Geometries,stabilities and electronic properties of small-sized Pd2-doped Sin (n = 1–11) clusters

The geometries, growth patterns, relative stabilities and electronic properties of small-sized Pd₂Si_n and Si_n+2 (n = 1–11) clusters are systematically studied using the hybrid density functional theory method B3LYP. The optimised structures revealed that the lowest energy Pd₂Si_n clusters are not similar to those of pure Si_n clusters. When n = 9, one Pd atom in Pd₂Si₉ completely falls into the centre of the Si outer frame, forming metal-encapsulated Si cages. On the basis of the optimised structures, the averaged binding energy, fragmentation energy, second-order energy difference and highest occupied–lowest unoccupied molecular orbital energy gap are calculated. It is found that the Pd₂Si₅ and Pd₂Si₇ clusters have stronger relative stabilities among the Pd₂Si_n clusters. Additionally, the stabilities of Si_n+2 clusters have been reduced by the doping of Pd impurity. The natural population and natural electronic configuration analysis indicated that the Pd atoms possess negative charges for n = 1–11 and there exist the spd hybridisation in the Pd atom. Finally, the chemical hardness, chemical potential, electrostatic potential and polarisability are discussed.     

Density functional study of Agn-1Y (n=2-10) clusters

Employing the density functional theory, we investigate the lowest-energy geometric, the stable and the electronic properties of Ag_n-1Y (n=2-10) clusters in this paper. The structural optimization and the frequency analysis are performed at the B3LYP/LANL2DZ level. Meanwhile, the differences in geometry, stability and electronic properties between Ag_n and Ag_n-1Y (n=2-10) clusters are also studied. The results show that for the doping of the yttrium atoms, the structures and the average binding lengths of the Ag_n clusters are greatly changed. In addition, the thermodynamic stabilities of the Ag_n clusters are enhanced generally with the doping of the Y atoms. In addition, the chemical stabilities of the Ag_n-1Y clusters are still improved compared with that of the three-dimensional Ag_n clusters.     

密度泛函理论研究ScnO(n=1—9)团簇的结构、稳定性与电子性质

采用基于密度泛函理论的BP86/CEP-121G （O原子采用6-311G^**基组）方法,对Sc_nO （n=1—9）团簇的几何结构、能量与稳定性、电子结构性质及其随团簇尺寸的变化趋势进行了研究.随着团簇原子个数的增加,O原子从位于Sc_n团簇结构的边缘转变为占据团簇的内部位置.O原子的掺入增加了Sc_n团簇的稳定性,使其能隙升高,并改变了其稳定性及电子结构性质随团簇尺寸变化的规律;含有偶数个Sc原子的氧化物团簇比其周围邻近的含有奇数个Sc原子的氧化物团簇具有相对较高的稳定性.Sc_nO团簇电离势的理论计算值与实验值符合得较好,而其电子亲和势呈现振荡交替上升的变化趋势;用最大化学硬度规律等方法表征了Sc_nO氧化物团簇的稳定性和电子结构性质. 关键词： nO团簇')" href="#">Sc_nO团簇 几何结构 电子性质 密度泛函理论     

Insights into the structures,stabilities, electronic and magnetic properties of X2Aun (X = La,Y, and Sc; n = 1–9) clusters: comparison with pure gold clusters

A systematic study of the X₂Au_n (X = La, Y, Sc; n = 1–9) clusters are performed by using the density functional theory at TPSS level. The structures, stabilities, electronic, and magnetic properties are investigated in comparison with pure gold clusters. The results show that the transition points of the doped clusters from two-dimensional to three-dimensional structure are obviously earlier than gold clusters. The impurity X atoms tend to occupy the most highly coordinated position and form the largest probable number of bonds with gold atoms. In addition, the impurity atoms can strongly enhance the stabilities of gold clusters. It indicates that the impurity atoms dramatically affect the geometries and stabilities of the Au_n clusters. The highest occupied molecular orbital–lowest occupied molecular orbital gap, vertical ionisation potential, and chemical hardness show that the X₂Au₆ clusters have higher stabilities than the others. In La₂Au_1–9, Y₂Au_1–7, and Sc₂Au_1–4 clusters, the charges transfer from X atoms to the Au_n frames. The total magnetic moments of X₂Au_n clusters exist distinctly odd–even alternation behaviours except for La₂Au₄ and Sc₂Au₄ clusters.     

