DFT study of size-dependent geometries,stabilities and electronic properties of Si2Agn clusters: comparison with pure silver clusters

The equilibrium geometric structures, stabilities and electronic properties of Si₂Ag_n (n = 1–8) and pure silver Ag_n (n ≤ 10) clusters have been systematically investigated by using meta-generalised gradient approximation. Due to sp³ hybridisation, the lowest energy structures of Si₂Ag_n clusters for n > 2 favour the three-dimensional structure. The silicon atoms prefer to be located at the surface of the host silver clusters. By analysing the relative stabilities, it is found that the di-bridged structure Si₂Ag₂ isomer is the most stable structure for Si₂Ag_n (n = 1–8) clusters. The highest occupied–lowest unoccupied molecular orbital gaps, exhibiting a pronounced even–odd alternation, indicate that the doped clusters with even number of atoms have enhanced chemical stability than those with odd number of atoms. The results of Wiberg bond indices and electronic localisation function show that the stronger Si–Si and Si–Ag interaction may be the main driving force for the higher stability of Si₂Ag_n 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.     

Geometries, stabilities, and electronic properties of gold-magnesium (AunMg) bimetallic clusters

The geometrical structures, relative stabilities, and electronic properties of bimetallic Au_nMg (n=1-8) clusters have been systematically investigated by means of first-principle density functional theory. The results show that the ground-state isomers have planar structures for n=1-7. Here, the calculated fragmentation energies, the second-order difference of energies, the highest occupied-lowest unoccupied molecular orbital energy gaps, and the hardness exhibit a pronounced odd-even alternation, manifesting that the clusters, especially Au₂Mg, with even-number gold atoms have a higher relative stability. On the basis of natural population analysis, the charge transfer and magnetic moment are also discussed.     

Formation of binary clusters by molecular ion irradiation

In the present study, we have observed silicon–carbon cluster ions (Si_nC_m⁺) emitted from a Si(1 0 0) surface under irradiation of reactive molecular ions, such as C₆F₅⁺, at 4 keV, 1 μA/cm². The cluster Si_n up to n=8 and “binary” cluster Si_nC up to n=6 are clearly detected for the C₆F₅⁺ irradiation. Stoichiometric clusters (Si_nC_m n=m) except SiC⁺ and other binary clusters which contain more than two carbon atoms (m≥2) were scarcely observed. The observed clusters show a yield alternation between odd and even n. The intensities of Si₄, Si₆ and Si₅C clusters are relatively higher than those of the neighboring clusters. In the case of Si₅C, it is considered that doped carbon atom acts as silicon atom. These results imply that the recombination through the nascent cluster emission and subsequent decomposition takes place during the cluster formation.     

Geometrical, electronic, and magnetic properties of small AunSc (n=1-8) clusters

Geometrical, electronic, and magnetic properties of the Sc-doped gold clusters, Au_nSc (n=1-8), have been studied using the density-functional theory within the generalized gradient approximation. An extensive structural search shows that the Sc atom in low-energy Au_nSc isomers tends to occupy the most highly coordinated position. The substitution of a Sc atom for an Au atom in the Au_n+1 cluster markedly changes the structure of the host cluster. Moreover, we confirm that the ground-state Au₆Sc cluster has a distortion to a lower D_2h symmetry. The relative stabilities and electronic properties of the lowest-energy Au_nSc clusters are analyzed based on the averaged binding energies, second-order energy differences, fragmentation energies, chemical hardnesses, and HOMO-LUMO gaps. It is found that the magic Au₃Sc cluster can be perceived as a superatom with high chemical stability and its HOMO-LUMO gap is larger than that of the closed-shell Zr@Au₁₄ cluster. The high symmetry and spin multiplicity of the Au₃Sc and Au₆Sc clusters are responsible for their large vertical ionization potential and electron affinity. The magnetism calculations indicate that the magnetic moment of the Sc atom in the ground-state Au_nSc (n=2-8) clusters gradually decreases for even n and is completely quenched for odd n.     

