Geometries and electronic properties of the neutral and charged rare earth Yb-doped Si(n) (n = 1-6) clusters: a relativistic density functional investigation

The neutral and charged YbSi(n) (n = 1-6) clusters considering different spin configurations have been systematically investigated by using the relativistic density functional theory with generalized gradient approximation. The total bonding energies, equilibrium geometries, Mulliken populations (MP), Hirshfeld charges (HC), fragmentation energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps are calculated and discussed. The optimized geometries indicate that the most stable YbSi(n) (n = 1-6) clusters keep basically the analogous frameworks as the low-lying Si(n)(+1) clusters, while the charged species deviate from their neutral counterparts, and that the doped Yb tends to occupy the substitutional site of the neutral and charged YbSi(n) isomers. The relative stabilities are investigated in terms of the calculated fragmentation energies, exhibiting enhanced stabilities for the remarkably stable neutral and charged YbSi2 and YbSi5 clusters. Furthermore, the calculated MP and HC values show that the charges of the neutral and charged YbSi(n) clusters transfer from the Yb atom to Si(n) atoms and the Yb atom acts as an electron donor, and that the f orbitals of the Yb atom in the neutral and charged YbSi(n) clusters behave as core without involvement in chemical bonding. The calculated HOMO-LUMO gaps indicate that the YbSi2 and YbSi4+ clusters have stronger chemical stabilities. Comparisons of the Yb-doped Si(n) (n = 1-6) with available theoretical results of transition-metal-doped silicon clusters are made. The growth pattern is investigated also.     

Geometries and magnetisms of the Zr(n) (n=2-8) clusters: the density functional investigations

The geometries, stabilities, and electronic and magnetic properties of small-sized Zr(n) (n=2-8) clusters with different spin configurations were systematically investigated by using density functional approach. Emphasis is placed on studies that focus on the total energies, equilibrium geometries, growth-pattern behaviors, fragmentation energies, and magnetic characteristics of zirconium clusters. The optimized geometries show that the large-sized low-lying Zr(n) (n=5-8) clusters become three-dimensional structures. Particularly, the relative stabilities of Zr(n) clusters in terms of the calculated fragmentation energies and second-order difference of energies are discussed, exhibiting that the magic numbers of stabilities are n=2, 5, and 7 and that the pentagonal bipyramidal D(5h) Zr(7) geometry is the most stable isomer and a nonmagnetic ground state. Furthermore, the investigated magnetic moments confirm that the atomic averaged magnetic moments of the Zr(n) (n not equal to 2) display an odd-even oscillation features and the tetrahedron C(s) Zr(4) structure has the biggest atomic averaged magnetic moment of 1.5 mu(B)/at. In addition, the calculated highest occupied molecular orbital-lowest unoccupied molecular orbital gaps indicate that the Zr(n) (n=2 and 7) clusters have dramatically enhanced chemical stabilities.     

Structural and electronic properties of TaSi(n) (n=1-13) clusters: a relativistic density functional investigation

The TaSi(n) (n=1-13) clusters with doublet, quartet, and sextet spin configurations have been systematically investigated by a relativistic density functional theory with the generalized gradient approximation available in Amsterdam density functional program. The total bonding energies, equilibrium geometries, Mulliken populations as well as Hirshfeld charges of TaSi(n) (n=1-13) clusters are calculated and presented. The emphasis on the stabilities and electronic properties is discussed. The most stable structures of the small TaSi(n) (n=1-6) clusters and the evolutional rule of low-lying geometries of the larger TaSi(n) (n=7-13) clusters are obtained. Theoretical results indicate that the most stable structure of TaSi(n) (n=1-6) clusters keeps the similar framework as the most stable structure of Si(n+1) clusters except for TaSi(3) cluster. The Ta atom in the lowest-energy TaSi(n) (n=1-13) isomers occupies a gradual sinking site, and the site moves from convex, to flatness, and to concave with the number of Si atom varying from 1 to 13. When n=12, the Ta atom in TaSi(12) cluster completely falls into the center of the Si frame, and a cagelike TaSi(12) geometry is formed. Meanwhile, the net Mulliken and Hirsheld populations of the Ta atom in the TaSi(n) (n=1-13) clusters vary from positive to negative, manifesting that the charges in TaSi(n) (n>/=12) clusters transfer from Si atoms to Ta atom. Additionally, the contribution of Si-Si and Si-Ta interactions to the stability of TaSi(n) clusters is briefly discussed. Furthermore, the investigations on atomic averaged binding energies and fragmentation energies show that the TaSi(n) (n=2,3,5,7,10,11,12) clusters have enhanced stabilities. Compared with pure silicon clusters, a universal narrowing of highest occupied molecular orbital-lowest unoccupied molecular orbital gap in TaSi(n) clusters is found.     

