Nature of valence transition and spin moment in Ag(n)V(+) clusters

Photoelectron Imaging Signature for Selective Formation of Icosahedral Anionic Silver Cages Encapsulating Group 5 Elements: M@Ag12- (M = V, Nb, and Ta)

An assembly of 13 atoms can form highly symmetric architectures like those belonging to D3h, Oh, D5h, and Ih point groups. Here, using photoelectron imaging spectroscopy in combination with density functional theory (DFT) calculations, we present a simple yet convincing experimental signature for the selective formation of icosahedral cages of anionic silver clusters encapsulating a dopant atom of group 5 elements: M@Ag12- (M = V, Nb, and Ta). Their photoelectron images obtained at 4 eV closely resemble one another: only a single ring is observed, which is assignable to photodetachment signals from a 5-fold degenerate superatomic 1D electronic shell in the 1S21P61D10 configuration of valence electrons. The perfect degeneracy represents an unambiguous fingerprint of an icosahedral symmetry, which would otherwise be lifted in all of the other structural isomers. DFT calculations confirm that Ih forms are the most stable and that D5h, Oh, and D3h structures are not found even in metastable states.

Structural Determination and Bonding Characteristics of the Gas-Phase Ta2Si2̅ Anion and Its Neutral: Anion Photoelectron Spectroscopy and Theoretical Studies

The structures and bonding characteristics of Ta2Si2̅/0 clusters are investigated using anion photoelectron spectroscopy and quantum chemical calculations. The vertical detachment energy of the Ta2Si2̅ anion is measured to be 2.00 ± 0.08 eV using the 266 nm photon. It is found that the Ta2Si2̅ anion has three low-energy isomers with a C2v symmetric Ta-Ta dibridged structural framework, all of which contribute to the experimental photoelectron spectrum, while the Ta2Si2 neutral also has a C2v symmetric Ta-Ta dibridged structural framework. The charge-transfer from Ta atoms to Si atoms is discovered using atomic dipole moment corrected Hirshfeld analysis for the Ta2Si2̅ anion and Ta2Si2 neutral. Chemical bonding investigations show that both the Ta2Si2̅ anion and Ta2Si2 neutral have a strong covalent Ta-Ta bond, as well as σ and π double bonding patterns. Furthermore, the Ta atoms are linked together by a single 2c-2e Ta2 σ bond, whereas the Si atoms are linked together with the Ta atoms via four 2c-2e TaSi σ bonds, two 3c-2e TaSi2 σ bonds, one 4c-2e Ta2Si2 σ bond, and one 4c-2e Ta2Si2 π bond.

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners. The format of the paper is that of a roundtable discussion, in which the participants express and exchange views on DFT in the form of 302 individual contributions, formulated as responses to a preset list of 26 questions. Supported by a bibliography of 777 entries, the paper represents a broad snapshot of DFT, anno 2022.

Exploring s-d, s-f, and d-f Electron Interactions in AgnCe+ and AgnSm+ by Chemical Reaction toward O2

We investigate gas-phase reactions of free Ag_nCe⁺ and Ag_nSm⁺ clusters with oxygen molecules to explore s-d, s-f, and d-f electron interactions in the finite size regime; a Ce atom has a 5d electron as well as a 4f electron, whereas a Sm atom has six 4f electrons without 5d electrons. In the reaction of Ag_nCe⁺ (n = 3-20), the Ce atom located on the cluster surface provides an active site except for n = 15 and 16, as inferred from the composition of the reaction products with oxygen bound to the Ce atom as well as from their relatively high reactivity. The extremely low reactivity for n = 15 and 16 is due to encapsulation of the Ce atom by Ag atoms. The minimum reactivity observed at n = 16 suggests that a closed electronic shell with 18 valence electrons is formed with a delocalized Ce 5d electron, while the localized Ce 4f electron does not contribute to the shell closure. As for Ag_nSm⁺ (n = 1-18), encapsulation of the Sm atom was observed for n ≥ 15. The lower reactivity at n = 17 than at n = 16 and 18 implies that an 18-valence-electron shell closure is formed with s electrons from Ag and Sm atoms; Sm 4f electrons are not involved in the shell closure as in the case of Ag_nCe⁺. The present results suggest that the 4f electrons tend to localize on the lanthanoid atom, whereas the 5d electron delocalizes to contribute to the electron shell closure.

