Block Symmetry Relegation Induces Mesopore and Abundant Open-Metal Sites in Metal–Organic Frameworks for Cancer Therapy

Controlled Metal Oxide and Porous Carbon Templation Using Metal-Organic Frameworks

Templated porous carbons are promising due to their robust chemical and thermal properties. However, investigations into the formation mechanisms and structure–property relationships are limited. We report a systematic study of the carbonization of two metal-organic frameworks (MOFs) with varying connectivities and metal centers to determine how the resulting porous carbon structure is affected by temperature and gas environment. Surface area analysis reveals that the porosity depends on the number of residual carbon species, while diffraction analysis shows the strong effect of carbonization temperature on the resulting metal oxide phase. A higher connectivity parent MOF also indicates a more controllable and typically higher-surface-area porous carbon. This effect is especially noticeable when coordinating gases are used as the calcination environment, suggesting that a kinetically controlled decoordination event is responsible for reducing the carbon surface area. Neutron total scattering and pair distribution function (PDF) analysis showed that larger carbon domain sizes also cause higher surface areas, which indicates that the formation of domains within the materials promotes rigid backbones and aids in the production of high surface areas. PDF analysis showed that the MOF template could also be used to maintain the symmetry of the parent cluster in the resulting carbon, with the Zr6O4(OH)4 of UiO-66 forming the cubic phase of the metal oxide.