Determination of structures, stabilities, and electronic properties for bimetallic cesium-doped gold clusters: a density functional theory study

The equilibrium geometric structures, stabilities, and electronic properties of bimetallic Au(n)Cs (n = 1-10) and pure gold Au(n) (n ≤ 11) clusters have been systematically investigated by using density functional theory with meta-generalized gradient approximation. The optimized geometries show that one Au atom capped on Au(n-1)Cs structures and Cs atom capped Au(n) structures for different sized Au(n)Cs (n = 1-10) clusters are two dominant growth patterns. Theoretical calculated results indicate that the most stable isomers have three-dimensional structures at n = 4 and 6-10. Averaged atomic binding energies, fragmentation energies, and second-order difference of energies exhibit a pronounced even-odd alternations phenomenon. The same even-odd alternations are found in the highest occupied-lowest unoccupied molecular orbital gaps, vertical ionization potential, vertical electron affinity, and hardnesses. In addition, it is found that the charge in corresponding Au(n)Cs clusters transfers from the Cs atom to the Au(n) host in the range of 0.851-1.036 electrons.     

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

First-principle density functional theory is used for studying the anion gold clusters doped with magnesium atom. By performing geometry optimizations, the equilibrium geometries, relative stabilities, and electronic and magnetic properties of [Au(n)Mg]? (n = 1-8) clusters have been investigated systematically in comparison with pure gold clusters. The results show that doping with a single Mg atom dramatically affects the geometries of the ground-state Au(n+1)? clusters for n = 2-7. Here, the relative stabilities are investigated in terms of the calculated fragmentation energies, second-order difference of energies, and highest occupied?lowest unoccupied molecular orbital energy gaps, manifesting that the ground-state [Au(n)Mg]? and Au(n+1)? clusters with odd-number gold atoms have a higher relative stability. In particular, it should be noted that the [Au?Mg]? cluster has the most enhanced chemical stability. The natural population analysis reveals that the charges in [Au(n)Mg]? (n = 2-8) clusters transfer from the Mg atom to the Au frames. In addition, the total magnetic moments of [Au(n)Mg]? clusters exhibit an odd-even oscillation as a function of cluster size, and the magnetic effects mainly come from the Au atoms.     

Geometries, stabilities, and electronic properties of different-sized ZrSi(n) (n=1-16) clusters: a density-functional investigation

The ZrSi(n) (n=1-16) clusters with different spin configurations have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, growth-pattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of different-sized ZrSi(n) clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable ZrSi(n) (n=1-7) geometries, except ZrSi3, keep the analogous frameworks as the lowest-energy or the second lowest-energy Si(n+1) clusters. However, for large ZrSi(n) (n=8-16) clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transition-metal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowest-energy sandwich-like ZrSi12 geometry is not a sealed structure and appears irregular as compared with other TM@Si12 (TM = Re,Ni). The growth patterns of ZrSi(n) (n=1-16) clusters are concerned showing the Zr-encapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the ZrSi(n) (n=1-16) clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerene-like ZrSi16 is the most stable structure, which is in good agreement with the calculated atomic binding energies of ZrSi(n) (n=8-16) and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable ZrSi(n) (n=1-16) structures exactly varies from positive to negative at the critical-sized ZrSi8 cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small- or middle-sized clusters and metallic in character for the large-sized clusters. Finally, the properties of frontier orbitals and polarizabilities of ZrSi(n) are also discussed.     

