Magic Clusters Research Articles

High symmetry Nbn and Tan (n = 12, 15, and 17) clusters: High magnetic moments and the finding of superatoms with doping

Using ab initio calculations, we study Nbn and Tan clusters with n=12, 15, and 17 and find superatoms made of transition metals. Nb12 and Ta12 have an empty cage icosahedral structure. Neutral Ta12 has icosahedral symmetry and 2μB magnetic moments while the cage for Nb12 is slightly distorted and has no magnetic moment. These clusters behave like a divalent superatom. Accordingly an oxygen atom interacts exohedrally on a 3-fold site of the icosahedral cage like an MgO molecule and leaves the cage intact while Fe, Ru, and Os atoms can be endohedrally doped in Ta12 to produce electronically closed shell clusters with large highest occupied-lowest unoccupied molecular orbital (HOMO–LUMO) gap. Also isoelectronic Co@X12 and Rh@X12 (X=Nb and Ta) cations have a large HOMO–LUMO gap of up to about 1eV. In these cases the magnetic moment is quenched. On the other hand doping with Ni leaves the magnetic behavior of Ta12 the same. Further anions of Nb15 and Ta15 have a closed electronic shell structure and a singlet ground state with a large HOMO–LUMO gap. We show that isoelectronic Nb14Mo, Nb14W, Ta14Mo, Ta14W, Nb14Mn+, Nb14Re+, Ta14Mn+, and Ta14Re+ all have a large HOMO–LUMO gap of up to about 1.0eV and are magic clusters. Most interestingly Ta17 has a tetrahedrally symmetric Z16 Frank–Kasper polyhedral structure with a large magnetic moment of 5μB. On the other hand the magnetic moment on Nb17 cluster is 1μB. The magnetic moment on Ta17 is surprisingly large and it is counter intuitive as normally the magnetic moments decrease as one goes down in a column in the periodic table but some tantalum clusters behave differently. Doping of the n=17 clusters with Zr at the center leaves Zr@Ta16 magnetic with 2μB and 6μB magnetic moments nearly degenerate while Zr@Nb16 has zero magnetic moment.

Electric response properties of neutral and charged Al13X (X = Li, Na, K) magic clusters. A comprehensive ab initio and density functional comparative study

A systematic analysis of the dipole polarizabilities and first hyperpolarizabilities of a cluster series based on the magic Al13 cluster is presented. Reliable values of the dipole polarizabilities and first hyperpolarizabilities of Al13X0/−1 (X=Li, Na, K) by means of ab initio and density functional theory clusters are for the first time provided and discussed. In addition, useful information involving the partitioning of the dipole polarizabilities in terms of intrinsic polarizabilities computed with the fractional occupation iterative Hirshfeld method (FOHI) are illustrated. Finally, a step by step study of the polarization mechanism dominating the hyperpolarizabilities of these species is illustrated and explained in a comprehensive manner. The presented outcomes point out a monotonic (hyper)polarizability evolution going from Li to K for both neutral and charged cluster families. Also, it is clearly shown that all neutral clusters become largely more (hyper)polarizable and more anisotropic after receiving one electron. Concerning the principal hyperpolarization mechanism in these species, the presented analysis suggests that is mainly unidirectional in character, involving intense charge transfer processes from the metal cluster to the alkali metal.

A Density Functional Study of the Gold Cages MAu16 (M = Si, Ge, and Sn)

Relativistic density functional calculations are performed to explore the promise of MAu16(M=Si, Ge, and Sn) clusters as magic clusters and building blocks in developing cluster-assembled materials. C1 and Cs, two isomers of SiAu16, GeAu16 and SnAu16 with M (Ge or Sn) at the center of the cage, named, respectively, as SiAu16—C1, SiAu16—Cs, GeAu16-center, and SnAu16-center, are calculated to be the most stable. The Au—M bond should have both ionic and covalent characteristics. Their static linear polarizabilities and first-order hyperpolarizabilities are found to be sensitive to the delocalization of the valence electrons of the M atom, as well as their structures and shapes.

