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.     

Computational investigation of TiSin (n=2-15) clusters by the density-functional theory

The geometries, stabilities, and electronic properties of TiSin (n=2-15) clusters with different spin configurations have been systematically investigated by using density-functional theory approach at B3LYP/LanL2DZ level. According to the optimum TiSin clusters, the equilibrium site of Ti atom gradually moves from convex to surface, and to a concave site as the number of Si atom increases from 2 to 15. When n=12, the Ti atom in TiSi12 completely falls into the center of the Si outer frame, forming metal-encapsulated Si cages, which can be explained by using 16-electron rule. On the basis of the optimized geometries, various energetic properties are calculated for the most stable isomers of TiSin clusters, including the average binding energy, the highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO-LUMO) gap, fragmentation energy, and the second-order difference of energy. It is found that at size n=6,8,12 the clusters are more stable than neighboring ones. According to the Mulliken charge population analysis, charges always transfer from Si atoms to Ti atom. Furthermore, the HOMO-LUMO gaps of the most stable TiSin clusters are usually smaller than those of Sin clusters.     

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.     

Trends in structural, electronic and energetic properties of bimetallic vanadium-gold clusters Au(n)V with n = 1-14

A systematic quantum chemical investigation on the electronic, geometric and energetic properties of Au(n)V clusters with n = 1-14 in both neutral and anionic states is performed using BP86/cc-pVTZ-PP calculations. Most clusters having an even number of electrons prefer a high spin state. For odd-electron systems, a quartet state is consistently favoured as the ground state up to Au(8)V. The larger sized Au(10)V, Au(12)V and Au(14)V prefer a doublet state. The clusters prefer 2D geometries up to Au(8)V involving a weak charge transfer. The larger systems bear 3D conformations with a more effective electron transfer from Au to V. The lowest-energy structure of a size Au(n)V is built upon the most stable form of Au(n-1)V. During the growth, V is endohedrally doped in order to maximize its coordination numbers and augment the charge transfer. Energetic properties, including the binding energies, embedding energies and second-order energy differences, show that the presence of a V atom enhances considerably the thermodynamic stability of odd-numbered gold clusters but reduces that of even-numbered systems. The atomic shape has an apparently more important effect on the clusters stability than the electronic structure. Especially, if both atomic shape and electronic condition are satisfied, the resulting cluster becomes particularly stable such as the anion Au(12)V(-), which can thus combine with the cation Au(+) to form a superatomic molecule of the type [Au(12)V]Au. Numerous lower-lying electronic states of these clusters are very close in energy, in such a way that DFT computations cannot clearly establish their ground electronic states. Calculated results demonstrate the existence of structural isomers with comparable energy content for several species including Au(9)V, Au(10)V, Au(13)V and Au(14)V.     

Effect of Ni and Pd on the geometry, electronic properties, and active sites of copper clusters

The geometry, electronic properties, and active sites of copper clusters doped with Ni or Pd atoms, Cu(n)()(-)(1)M (n = 2-6; M = Ni, Pd) have been investigated using first-principles methods. Planar structures are energetically favorable in Cu(n)()(-)(1)Ni (n = 2-6). However, for Pd-doped clusters, three-dimensional structures are competitive in energy, and for n = 6, the most stable structure is not planar. Several properties of doped copper clusters present odd-even oscillations as the number of copper atoms grow. The different atomic ground-state configuration of Ni and Pd determines the bonding and electronic properties of doped copper clusters. The interaction between impurities and copper atoms can modify the chemical hardness and active sites of doped copper clusters markedly inducing directionality in the reactivity. This effect is relevant to the behavior of catalysts as well as in the growth of metallic films.     

Evolution of the properties of Al(n)N(n) clusters with size

A global optimization of stoichiometric (AlN)(n) clusters (n = 1-25, 30, 35, ..., 95, 100) has been performed using the basin-hopping (BH) method and describing the interactions with simple and yet realistic interatomic potentials. The results for the smaller isomers agree with those of previous electronic structure calculations, thus validating the present scheme. The lowest-energy isomers found can be classified in three different categories according to their structural motifs: (i) small clusters (n = 2-5), with planar ring structures and 2-fold coordination, (ii) medium clusters (n = 6-40), where a competition between stacked rings and globular-like empty cages exists, and (iii) large clusters (n > 40), large enough to mix different elements of the previous stage. All the atoms in small and medium-sized clusters are in the surface, while large clusters start to display interior atoms. Large clusters display a competition between tetrahedral and octahedral-like features: the former lead to a lower energy interior in the cluster, while the latter allow for surface terminations with a lower energy. All of the properties studied present different regimes according to the above classification. It is of particular interest that the local properties of the interior atoms do converge to the bulk limit. The isomers with n = 6 and 12 are specially stable with respect to the gain or loss of AlN molecules.     