A computational investigation of copper-doped germanium and germanium clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Ge(n) and CuGe(n) (n = 2-13) clusters have been systematically investigated by using density-functional approach. According to optimized CuGe(n) geometries, growth patterns of Cu-capped Ge(n) or Cu-substituted Ge(n+1) clusters for the small- or middle-sized CuGe(n) clusters as well as growth patterns of Cu-concaved Ge(n) or Ge-capped CuGe(n-1) clusters for the large-sized CuGe(n) clusters are apparently dominant. The average atomic binding energies and fragmentation energies are calculated and discussed; particularly, the relative stabilities of CuGe10 and Ge10 are the strongest among all different sized CuGe(n) and Ge(n) clusters, respectively. These findings are in good agreement with the available experimental results on CoGe10- and Ge10 clusters. Consequently, unlike some transition metal (TM)Si12, the hexagonal prism CuGe12 is only low-lying structure; however, the basket-like structure is located as the lowest-energy structure. Different from some TM-doped silicon clusters, charge always transfers from copper to germanium atoms in all different sized clusters. Furthermore, the calculated highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gaps are obviously decreased when Cu is doped into the Ge(n) clusters, together with the decrease of HOMO-LUMO gaps, as the size of clusters increases. Additionally, the contribution of the doped Cu atom to bond properties and polarizabilities of the Ge(n) clusters is also discussed.     

Small ScCn cyclic clusters: a density functional study of their structure and stability

A theoretical study of the ScCn, ScCn+, and ScCn- (n = 1-10) cyclic clusters has been carried out employing the B3LYP density functional method. Predictions for several molecular properties that could help in their possible experimental characterization, such as equilibrium geometries, electronic structures, dipole moments, and vibrational frequencies, are reported. All ScCn cyclic clusters are predicted to have doublet ground states. For cationic clusters the ground state is alternate between singlets (n-even species) and triplets (n-odd members). In the case of anionic clusters the singlet-triplet separation is relatively small, with the singlets being favored in most cases. In general, even-odd parity effects are also observed for different properties, such as incremental binding energies, ionization energies, and electron affinities. For all neutral, cationic, and anionic clusters it is found that cyclic species are more stable than their open-chain counterparts. Therefore, cyclic structures are the most interesting possible targets for an experimental search of scandium-doped carbon clusters.     

Equilibrium geometries, stabilities, and electronic properties of the bimetallic M2-doped Au(n) (M = Ag, Cu; n = 1-10) clusters: comparison with pure gold clusters

The density functional method with relativistic effective core potential has been employed to investigate systematically the geometrical structures, relative stabilities, growth-pattern behaviors, and electronic properties of small bimetallic M(2)Au(n) (M = Ag, Cu; n = 1-10) and pure gold Au(n) (n ≤ 12) clusters. The optimized geometries reveal that M(2) substituted Au(n+2) clusters and one Au atom capped M(2)Au(n-1) structures are dominant growth patterns of the stable alloyed M(2)Au(n) clusters. The calculated averaged atomic binding energies, fragmentation energies, and the second-order difference of energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The analytic results exhibit that the planar structure Ag(2)Au(4) and Cu(2)Au(2) isomers are the most stable geometries of Ag(2)Au(n) and Cu(2)Au(n) clusters, respectively. In addition, the HOMO-LUMO gaps, charge transfers, chemical hardnesses and polarizabilities have been analyzed and compared further.     

