Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.     

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.     

Stable Tin (n = 2-15) clusters and their geometries: DFT calculations

We present a detailed structural analysis for small Tin (n = 2-15) clusters based on ab initio quantum mechanical calculations of their binding energies, frontier orbital gaps, and second energy derivatives. Local density approximation calculations revealed that while the smaller clusters (n < or = 8) prefer hexagonal atomic arrays with bulklike crystal symmetry, the bigger clusters prefer pentagonal atomic arrays. From the stability criteria of the magic number clusters we could identify three magic number clusters Ti7, Ti13, and Ti15. While the most stable configuration of Ti7 is a decahedral bipyramid induced by tetrahedral atomic arrays, the most stable configuration of Ti13 is an icosahedron. The other stable cluster Ti15 takes a closed-shell icosahedron-like configuration with both pentagonal and hexagonal symmetries. The stability of the Tin clusters strongly depends on their geometries and charge states. The HOMO-LUMO gap of the Tin clusters approaches its bulk value for n > 8. While there is not much difference between the HOMO and LUMO isosurface charge distributions for the Ti7 and Ti13 clusters in their most stable configurations, they are very different in the case of Ti15. Such a distinct charge distribution in Ti15 indicates its singular chemical selectivity over the other two magic number clusters.     

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.     

Electronic structure calculations of small Al n (n=2–8) clusters

The electronic states of small Al _n (n=2–8) clusters have been calculated with a relativistic ab-initio MO-LCAO Dirac-Fock-Slater method using numerical atomic DFS wave-functions. The excitation energies were obtained from a ground state calculation of neutral clusters, and in addition from negative clusters charged by half an electron in order to account for part of the relaxation. These energies are compared with experimental photo-electron spectra.     

Structures, spectra, and energies of niobium clusters from Nb13 to Nb20

A comprehensive theoretical investigation on structures and properties of niobium clusters in the range from 13 to 20 atoms, in three different charged states, is performed by using the BPW91 and M06 functionals and the cc-pVDZ-PP basis set. These species are predicted to prefer low spin ground state, i.e., singlet (for even electron) and doublet (for odd electron) systems. In terms of growth mechanism, a compact structure with one Nb encapsulated by a cage formed from five and six triangles is found to be favored over an icosahedral evolution. Unlike many 3d metals, whose volumes are much smaller, 13 and 19 Nb atoms clusters do not exist as icosahedra and double-icosahedra. A distinct case is Nb(15) as it bears a slightly distorted bcc structure. For some systems, several lower lying isomers are computed to be so close in energy that DFT computations cannot clearly establish their ground electronic states. The existence of structural isomers with comparable energy content is established for Nb(n) species with n = 13, 18, 19, and 20 in both neutral and charged states. The vibrational (IR) spectra are also calculated. While the spectra of smaller systems are strongly dependent on addition or removal of an electron from the neutral, the spectra of the larger size clusters are mostly independent of the charged state. The neutrals and their corresponding ions usually have a quite similar IR pattern. Electron affinities (EA), ionization energies (IE), average binding energies, dissociation energies, and frontier orbital energy gaps are evaluated. The computed EAs and IEs are generally in fair agreement with experiment. The Nb(15) system is observed to be stable and it can form a highly symmetric structure in all charged states with both open and closed electron shells.     

Adsorption of small Au(n) (n = 1-5) and Au-Pd clusters inside the TS-1 and S-1 pores

We used a hybrid quantum-mechanics/molecular-mechanics (QM/MM) approach to simulate the adsorption of Au(n)() (n = 1-5), AuPd, and Au(2)Pd(2) clusters inside the TS-1 and S-1 pores. We studied nondefect and metal-vacancy defect sites in TS-1 and S-1 for a total of four different environments around the T6 crystallographic site. We predict stronger binding of all clusters near Ti sites in Ti-substituted framework compared to adsorption near Si sites-consistent with the experimental finding of a direct correlation between the Ti-loading and the Au-loading on the Au/TS-1 catalysts with high Si/Ti ratio. The cluster binding is also stronger near lattice-metal vacancies compared to fully coordinated, nondefect sites. In all the cases, a trend of binding energy (BE) versus Au cluster size (n) shows a peak at around n = 3-4. Our results show that there is enough room for the attack of H(2)O(2) on the Ti-defect site even with Au(1-4) adsorbed-a result that supports the possibility of H(2)O(2) spillover from the Au clusters to the adjacent Ti-defect sites. Mulliken charge analysis indicates that in all the cases there is electron density transfer to adsorbed clusters from the zeolite lattice. In the case of both gas-phase and adsorbed Au-Pd clusters, all the Pd atoms were positively charged, and all the Au atoms were negatively charged due to the higher electron-affinity of Au. We also found a correlation between the BE and the charge transfer to the clusters (the higher the charge transfer to the clusters, the higher the BE), and a universal correlation was found for Au(2-5) when BE and charge transfer were plotted on a per atom basis. A relatively larger charge transfer to the adsorbed clusters was found for the Ti sites versus the Si sites, and for the defect sites versus the nondefect sites. The trends in the BE were corroborated using Gibbs free energy of adsorption (DeltaG(ads)), and the implications of DeltaG(ads) in sintering of Au clusters are also discussed. Our results confirm that electronic factors such as cluster-charging are potentially important support effects for the Au/TS-1 catalyst.     

