General principles governing structures of small clusters

General rules which govern electronic and geometric structures of small clusters are formulated, and their validity is documented with the results of the MRD - CI investigations for Li _n , BeLi _k , Be _l (n=2?14,k=2?6,l=2?13) as well as on IIa and IVa tetramers. The MRD - CI results are compared with investigations performed with other methods.     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

Structural, Electronic, and Magnetic Properties of MB n (M?=?Y, Zr, Nb, Mo, Tc, Ru, n?≤?8) Clusters

The geometries, stabilities, electronic, and magnetic properties of MB _n (M?=?Y, Zr, Nb, Mo, Tc, Ru, n????8) clusters have been systematically investigated by density functional theory. It is shown that the lowest energy structures of MB _n (n????3) clusters can be obtained by substituting one B atom in the lowest energy structures of B _n+1 clusters in most cases. After n????8, the 3D configurations prevail and become the lowest-energy structures. The second-order energy difference and the dissociation energy show YB₇, ZrB₇, NbB₆, MoB₆, TcB₆, RuB₆ clusters possess relatively higher stabilities. The doped-M atoms improve the chemical activity of the host clusters in most cases; but different M atom has different effect on B atom??s electronic structure. The binding strengths are strong between M and B _n , which plays an important role in the M?CB growth mechanisms. It is interesting that the relative orientation between the magnetic moments of the M (M?=?Zr, Nb, Mo, Tc, Ru) atoms and those of its neighboring B atoms exhibits ferromagnetic or antiferromagnetic alignment in contrast to the ferromagnetic alignment of YB _n .     

Electronic shells and shells of atoms in metallic clusters

Intensity anomalies (magic numbers) have been observed in the mass spectra of sodium clusters containing up to 22 000 atoms. For small clusters (Na _n ,n≤1500) the anomalies appear to be due to the filling of electronic shells (groups of subshells having the same energy). The shells can be characterized rather well by a pseudoquantum-number, indicating the possible existence of a symmetry higher than spherical. The mass spectra of larger clusters (1500≤n≤22 000) are well explained by the completion of icosahedral or cuboctahedral shells of atoms. The fact that the two types of shells (electron and atom) occur in distinct and non-overlapping size intervals might indicate the existence of a “liquid” to “solid” transition in going from small to large clusters.     

Electronic stress tensor analysis of hydrogenated palladium clusters

We study the chemical bonds of small palladium clusters Pd _n (n?=?2?9) saturated by hydrogen atoms using electronic stress tensor. Our calculation includes bond orders which are recently proposed based on the stress tensor. It is shown that our bond orders can classify the different types of chemical bonds in those clusters. In particular, we discuss Pd?CH bonds associated with the H atoms with high coordination numbers and the difference of H?CH bonds in the different Pd clusters from viewpoint of the electronic stress tensor. The notion of ??pseudo-spindle structure?? is proposed as the region between two atoms where the largest eigenvalue of the electronic stress tensor is negative and corresponding eigenvectors forming a pattern which connects them.     

Structures and stabilities of 3d-transition metal-benzene organometallic clusters

In the gas phase, we have successfully synthesized organometallic clusters, M_n(benzene)_m (M=3d transition metal atoms), by using a laser vaporization method. The measurements of mass spectra and ionization energies (E_i) have revealed that the organometallic clusters can take two types of structures; layered sandwich structures (m = n + 1) and metal clusters saturatedly covered with benzenes. For early transition metals of Sc, Ti, and V, only the multiple decker sandwich structure clusters were preferentially produced, in which benzene and metal atoms are alternately piled up. For late transition metals of Co and Ni, the metal clusters saturatedly surrounded by benzenes were also produced as well as the sandwich clusters. Furthermore, the E_is of M₁(benzene)₂ (M = Sc-Ni) were systematically measured and their electronic properties will be discussed.     

Density functional theory of the collective electronic excitations in NanKn clusters

The collective electronic response of Na_nK_n clusters has been studied for some model structures. In their low-temperature lowest-energy structure, those clusters have all the K atoms on the surface. The collective oscillation frequencies for clusters with the K atoms segregated to the surface are red-shifted with respect to the corresponding frequencies for isomers with a very similar underlying skeleton but with the Na atoms segregated to the surface. The collective frequency varies smoothly with respect to the degree of relative segregation. These results may be useful in the analysis of the collective response of large alloy clusters and microcrystals. © 1995 John Wiley & Sons, Inc.     