Structural and electronic properties of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13): Theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n)-, and PSi(n-1) clusters (2 < or = n < or = 13) have been investigated using the ab initio molecular orbital theory formalism. The hybrid exchange-correlation energy functional (B3LYP) and a standard split-valence basis set with polarization functions (6-31+G(d)) were employed to optimize geometrical configurations. The total energies of the lowest energy isomers thus obtained were recalculated at the MP2/aug-cc-pVTZ level of theory. Unlike positively charged clusters, which showed similar structural behavior as that of neutral clusters [Nigam et al., J. Chem. Phys. 121, 7756 (2004)], significant geometrical changes were observed between Si(n) and Si(n)- clusters for n = 6, 8, 11, and 13. However, the geometries of P substituted silicon clusters show similar growth as that of negatively charged Si(n) clusters with small local distortions. The relative stability as a function of cluster size has been verified based on their binding energies, second difference in energy (Delta2 E), and fragmentation behavior. In general, the average binding energy of Si(n)- clusters is found to be higher than that of Si(n) clusters. For isoelectronic PSi(n-1) clusters, it is found that although for small clusters (n < 4) substitution of P atom improves the binding energy of Si(n) clusters, for larger clusters (n > or = 4) the effect is opposite. The fragmentation behavior of these clusters reveals that while small clusters prefer to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size. The adiabatic electron affinities of Si(n) clusters and vertical detachment energies of Si(n)- clusters were calculated and compared with available experimental results. Finally, a good agreement between experimental and our theoretical results suggests good prediction of the lowest energy isomeric structures for all clusters calculated in the present study.     

Structure and stability of Al-doped boron clusters by the density-functional theory

The geometries, stabilities, and electronic properties of Bn and AlBn clusters, up to n=12, have been systematically investigated by using the density-functional approach. The results of Bn clusters are in good agreement with previous conclusions. When the Al atom is doped in Bn clusters, the lowest-energy structures of the AlBn clusters favor two-dimensional and can be obtained by adding one Al atom on the peripheral site of the stable Bn when n相似文献   

TbSin(n=2-13)团簇的结构、电子及磁学性质

利用相对论密度泛函理论在广义梯度近似下研究TbSi_n (n=2-13)团簇的结构、稳定性、电子和磁学性质. 对团簇的平均结合能、离解能、电荷转移、最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能级差、Mulliken 电荷分析和磁学性质进行了计算和讨论. TbSi_n团簇并没有像实验推测的那样在n=10形成嵌入式的结构. 我们推断电子亲和势的急剧变化不仅与嵌入式的结构有关, 而且与电子的固有稳定性相关.Mulliken 电荷分析表明电荷总是从Tb 原子转向Si 原子. 团簇的磁矩主要局域在Tb 原子的周围, 并且主要由f电子贡献, f 电子表现出局域性并且不参与化学成键. 以TbSi₁₀为例的分波态密度分析表明Tb与Si 原子间存在很强的sp轨道杂化.     

线性簇合物SC2nS2－(n =1～12)电子吸收光谱

应用密度泛函理论,在B3LYP/6-31G*水平上优化了线性簇合物SC2nS2－(n =1～12)的基态平衡几何结构,并计算了它们的谐振动频率.在基态平衡构型下,通过TD-B3LYP/cc-pvTZ和TD-B3LYP/cc-pvDZ计算,确定了簇合物SC2nS2－(n =1～10) 电子跃迁的垂直激发能和对应的振子强度.基于计算结果,导出了电子跃迁吸收波长与体系大小n的解析关系式,以及SC2nS2－体系第一电离能与体系大小n的解析表达式,并讨论了不同端位原子对碳链体系激发态性质的影响.     