Electronic excitation spectra of the [Ir(ppy)2(bpy)]+ photosensitizer bound to small silver clusters Ag(n) (n = 1-6)

The changes in nature and order of the excited electronic states of the photosensitizer [Ir(ppy)(2)(bpy)](+) upon binding to small silver clusters, Ag(n) (n = 1-6), were studied theoretically using the linear response TDDFT method with the range-separated LC-BLYP functional. Binding energies and localization of HOMO and LUMO orbitals are found to oscillate with the number of silver atoms. Special emphasis is put on the discussion of long-range charge transfer transitions between the photosensitizer and the silver cluster. The energies of these transitions were found to be only slightly dependent on the relative orientations of both fragments, but strongly dependent on the intermolecular distance. The absorption spectrum of the combined system does not show a systematic trend with respect to cluster size, but it is strongly modified by the charge transfer transitions. Possible photophysical processes of the systems containing larger clusters are discussed.     

Theoretical study of oxygen adsorption on pure Au(n+1)+ and doped MAu(n)+ cationic gold clusters for M = Ti, Fe and n = 3-7

A comparative study of the adsorption of an O2 molecule on pure Au(n+1)+ and doped MAu(n)+ cationic gold clusters for n = 3-7 and M = Ti, Fe is presented. The simultaneous adsorption of two oxygen atoms also was studied. This work was performed by means of first principles calculations based on norm-conserving pseudo-potentials and numerical basis sets. For pure Au4 +, Au6+, and Au7+ clusters, the O2 molecule is adsorbed preferably on top of low coordinated Au atoms, with an adsorption energy smaller than 0.5 eV. Instead, for Au5+ and Au8+, bridge adsorption sites are preferred with adsorption energies of 0.56 and 0.69 eV, respectively. The ground-state geometry of Au(n)+ is almost unperturbed after O2 adsorption. The electronic charge flows towards O2 when the molecule is adsorbed in bridge positions and towards the gold cluster when O2 is adsorbed on top of Au atoms, and both the adsorption energy and the O-O bond length of adsorbed oxygen increase when the amount of electronic charge on O2 increases. On the other hand, we studied the adsorption of an O2 molecule on doped MAu(n)+ clusters, leading to the formation of (MAu(n)O2+) ad complexes with different equilibrium configurations. The highest adsorption energy was obtained when both atoms of O2 bind on top of the M impurity, and it is larger for Ti doped clusters than for Fe doped clusters, showing an odd-even effect trend with size n, which is opposite for Ti as compared to Fe complexes. For those adsorption configurations of (MAu(n)O2+) ad involving only Au sites, the adsorption energy is similar to or smaller than that for similar configurations of Au(n)+1O2 + complexes. However, the highest adsorption energy of (MAu(n)O2+) ad is higher than that for (Au(n)+1O2+) ad by a factor of approximately 4.0 (1.2) for M = Ti (M = Fe). The trends with size n are rationalized in terms of O-O and O-M bond distances, as well as charge transfer between oxygen and cluster substrates. The spin multiplicity of those (MAu(n)O2+) ad complexes with the highest O2 adsorption energy is a maximum (minimum) for M = Fe (Ti), corresponding to parallel (anti-parallel) spin coupling of MAu(n)+ clusters and O2 molecules. Finally, we obtained the minimum energy equilibrium structure of complexes (Au(n)O2+) dis and (MAu(n)O2+) dis containing two separated O atoms bonded at different sites of Au(n)+ and MAu(n)+ clusters, respectively. For (MAu(n)O2 (+)) dis, the equilibrium configuration with the highest adsorption energy is stable against separation in MAu(n)+ and O2 fragments, respectively. Instead, for (Au(n)O2+) dis, only the complex n = 6 is stable against separation in Au(n)+ and O2 fragments. The maximum separation energy of (MAu(n)O2+) dis is higher than the O2 adsorption energy of (MAu(n)O2+) ad complexes by factors of approximately 1.6 (2.5), 1.6 (1.7), 1.5 (2.4), 1.5 (1.3), and 1.6 (1.8) for M = Ti (Fe) complexes in the range n = 3-7, respectively.     