Electron counting in cationic and anionic silver clusters doped with a 3d transition-metal atom: endo- vs. exohedral geometry

Cationic and anionic AgNM+/− (M = Sc–Ni) clusters are explored to examine the electron-counting rule. Among 18-valence-electron clusters, endohedrally doped ones are stable due to superatomic electron-shell closure involving delocalized 3d electrons.

Reaction of nitric oxide molecules on transition-metal-doped silver cluster cations: size- and dopant-dependent reaction pathways

We report size- and dopant-dependent reaction pathways as well as reactivity of gas-phase free Ag_nM⁺ (M = Sc-Ni) clusters interacting with NO. The reactivity of Ag_nM⁺, except for M = Cr and Mn, exhibits a minimum at a specific size, where the cluster cation possesses 18 or 20 valence electrons consisting of Ag 5s and dopant's 3d and 4s. The product ions range from NO adducts, Ag_nM(NO)_m⁺, and oxygen adducts, Ag_nMO_m⁺, to NO₂ adducts, Ag_nM(NO₂)_m⁺. At small sizes, Ag_nMO_m⁺ are the major products for M = Sc-V, whereas Ag_nM(NO)_m⁺ dominate the products for M = Cr-Ni in striking contrast. In both cases, these reaction products are reminiscent of those from an atomic transition metal. However, the reaction pathways are different at least for M = Sc and Ti; kinetics measurements reveal that the present oxygen adducts are formed via NO adducts, while, for example, Ti⁺ is known to produce TiO⁺ directly by reaction with a single NO molecule. At larger sizes, on the other hand, Ag_nM(NO₂)_m⁺ are dominantly produced regardless of the dopant element because the dopant atom is encapsulated by the Ag host; the NO₂ formation on the cluster is similar to that reported for undoped Ag_n⁺.

The superatomic state beyond conventional magic numbers: Ligated metal chalcogenide superatoms

The field of cluster science is drawing increasing attention due to the strong size and composition-dependent properties of clusters and the exciting prospect of clusters serving as the building blocks for materials with tailored properties. However, identifying a unifying central paradigm that provides a framework for classifying and understanding the diverse behaviors is an outstanding challenge. One such central paradigm is the superatom concept that was developed for metallic and ligand-protected metallic clusters. The periodic electronic and geometric closed shells in clusters result in their properties being based on the stability they gain when they achieve closed shells. This stabilization results in the clusters having a well-defined valence, allowing them to be classified as superatoms-thus extending the Periodic Table to a third dimension. This Perspective focuses on extending the superatomic concept to ligated metal-chalcogen clusters that have recently been synthesized in solutions and form assemblies with counterions that have wide-ranging applications. Here, we illustrate that the periodic patterns emerge in the electronic structure of ligated metal-chalcogenide clusters. The stabilization gained by the closing of their electronic shells allows for the prediction of their redox properties. Further investigations reveal how the selection of ligands may control the redox properties of the superatoms. These ligated clusters may serve as chemical dopants for two-dimensional semiconductors to control their transport characteristics. Superatomic molecules of multiple metal-chalcogen superatoms allow for the formation of nano-p-n junctions ideal for directed transport and photon harvesting. This Perspective outlines future developments, including the synthesis of magnetic superatoms.

