Study on the Geometric and Electronic Structures of Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Si<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> (n = 3, 4, 5; m = 1, 2, 3, 4) Clusters

Genetic algorithm combined with the semi-empirical Hamitonian AM1/PM3 is used to search the low energy isomers of Al _n Si _m (n = 3, 5, m ≤ 3 and n = 4, m ≤ 4) and the charged clusters with 20 and 28 valence electrons. The candidate structures were optimized by the density functional theory PBE0 and B3LYP models with the triply split basis sets including polarization functions. The electronic structures show that Al–Si binary clusters behave like metal clusters. The molecular orbitals accord with that predicted by the jellium model, and the electron localization function shows the valence electrons are delocalized over the entire clusters. The clusters having 20 and 28 valence electrons exhibit pronounced stabilities and large energy gaps. The 20 valence electrons of Al₄Si₂ and Al₃Si₃ ⁺, Al₅Si^? form closed shells 1S ²1P ⁶2S ²1D ¹⁰. Al₄Si₄ and Al₅Si₃ ^? have oblate structures and the P, D, F levels spilt considerably in these clusters. The electron density distributions suggest that doping silicon in the aluminum clusters enhances the stability considerably.     

Polyhedral structures with three-, four-, and five fold symmetry in metal-centered ten-vertex germanium clusters

Studies using density functional theory (DFT) at the hybrid B3LYP level indicate that the relative energies of structures with three-fold, four-fold, and five-fold symmetry for centered 10-vertex bare germanium clusters of the general type M@Ge(10) (z) depend on the central metal atom M and the skeletal electron count. For M@Ge(10) clusters with 20 skeletal electrons the DFT results agree with experimental data on the isoelectronic centered 10-vertex bare metal clusters. Thus the lowest energy structure for Ni@Ge(10), isoelectronic with the known Ni@In(10) (10-), is a C(3v) polyhedron derived from the tetracapped trigonal prism. However, Zn@Ge(10) (2+) is isoelectronic with the known cluster Zn@In(10) (8-), which has the lowest energy structure, a D(4d) bicapped square antiprism. For the clusters Ni@Ge(10) (2-), Cu@Ge(10) (-), and Zn@Ge(10) that have 22 skeletal electrons the lowest energy structures are the D(4d) bicapped square antiprism predicted by the Wade-Mingos rules. For the clusters Ni@Ge(10) (4-), Cu@Ge(10) (3-), and Zn@Ge(10) (2-) that have 24 skeletal electrons the lowest energy structures are C(3v) polyhedra with 10 triangular faces and 3 quadrilateral faces derived from a tetracapped trigonal prism by extreme lengthening of the edges of the capped triangular face of the underlying trigonal prism. For the clusters Cu@Ge(10) (5-) and Zn@Ge(10) (4-) that have 26 skeletal electrons the lowest energy structures are the D(5d) pentagonal antiprisms predicted by the Wade-Mingos rules and the C(3v) tetracapped trigonal prism as a somewhat higher energy structure. However, for the isoelectronic Ni@Ge(10) (6-) the relative energies of these two structure types are reversed so that the C(3v) tetracapped trigonal prism becomes the global minimum. The effects of electron count on the geometries of the D(5d) pentagonal prism and D(4d) bicapped square antiprism centered metal cluster structures are consistent with the bonding/antibonding characteristics of the corresponding HOMO and LUMO frontier molecular orbitals.     