Small clusters made up of three kinds of neutral alkali atoms

Small clusters made up of three kinds of neutral alkali atoms, i.e. clusters of the form X _? Y _m Z _n , are theoretically studied. These clusters exhibit three series of magic numbers, one for each kind of atoms. That is,?,m, andn independently can be magic numbers rather than their cumulative number?+m+n or, in other words, magic numbers in alkali clusters composed of neutral atoms are due to atoms rather than to delocalized electrons as in jellium model. Of course, if conditions favor delocalization of electrons,?+m+n can be magic but then we have no neutral atoms which are prerequisite for an application of the present model.     

Spatial structure and electronic spectrum of TiSi n − clusters (n = 6–18)

Results from optimizing the spatial structure and calculated electronic spectra of anion clusters TiSi _n ^? (n = 6–18) are presented. Calculations are performed within the density functional theory. Spatial structures of clusters detected experimentally are established by comparing the calculated and experimental data. It is shown that prismatic and fullerene-like structures are the ones most energetically favorable for clusters TiSi _n ^? . It is concluded that these structures are basic when building clusters with close numbers of silicon atoms.     

Radiative neutralization of small clusters impinging on solid surfaces

Light emission during the interaction of slow singly-charged clusters with solid surfaces is studied theoretically. More precisely, we consider positive ions of Ag _n clusters (n = 1...5) impinging on silver surfaces. In such systems, the charge transfer process involved during the cluster-surface interaction is mainly resonant capture. However, photon emission due to radiative capture is also a possible charge transfer channel. Our simple theoretical model including both processes allows us to calculate the light spectra and the total photon yield for the different cluster sizes, n. Our results show that light emission strongly depends on the electronic level dynamics of the clusters in front of the surface, providing a tool for electronic structure analysis of atoms, clusters and solid surfaces.     

The effect of silicon doping on the geometrical structures,stability, and electronic and spectral properties of magnesium clusters: DFT study of SiMgn (n = 1-12) clusters

Using the density functional theory (DFT) method at the B3LYP /6−311G (D) level, we studied how silicon doping affects the geometrical structure, stability, and electronic and spectral properties of magnesium clusters. The stable isomers of SiMg _n (n = 1-12) clusters were calculated by searching numerous initial configurations using the CALYPSO program. The geometrical structure optimization shows that most stable SiMg _n (n = 3-12) clusters are three-dimensional. In addition, geometrical structure growth patterns show that some structures of SiMg _n clusters can be directly formed by replacing one Mg atom in the corresponding Mg _{n + 1} cluster with one silicon atom, such as SiMg₈ and Mg₉ clusters. The stability of SiMg _n clusters is analyzed by calculating the average binding energy, fragmentation energy, and second-order energy difference. The results show that SiMg _n clusters with n = 5 and 8 are more stable than others. MO contents analysis show that the Si 3p-orbitals and Mg 3s-orbital are mainly responsible for the stability of these two clusters. The results of the natural charge population (NCP) and natural electronic configure (NEC) analysis of the electronic properties reveal that the charges in SiMg_n (n = 1-12) clusters transfer from magnesium atoms to silicon frame, and electronic charge distributions are primarily governed by s- and p-orbital interactions. In addition, the Vertical ionization potential (VIP), vertical electron affinity (VEA), and chemical hardness of ground sates of SiMg _n (n = 1-12) clusters were studied in detail and compared with the experimental results. The conclusions show that the chemical hardness of most SiMg _n clusters are lower than that of pure Mg _{n + 1} (n = 1-12) clusters, except for n = 1 and 8. This indicates that the doping of silicon atom can always reduce the chemical hardness of pure magnesium clusters. Finally, the infrared and Raman spectral properties of SiMg₅ and SiMg₈ clusters were calculated and discussed in detail.     

Geometry and electronic properties of alkali metal (rubidium) doped boron clusters

Alkali metal-doped boron clusters have captured much attention because of their novel electronic properties and structural evolution. In the study of RbB_n^0/− (n = 2–12) clusters, the minimum global search of the potential energy surface and structure optimization at the level of PBE1PBE by using the CALYPSO method and Gaussian package coupled with DFT calculation; the geometrical structures and electronic properties are systematically investigated. At n = 8, the ground-state structures are composed of an Rb atom above B atoms, forming a structurally stable pagoda cone. By stability analysis and charge transfer calculation, the RbB₈⁻ cluster shows more stability. It found that s-p hybridization between Rb atom and B atoms as well as s-p hybridization between B atoms is one of the reasons for the outstanding stability exhibited in the RbB₈^0/− clusters by using DOS and HOMO–LUMO orbital contour maps. The chemical bonding of the RbB₈^0/− groups was analyzed by using the AdNDP method, and B atoms with larger numbers readily form multi-center chemical bonds with the Rb atom. From the results of the bonding analysis, the interaction between the Rb atom and B atoms strengthens the stability of the RbB₈^0/− clusters. It is hoped that this work provides a direction for experimental manipulation.     