Tight-binding study of structural and electronic properties of silver clusters

Tight-binding model is developed to study the structural and electronic properties of silver clusters. The ground state structures of Ag clusters up to 21 atoms are optimized by molecular dynamics-based genetic algorithm. The results on small Ag_n clusters (n = 3-9) are comparable to ab initio calculations. The size dependence of electronic properties such as density of states, s-d band separation, HOMO-LUMO gap, and ionization potentials are discussed. Magic number behavior at Ag₂, Ag₈, Ag₁₄, Ag₁₈, Ag₂₀ is obtained, in agreement with the prediction of electronic ellipsoid shell model. We suggest that both the electronic and geometrical effect play significant role in the coinage metal clusters. Received 7 August 2000     

Structures,stabilities and electronic properties of boron-doped silicon clusters B3Sin (n=1–17) and their anions

The structures, stabilities and electronic properties of neutral and anionic B₃Si_n (n?=?1–17) clusters have been systemically investigated on the basis of density functional theory at the B3LYP/6-311?+?G(d) level and CALYPSO structure prediction method. The structural searches show that three boron atoms tend to form B₃ triangle encapsulated into Si_n cages with the increasing number of silicon atoms. Most of the lowest energy structures can be derived by using the squashed pentagonal bipyramid structure of B₃Si₄ and B₃Si₄^? as the major building unit. The relative stabilities are studied based on the calculated binding energies, second-order difference of energies and HOMO–LUMO gaps of the lowest energy structures. In addition, Hirshfeld, natural population analysis, Bader approaches and natural electronic configuration are performed to explore the charge transfer. At last, molecular orbital, magnetic properties, IR, Raman and UV–vis spectra are also, respectively, analysed for providing strong support for essential theoretical and experimental research.     

Density-functional theory study of structures,stabilities, and electronic properties of the Cu2-doped silicon clusters: Comparison with pure silicon clusters

Equilibrium geometric structures, stabilities, and electronic properties of Si_nCu₂ (n=1–8) clusters and pure silicon Si_n (n=3–10) clusters are investigated systematically by exchange-correlation density functional (B3LYP). The optimized geometries show that the most stable isomers have 3D structure for n=2, 4–8, and Cu-substituted Si_n+2 clusters is dominating growth pattern for the Si_nCu₂ clusters. The calculated averaged binding energies, fragmentation energies, second-order difference of energies, and the HOMO–LUMO gaps show that Si₂Cu₂ and Si₅Cu₂ clusters have enhanced relative stabilities and chemical stability than their neighboring clusters. Electronic properties of Si_nCu₂ (n=1–8) clusters are studied by calculating the natural population analysis and electrostatic potential, where the results show that the two copper atoms always possess positive charge and positive potential surround them. In addition, the VIP, VEA and the chemical hardness (η) are also analyzed and compared.     

Density function study transition metal chromium-doped alkali clusters: the finding of magnetic superatom

The structures, stabilities and magnetic properties of CrX_n (X = Na, Rb and Cs; n up to 9) clusters are studied using density functional theory to search for the stable magnetic superatoms. The geometrical optimisations indicate the ground-state structures of CrX_n evolve toward a close packed structure with an interior Cr atom surrounded by X atoms as the cluster size increase. Their stabilities are analysed by the relative energy, gain in energy (ΔE(n)) and the highest unoccupied molecular orbital and lowest unoccupied molecular orbital gaps. Furthermore, the magnetic moments of CrX_n clusters show an odd–even oscillation. Here, we mainly focus on the CrX₇ (X = Na, Rb and Cs) clusters due to the same valence count as the known stable magnetic superatoms VNa₈, VCs₈ and TiNa₉. Although these clusters all have a filled electronic configuration 1S²1P⁶ and large magnetic moment 5 μ_B, our studies indicate that only CrNa₇ is highly stable compared to its nearest neighbours, while CrRb₇ and CrCs₇ clusters are less stable. This suggests that Cr-doped Na₇ is most appropriate for filled electronic configuration and CrNa₇ is shown to be a stable magnetic superatom. More interesting, we find CrRb₈ and CrCs₈ with the filled electronic configuration 1S²1P⁶ have higher stability and large magnetic moment 6 μ_B in their respective series.     