Endohedral nickel and palladium atoms in metal clusters: analogy to endohedral noble gas atoms in fullerenes in polyhedra with five-fold symmetry

Nickel and palladium atoms with their closed-shell d(10) electronic configurations are encapsulated in the icosahedral clusters [Ni@Ni(10)E(2)(CO)(18)](4-)(E = Sb, Bi, Sb[rightward arrow]Ni(CO)(3), CH(3)Sn and n-C(4)H(9)Sn) and the geometrically related pentagonal antiprismatic cluster Pd@Bi(10)(4+) found in Bi(14)PdBr(16). Such endohedral d(10) atoms in pentagonal antiprismatic clusters are donors of zero skeletal electrons and interact only weakly with the atoms in the surrounding polyhedron so that they may be regarded as analogous to endohedral noble gases in fullerenes such as He@C(60). On the other hand, endohedral nickel and palladium atoms in 10- and 11-vertex flattened deltahedral bare metal clusters of group 13 metals without five-fold symmetry, such as Ni@E(10)(10-) found in Na(10)NiE(10)(E = Ga, In) and Pd@Tl(11)(7-) found in A(8)Tl(11)Pd (A = Cs, Rb, K), interact significantly with the cluster atoms, particularly those at the flattened vertices of the deltahedron. The role of endohedral d(10) atoms Ni and Pd in polyhedra with five-fold symmetry as "pseudo-noble-gases" can be related to their positions at the "composite divide" of the "Metallurgists' Periodic Table" proposed by H. E. N. Stone on the basis of alloy systematics as well as the equivalence of the five d orbitals in polyhedra with five-fold symmetry.     

Electron counts for face-bridged octahedral transition metal clusters

Kohn-Sham orbital energy patterns were used to rationalize valence electron counts for stable face-capped octahedral clusters [M(6)E(8)L(6)] (E=S, Se, Te, Cl; L=CO, PMe(3), Cl(-)). When L is a pi acceptor such as CO or PMe(3), stable closed-shell clusters are found for 80, 84, and 98 electrons. For L=Cl(-) (i.e. a pi-electron donor), only a count of 84 electrons appears favorable, as is found in [Mo(6)Cl(14)](2-). These counting rules apply to fivefold coordination of M, which becomes unstable if the electron count exceeds 98, for example, for M=Ni. In this case structures with tetrahedrally coordinated M are energetically favored, and this leads to different cluster structures.     

Syntheses of the 47 electron clusters [(Cp*Fe)3(mu3-X)2] (X = S, Se) and the First Fe/Sn/Se Heterocubane Cluster [(CpFe)3(SnCl3)(mu3-Se)4] x DME by the use of chalcogenostannate salts

By reacting 1-aminoethylammonium (H2NCH2CH2NH3+ = enH+) salts of [Sn2E6]4- anions (E = S, Se), [enH]4[Sn2S6] (1) and [enH]4[Sn2Se6] x en (2), with FeCl2/LiCp, three novel (partly) oxidized, Cp* ligated iron chalcogenide clusters were synthesized. Two of them, [(CpFe)3(mu3-S)2] (3) and [(Cp*Fe)3(mu3-Se)2] (4), contain formally 47 valence electrons. [(Cp*Fe)3(SnCl3)(mu3-Se)4] x DME (5) represents the first known mixed metal Fe/Sn/Se heterocubane type cluster. Compounds 3-5 were structurally characterized by single-crystal X-ray diffraction, and the odd valence electron number of the [Fe3E2] clusters (E = S, Se) was confirmed by density functional (DFT) investigations, mass spectrometry, cyclic voltammetry and a susceptibility measurement of 3.     

"n-Doping" of deltahedral Zintl ions

We report a simple and efficient method for replacing germanium atoms in deltahedral Ge(9)(4-) clusters with Sb or Bi. While reactions of Ge(9)(4-) with EPh(3) (E = Sb, Bi) at room temperature are known to produce mono- and disubstituted clusters [Ph(2)E-Ge(9)-Ge(9)-EPh(2)](4-) and [Ph(2)E-Ge(9)-EPh(2)](2-), respectively, at elevated temperatures or with sonication they result in exchange of Ge cluster atoms with Sb or Bi. Structurally characterized from such reactions are the novel "n-doped" deltahedral Zintl ions [(EGe(8))-(Ge(8)E)](4-), (Sb(2)Ge(7))(2-), and [(SbGe(8))-SbPh(2)](2-).     