Small carbon clusters doped with early transition metals: a theoretical study of ScCn, ScCn+, and ScCn- (n = 1-8) open-chain clusters

A theoretical study of the ScCn, ScCn+, and ScCn- (n = 1-8) open-chain clusters has been carried out. Predictions for their electronic energies, rotational constants, dipole moments and vibrational frequencies have been made using the B3LYP method with different basis set including effective core potentials, ECPs. For the ScCn open-chain clusters the lowest-lying states correspond to quartet states for n-odd members, whereas for n-even species the ground state is found to be a doublet. In the cationic and anionic species, the electronic ground state is found to be a singlet for even n and a triplet for odd n. An even-odd parity effect (n-even clusters being more stable than n-odd ones) is observed in neutral and charged clusters. Ionization energies and electron affinities also exhibit a clear parity alternation trend, with n-even clusters having higher values than n-odd ones.     

Geometric and electronic structures of multiple-decker one-end open sandwich clusters: Eu(n)(C8H8)n- (n = 1-4)

We have measured the photoelectron spectra of the multiple-decker 1:1 sandwich clusters of Eu(n)(COT)n- (n = 1-4; COT = 1,3,5,7-cyclooctatetraene), synthesized in the gas phase, and studied theoretically the bonding scheme, charge distribution, valence orbital energies, and photodetachment energies. We calculated the ground electronic state X- and the first excited electronic state A-, both of which have strong ionic bonding and a characteristic charge distribution. Moreover, we found that the valence orbital energies of Eu (6s) and COT (L delta) depend strongly on cluster size and their positions in the clusters. With the calculated vertical detachment energies for these valence orbitals, we assigned the peaks in the experimental photoelectron spectra and analyzed the origin of their interesting behavior by employing simple point charge models. From these analyses, it became clear that the characteristic behavior of the spectra is due to the strong ionic bonding and the charge distribution. In addition, using the point charge models, we estimated the vertical detachment energies of the one-dimensional polymer [Eu(COT)]infinity-.     

AlnO2±团簇结构的几何特征与稳定性

采用密度泛函理论(DFT)的B3LYP方法,在6-311G**水平上对AlnO2±(n=1-10)团簇的几何和电子结构进行了理论计算.讨论了混合团簇的基态结构与振动频率,以及电荷转移与分子轨道.结果表明,AlnO2±(n>1)团簇的基态结构都是2个较小的AlmO(m相似文献   

A new magic titanium-doped gold cluster and orientation dependent cluster-cluster interaction

The stability and structures of titanium-doped gold clusters Au(n)Ti (n=2-16) are studied by the relativistic all-electron density-functional calculations. The most stable structures for Au(n)Ti clusters with n=2-7 are found to be planar. A structural transition of Au(n)Ti clusters from two-dimensional to three-dimensional geometry occurs at n=8, while the Au(n)Ti (n=12-16) prefer a gold cage structure with Ti atom locating at the center. Binding energy and second-order energy differences indicate that the Au(14)Ti has a significantly higher stability than its neighbors. A high ionization potential, low electron affinity, and large energy gap being the typical characters of a magic cluster are found for the Au(14)Ti. For cluster-cluster interaction between magic transition-metal-doped gold clusters, calculations were performed for cluster dimers, in which the clusters have an icosahedral or nonicosahedral structure. It is concluded that both electronic shell effect and relative orientation of clusters are responsible for the cluster-cluster interaction.     

Geometrical and electronic structures of Au(m)Ag(n) (2 < or = m + n < or = 8)

The structural and electronic properties of Au(m)Ag(n) binary clusters (2 < or = m + n < or = 8) have been investigated by density functional theory with relativistic effective core potentials. The results indicate that Au atoms tend to occupy the surface of Au(m)Ag(n) clusters (n > or = 2 and m > or = 2). As a result, segregation of small or big bimetallic clusters can be explained according to the atomic mass. The binding energies of the most stable Au(m)Ag(n) clusters increase with increasing m+n. The vertical ionization potentials of the most stable Au(m)Ag(n) clusters show odd-even oscillations with changing m+n. The possible dissociation channels of the clusters considered are also discussed.     