A comparative study on geometries,stabilities, and electronic properties between bimetallic AgnX（X=Au,Cu;n=1-8）and pure silver clusters

Using the meta-generalized gradient approximation (meta-GGA) exchange correlation TPSS functional, the geo- metric structures, the relative stabilities, and the electronic properties of bimetallic Ag n X (X=Au, Cu; n=1–8) clusters are systematically investigated and compared with those of pure silver clusters. The optimized structures show that the transition point from preferentially planar to three-dimensional structure occurs at n = 6 for the Ag n Au clusters, and at n = 5 for Ag n Cu clusters. For different-sized Ag n X clusters, one X (X=Au or Cu) atom substituted Ag n+1 structure is a dominant growth pattern. The calculated fragmentation energies, second-order differences in energies, and the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps show interesting odd–even oscillation behaviours, indicating that Ag 2,4,6,8 and Ag 1,3,5,7 X (X=Au, Cu) clusters keep high stabilities in comparison with their neighbouring clusters. The natural population analysis reveals that the charges transfer from the Ag n host to the impurity atom except for the Ag 2 Cu cluster. Moreover, vertical ionization potential (VIP), vertical electronic affinity (VEA), and chemical hardness (η) are discussed and compared in depth. The same odd–even oscillations are found for the VIP and η of the Ag n X (X=Au, Cu; n=1–8) clusters.     

Systematic theoretical investigation of structure and electronic properties of pure copper and lithium doped copper clusters

The pure copper and lithium-doped copper clusters are studied using the unbiased CALYPSO structure searching method and density function theory to understand the evolution of various structure and electronic properties. Theoretical results show the growth behaviours of doped clusters are organised as follows: Li capped Cu_n clusters or Li substituted Cu_n+1 clusters as well as Cu capped Cu_n-1Li clusters. Moreover, the lowest energy structures of Cu_nLi favour planar structures for n ≤ 3 and three-dimensional structures for n = 4–12. In addition, the calculated averaged binding energies, fragmentation energies and second-order difference of energies exhibit obvious odd–even alternations as cluster size increasing. At last, the highest occupied-lowest unoccupied molecular orbital gaps, molecular orbital energy, magnetic property, natural population analysis, natural electron configurations, electrostatic potential, electron density difference, Infrared and Raman spectra and density of states are also, respectively, operative for characterising and rationalising the electronic properties of doped clusters.     

Geometries, stabilities, and electronic properties of Be-doped gold clusters: a density functional theory study

We have systematically investigated the geometrical structures, relative stabilities and electronic properties of small bimetallic AunBe (n = 1, 2, . . . , 8) clusters using a density functional method at BP86 level. The optimized geometries reveal that the impurity beryllium atom dramatically affects the structures of the Aun clusters. The averaged binding energies, fragmentation energies, second-order difference of energies, the highest occupied-lowest unoccupied molecular orbital energy gaps and chemical hardness are investigated. All of them exhibit a pronounced odd-even alternation, manifesting that the clusters with even number of gold atoms possess relatively higher stabilities. Especially, the linear Au2Be cluster is magic cluster with the most stable chemical stability. According to the natural population analysis, it is found that charge-transferring direction between Au atom and Be atom changes at the size of n = 4.     

DFT study on size-dependent geometries, stabilities, and electronic properties of AunM2 (M = Si, P; n = 1–8) clusters

The ab initio method based on density functional theory at the PW91PW91 level has been employed to systematically study the structures, stabilities, electronic, and magnetic properties of gold clusters with or without silicon/phosphorus doping. The optimized geometries show that the most stable isomers for Au _n Si₂ and Au _n P₂ (n = 1–8) clusters prefer a three-dimensional structure when n = 2 and n = 3 upwards, respectively, and they can be viewed as grown from the already observed Au _n−1M₂ (M = Si, P). The relative stabilities of calculated Au _n M₂ (M = Si, P) clusters have been analyzed through the atomic average binding energy, fragmentation energy, second-order difference of energy, and HOMO-LUMO gap. A pronounced odd-even alternative phenomenon indicates that the clusters with even-numbered valence electrons possess a higher stability than their neighboring ones. For both systems, natural population analysis reveals that electronic properties of dopant atoms in the corresponding configuration are mainly related to s and p states. We also investigated magnetic effects of clusters as a function of cluster size, however, their oscillatory magnetic moments were found to vary inversely to the fragmentation energy, second-order difference of energy, and HOMO-LUMO gap.     