An evaluation by density functional theory of M-M interactions in organometallic clusters with the [Fe(3)MoS(3)](2+) cores

Density functional theory calculations were carried out on the structurally characterized [(Cl(4)-cat)Mo(py)Fe(3)S(3) (CO)(4)(P(n)Pr(3))(3)], A, and (Cl(4)-cat)Mo(py)Fe(3)S(3)(CO)(6)(PEt(3))(2), B, and also on A(2)(-) and B(2+) clusters. The Fe-Fe distances in these molecules depend on the total number of valence electrons (60 e(-) in A and B(2)(+) and 62 e(-) in A(2)(-) and B) and undergo great structural changes upon addition or removal of electrons. The changes are consistent with known electron-counting rules in organometallic chemistry. The weak nature of the Fe-Fe bonding interactions in these clusters is apparent in the very similar energies of states with widely different Fe-Fe distances.     

Many-body origin of the plasmon resonance in small metal clusters

The origin of the plasmon excitation in small metal clusters is studied within the jellium model through ab initio electronic-structure calculations based on the nuclear shell model. In the limit of infinite size, the plasmon classically represents pure harmonic motion of the center of mass of the valence electrons. It is shown that this limit is already well approximated by clusters of only eight electrons.     

Electron delocalization and electrostatic repulsion at the origin of the strong spin coupling in mixed-valence keggin polyoxometalates: ab initio calculations of the one- and two-electron processes

We present here a general theoretical procedure to treat the problem of electron delocalization and magnetic interactions in high-nuclearity mixed valence clusters based on polyoxometalates. The main interactions between the delocalized electrons of mixed-valence polyoxometalate anions are extracted from valence spectroscopy ab initio calculations on embedded fragments. Electron transfer, magnetic coupling and exchange transfer parameters between nearest and next-nearest-neighbor metal ions, as well as the value of the electrostatic repulsion between pairs of metal ions are determined. These parameters are introduced in a model Hamiltonian that considers the whole anion. It thus provides macroscopic properties that should be compared with the experimental data. This method is applied to a two-electron-reduced polyoxowolframate Keggin anion. The results demonstrate that the electron transfer processes, combined with the Coulombic repulsion between the "extra" electrons, induce a strong antiferromagnetic coupling between the two delocalized spins providing a definite explanation of the diamagnetic properties of these high nuclearity mixed-valence clusters.     

B(14) (2+): A magic number double-ring cluster

B(20) is a "magic number" cluster with double-ring structure. Surprisingly, we also find that B(14) (2+) is a "magic number" cluster with double-ring structure, which has the largest HOMO-LUMO gap (3.31 eV) and the highest aromaticity in double-ring clusters. This double-ring B(14) (2+) cluster is energetically lower than the quasi-planar one by even ～1.2 eV using high level ab initio calculations. B(14) (2+) also has 40 valence electrons as in Al(13) (-) cluster. The reason leading to the unusual properties of B(14) (2+) may be the electronic shell closing as in Al(13) (-) cluster based on the jellium model, besides the double aromaticity in all double-ring clusters.     

Pseudopotential approach of the electronic structure in clusters: application to Alkali Halides and Rare Gases

We examine here the use of pseudopotentials in limit cases where only a very small number of electrons (much less than the usual number of valence electrons), eventually excited, can be singled out and considered as active to determine the electronic structure. Two applications are considered. The first one concerns the family of nonstoechiometric ionic clusters for which only the excess electrons are active. The relevance and accuracy of such ab initio determined pseudopotentials is illustrated on Na_nF_n-1 clusters which are treated as one-electron systems. The second application concerns excited states of neutral rare gas clusters Rg _n ^* . In this case, the excited electron may be coupled to different core states and a resonant hole-particle treatment involving e-Rg and e-Rg ⁺ pseudopotentials is presented.     