Gold adatoms and clusters on PPV: An ab initio investigation

We have performed an ab initio investigation of the energetic, structural, electronic, and vibrational properties of Au atoms and clusters adsorbed on poly-p-phenylene vinylene (PPV) chains, Au(n)/PPV (with n =?1, 2, 6, 7, 10, and 12). We find that the Au(n)/PPV systems are energetically stable by 0.5 eV, compared with the isolated systems, viz., PPV chain and Au(n) clusters, thus supporting the formation of Au(n)/PPV nanocomposites. Further support to the formation of Au(n)/PPV has been provided by examining the vibrational properties of pristine PPV and Au(n)/PPV systems. In agreement with experimental measurements, we find a reduction on the in-plane vibrational frequency of C-C bonds of Au(n)/PPV, when compared with the same vibrational modes of pristine PPV. The electronic properties of isolated Au(n) clusters are modified when adsorbed on PPV. The highest occupied states of Au(n)/PPV are mostly concentrated on the Au(n) cluster, while the lowest unoccupied states are mainly localized along the PPV chain. The HOMO-LUMO energy gap of the Au(n)/PPV systems are smaller than the energy gap of the isolated systems, Au(n) clusters, and pristime PPV chains.     

Optical properties of (GaAs)n clusters (n = 2-16)

The electronic and geometrical structures of the lowest triplet states of (GaAs) n clusters ( n = 2-16) are studied using density functional theory with generalized gradient approximation (DFT-GGA). It is found that the triplet-state geometries are different from the corresponding singlet-state geometries; for n = 2-8, 10, and 11, the triplets and singlets have different topologies, while the (GaAs) 9, (GaAs) 12, (GaAs) 15, and (GaAs) 16 triplets possess a reduced symmetry, due to Jahn-Teller distortions. Except for GaAs, the singlet states are the ground states. Excitation energies and oscillator strengths are computed for excitations from the ground state to ten singlet states of all (GaAs) n clusters using time-dependent density functional theory. The adiabatic singlet-triplet gap is compared to the vertical gap, and the difference in the eigenvalues of the highest-occupied and lowest-unoccupied molecular orbitals (the HOMO-LUMO gap). While these three values show large oscillations for small n, they approach each other as the cluster size grows. Thus, the HOMO-LUMO gap computed using the DFT-GGA approach presents a rather reliable estimate of the adiabatic singlet-triplet gap.     

金钯二元小团簇的几何结构与电子性质

在UBP86/LANL2DZ和UB3LYP/def2-TZVP水平下详细研究了AumPdn(m+n≤6)团簇的几何结构和电子性质.阐明了团簇的结构特征、平均结合能、垂直电离势、垂直电子亲和能、电荷转移以及成键特征.除单取代混合团簇(AunPd和AuPdn,n=5或6)外,五和六原子混合团簇中钯原子趋于聚集到一起形成Pdcore,金原子分布在Pdcore周围形成PdcoreAushell结构.含一个和两个钯原子团簇的电子性质与纯金团簇类似,呈现一定奇偶振荡.混合团簇的电子性质,如最高占据分子轨道(HOMO),最低未占据分子轨道(LUMO),垂直电离势,垂直电子亲和能,Fermi能级和化学硬度等均与团簇空间结构和金、钯原子数之比直接相关.混合团簇中存在钯原子到金原子间的电荷转移,表明团簇中存在明显金钯间成键作用.分析团簇的电荷分布、前线轨道和化学硬度表明,金钯混合团簇对小分子如O2、H2和CO等的反应活性要强于纯金团簇.     

用密度泛函理论研究ZrnB(n=1-13)团簇的结构及性质

利用密度泛函理论, 得到了ZrnB(n=1-13)团簇的基态结构, 计算并讨论了团簇能量的二阶差分和离解能. 结果表明, n=2, 5, 12时, 相应团簇较稳定, 特别是Zr5B团簇的稳定性最高. 同时分析了ZrnB团簇的电子性质及磁性, 结果显示能隙随n值的增大出现奇偶振荡趋势, 特别是Zr12B团簇的能隙只有0.015 eV, 表明该团簇已具有金属性. 电荷转移随n值增大, 整体呈增大趋势, 除了二聚体ZrB, 电荷由B原子转移到Zr原子. 利用Mulliken布居分析得到二聚体ZrB(5.000 μB)和团簇Zr4B(3.000 μB)的磁矩较大, ZrnB团簇中总磁矩主要来自Zr原子的4d轨道.     

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 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.