Systematic Investigation of the Structure, Stability, and Spin Magnetic Moment of CrM n Clusters (M = Cu, Ag, Au, and n = 2-20) by DFT Calculations

Binary clusters of transition-metal and noble-metal elements have been gathering momentum for not only advanced fundamental understanding but also potential as elementary blocks of novel nanostructured materials. In this regard, the geometries, electronic structures, stability, and magnetic properties of Cr-doped Cu _n , Ag _n , and Au _n clusters (n = 2-20) have been systematically studied by means of density functional theory calculations. It is found that the structural evolutions of CrCu _n and CrAg _n clusters are identical. The icosahedral CrCu₁₂ and CrAg₁₂ are crucial sizes for doped copper and silver species. Small CrAu _n clusters prefer the planar geometries, while the larger ones appear as on the way to establish the tetrahedral CrAu₁₉. Our results show that while each noble atom contributes one s valence electron to the cluster shell, the number of chromium delocalized electrons is strongly size-dependent. The localization and delocalization behavior of 3d orbitals of the chromium decide how they participate in metallic bonding, stabilize the cluster, and give rise to and eventually quench the spin magnetic moment. Moreover, molecular orbital analysis in combination with a qualitative interpretation using the phenomenological shell model is applied to reveal the complex interplay between geometric structure, electronic structure, and magnetic moment of clusters. The finding results are expected to provide greater insight into how a host material electronic structure influences the geometry, stability, and formation of spin magnetic moments in doped systems.

First-principle study of the structures, growth pattern, and properties of (Pt3Cu)n, n = 1-9, clusters

In this work, a first-principles systematic study of (Pt₃Cu)_n, n = 1-9, clusters was performed employing the linear combination of Gaussian-type orbital auxiliary density functional theory approach. The growth of the clusters has been achieved by increasing the previous cluster by one Pt₃Cu unit at a time. To explore in detail the potential energy surface of these clusters, initial structures were obtained from Born-Oppenheimer molecular dynamics trajectories generated at different temperatures and spin multiplicities. For each cluster size, several dozens of structures were optimized without any constraints. The most stable structures were characterized by frequency analysis calculations. This study demonstrates that the obtained most stable structures prefer low spin multiplicities. To gain insight into the growing pattern of these systems, average bond lengths were calculated for the lowest stable structures. This work reveals that the Cu atoms prefer to be together and to localize inside the cluster structures. Moreover, these systems tend to form octahedra moieties in the size range of n going from 4 to 9 Pt₃Cu units. Magnetic moment per atom and spin density plots were obtained for the neutral, cationic, and anionic ground state structures. Dissociation energies, ionization potential, and electron affinity were calculated, too. The dissociation energy and the electron affinity increase as the number of Pt₃Cu units grows, whereas the ionization potential decreases.

Stability of cationic silver doped gold clusters and the subshell-closed electronic configuration of AgAu14. J Chem Phys 2020;153:244304. [PMID: 33380086 DOI: 10.1063/5.0033487]

Silver doping is a valuable route to modulate the structural, electronic, and optical properties of gold clusters. We combine photofragmentation experiments with density functional theory calculations to investigate the relative stability of cationic Ag doped Au clusters, AgAu_N-1 ⁺ (N ≤ 40). The mass spectra of the clusters after photofragmentation reveal marked drops in the intensity of AgAu₈ ⁺, AgAu₁₄ ⁺, and AgAu₃₄ ⁺, indicating a higher relative stability of these sizes. This is confirmed by the calculated AgAu_N-1 ⁺ (N ≤ 17) dissociation energies peaking for AgAu₆ ⁺, AgAu₈ ⁺, and AgAu₁₄ ⁺. While the stability of AgAu₆ ⁺ and AgAu₈ ⁺ can be explained by the accepted electronic shell model for metal clusters, density of states analysis shows that the geometry plays an important role in the higher relative stability of AgAu₁₄ ⁺. For this size, there is a degeneracy lifting of the 1D shell, which opens a relatively large HOMO-LUMO gap with a subshell-closed 1S²1P⁴1P²1D⁶ electronic configuration.