Negative ions of nitroethane and its clusters

Valence and dipole-bound negative ions of the nitroethane (NE) molecule and its clusters are studied using photoelectron spectroscopy (PES), Rydberg electron transfer (RET) techniques, and ab initio methods. Valence adiabatic electron affinities (EA(a)s) of NE, C(2)H(5)NO(2), and its clusters, (C(2)H(5)NO(2))(n), n=2-5, are estimated using vibrationally unresolved PES to be 0.3+/-0.2 eV (n=1), 0.9+/-0.2 eV (n=2), 1.5+/-0.2 eV (n=3), 1.9+/-0.2 eV (n=4), and 2.1+/-0.2 eV (n=5). These energies were then used to determine stepwise anion-neutral solvation energies and compared with previous literature values. Vertical detachment energies for (C(2)H(5)NO(2))(n)(-) were also measured to be 0.92+/-0.10 eV (n=1), 1.63+/-0.10 eV (n=2), 2.04+/-0.10 eV (n=3), and 2.3+/-0.1 eV (n=4). RET experiments show that Rydberg electrons can be attached to NE both as dipole-bound and valence bound anion states. The results are similar to those found for nitromethane (NM), where it was argued that the diffuse dipole state act as a "doorway state" to the more tightly bound valence anion. Using previous models for relating the maximum in the RET dependence of the Rydberg effective principle number n(max)(*), the dipole-bound electron affinity is predicted to be approximately 25 meV. However, a close examination of the RET cross section data for NE and a re-examination of such data for NM finds a much broader dependence on n(*) than is seen for RET in conventional dipole bound states and, more importantly, a pronounced [l] dependence is found in n(max)(*) (n(max)(*) increases with [l]). Ab initio calculations agree well with the experimental results apart from the vertical electron affinity value associated with the dipole bound state which is predicted to be 8 meV. Moreover, the calculations help to visualize the dramatic difference in the distributions of the excess electron for dipole-bound and valence states, and suggest that NE clusters form only anions where the excess electron localizes on a single monomer.     

Density functional theory study of 10-atom germanium clusters: effect of electron count on cluster geometry

Density functional theory (DFT) at the hybrid B3LYP level has been applied to Ge10z germanium clusters (z = -6, -4, -2, 0, +2, +4, +6) starting from 12 different initial configurations. The D4d 4,4-bicapped square antiprism found experimentally in B10H102- and other 10-vertex clusters with 22 skeletal electrons is calculated for the isoelectronic Ge102- to be the global minimum by more than 15 kcal/mol. The global minima found for electron-rich clusters Ge104- and Ge106- are not those known experimentally. However, experimentally known structures for nido-B10H14 and the pentagonal antiprism of arachno-Pd@Bi104+ are found at higher but potentially accessible energies for Ge104- and Ge106-. The global minimum for Ge10 is the C3v 3,4,4,4-tetracapped trigonal prism predicted by the Wade-Mingos rules and found experimentally in isoelectronic Ni@Ga1010-. However, only slightly above this global minimum for Ge10 (+3.3 kcal/mol) is the likewise C3v isocloso 10-vertex deltahedron found in metallaboranes such as (eta6-arene)RuB9H9 derivatives. Structures found for more electron-poor clusters Ge102+ and Ge104+ include various capped octahedra and pentagonal bipyramids. This study predicts a number of 10-vertex cluster structures that have not yet been realized experimentally but would be interesting targets for future synthetic 10-vertex cluster chemistry using vertex units isolobal with the germanium vertices used in this work.     