Geometries, stabilities, and electronic properties of Pt-group-doped gold clusters, their relationship to cluster size, and comparison with pure gold clusters

A systematic study of bimetallic Au(n)M(2) (n = 1-6, M = Ni, Pd, and Pt) clusters is performed by using density functional theory at the B3LYP level. The geometric structures, relative stabilities, HOMO-LUMO gaps, natural charges and electronic magnetic moments of these clusters are investigated, and compared with pure gold clusters. The results indicate that the properties of Au(n)M(2) clusters for n = 1-3 diverge more from pure gold clusters, while those for n = 4-6 show good agreement with Au(n) clusters. The dissociation energies, the second-order difference of energies, and HOMO-LUMO energy gaps, exhibiting an odd-even alternation, indicate that the Au(4)M(2) clusters are the most stable structures for Au(n)M(2) (n = 1-6, M = Ni, Pd, and Pt) clusters. Moreover, we predict that the average atomic binding energies of these clusters should tend to a limit in the range 1.56-2.00 eV.     

A G3 study of the structure of carbon-nitrogen nanoclusters

Possible structures of the carbon-nitrogen clusters of the form C(m)N(n) (m = 1-4, n = 1-4, m + n = 2-5) were predicted for the neutral, anion, and cation species in the singlet, doublet, and triplet states, whenever appropriate. The calculations were performed at the G3, MP2(fc)/6-311+G*, and B3LYP/6-311+G* levels of theory. Several molecular properties related to the experimental data--such as the electronic energy, equilibrium geometry, binding energy, HOMO-LUMO gap (HLG), and spin contamination --were calculated. In addition the vertical electron attachment, the adiabatic electron affinity, and vertical ionization energy, of the neutral clusters were calculated. Most of the predicted lowest energy structures were linear, whereas bent structures became more stable with the increase of the cluster size and increase of the number of the N atoms. In most of the predicted lowest energy structures, the N atom prefers the terminal position with acetylenic bond. The calculated BE of the predicted clusters increases with the increase of the cluster size for the neutral and cation clusters but decreases with the increase of the cluster size for the anion clusters. The predicted clusters are characterized by high HLG of about 11 eV on the average, with that of the anion clusters is smaller than that for the neutral and cation clusters. It is concluded then that the anion clusters are less stable than the corresponding neutral and cation clusters. Finally, the N(2) loss reaction is treated.     

First-principles local density approximation (generalized gradient approximation) +U study of catalytic CenOm clusters: U value differs from bulk

Ceria possesses strong catalytic properties for CONO(x) removal and H(2) production. Clusters often show more intriguing functionalities than their bulk counterparts. Here, the geometric and electronic structures of Ce(n)O(m) (n=1-4,m=2n-1,2n) clusters are studied for the first time using the projected augmented wave method in density functional theory with detailed assessment of the exchange-correlation functional and the Hubbard parameter U. We note that the U value strongly affects the electronic structures of the oxygen-deficient Ce(n)O(2n-1) clusters, though less so on the stoichiometric Ce(n)O(2n). Furthermore, the local density approximation (LDA)+U method is more accurate than the generalized gradient approximation+U in describing the localization of the 4f electrons of the Ce(n)O(m) clusters. The calculated vibration frequency of the CeO molecule with the LDA+U (U=4 eV) is 818.4 cm(-1), in close agreement with experimental values of 820-825 cm(-1) for the low lying states. Different optimal U values were noted for the ceria cluster (4 eV) and its bulk (6 eV), due to quantum-size and geometric effects. The largely reduced formation energy of an oxygen vacancy indicates that the catalytic effect of the Ce(n)O(m) clusters are far greater than bulk CeO(2).     

FMBen（FM=Fe,Co,Ni;n=1-12）团簇结构和电子性质

采用密度泛函理论中的广义梯度近似对FMBen(FM=Fe,Co,Ni;n=1-12)团簇的几何构型进行优化,并对能量、频率和磁性进行了计算,同时考虑了电子的自旋多重度.结果表明,纯铍团簇的幻数是由电子的壳层模型确定,而FMBen团簇的幻数主要由几何效应来解释;掺杂铁磁性的过渡金属(Fe,Co,Ni)提高了纯团簇的稳定性.二阶能量差分表明FMBen(FM=Fe,Co,Ni)的幻数分别为5,10;5,10;4,10.通过对磁性质的研究发现掺杂不同的过渡金属时,磁矩出现了不同的变化规律.     