Structural Evolution and Electronic Properties of TaSin-/0 (n = 2-15) Clusters: Size-Selected Anion Photoelectron Spectroscopy and Theoretical Calculations

The structural evolution and electronic properties of TaSi_n^-/0 (n = 2-15) clusters are explored using anion photoelectron spectroscopy accompanied by quantum chemical calculations. The Ta atom in TaSi_n^-/0 is inclined to interact with more Si atoms and has high coordination numbers. The theoretical calculations show that TaSi₂^-/0 have trianglur structures and TaSi₃^-/0 adopt pyramid structures, while the geometries of TaSi_n^-/0 (n = 4-7) are all exohedral structures dominated by bipyramid-based configurations with the Ta atom face-capping the Si_n motifs. TaSi₈^-/0 and TaSi_9-10^- have boat-shaped geometries, whereas TaSi_9-10 neutrals adopt bipyramid-based geometries instead of boat-shaped ones. TaSi₁₁^- and TaSi₁₂ are confirmed as the critical size of transiting from exohedral to endohedral structures for anionic and neutral clusters, respectively. TaSi_12-15^-/0 have pentagonal or hexagonal prism-based geometries. Natural population analysis shows that the electron transfers from Si_n skeletons to Ta atom. The second-order energy differences (Δ₂E) and incremental binding energy (ΔE^I) values exhibit strong odd-even alternations, suggesting that the TaSi_n-odd^-/0 clusters are more stable than the adjacent TaSi_n-even^-/0 ones, except that TaSi_12^-/0 are more stable than TaSi_11^-/0 and TaSi_13^-/0.

Relative Stability of Small Silver, Platinum, and Palladium Doped Gold Cluster Cations

The stability patterns of single silver, platinum, and palladium atom doped gold cluster cations, MAuN−1+ (M = Ag, Pt, Pd; N = 3–6), are investigated by a combination of photofragmentation experiments and density functional theory calculations. The mass spectra of the photofragmented clusters reveal an odd-even pattern in the abundances of AgAuN−1+, with local maxima for clusters containing an even number of valence electrons, similarly to pure AuN+. The odd-even pattern, however, disappears upon Pt and Pd doping. Computed dissociation energies agree well with the experimental findings for the different doped clusters. The effect of Ag, Pt, and Pd doping is discussed on the basis of an analysis of the density of states of the N = 3–5 clusters. Whereas Ag delocalizes its 5s valence electron in all sizes, this process is size-specific for Pt and Pd.

Stability of small cationic platinum clusters

The relative stability of small cationic platinum clusters is investigated by photofragmentation experiments and density functional theory calculations.

Probing the Structural, Electronic, and Magnetic Properties of Ag n V (n = 1-12) Clusters

The structural, electronic, and magnetic properties of Ag _n V (n = 1-12) clusters have been studied using density functional theory and CALYPSO structure searching method. Geometry optimizations manifest that a vanadium atom in low-energy Ag_nV clusters favors the most highly coordinated location. The substitution of one V atom for an Ag atom in Ag _n + 1 (n ≥ 5) cluster modifies the lowest energy structure of the host cluster. The infrared spectra, Raman spectra, and photoelectron spectra of Ag _n V (n = 1-12) clusters are simulated and can be used to determine the most stable structure in the future. The relative stability, dissociation channel, and chemical activity of the ground states are analyzed through atomic averaged binding energy, dissociation energy, and energy gap. It is found that V atom can improve the stability of the host cluster, Ag₂ excepted. The most possible dissociation channels are Ag _n V = Ag + Ag _n - 1V for n = 1 and 4-12 and Ag _n V = Ag₂ + Ag _n - 2V for n = 2 and 3. The energy gap of Ag _n V cluster with odd n is much smaller than that of Ag _n + 1 cluster. Analyses of magnetic property indicate that the total magnetic moment of Ag _n V cluster mostly comes from V atom and varies from 1 to 5 μ _B. The charge transfer between V and Ag atoms should be responsible for the change of magnetic moment.