Role of the electron transfer and magnetic exchange interactions in the magnetic properties of mixed-valence polyoxovanadate complexes

Modeling the properties of high-nuclearity, high-electron-population, mixed-valence (MV) magnetic systems remains one of the open challenges in molecular magnetism. In this work, we analyze the magnetic properties of a series of polyoxovananadate clusters of formula [V 18O 42] (12-) and [V 18O 42] (4-). The first compound is a fully localized spin cluster that contains 18 unpaired electrons located at the metal sites, while the second one is a MV cluster with 10 unpaired electrons largely delocalized over the 18 metal sites. A theoretical model that takes into account the interplay between electron transfer and magnetic exchange interactions is developed to explain the unexpected enhancement of the antiferromagnetic coupling when the number of unpaired electrons is reduced from 18 to 10 in these clusters. In the MV area, these systems represent the most complex magnetic clusters studied theoretically so far. Because of the high complexity of the systems, the number of relevant parameters is too large for a conventional model Hamiltonian approach. We therefore perform a theoretical study that combines ab initio calculations with the model Hamiltonian. In this way, we use ab initio calculations performed on small fragments of the cluster to lower the degrees of freedom of the parameter set of the model Hamiltonian that operates in the whole MV cluster. This approach shows the usefulness of combining ab initio calculations with model Hamiltonians in order to explore the magnetic properties of large and complex molecular systems, emphasizing the key role played by the electron transfer in these model magnetic materials.     

Accuracy and limitations of second-order many-body perturbation theory for predicting vertical detachment energies of solvated-electron clusters

Vertical electron detachment energies (VDEs) are calculated for a variety of (H(2)O)(n)(-) and (HF)(n)(-) isomers, using different electronic structure methodologies but focusing in particular on a comparison between second-order M?ller-Plesset perturbation theory (MP2) and coupled-cluster theory with noniterative triples, CCSD(T). For the surface-bound electrons that characterize small (H(2)O)(n)(-) clusters (n< or = 7), the correlation energy associated with the unpaired electron grows linearly as a function of the VDE but is unrelated to the number of monomers, n. In every example considered here, including strongly-bound "cavity" isomers of (H(2)O)(24)(-), the correlation energy associated with the unpaired electron is significantly smaller than that associated with typical valence electrons. As a result, the error in the MP2 detachment energy, as a fraction of the CCSD(T) value, approaches a limit of about -7% for (H(2)O)(n)(-) clusters with VDEs larger than about 0.4 eV. CCSD(T) detachment energies are bounded from below by MP2 values and from above by VDEs calculated using second-order many-body perturbation theory with molecular orbitals obtained from density functional theory. For a variety of both strongly- and weakly-bound isomers of (H(2)O)(20)(-) and (H(2)O)(24)(-), including both surface states and cavity states, these bounds afford typical error bars of +/-0.1 eV. We have found only one case where the Hartree-Fock and density functional orbitals differ qualitatively; in this case the aforementioned bounds lie 0.4 eV apart, and second-order perturbation theory may not be reliable.     

铬/磷二元团簇的形成和光解

用532nm的Nd:YAG激光直接溅射铬/磷粉末混合物样品产生铬/磷团簇,并用串级飞行时间质谱仪研究了二元团簇的组份分布及紫外激光光解规律.实验表明,铬/磷极易形成富磷的二元团簇离子,CrP_m⁺团簇离子系列表现出明显的奇偶振荡效应,且CrP₄⁺,Cr_nP₈⁺(n=1～4),Cr₄P₉⁺,Cr₅P₁₁⁺,Cr₆P₁₂⁺和Cr₈P₁₄⁺等为质谱中丰度较大的离子,不随样品组成的变化而变化,光解时主要以失去中性P₂和P₄的方式进行解离,尝试对其电子结构进行推测.并与铬/硫二元团簇的形成和光解结果作简单对比.     