A density functional theory study of structural, electronic, optical and magnetic properties of small Ag–Cu nanoalloys

The structures and properties of 13-atom silver and copper bimetallic clusters are systematically investigated by density functional theory (DFT) in the theoretical frame of the generalised gradient approximation (GGA) exchange-collection function. Optical absorption, Raman spectra, vibrational spectra, as well as electronic and magnetic properties are calculated by DFT/GGA and semi-core pseudopotentials. The following lowest-energy structures in the 13-atom Ag–Cu clusters are obtained: cuboctahedron for pure Ag13, icosahedrons for pure Cu13, Ag1Cu12, Ag6Cu7 and Ag12Cu1; and amorphous motifs for Ag m Cu13−m when m = 2–5 and 7–11. Ag2Cu11, Ag7Cu6 and Ag11Cu2 are magic clusters. The Ag2Cu11 cluster exhibits high energetic stability, strong electronic stability, multipole surface plasmon resonance (SPR) mode and small dipole moment. The Ag6Cu7 cluster is a Janus-separated cluster that possesses the strongest electronic stability with a band gap of 0.424 eV and a vertical ionisation potential of 5.8417 eV. The amorphous Ag7Cu6 cluster shows an Ag–Cu alloyed motif. The blue shift of the maximum SPR peak becomes increasingly evident as silver atoms are added. All Raman and vibrational spectra exhibit many significant vibration modes within the wavenumber ranges of 0–270 and 0–306.55 cm−1, respectively. Ferroelectric and ferromagnetic behaviours are observed in the 13-atom Ag–Cu nanoalloys, indicating their new potential applications in nonlinear optical devices.

New structural model for Na6Si3 surface magic cluster on the Si(111)-7 × 7 surface

The adsorption of Na atoms on the Si(111)-7×7 surface is studied using first-principles calculations. Compared to the Triangle-Trimer model reported previously, we propose a more stable and robust Na6Si3 Hexagon-Trimer model which has six Na atoms with hexagon shape and three Si edge adatoms moving inward to form a trimer. The total energy of Hexagon-Trimer model is 0.252eV lower than that of Triangle-Trimer model and 0.552eV lower than that of Hexagon model. The simulated STM images of Hexagon-Trimer model are in good agreement with experimental STM observations. The most probable formation process of Hexagon-Trimer model is analyzed. The reaction is catalyzed by a Na atom and the energy barrier is reduced from 0.89 to 0.44eV. These results have provided a complete picture for the formation mechanism of Na6Si3 surface magic clusters on the Si(111)-7×7 surface.

Endohedrally doping the gold cage [formula omitted] with an trivalent atom B, Al, Ga, and In: Density functional studies

The relativistic density functional calculations explore that M@Au16- (M=B, Al, Ga, and In) with M at the cage center, named as M@Au16--center, should be the most stable. The M@Au16--center (M=B, Al, Ga, and In) clusters have closed-shell electronic structures and large energy gaps. All of these properties are characteristic of a magic cluster and can be well understood by the jellium model. Therefore, we strongly suggest M@Au16--center (M=B, Al, Ga, and In) are magic clusters and promising as building blocks in developing cluster-assembled materials. The energy levels and the wavefunctions of frontier orbitals explore that the HOMOs of M@Au16--center should be partly occupied by the M atom, while the LUMOs of them should be mostly from the Au16- bodies. The difference charge densities and the natural bonding orbital charge analyses imply the Au–M bonds have both the ionic and covalent characters. Finally, the mean static linear polarizabilities and first-order hyperpolarizabilities of M@Au16--center are larger than those of Au16-, while their anisotropies of the polarizability tensors are smaller than those of Au16-. We rationalize the nonlinear properties by studying the low-energy optical absorption band obtained by employing time-dependent density functional theory.