砷化镓离子团簇的稳定性研究

采用全势能线性糕模轨道分子动力学方法，详细研究了砷化镓离子团簇Ga_nAs_n(n=4，5，6)的几何结构和稳定性.分别找到了这些离子团簇的最低能量结构，通过计算发现这些结构明显不同于中性团簇的基态结构.还发现离子团簇的其他稳定结构与对应的中性结构相比也有较大的结构畸变.在这些砷化镓离子团簇中，相对于砷原子而言，镓原子更容易处在帽原子的位置上. 关键词： 离子团簇 基态结构 稳定性     

Probing the structural and electronic properties of cationic rubidium–gold clusters: [AunRb]+ (n = 1–10)

Density functional theory has been applied to study the geometric structures, relative stabilities, and electronic properties of cationic [Au_nRb]⁺ and Au_{n + 1}⁺ (n = 1–10) clusters. For the lowest energy structures of [Au_nRb]⁺ clusters, the planar to three-dimensional transformation is found to occur at cluster size n = 4 and the Rb atoms prefer being located at the most highly coordinated position. The trends of the averaged atomic binding energies, fragmentation energies, second-order difference of energies, and energy gaps show pronounced even–odd alternations. It indicated that the clusters containing odd number of atoms maintain greater stability than the clusters in the vicinity. In particular, the [Au₆Rb]⁺ clusters are the most stable isomer for [Au_nRb]⁺ clusters in the region of n = 1–10. The charges in [Au_nRb]⁺ clusters transfer from the Rb atoms to Au_n host. Density of states revealed that the Au-5d, Au-5p, and Rb-4p orbitals hardly participated in bonding. In addition, it is found that the most favourable channel of the [Au_nRb]⁺ clusters is Rb⁺ cation ejection. The electronic localisation function (ELF) analysis of the [Au_nRb]⁺ clusters shown that strong interactions are not revealed in this study.     

Evolution of structures,stabilities, and electronic properties of anionic [AunRb]− (n = 1–10) clusters: comparison with pure gold clusters

The geometric structures, stabilities, and electronic properties of small size anionic [Au_nRb]^? and Au_n+1^? (n = 1–10) clusters have been systematically investigated by using density functional theory. The optimised geometries show that the structures of [Au_nRb]^? clusters favour the three-dimensional structure at n ≥ 8. The Rb atoms tend to occupy the most highly coordinated position and form the largest probable number of bonds with gold atoms. One Au atom capped on [Au_n-1Rb]^? structures is the dominant growth pattern for n = 2–8 and Rb atom capped on Au_n^? structures for n = 9–10. The averaged atomic bonding energies, fragmentation energies, second-order difference of energies, and highest occupied molecular orbital–lowest unoccupied molecular orbital gaps exhibit a pronounced even–odd alternations phenomenon. The charges in [Au_nRb]^? clusters transfer from the Rb atoms to Au_n host. In addition, it is found that the most favourable dissociation channel of the [Au_nRb]^? clusters is to eject a Rb atom and the highest energy dissociation path is Rb^? anion ejection.     

Experimental and theoretical studies of interactions between Si<Subscript>7</Subscript> clusters

The possibility of using magic Si₇ clusters to form a cluster material was studied experimentally and theoretically. In experiments Si₇ clusters were deposited on carbon surfaces, and the electronic structure and chemical properties of the deposited clusters were measured using X-ray photoelectron spectroscopy (XPS). A non bulk-like electronic structure of Si₇ was found in the Si 2p core level spectra. Si₇ is suggested to form a more stable structure than the non-magic Si₈ cluster and Si atoms upon deposition on carbon surfaces. Theoretically it was possible to study the interaction between the clusters without the effect of a surface. Density functional theory (DFT) calculations of potential curves of two free Si₇ clusters approaching each other in various orientations hint at the formation of cluster materials rather than the fusion of clusters forming bulk-like structures.     