原子簇与有关分子的结构规则(Ⅰ)-(nxcπ)格式

包括原子簇在内的无机和有机分子可认为由若干分子片所组成,它们的结构类型可由四个数(nxcπ)来规定。文中提出七条结构规则来阐明原子簇及有关分子的结构和成键能力,并举例说明这些结构规则和(nxcπ)格式的应用,如由分子式估算结构类型,预测新的原子簇化合物及其可能的合成途径等。     

Enhanced Zintl anions by carbon doping in Al-Na clusters and new magic structure Al6Na4C

This article investigated the low-energy structures of Al₆Na _mC (m = 2, 4, 6, 8) clusters and their electronic structures by using genetic algorithm combined with density functional theory and configuration interaction methods. The computations show that the C atoms prefer sitting at the center, whereas the Na atoms tend to locate at the outside of the clusters. The valence molecular orbitals (MOs) agree well with the prediction of the jellium model. The stronger attraction of the central carbon to the valence electrons will depress the potential energies locally, which makes the 2S level go obviously lower and the 2P and 1D orbitals form a sub-band. The 26 valence electrons in Al₆Na₄C form closed 1S²1P⁶2S²1D¹⁰2P⁶ shells and correspond to a new magic structure. The MOs and electron localization function show that the sodium cores are exposed at the outside of the valence electrons and form naked cations. The contraction of the valence electrons because of the carbon doping enhances the charges on the Al₆C moieties, and the Na⁺ cores on the peripheries are ionically bonded to the Zintl anions (Al₆C)^q−. The Al₆Na₄C has a tetrahedral structure with symmetry T_d, and it may be used as building blocks to synthesize Zintl solid.     

Studies on the Stability of On-top Al13Inm (n = 1～12,m =-1,0,+1) Clusters

Energetic and electronic structures of the on-top Al13Inm (n = 1 ～12,m = -1,0,+1)clusters have been investigated by employing a first-principles pseudo-potential plane wave method.Several parameters such as binding energies,second differences of energy and vertical-electron detachment energies have been adopted to characterize and evaluate the structure stability of Al13In (n = 1 ～ 12) clusters.The optimized models show that the Al13 moieties in the clusters can not retain the original regular icosahedron structure.Results from binding energy and second difference of energy show that Al13In and Al13In- clusters with even n are more stable than those with odd n in contrast with Al13In+ clusters.The calculation of vertical-electron detachment energies (VDE) of Al13In clusters indicates that Al13In and Al13In- clusters with even n are closer to the closed shell of the Jellium model.Further analysis of electron density of states and electron density differences reveals that the enhanced stability of Al13In- clusters is not only associated with the closed shell of valence electrons but also with the bonding type between I and associated Al atoms.     

Preparative and electrochemical investigations on the electron sponge behavior of cobalt telluride clusters: CO substitution in [Co11Te7(CO)10]n- ions (n=1, 2) by PMe2Ph and crystal structure of [Co11Te7(CO)5(PMe2Ph)5

The reaction of the cluster salts [Cp(2*) Nb(CO)(2)](n)[Co(11)Te(7)(CO)(10)] (Cp*=C(5)Me(5); n=1, 2) with excess PMe(2)Ph gave the neutral, dark brown clusters [Co(11)Te(7)(CO)(6)(PMe(2)Ph)(4)] (5) and [Co(11)Te(7)(CO)(5)(PMe(2)Ph)(5)] (6) with 147 metal valence electrons. The new compounds were characterized by IR spectroscopy, elemental analyses, and mass spectrometry. The molecular structure of 6 was determined by X-ray crystallography. Like its precursor anion, it consists of a pentagonal-prismatic [Co(11)Te(7)] core, but with a ligand sphere composed of five CO and five PMe(2)Ph ligands. Detailed electrochemical studies of both reactions reveal that a stepwise substitution of CO ligands in the initial cluster anions takes place leading to intermediate [Co(11)Te(7)(CO)(10-m)(PMe(2)Ph)(m)](n-) ions (m=1-5; n=1, 2). Each of these intermediates is distinguished by at least one oxidation and two reduction waves, giving rise to a total of 21 redox couples and 27 electroactive species. The electron sponge character of the new compounds is particularly pronounced in 5, which exhibits charges n between +1 and -4 corresponding to metal valence electron counts of between 146 and 151.