Evolution of the Spin Magnetic Moments and Atomic Valence of Vanadium in VCux+, VAgx+, and VAux+ Clusters (x = 3-14)

The atomic structures, bonding characteristics, spin magnetic moments, and stability of VCu_x⁺, VAg_x⁺, and VAu_x⁺ (x = 3-14) clusters were examined using density functional theory. Our studies indicate that the effective valence of vanadium is size-dependent and that at small sizes some of the valence electrons of vanadium are localized on vanadium, while at larger sizes the 3d orbitals of the vanadium participate in metallic bonding eventually quenching the spin magnetic moment. The electronic stability of the clusters may be understood through a split-shell model that partitions the valence electrons in either a delocalized shell or localized on the vanadium atom. A molecular orbital analysis reveals that in planar clusters the delocalization of the 3d orbital of vanadium is enhanced when surrounded by gold due to enhanced 6s-5d hybridization. Once the clusters become three-dimensional, this hybridization is reduced, and copper most readily delocalizes the vanadium's valence electrons. By understanding these unique features, greater insight is offered into the role of a host material's electronic structure in determining the bonding characteristics and stability of localized spin magnetic moments in quantum confined systems.

Superatoms: Electronic and Geometric Effects on Reactivity

The relative role of electronic and geometric effects on the stability of clusters has been a contentious topic for quite some time, with the focus on electronic structure generally gaining the upper hand. In this Account, we hope to demonstrate that both electronic shell filling and geometric shell filling are necessary concepts for an intuitive understanding of the reactivity of metal clusters. This work will focus on the reactivity of aluminum based clusters, although these concepts may be applied to clusters of different metals and ligand protected clusters. First we highlight the importance of electronic shell closure in the stability of metallic clusters. Quantum confinement in small compact metal clusters results in the bunching of quantum states that are reminiscent of the electronic shells in atoms. Clusters with closed electronic shells and large HOMO-LUMO (highest occupied molecular orbital-lowest unoccupied molecular orbital) gaps have enhanced stability and reduced reactivity with O₂ due to the need for the cluster to accommodate the spin of molecular oxygen during activation of the molecule. To intuitively understand the reactivity of clusters with protic species such as water and methanol, geometric effects are needed. Clusters with unsymmetrical structures and defects usually result in uneven charge distribution over the surface of the cluster, forming active sites. To reduce reactivity, these sites must be quenched. These concepts can also be applied to ligand protected clusters. Clusters with ligands that are balanced across the cluster are less reactive, while clusters with unbalanced ligands can result in induced active sites. Adatoms on the surface of a cluster that are bound to a ligand result in an activated adatom that reacts readily with protic species, offering a mechanism by which the defects will be etched off returning the cluster to a closed geometric shell. The goal of this Account is to argue that both geometric and electronic shell filling concepts serve as valuable organizational principles that explain a wide variety of phenomena in the reactivity of clusters. These concepts help to explain the fundamental interactions that allow for specific clusters to be described as superatoms. Superatoms are clusters that exhibit a well-defined valence. A superatom cluster's properties may be intuitively understood and predicted based on the energy gained when the cluster obtains its optimal electronic and geometric structure. This concept has been found to be a unifying principle among a wide variety of metal clusters ranging from free aluminum clusters to ligand protected noble metal clusters and even metal-chalcogenide ligand protected clusters. Thus, the importance of electronic and geometric shell closing concepts supports the superatom concept, because the properties of certain clusters with well-defined valence are controlled by the stability that is enhanced when they retain their closed electronic and geometric shells.