Magic number effect on cluster formation of polyhydroxylated fullerenes in water–alcohol binary solution

Due to the spherical shape with a diameter of ca. 1 nm, the aggregation behaviour of fullerene C60 is very interesting in view of the possible formation of magic number particle in a similar manner as metal cluster in gas phase. Herein, we report for the first time the magic number aggregation behaviours of polyhydroxylated fullerenol C60(OH)36 in water–alcohol (methanol, ethanol and 1-propanol) binary solution with increasing alcohol component. The diameters of particle were ca. 6–8 nm depending on the alcohol used. The particle sizes were precisely measured by the novel-induced grating method which is superior for the particle-size measurement in single-nano region (1–10 nm). The magic number cluster was also detected by scanning probe microscopy observation. However, such aggregation behaviours were not found in DMSO–alcohol system or for the use of less hydroxylated C60(OH)10.

Thermodynamic properties of carbon dioxide clusters by M06-2X and dispersion-corrected B2PLYP-D theory

The M06-2X and B2PLYP-D functionals have been applied to predict structures and energies for (CO2)n clusters up to n=16. A comparison between M06-2X, B2PLYP-D and benchmark CCSD(T) results indicates that M06-2X is capable of providing accurate binding energies. Stepwise M06-2X (CO2)n clustering free energies exhibit a sharp discontinuity at the magic cluster size n=13 and systematically shift to more exergonic values with decreasing temperature, in particular for larger clusters. These results indicate that the M06-2X method provides an accurate and cost effective description of non-covalent interactions in (CO2)n clusters and therefore may provide important information on CO2 nucleation phenomena.

Size-selective self-assembly of magnetic Mn nanoclusters on Si(111)

We show by first-principles calculations two types of magnetic magic Mn clusters on the Si(111)-(7 × 7) surface. The first is a small triangular Mn7 cluster stabilized by the solid-centered Mn-Si3 bonds on the top layer, and the second is a large hexagonal Mn13 cluster favored by the confining potential wells of the faulted half unit cells on the Si(111) surface. These two structural models are distinct from that of the planar group-III clusters on Si(111) and produce simulated scanning tunneling microscopy images in reasonable agreement with recent experimental observations. These results offer key insights for understanding the complex energetic landscape on the Si(111)-(7 × 7) surface, which is critical to precisely controlled growth of Mn nanocluster arrays with specific size, magnetic moment, and good uniformity.

Density functional studies of magic clusters Ga13M(M = Li, Na, K, and Rb)

Density functional studies are performed on the structures, stabilities, electronic properties, and polarizabilities of the Ga13M(M=Li, Na, K, and Rb) clusters, which have closed electronic shell structures, enhanced stabilities, large HOMO–LUMO energy gaps, high vertical ionization potentials, and low vertical electron affinities. All of these properties are characteristic of a magic cluster and can be well understood by the jellium model. Therefore, we strongly suggest Ga13M(M=Li, Na, K, and Rb) are magic clusters and promising as building blocks in developing cluster-assembled materials. The calculated vertical electron affinity of Ga13 is close to that of bromine, implying it would be like a halogen atom in the Ga13M molecule. The static linear polarizabilities and first-order hyperpolarizabilities of Ga13M clusters are significantly larger than those of Ga13 because of their lower symmetries and higher delocalization of p electrons.

Large mixed complexes involving uracil, cytosine, thymine and/or 1‐methyl uracil around Ca2+ ions: an electrospray ionization/MS study

We investigated the possible formation of mixed B(n)B'(n')Ca(2+) complexes where B and B' are two different nucleobases. Electrospray ionization (ESI) mass spectrometric experiments from solutions containing two different kinds of nucleobases and calcium ions were carried out to investigate the formation of magic number clusters that may be relevant in a biological point of view. The results presented here clearly show that mixed complexes can be formed and are stable in the gas phase. This represents an important step toward more complex solutions in which several nucleobases are present simultaneously and may compete in the formation of cationized clusters. We believe that thorough investigations on such systems may help understanding biological processes that may effect the tridimensional structure of the DNA macromolecule. The formation of mixed hexamers, decamers, dodecamers and tetradecamers are clearly favored from solution containing uracil (Ura), thymine (Thy) and Ca(2+), whereas mixed octamers are preferred from 1-methyl uracil (MeU), uracil and Ca(2+) mixtures. Cytosine (Cyto) can form mixed complexes with either uracil or 1-methyl uracil or thymine. On the other hand, the main species formed in these latter cases are mixed tetramers.