Chromium-doped germanium clusters CrGen (n = 1-5): geometry, electronic structure, and topology of chemical bonding

The structure and properties of small neutral and cationic CrGen(0,+) clusters, with n from 1 to 5, were investigated using quantum chemical calculations at the CASSCF/CASPT2 and DFT/B3LYP levels. Smaller clusters prefer planar geometries, whereas the lowest-lying electronic states of the neutral CrGe4, CrGe5, and cationic CrGe5+ forms exhibit nonplanar geometries. Most of the clusters considered prefer structures with high-spin ground state and large magnetic moments. Relative to the values obtained for the pure Gen clusters, fragmentation energies of doped CrGen clusters are smaller when n is 3 and 4 and larger when n = 5. The averaged binding energy tends to increase with the increasing number of Ge atoms. For n = 5, the binding energies for Ge5, CrGe5, and CrGe5+ are similar to each other, amounting to approximately 2.5 eV. The Cr atom acts as a general electron donor in neutral CrGen clusters. Electron localization function (ELF) analyses suggest that the chemical bonding in chromium-doped germanium clusters differs from that of their pure or Li-doped counterparts and allow the origin of the inherent high-spin ground state to be understood. The differential DeltaELF picture, obtained in separating both alpha and beta electron components, is consistent with that derived from spin density calculations. For CrGen, n = 2 and 3, a small amount of d-pi back-donation is anticipated within the framework of the proposed bonding model.     

An ab initio investigation on (CO2)n and CO2(Ar)m clusters: geometries and IR spectra

An ab initio investigation on CO(2) homoclusters is done at MPWB1K6-31++G(2d) level of theory. Electrostatic guidelines are found to be useful for generating initial structures of (CO(2))(n) clusters. The ab initio minimum energy geometries of (CO(2))(n) with n=2-8 are T shaped, cyclic, trigonal pyramidal, tetragonal pyramidal, tetragonal bipyramidal, pentagonal bipyramidal, and pentagonal bipyramid with one CO(2) molecule attached to it. A test calculation on (CO(2))(20) cluster is also reported. The geometric parameters of the energetically most favored (CO(2))(n) clusters match quite well their experimental counterparts (wherever available) as well as those derived from molecular dynamics studies. The effect of clustering is quantified through the asymmetric C-O stretching frequency shift relative to the single CO(2) molecule. (CO(2))(n) clusters show an increasing blueshift from 1.8 to 9.6 cm(-1) on increasing number of CO(2) molecules from n=2 to 8. The energetics and geometries of CO(2)(Ar)(m) clusters have also been explored at the same level of theory. The geometries for m=1-6 show a predominant T type of the argon-CO(2) molecule interaction. Higher clusters with m=7-12 show that the argon atoms cluster around the oxygen atom after the saturation of the central carbon atom. The CO(2)(Ar)(m) clusters exhibit an increasing redshift in the C-O asymmetric stretch relative to CO(2) molecule of 0.7-5.6 cm(-1) with increasing number of argon atoms through m=1-8.     

Prediction of a family of cage-shaped boric acid clusters

Equilibrium geometries, energies, and vibrational frequencies of cage-shaped boric acid clusters including the onion-like structure have been calculated at the HF/6-31G and B3LYP/6-31G(d) levels of theory. A family of cage-shaped boric acid clusters becomes evident according to our calculations. Each member of the family is formed by strong O-H...O hydrogen bonds. Higher cage-shaped boric acid clusters are more stable. The calculated stabilization energies for the cage-shaped boric acid clusters appear to steadily increase with the number of boric acid molecules (n) and are nearly linear in n. Similarities between cage-shaped boric acid clusters and fullerenes are also discussed.     

Density Functional Theory Study on the Structural and Electronic Properties of Ge（SiO_2）_n Clusters

The geometry,stability,binding energy and electronic properties of(SiO2)n and Ge(SiO2)n clusters(n = 7) have been investigated by Density functional theory(DFT).The results show that the lowest energy structures of Ge(SiO2)n are obtained by adding one Ge on the end site of the O atom or the Si near end site of the O atom in(SiO2)n.The chemical activation of Ge-(SiO2)n is improved compared with(SiO2)n.The calculated second-order difference of energies and fragmentation energies show that the Ge(SiO2)n clusters with n = 2 or 5 are stable.     