Electronic structures of Al–Si clusters and the magic number structure Al8Si4

The low-energy structures of Al₈Si_m (m = 1–6) have been determined by using the genetic algorithm combined with density functional theory and the Second-order Moller-Plesset perturbation theory (MP2) models. The results show that the close-packed structures are preferable in energy for Al–Si clusters and in most cases there exist a few isomers with close energies. The valence molecular orbitals, the orbital level structures and the electron localisation function (ELF) consistently demonstrate that the electronic structures of Al–Si clusters can be described by the jellium model. Al₈Si₄ corresponds to a magic number structure with pronounced stability and large energy gap; the 40 valence electrons form closed 1S²1P⁶1D¹⁰2S²1F¹⁴2P⁶ shells. The ELF attractors also suggest weak covalent Si–Si, Si–Al and Al–Al bonding, and doping Si in aluminium clusters promotes the covalent interaction between Al atoms.     

Ab initio calculation of the geometric,electronic and magnetic properties of neutral and anionic Au n Pd (n = 1–9) clusters

The ab initio method based on density functional theory at the B3PW91 level has been applied to study the geometric, electronic, and magnetic properties of neutral and anionic Au _n Pd (n?=?1–9) clusters. The results show that the most stable geometric structures adopt a three-dimensional structure for neutral Au₇Pd and Au₈Pd clusters, but for anionic clusters, no three-dimensional lowest-energy structures were obtained. The relative stabilities of neutral and anionic Au _n Pd clusters were analysed by means of the dependent relationships between the binding energies per atom, the dissociation energies, the second-order difference of energies, the HOMO–LUMO energy gaps and the cluster size n, and a local odd–even alternation phenomenon was found. Natural population analysis indicates the sequential transfer from the Pd atom to the Au _n frame in Au_1,2,3,5Pd and Au_2,3Pd^? clusters, and from the Au _n frame to the Pd atom in other clusters. Much to our surprise, irrespective of whether it is the total magnetic moment or the local magnetic moment, the magnetic moment presents an odd–even alternation phenomenon as a function of the cluster size n. The magnetic effects are mainly localized on the various atoms (Au or Pd) for different cluster size n.     

Metastable fragmentation of silver bromide clusters

The abundance spectra and the fragmentation channels of silver bromide clusters have been measured and analyzed. The most abundant species are Ag_nBr_{n - 1} ⁺ and Ag_nBr_{n + 1} ^- and Ag₁₄Br₁₃ ⁺ is a magic number, revealing their ionic nature. However, some features depart from what is generally observed for alkali-halide ionic clusters. From a certain size, Ag_nBr_{n - 1} ⁺ is no more the main series, and Ag_nBr _{n - 2, 3} ⁺ series become almost as important. The fast fragmentation induced by a UV laser makes the cations lose more bromine than silver ions and lead to more silver-rich clusters. Negative ions mass spectra contain also species with more silver atoms than required by stoichiometry. We have investigated the metastable fragmentation of the cations using a new experimental method. The large majority of the cations release mainly a neutral Ag₃Br₃ cluster. These decay channels are in full agreement with our recent ab initio DFT calculations, which show that Ag⁺-Ag⁺ repulsion is reduced due to a globally attractive interaction of their d orbitals. This effect leads to a particularly stable trimer (AgBr)₃ and to quasi-planar cyclic structures of (AgBr)_n clusters up to n = 6. We have shown that these two features may be extended to other silver halides, to silver hydroxides (AgOH)_n, and to cuprous halide compounds. Received 9 November 2000 and Received in final form 25 January 2001     

Odd-even effect of the number of free valence electrons on the electronic structure properties of gold-thiolate clusters

ABSTRACT

It is essential to understand the intrinsic stability of the gold-thiolate clusters, which present extensive potential applications in many fields such as the catalysis, biomedicines and molecular machines. The electronic structures and aromaticity indexes of a series of Au_m(SH)_n (m, n?=?5–12) were comprehensively investigated through energetic, vibrational, magnetic, and electronic density properties, which are highly sensitive to the size and topological structure of the cluster. Generally, computational results of energy gap between the frontier molecular orbitals, normalized atomization energy (NAE), and electron localization function (ELF)-σ values exhibit the odd-even effect, in which clusters with the even number of free valence electrons, being reflected by the value of (m–n), possess relatively higher stability than the odd one. However, it is difficult to describe the stability of cluster with the sophisticated three-dimensional structure through one single aromaticity index such as the nucleus-independent chemical shift (NICS) value. Principal component analysis and clustering analysis of the calculation results of Au_m(SR)_n clusters suggest that the value of (m–n) and the Au₄ unit are important for predicting the stability of the Au clusters.