4d and 5d bimetal doped tubular silicon clusters Si12M2 with M = Nb, Ta, Mo and W: a bimetallic configuration model

M₂Si₁₂ clusters are found in a bimetallic tubular structure where one metal atom is located in the central region of a (6/6) tube, and the other is capped outside to a hexagonal face. A bimetallic configuration containing 11 MOs, partially or fully occupied by up to 22 electrons, was established to interpret their stability.

The structural and electronic properties of NbSin-/0 (n = 3-12) clusters: anion photoelectron spectroscopy and ab initio calculations

Niobium-doped silicon clusters, NbSi_n^- (n = 3-12), were generated by laser vaporization and investigated by anion photoelectron spectroscopy. The structures and electronic properties of NbSi_n^- anions and their neutral counterparts were investigated with ab initio calculations and compared with the experimental results. It is found that the Nb atom in NbSi_n^-/0 prefers to occupy the high coordination sites to form more Nb-Si bonds. The most stable structures of NbSi_3-7^-/0 are all exohedral structures with the Nb atom face-capping the Si_n frameworks. At n = 8, both the anion and neutral adopt a boat-shaped structure and the openings of the boat-shaped structures remain unclosed in NbSi_9-10^-/0 clusters. The most stable structure of the NbSi₁₁^- anion is endohedral, while that of neutral NbSi₁₁ is exohedral. The global minima of both the NbSi₁₂^- anion and neutral NbSi₁₂ are D_6h symmetric hexagonal prisms with the Nb atom at the center. The perfect D_6h symmetric hexagonal prism of NbSi₁₂^- is electronically stable as it obeys the 18-electron rule and has a shell-closed electronic structure with a large HOMO-LUMO gap of 2.70 eV. The molecular orbital analysis of NbSi₁₂^- suggests that the delocalized Nb-Si₁₂ ligand interactions may contribute to the stability of the D_6h symmetric hexagonal prism. The AdNDP analysis shows that the delocalized 2c-2e Si-Si bonds and multicenter-2e NbSi_n bonds are important for the structural stability of the NbSi₁₂^- anion.

A Systematic Investigation on CrCun Clusters with n = 9-16: Noble Gas and Tunable Magnetic Property

A systematic investigation on structure, dissociation behavior, chemical bonding, and magnetic property of Cr-doped Cun clusters (n = 9-16) is carried out using the mean of density functional theory calculations. It is found that CrCu12 is a crucial size, preferring an icosahedral Cu12 cage with the central Cr dopant. Smaller cluster sizes appear as on the way to form the CrCu12 icosahedron while larger ones are produced by attaching additional Cu atoms to the CrCu12 core. The presence of Cr dopant obviously enhances the stability of CrCun clusters in comparison to that of pure counterparts. Exceptionally stable CrCu12 has an 18-electron closed-shell electronic structure, mimicking a noble gas in the viewpoint of superatom concept. Analysis on cluster electronic structure shows that the interplay between 3d orbitals of Cr and 4s orbitals of Cu has a vital role on the magnetic properties of CrCun clusters.

Probing the low-energy structures of aluminum–magnesium alloy clusters: a detailed study

The effect of Mg doping on the growth behavior and the electronic properties of aluminum clusters has been investigated theoretically using the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) method in combination with density functional theory calculations.

Influence of spin multiplicity on the melting of Na55(+)

The influence of spin multiplicity on the melting of the Na55(+) cluster has been investigated by means of all-electron Kohn-Sham Born-Oppenheimer molecular dynamics simulations. On the basis of the quantitative agreement between the experimental and theoretical melting temperature and latent heat a detailed analysis of the cluster dynamics was performed. This analysis showed a significant structure deformation of the cluster that is inconsistent with the geometrical shell closing concept. In subsequent structure optimizations a high-spin ground state in perfect icosahedral symmetry was found for the Na55(+) cluster. The Born-Oppenheimer molecular dynamics of this high-spin Na55(+) cluster indicates a particular thermal stability of the icosahedral cluster structure. A new electronic mechanism, named subshell closing, is suggested as the origin for this enhanced thermal stability of the icosahedral cluster structure. This mechanism is a natural extension of the common jellium model. By its nature, the subshell closing mechanism is general for finite systems and expected to be found in many other clusters for which the jellium model is applicable.