Laser desorption dual spray post‐ionization mass spectrometry for direct analysis of samples via two informative channels

A laser desorption dual spray post-ionization mass spectrometry method is described, and its usefulness is demonstrated with the examples of selective detection of food components, manipulation of protein charge state distribution and investigation on the formation of magic number clusters. The method is carried out by adopting two spray emitters for post-ionization of analytes desorbed by a pulsed infrared laser. Various components in a complex sample or distinct behavior of an analyte in two different spray reagents can be rapidly probed by the method quasi-simultaneously, highlighting the potential applications of this method for protein characterization, reaction study and food analysis.

Step Flow Versus Mosaic Film Growth in Hexagonal Boron Nitride

Many emerging applications of hexagonal boron nitride (h-BN) in graphene-based nanoelectronics require high-quality monolayers as the ultrathin dielectric. Here, the nucleation and growth of h-BN monolayer on Ru(0001) surface are investigated using scanning tunneling microscopy with a view toward understanding the process of defect formation on a strongly interacted interface. In contrast to homoelemental bonding in graphene, the heteroelemental nature of h-BN gives rise to growth fronts with elemental polarity. This can have consequences in the different stages of film growth, from the nucleation of h-BN magic clusters and their sintering to form compact triangular islands to the growth of patchwork mosaic monolayer with a high density of misfit boundaries. The parallel alignment of triangular islands on the same terrace produces translational fault lines when growth fronts merge, while antiparallel alignment of islands on adjacent terraces produces non-bonded fault lines between domains terminated by like atoms. With these insights into the generation of void defects and fault lines at grain boundaries, we demonstrate a strategy to obtain high-quality h-BN monolayer film based on step flow growth.

A density functional study of the structure of small OCS@3HeN clusters

Kohn-Sham density functional calculations are reported for the structures of clusters consisting of a carbonyl sulfide (OCS) molecule with N = 1, 8, 18, and 40 attached (3)He atoms. The N = 1 cluster ground state is highly localized at the molecular waist (donut ring position), but for higher levels of excitation becomes increasingly delocalized. The first magic cluster with 8 atoms has a significant density at both ends of the molecule in addition to the donut ring. With N = 18 (3)He atoms the molecule is enclosed by a magic number closed shell. Another magic stable structure consisting of two nearly isotropically spherical closed shells is found at N = 40. A comparison with calculations for the same sized (4)He clusters show some important similarities, e.g., pile up at the donut ring position but altogether a more diffuse, less anisotropic structure. These results are discussed in the light of the recently analyzed infrared spectra measured in large pure (3)He droplets (N ≈ 1.2 × 10(4)) [B. Sartakov, J. P. Toennies, and A. F. Vilesov, J. Chem. Phys. 136, 134316 (2012)]. The moments of inertia of the 11 atom spherical shell structure, which is consistent with the experimental spectrum, lies between the predicted moments of inertia for N = 8 and N = 18 clusters. Overall the calculations reveal that the structures and energies of small doped (3)He are only slightly more diffuse and less energetic than the same (4)He clusters.

安定かつ高機能なナノ物質の創製を目指して：魔法数金クラスターの高機能化

Nanomaterials which exhibit both stability and functionality are currently considered to hold the most promise as components of nanotechnology devices. Thiolate (RS)-protected gold nanoclusters (Aun(SR)m) have attracted significant attention in this regard and, among these, the magic clusters are believed to be the best candidates since they are the most stable. We have investigated the effects of heteroatom doping, protection by selenolate ligands and protection by photoresponsive thiolates on the stability and physical/chemical properties of these clusters. Through such studies, we have attempted to establish methods of modifying magic Aun(SR)m clusters as a means of creating metal clusters that are both robust and functional. This paper summarizes our studies towards this goal and the obtained results.