FMBen(FM=Fe,Co, Ni; n=1-12)团簇结构和电子性质

采用密度泛函理论中的广义梯度近似对FMBen(FM=Fe, Co, Ni; n=1-12)团簇的几何构型进行优化, 并对能量、频率和磁性进行了计算, 同时考虑了电子的自旋多重度. 结果表明, 纯铍团簇的幻数是由电子的壳层模型确定, 而FMBen团簇的幻数主要由几何效应来解释; 掺杂铁磁性的过渡金属(Fe, Co, Ni)提高了纯团簇的稳定性. 二阶能量差分表明FMBen(FM=Fe, Co, Ni)的幻数分别为5, 10; 5, 10; 4, 10. 通过对磁性质的研究发现掺杂不同的过渡金属时, 磁矩出现了不同的变化规律.     

Evolution of the electronic properties of Snn- clusters (n=4-45) and the semiconductor-to-metal transition

The electronic structure of Sn(n) (-) clusters (n=4-45) was examined using photoelectron spectroscopy at photon energies of 6.424 eV (193 nm) and 4.661 eV (266 nm) to probe the semiconductor-to-metal transition. Well resolved photoelectron spectra were obtained for small Sn(n) (-) clusters (n< or =25), whereas more congested spectra were observed with increasing cluster size. A distinct energy gap was observed in the photoelectron spectra of Sn(n) (-) clusters with n< or =41, suggesting the semiconductor nature of small neutral tin clusters. For Sn(n) (-) clusters with n> or =42, the photoelectron spectra became continuous and no well-defined energy gap was observed, indicating the onset of metallic behavior for the large Sn(n) clusters. The photoelectron spectra thus revealed a distinct semiconductor-to-metal transition for Sn(n) clusters at n=42. The spectra of small Sn(n) (-) clusters (n< or =13) were also compared with those of the corresponding Si(n) (-) and Ge(n) (-) clusters, and similarities were found between the spectra of Sn(n) (-) and those of Ge(n) (-) in this size range, except for Sn(12) (-), which led to the discovery of stannaspherene (the icosahedral Sn(12) (2-)) previously [L. F. Cui et al., J. Am. Chem. Soc. 128, 8391 (2006)].     

A theoretical study on small iridium clusters: structural evolution, electronic and magnetic properties, and reactivity predictors

The structural, electronic, and magnetic properties of iridium clusters with sizes of n = 2-15 are investigated by employing the generalized gradient approximation of density functional theory. Simple cube evolution pattern is revealed for Ir(2-15) clusters, as predicted by previous reports. It is remarkable that for Ir(10), Ir(11) clusters, new generated isomers with higher stabilities relative to those reported in previous studies are obtained. The even-sized clusters are more stable than the odd-sized species. The Ir-Ir bonds in the cubic Ir(8) and Ir(12) clusters, which are considered as the basic units in the structural evolution present covalent character. Starting from n = 8, the magnetic moments of Ir(n) clusters decrease sharply. The moments of magnetic clusters show 5d characters. The reactive site selectivity of studied clusters with n = 5-15 is analyzed with condensed Fukui function. The capped atoms in certain clusters (Ir(9), Ir(10), Ir(11), and Ir(13)) generally show extraordinary activity for both nucleophilic and electrophilic attack.     

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

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

Growth pattern and electronic properties of acetonitrile clusters: a density functional study

We report a systematic theoretical study on the growth pattern and electronic properties of acetonitrile clusters [(CH(3)CN)(n) (n = 1, 9, 12)] using density functional approach at the B3LYP6-31++G(d,p) level. Although we have considered a large number of configurations for each cluster, the stability of the lowest energy isomer was verified from the Hessian calculation. It is found that the lowest energy isomer of the dimer adopts an antiparallel configuration. For trimer and tetramer, cyclic ring structures were found to be favored over the dipole stabilized structure. In general, it is found that the intermolecular CH...N interactions play a significant role in the stabilization of the cyclic layered geometry of acetonitrile clusters. A critical comparison between trimer and tetramer clusters suggests that the three member cyclic ring is more stable than four member rings. The growth motif for larger clusters (n = 5-9, 12) follows a layered pattern consisting of three or four membered rings, which, in fact, is used as the building block. Based on the stability analysis, it is found that clusters with an even number of molecular entities are more stable than the odd clusters, except trimer and nonamer. The exceptional stability of these two clusters is attributed to the formation of trimembered cyclic rings, which have been found to form the building blocks for larger clusters.     