Structures, Stabilities, and Electronic Properties of Small-Sized Zr2Si n (n=1–11) Clusters: A Density Functional Study

Ab initio methods based on density functional theory at B3LYP level have been applied in investigating the equilibrium geometries, growth patterns, relative stabilities, and electronic properties of Zr2-doped Si n clusters. The optimisation results shown that the lowest-energy configurations for Zr2Si n clusters do not keep the corresponding silicon framework unchanged, which reflects that the doped Zr atoms dramatically affect the most stable structures of the Si n clusters. By analysing the relative stabilities, it is found that the doping of zirconium atoms reduces the chemical stabilities of silicon host. The Zr2Si4 and Zr2Si7 clusters are the magic numbers. The natural population and natural electronic configuration analyses indicated that the Zr atoms possess positive charge for n=1–6 and negative charge for n=7–11. In addition, the chemical hardness, chemical potential, infrared, and Raman spectra are also discussed.

Effects of bimetallic doping on small cyclic and tubular boron clusters: B7M2 and B14M2 structures with M = Fe, Co

Using density functional theory with the TPSSh functional and the 6-311+G(d) basis set, we extensively searched for the global minima of two metallic atoms doped boron clusters B6M2, B7M2, B12M2 and B14M2 with transition metal element M being Co and Fe. Structural identifications reveal that B7Co2, B7Fe2 and B7CoFe clusters have global minima in a B-cyclic motif, in which a perfectly planar B7 is coordinated with two metallic atoms placed along the C7 axis. The B6 cluster is too small to form a cycle with the presence of two metals. Similarly, the B12 cluster is not large enough to stabilize the metallic dimer within a double ring 2 × B6 tube. The doped B14M2 clusters including B14Co2, B14Fe2 and B14CoFe have a double ring 2 × B7 tubular shape in which one metal atom is encapsulated by the B14 tube and the other is located at an exposed position. Dissociation energies demonstrate that while bimetallic cyclic cluster B7M2 prefers a fragmentation channel that generates the B7 global minimum plus metallic dimer, the tubular structure B14M2 tends to dissociate giving a bimetallic cyclic structure B7M2 and a B@B6 cluster. The enhanced stability of the bimetallic doped boron clusters considered can be understood from the stabilizing interactions between the anti-bonding MOs of metal-metal dimers and the levels of a disk aromatic configuration (for bimetallic cyclic structures), or the eigenstates of the B14 tubular form (in case of bimetallic tubular structure).

Geometries, stabilities and fragmental channels of neutral and charged sulfur clusters: SnQ(n = 3–20, Q = 0, ±1)

We have performed unbiased searches for the global minimum structures of neutral and charged sulfur clusters relying on the CALYPSO method combined with DFT geometric optimization.

Mn2@Si15: the smallest triple ring tubular silicon cluster

The smallest triple ring tubular silicon cluster Mn₂@Si₁₅ is reported for the first time.

Does the 18-Electron Rule Apply to CrSi12?

Understanding the bonding between silicon and transition metals is valuable for devising strategies for incorporating magnetic species into silicon. CrSi12 is the standard example of a cluster whose apparent high stability has been explained by the 18-electron rule. We critically examine the bonding and nature of stability of CrSi12 and show that its electronic structure does not conform to the 18-electron rule. Through theoretical studies, we find that CrSi12 has 16 effective valence electrons assigned to the Cr atom and an unoccupied 3dz(2) orbital. We demonstrate that the cluster's apparent stability is rooted in a crystal field-like splitting of the 3d orbitals analogous to that of square planar complexes. CrSi14 is shown to follow the 18-electron rule and exhibits all conventional markers characteristic of a magic cluster.