Structures, chemical bonding, magnetisms of small Al-doped zirconium clusters

The geometrical and electronic properties of small Al-doped Zrn−1 and host Zrn clusters (n=2-8) are investigated with hybrid HF/DFT functional: B3LYP. For the most favorable configurations of Zrn−1Al clusters, the Al atom prefers to be located on the surface of host zirconium clusters. The isomers that correspond to low coordination number of Zr-Al bonds are found to be more stable. The doping of Al atom in Zrn−1 clusters improves the chemical activities of host clusters. The Zr₅, Zr₇, Zr₄Al and Zr₆Al clusters behave the stronger stabilities relative to their respective neighbors. The strong s-d hybridizations are presented in all bonding Zr atoms. The values of WBI together with AIM analysis suggest that the Zr-Zr interactions are stronger than those between Zr and Al atoms. The doping of Al atom results into the decrease of spin magnetic moments for host zirconium clusters. The moments are mainly derived from the 4d electrons of bonding Zr atoms.     

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.     

Enhancement of the secondary ion emission induced by fast clusters

The emission yields of the secondary ions are measured by using a conventional time of flight (TOF) technique under bombardments of Mg and C₂, Ni and Si₂ with different energies, and C_n, Si_n and Ni_n (n = 1-3) with the different charge states and with energy of 1.5 MeV per atom, respectively. For the bombardments of C_n, Si_n and Ni_n, the enhancements of the secondary ion emissions increase with increasing cluster sizes and charge states. For the bombardments of Mg and C₂, Ni and Si₂, although the mass and the nuclear charges of C₂ and Si₂ are the same as or equivalent to Mg or Ni, respectively, the enhancements of the secondary ion emissions induced by the clusters of C₂ and Si₂ in a wide energy range are also clearly indicated. The instantaneous collective interaction of the cluster constituents plays an important role in the secondary ion emissions.     

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.     

Copper clusters: electronic effect dominates over geometric effect

A minimal parameter tight binding molecular dynamics scheme is used to study Cu _n clusters with . We present results for relaxed configurations of different symmetries, binding energies, relative stabilities and HOMO-LUMO gap energies for these clusters. Detailed comparison for small clusters n = 3-9 with ab initio and available experimental results shows very good agreement. Even-odd alternation due to electron pairing and magic behaviour for Cu₂, Cu₈, Cu₁₈ and Cu₂₀ due to electronic shell closing are found. We found electronic effects, electronic shell closing and electron pairing in the HOMO dominates over the geometrical effect to determine the relative stability of copper clusters. The present results indicate that tight-binding molecular dynamics scheme can be relied on to provide a useful semiempirical scheme in modeling interactions in metallic systems.Received: 3 May 2004, Published online: 26 October 2004PACS: 36.40.Cg Electronic and magnetic properties of clusters - 36.40.Mr Spectroscopy and geometrical structure of clusters - 36.40.Qv Stability and fragmentation of clusters     

Structural, electronic and magnetic properties of ConRh (n=1-8) clusters from density functional calculations

The geometries, stabilities, electronic and magnetic properties of Co_nRh (n=1-8) clusters have been investigated systematically within the framework of the generalized gradient approximation density-functional theory. The results indicate that the most stable structures of Co_nRh (n=1-8) clusters are all similar to those of corresponding Co_n+1 clusters. Maximum peaks of second-order energy difference are found at n=2, 4 and 7, indicating that these clusters possess relatively higher stability than their respective neighbors. The magnetism of the ground state of alloy clusters all displays ferromagnetic coupling except for Co₃Rh. In addition, the doped Rh atom exhibits an important influence on the magnetism of alloy clusters, e.g., compared with corresponding pure Co_n clusters, the local moment of Co atom is noticeably enhanced in Co_nRh alloy clusters at n=1, 2, 5, 6, 7 and 8, while reduced at n=3 and 4. Further analysis based on the average bond length, the charge transfer and the spin polarization has been made to clarify the different magnetic responses to Rh doping.     

密度泛函理论对ZrnPd团簇结构和性质的研究

用B3LYP/LANL2DZ方法对Zr_nPd(n =1—13)团簇的平衡几何结构、能量、频率、电子性质和磁性进行了计算.研究表明,Pd原子位于表面的异构体更为稳定,其中Zr₇Pd,Zr₁₂Pd团簇稳定性高,是幻数团簇,此外,相对于Zr_nCo与Zr_nFe团簇,Zr_nPd团簇参与化学反应的能力较弱,化学稳定性更     

Density functional theory study of MgnNi2 (n=1-6) clusters

The geometries of Mg_nNi₂ (n=1-6) clusters are studied by using the hybrid density functional theory (B3LYP) with LANL2DZ basis sets. For the ground-state structures of Mg_nNi₂ clusters, the stabilities and the electronic properties are investigated. The results show that the groundstate structures and symmetries of Mg clusters change greatly due to the Ni atoms. The average binding energies have a growing tendency while the energy gaps have a declining tendency. In addition, the ionization energies exhibit an odd-even oscillation feature. We also conclude that n=3, 5 are the magic numbers of the Mg_nNi₂ clusters. The Mg₃ Ni₂ and Mg₅Ni₂ clusters are more stable than neighbouring clusters, and the Mg₄Ni₂ cluster exhibits a higher chemical activity.     