Time-resolved intraband electronic relaxation dynamics of Hg(n) (-) clusters (n=7-13,15,18) excited at 1.0 eV

Time-resolved photoelectron imaging has been used to study the relaxation dynamics of small Hg(n) (-) clusters (n=7-13,15,18) following intraband electronic excitation at 1250 nm (1.0 eV). This study furthers our previous investigation of single electron, intraband relaxation dynamics in Hg(n) (-) clusters at 790 nm by exploring the dynamics of smaller clusters (n=7-10), as well as those of larger clusters (n=11-13,15,18) at a lower excitation energy. We measure relaxation time scales of 2-9 ps, two to three times faster than seen previously after 790 nm excitation of Hg(n) (-), n=11-18. These results, along with size-dependent trends in the absorption cross-section and photoelectron angular distribution anisotropy, suggest significant evolution of the cluster anion electronic structure in the size range studied here. Furthermore, the smallest clusters studied here exhibit 35-45 cm(-1) oscillations in pump-probe signal at earliest temporal delays that are interpreted as early coherent nuclear motion on the excited potential energy surfaces of these clusters. Evidence for evaporation of one or two Hg atoms is seen on a time scale of tens of picoseconds.     

The Kohn-Sham density of states and band gap of water: from small clusters to liquid water

Electronic properties of water clusters (H2O)(n), with n=2, 4, 8, 10, 15, 20, and 30 molecules were investigated by sequential Monte Carlo/density-functional theory (DFT) calculations. DFT calculations were carried out over uncorrelated configurations generated by Monte Carlo simulations of liquid water with a reparametrized exchange-correlation functional that reproduces the experimental information on the electronic properties (first ionization energy and highest occupied molecular orbital-lowest unoccupied molecular orbital gap) of the water dimer. The dependence of electronic properties on the cluster size (n) shows that the density of states (DOS) of small water clusters (n>10) exhibits the same basic features that are typical of larger aggregates, such as the mixing of the 3a1 and 1b1 valence bands. When long-ranged polarization effects are taken into account by the introduction of embedding charges, the DOS associated with 3a1 orbitals is significantly enhanced. In agreement with valence-band photoelectron spectra of liquid water, the 1b1, 3a1, and 1b2 electron binding energies in water aggregates are redshifted by approximately 1 eV relative to the isolated molecule. By extrapolating the results for larger clusters the threshold energy for photoelectron emission is 9.6+/-0.15 eV (free clusters) and 10.58+/-0.10 eV (embedded clusters). Our results for the electron affinity (V0=-0.17+/-0.05 eV) and adiabatic band gap (E(G,Ad)=6.83+/-0.05 eV) of liquid water are in excellent agreement with recent information from theoretical and experimental works.     

Theoretical study of Al(n) and Al(n)O (n = 2-10) clusters

The stable structures, energies, and electronic properties of neutral, cationic, and anionic clusters of Al(n) (n = 2-10) are studied systematically at the B3LYP/6-311G(2d) level. We find that our optimized structures of Al5(+), Al9(+), Al9(-), Al10, Al10(+), and Al10(-) clusters are more stable than the corresponding ones proposed in previous literature reports. For the studied neutral aluminum clusters, our results show that the stability has an odd/even alternation phenomenon. We also find that the Al3, Al7, Al7(+), and Al7(-) structures are more stable than their neighbors according to their binding energies. For Al7(+) with a special stability, the nucleus-independent chemical shifts and resonance energies are calculated to evaluate its aromaticity. In addition, we present results on hardness, ionization potential, and electron detachment energy. On the basis of the stable structures of the neutral Al(n) (n = 2-10) clusters, the Al(n)O (n = 2-10) clusters are further investigated at the B3LYP/6-311G(2d), and the lowest-energy structures are searched. The structures show that oxygen tends to either be absorbed at the surface of the aluminum clusters or be inserted between Al atoms to form an Al(n-1)OAl motif, of which the Al(n-1) part retains the stable structure of pure aluminum clusters.     

Structures, rugged energetic landscapes, and nanothermodynamics of Al(n) (2 <or= n <or= 65) particles

Metal nanoparticles are important in several emerging technologies, but their size-selected thermodynamic properties are hard to obtain from experiment. We have characterized the energetic and structural properties of unsupported neutral Aln (2 相似文献