Toward the creation of stable, functionalized metal clusters

Nanomaterials which exhibit both stability and functionality are currently considered to hold the most promise as components of nanotechnology devices. Thiolate (RS)-protected gold nanoclusters (Aun(SR)m) have attracted significant attention in this regard and, among these, the magic clusters are believed to be the best candidates since they are the most stable. We have investigated the effects of heteroatom doping, protection by selenolate ligands and protection by photoresponsive thiolates on the stability and physical/chemical properties of these clusters. Through such studies, we have attempted to establish methods of modifying magic Aun(SR)m clusters as a means of creating metal clusters that are both robust and functional. This paper summarizes our studies towards this goal and the obtained results.

Effect of spin ordering on structure and structural transitions in the (MnS)6 magic cluster

Many manganese-based magnetic materials exhibit exciting technologically important properties (e.g. colossal magnetoresistance, giant magnetocaloric effect) but, as yet, relatively little is known at the nanoscale. Recently, manganese sulfide clusters were produced in a laser ablation experiment, revealing sizes with special stability, i.e. magic clusters. Here, we use density functional calculations to investigate the (MnS)6 magic cluster. Specifically, the interplay between magnetism, structure and energetic stability in nine low lying minima (MnS)6 structures is investigated and rationalized. We further calculate the energetic barriers for interconversion between the two lowest lying (MnS)6 isomers and discuss their possible relevance to premelting cluster dynamics.

Evolution of (GaAl) n Clusters and Chemisorptions of H2 on (GaAl) n Clusters

The growth behavior of (GaAl) n (n = 1–12) and the chemisorptions of hydrogen on the ground state geometries have been studied with the three-parameter hybrid generalized gradient approximation due to Becke-Lee–Yang–Parr (B3LYP). The dissociation energy, the second-order energy differences, and the HOMO–LUMO gaps indicate that the magic numbers of the calculated (GaAl) n clusters are n = 4 and 6. To my knowledge, this is the first time that a systematic study of chemisorptions of hydrogen on gallium aluminum clusters. The onefold top site of aluminum atom is identified to be the most favorable chemisorptions site for one hydrogen chemisorptions on most (GaAl) n clusters. In general, dissociative chemisorptions of a hydrogen molecule on a top site of aluminum atom is found common for all sizes clusters considered here except for (GaAl) n (n = 1–3) clusters. The stability of the (GaAl) n H m complexes shows that both large second-order difference and large fragmentation energies for (GaAl)10H2 and (GaAl)11H2 make these species behaving like magic clusters.

Endohedral cage and layered structures of Al46

First-principles calculations were performed to study the structure and stability of the Al46 cluster. The results suggest two competing structural motifs, the spherical endohedral cage and layer-stacking structures. It is shown that although medium-sized Al clusters tend to form layered structures (i.e., fcc fragments with a stacking fault), a spherical endohedral cage configuration is also an important structural motif for the magic Al46 cluster. Besides, the cluster ions were also studied, and the calculated PES of the Al46- isomer with the minimum of free energy is in better agreement with the experimental PES data.

Infrared spectroscopy of large protonated water clusters H+(H2O)20–50 cooled by inert gas attachment

We report infrared spectra of protonated water clusters H+(H2O)n (n=20–50) cooled by H2 tagging. IR spectra show sharper features, validating the cooling effect of the H2 attachment even for the large clusters. Furthermore, the H2–mediated spectrum has indicated the origin of the first antimagic number (n=22), which is a dangling water molecule on the cluster surface [K. Mizuse, A. Fujii, J. Phys. Chem. Lett. 2 (2011) 2130]. On the other hand, for the second magic (n=28) and antimagic (n=29) number clusters, no apparent difference is observed by the H2 tagging. IR spectra of Ar-tagged H+(H2O)20–22 are also measured. These spectra also show sharper features, however, no signature for the dangling water molecule is seen in n=22. This result implies there are multiple isomer types in the n=22 cluster and the observable type might vary with the choice of the inert gas for tagging.