Density functional theoretical study of Cun, Aln (n = 4-31) and copper doped aluminum clusters: Electronic properties and reactivity with atomic oxygen

A DFT study of the electronic properties of copper doped aluminum clusters and their reactivity with atomic oxygen is reported. Firstly we performed calculations for the pure Cu_n and Al_n (n = 4, 9, 10, 13, 25 and 31) clusters and we determined their atomization energy for some frozen conformations at the B3PW91 level. The calculated work functions and M-M (M = Cu, Al) bond energies of the largest clusters are comparable with experimental data. Secondly, we focused our attention on the change of the electronic properties of the systems upon the substitution of an Al atom by a Cu one. This latter stabilizes the system as the atomization energy of the 31-atoms cluster increases of 0.31 eV when the substitution is done on the surface and of 1.18 eV when it is done inside the cluster. We show that the electronic transfer from the Al cluster to the Cu atom located at the surface is large (equal to 0.7 e⁻) while it is negligible when Cu is inserted in the Al_n cluster. Moreover, the DOS of the Al₃₁ and Al₃₀Cu systems are compared. Finally, the chemisorption energies of atomic oxygen in threefold sites of the Al₃₁, Cu₃₁ and Al₃₀Cu clusters are calculated and discussed. We show that the chemisorption energy of O is decreasing on the bimetallic systems compared to the pure aluminum cluster.     

On a presence of SimHn clusters in a-Si:H/c-Si structures

Dominant aim of the paper was to verify the existence of the Si_mH_n clusters in a-Si:H layers. Thin layers were deposited by plasma-enhanced chemical vapor deposition (PECVD) on both glass and crystalline silicon substrates. Their IR and structural properties were investigated by Fourier transform infrared spectroscopy (FTIR) and X-ray diffraction at grazing incidence angle (XRDGI). We have found that the layer probably consists of larger structurally ordered parts corresponding to Si_mH_n clusters and separated groups of (Si-H_x)_N. The ordered parts could be identified as some of Si_mH_n clusters ranging from (10, 16) to (84, 64) represented by corresponding vibration frequencies in three following IR regions: 600-750, 830-900 and 2080-2180 cm⁻¹. XRDGI measurement indicates that diffraction maximum at around 2Θ = 28° can be attributed to an existing Si_mH_n cluster.     

Pt_nAl(n=1—8)小团簇的密度泛函理论研究

采用密度泛函理论方法,在BPW91/LANL2DZ水平下详细研究了Pt n Al(n=1—8)团簇的几何结构、稳定性和电子性质.同时,分析了团簇的结构演化规律、平均结合能、二阶能量差分、能隙、磁性、Mulliken电荷和电极化率.结果表明:除Pt2Al外,所有Pt n Al(n=1—8)团簇的基态几何结构都可以用Al原子替换Pt n+1基态构型中的Pt原子得到,且Al原子位于较高的配位点上.二阶能量差分、能隙的分析结果表明,PtAl和Pt4Al团簇相对其他团簇具有较高的稳定性.Mulliken电荷分析表明,Al原子所带的电荷转移到Pt原子上,Al原子是电荷的捐赠者.磁性的分析说明,单个Al原子的加入对Pt n团簇的平均每原子磁矩随尺寸的变化趋势没有影响,但总体上降低了Pt n团簇的平均磁矩.极化率的研究表明,富Pt团簇的非线形光学效应强,容易被外场极化.     