Electronic structure of Lanthanum-carbon clusters

As the attachment of a metal change the molecular and electronic structure of carbon clusters, the electronic properties as ionization potentials (IP) and electron affinities (EA) for small Lanthanum-carbon clusters LaC _n with n=1–6 have been investigated theoretically. They were studied by density-functional-theory (DFT) within LDA and considering Gradient corrections (GC) for the exchange-correlation potential ( Becke-Perdew). The results for both quantities were obtained in good agreement with the experimental data: odd-even alternating IP’s, and no alternations for the EA’s. The different charge location in the carbon chains or at the La atom can explain the different trends of both quantities, respectively.     

Threshold photoionization behaviour of (Li2O)Lin clusters produced by a laser vaporization source

We report on the production of small and medium size lithium and lithium oxide clusters by a laser vaporization cluster source. The isotopomeric distribution of natural lithium allowed to identify Li_kO clusters as the most abundant components in the mass spectrum. Photoionization efficiency curves of Li_kO clusters with photon energies from 3.4 to 4.7 eV were measured for 8 ≤ k ≤ 27. Using linear extrapolation of the increase in photoionization efficiency with photon energy, ionization potentials were extracted. With the chemical bond of the O^2- anion to two Li atoms, leaving n = k-2 valence electrons in the (Li₂O)Li_n clusters, clear shell closure effects are present at n = 8 and n = 20.     

Semiempirical and ab-initio calculations of semiconductor clusters: variation of structure and symmetry with size for different compounds

Semiempirical (by extended Hückel method) and ab initio RHF SCF calculations are used for the wide range of cluster structures M_xX_y, where M = Cd,Ag; X = S,I: semiempirical - up to M₂₀X₃₅, and ab initio - for small clusters less than ten atoms. Variation of electronic structure with size for the fragments with tetrahedral coordination (bulklike sphalerite structures) and for some clusters of the lower symmetry allows to predict their possible geometries which are compared with experimental data. The chemical bonding factor (the chemical nature of bounded atoms, coordination number for metal and non-metal atoms, hybridization, etc) is of more importance in properties of the clusters than the familiar quantum confinement effect of semiconductor clusters (like CdS, CdSe, PbS, etc. ). The essential difference in regularities of small cluster formation is analysed for CdS- and AgI- based structures.     

Molecular and electronic structure of some binary polyhedral clusters

The molecular and electronic structures of some polyhedral alternate molecules X_nY_n, where n=12, 16; X=B, Al, Si; Y=N,P,C, and of homoatomic clusters C₂₄, Si₂₄, C₃₂, and Si₃₂ are calculated in a valence approximation by the MNDO method. It is suggested that the σ-frameworks of these molecules are formed of four- and six-membered rings, with each X atom having only Y atoms as neighbors. The singlet states of all these systems have local minima on the corresponding potential energy surfaces with T_h symmetry for n=12 and T_d symmetry for n=16. The main structural parameters, heats of formation, ionization potentials, and effective charge distributions are given. It is concluded that the X_nY_n heteroatomic clusters can exist when X and Y are atoms of Group III and V elements, respectively, or both are atoms of Group IV elements. A. N. Nesmeyanov Institute of Organoelement Compounds, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 6, pp.976–982, November–December, 1995. Translated by L. Smolina     

Observable Structures of Small Neutral and Anionic Gold Clusters

Since gold clusters have mostly been studied theoretically by using DFT calculations, more accurate studies are of importance. Thus, small neutral and anionic gold clusters (Au_n and Au_n^?, n=4–7) were investigated by means of coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] calculations with large basis sets, and some differences between DFT and CCSD(T) results are discussed. Interesting isomeric structures that have dangling atoms were obtained. Structures having dangling atoms appear to be stable up to n=4 for neutral gold clusters and up to n=7 for anionic clusters. The relative stabilities and electronic properties of some isomers and major structures are discussed on the basis of the CCSD(T) calculations. This accurate structure prediction of small gold clusters corresponding to experimental photoelectron spectral peaks is valuable in the field of atom‐scale materials science including nanocatalysts.     

Electronic properties of aluminum clusters compared with the jellium model

The experimental polarizabilities, ionization potentials and electron affinities of aluminum clusters are compared with jellium predictions. It is found that the clusters have radii and work functions which are close to the jellium model predictions for clusters with more than 13 atoms. The polarizabilities of Al _n correspond with the jellium only forn>40 and the shell structure features in the ionization potentials are anomalous up to 37. We conclude that nonjellium effects are important up ton=40.