Self-consistent field tight-binding model for neutral and (multi-) charged carbon clusters

A semiempirical model for carbon clusters modeling is presented, along with structural and dynamical applications. The model is a tight-binding scheme with additional one- and two-center distance-dependent electrostatic interactions treated self-consistently. This approach, which explicitly accounts for charge relaxation, allows us to treat neutral and (multi-) charged clusters not only at equilibrium but also in dissociative regions. The equilibrium properties, geometries, harmonic spectra, and relative stabilities of the stable isomers of neutral and singly charged clusters in the range n=1-14, for C(20) and C(60), are found to reproduce the results of ab initio calculations. The model is also shown to be successful in describing the stability and fragmentation energies of dictations in the range n=2-10 and allows the determination of their Coulomb barriers, as examplified for the smallest sizes (C(2) (2+),C(3) (2+),C(4) (2+)). We also present time-dependent mean-field and linear response optical spectra for the C(8) and C(60) clusters and discuss their relevance with respect to existing calculations.     

Geometries, stabilities, and growth patterns of the bimetal Mo2-doped Sin (n=9-16) clusters: a density functional investigation

The behaviors of the bimetal Mo-Mo doped cagelike silicon clusters Mo2Sin at the size of n=9-16 have been investigated systematically with the density functional approach. The growth-pattern behaviors, relative stabilities, and charge-transfer of these clusters are presented and discussed. The optimized geometries reveal that the dominant growth patterns of the bimetal Mo-Mo doped on opened cagelike silicon clusters (n=9-13) are based on pentagon prism MoSi10 and hexagonal prism MoSi12 clusters, while the Mo2 encapsulated Sin(n=14-16) frames are dominant growth behaviors for the large-sized clusters. The doped Mo2 dimer in the Sin frames is dissociated under the interactions of the Mo2 and Sin frames which are examined in term of the calculated Mo-Mo distance. The calculated fragmentation energies manifest that the remarkable local maximums of stable clusters are Mo2-doped Sin with n=10 and 12; the obtained relative stabilities exhibit that the Mo2-doped Si10 cluster is the most stable species in all different sized clusters. Natural population analysis shows that the charge-transfer phenomena appearing in the Mo2-doped Sin clusters are analogous to the single transition metal Re or W doped silicon clusters. In addition, the properties of frontier orbitals of Mo2-doped Sin (n=10 and 12) clusters show that the Mo2Si10 and Mo2Si12 isomers have enhanced chemical stabilities because of their larger HOMO-LUMO gaps. Interestingly, the geometry of the most stable Mo2Si9 cluster has the framework which is analogous to that of Ni2Ge9 cluster confirmed by recent experimental observation (Goicoechea, J. M.; Sevov, S. C. J. Am Chem. Soc. 2006, 128, 4155).     

Superhalogen properties of CumCln clusters: theory and experiment

Using a combination of density functional theory and anion photoelectron spectroscopy experiment, we have studied the structure and electronic properties of CuCl(n)(-) (n = 1-5) and Cu(2)Cl(n)(-) (n = 2-5) clusters. Prominent peaks in the mass spectrum of these clusters occurring at n = 2, 3, and 4 in CuCl(n)(-) and at n = 3, 4, and 5 in Cu(2)Cl(n)(-) are shown to be associated with the large electron affinities of their neutral clusters that far exceed the value of Cl. While CuCl(n) (n ≥ 2) clusters are conventional superhalogens with a metal atom at the core surrounded by halogen atoms, Cu(2)Cl(n) (n ≥ 3) clusters are also superhalogens but with (CuCl)(2) forming the core. The good agreement between our calculated and measured electron affinities and vertical detachment energies confirm not only the calculated geometries of these superhalogens but also our interpretation of their electronic structure and relative stability.