Geometries, stabilities and electronic properties of small Nb-doped gallium clusters: A density functional theory study

The host Ga_n+1 and doped Ga_nNb (n=1-9) clusters with several spin configurations have been systematically investigated by a relativistic density functional theory (DFT) with the generalized gradient approximation. The optimized equilibrium geometries tend to prefer the close-packed configurations for small Nb-doped gallium clusters up to n=9. The average binding energies per atom (E_b/atom), second-order differences of total energies (Δ₂E), fragmentation energies (E_f) and HOMO-LUMO gaps of Ga_n+1 and Ga_nNb (n=1-9) clusters are studied. The results indicate the doping of Nb atom in gallium clusters improves the chemical activities. In particular, the clusters with sizes of Ga₄Nb and Ga₇Nb are found to be more stable with respect to their respective neighbors. Our calculated vertical ionization potentials (VIPs) exhibit an obvious oscillating behavior with the cluster size increasing, except for Ga₃ and Ga₄Nb, suggesting the Ga₃, Ga₅, Ga₇, GaNb, Ga₃Nb, Ga₆Nb and Ga₈Nb clusters corresponding to the high VIPs. In the case of vertical electron affinities (VEAs) and chemical hardness η, VEAs are slightly increasing whereas chemical hardness η decreasing as Ga_nNb cluster size increases. Besides, the doping of Nb atom also brings the decrease as the cluster sizes increases for atomic spin magnetic moments (μ_b).     

Density functional theory study of AunMn(n=1-8) clusters

Equilibrium geometries, relative stabilities, and magnetic properties of small Au_nMn (n=1-8) clusters have been investigated using density functional theory at the PW91P86 level. It is found that Mn atoms in the ground state Au_nMn isomers tend to occupy the most highly coordinated position and the lowest energy structure of Au_nMn clusters with even n is similar to that of pure Au_n+1 clusters, except for n=2. The substitution of Au atom in Au_n+1 cluster by a Mn atom improves the stability of the host clusters. Maximum peaks are observed for Au_nMn clusters at n=2, 4 on the size dependence of second-order energy differences and fragmentation energies, implying that the two clusters possess relatively higher stability. The HOMO-LUMO energy gaps of the ground state Au_nMn clusters show a pronounced odd-even oscillation with the number of Au atoms, and the energy gap of Au₂Mn cluster is the biggest among all the clusters. The magnetism calculations indicate that the total magnetic moment of Au_nMn cluster, which has a very large magnetic moment in comparison to the pure Au_n+1 cluster, is mainly localized on Mn atom.     

Density functional study of small cobalt-platinum nanoalloy clusters

The structural, energetic, electronic and magnetic properties of small bimetallic Co_nPt_m (n+m≤5) nanoalloy clusters are investigated by density functional theory within the generalized gradient approximation. A plausible candidate for the ground state isomer and the other possible local minima, binding energies, relative stabilities, magnetic moments, the highest occupied and the lowest unoccupied molecular orbital energy gaps have been calculated. It is found as a general trend that average binding energies of Co-Pt bimetallic clusters increase with Pt doping. Planar structures of pure Co clusters become 3D with the addition of Pt atoms. CoPt₂, Co₂Pt₂, Co₃Pt₂, and CoPt₄ nanoalloys are identified as the most stable species since they have higher second finite difference in energy than the others. Pt doping decreases the total spin magnetic moment gradually. A rule for the prediction of the total spin moments of small Co-Pt bimetallic clusters is derived.     

Geometrical,electronic, and magnetic properties of CunFe (n=1–12) clusters: A density functional study

The geometrical, electronic, and magnetic properties of small Cu_nFe (n=1–12) clusters have been investigated by using density functional method B3LYP and LanL2DZ basis set. The structural search reveals that Fe atoms in low-energy Cu_nFe isomers tend to occupy the position with the maximum coordination number. The ground state Cu_nFe clusters possess planar structure for n=2–5 and three-dimensional (3D) structure for n=6–12. The electronic properties of Cu_nFe clusters are analyzed through the averaged binding energy, the second-order energy difference and HOMO–LUMO energy gap. It is found that the magic numbers of stability are 1, 3, 7 and 9 for the ground state Cu_nFe clusters. The energy gap of Fe-encapsulated cage clusters is smaller than that of other configurations. The Cu₅Fe and Cu₇Fe clusters have a very large energy gap (>2.4 eV). The vertical ionization potential (VIP), electron affinity (EA) and photoelectron spectra are also calculated and simulated theoretically for all the ground-state clusters. The magnetic moment analyses for the ground-state Cu_nFe clusters show that Fe atom can enhance the magnetic moment of the host cluster and carries most of the total magnetic moment.