Ground state, growth, and electronic properties of small lanthanum clusters

The DMol cluster method based on density-functional theory has been employed to study the structural stability and electronic structure of La(n) (n=2-14) clusters. The ground states have been found out for lanthanum clusters. The Jahn-Teller effect plays an important role in this process because there are many isomers near the ground state. The magnetism is not sensitive to interatomic spacing when the change of interatomic spacing is in a small range. Lanthanum clusters grow in an icosahedral pattern. The results of the mean binding energy, of the second derivative of binding energy, and of the formation energy show strong odd-even alternation and that 7- and 13-atom clusters are magic. Further, the HOMO-LUMO gap, the mean nearest bond lengths, and the mean magnetic moments suggest that the convergence to bulk is slow and it shows an oscillatory behavior for small lanthanum clusters.     

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.     

Phenyl-coinage metal (Ag, Au) complexes: an anion photoelectron spectroscopy and density functional study

The important intermediate phenyl-coinage metal complexes (Ag(m)C6H5(-), Au(m)C6H5(-)), which are produced from the reactions between coinage metal clusters formed by laser ablation and the benzene molecules seeded in argon carrier gas, are studied by PES (photoelectron spectroscopy) and DFT (density functional theory). The EAs (adiabatic electron affinities) of these complexes are obtained from PES at both 308 and 193 nm photon energies and show odd-even alternation. Calculations with DFT are carried out on the structural and electronic properties of Ag(m)C6H5(-) and Au(m)C6H5(-); the adiabatic detachment energy and the calculated DOS (density of states) for the ground state of a given anion are in good agreement with the experimental PES results. The observed spectra are also compared with those of the pure coinage metal clusters, which reveal that there are some similarities between them and the phenyl acts like an additional metal atom in the clusters. Furthermore, the bonding between phenyl and metal is analyzed, suggesting that phenyl group binds perpendicularly on metal clusters through C-M sigma bond.     

Theoretical Study of the Structural,Electronic, and Magnetic Properties of Zirconium-doped Aluminum Clusters:Al_nZr(n = 1～14)

The geometrical structures, stabilities, electronic and magnetic properties of Al_nZr(n = 1~14) clusters have been systematically investigated using density functional theory. It is found that for the optimized clusters the zirconium atom prefers to remain on the surface, and the growth patterns are organized as follows: Zr substituted Al_(n+1) clusters or Zr capped Aln clusters as well as Al added Al_(n-1)Zr clusters. All doped clusters exhibit relatively larger average binding energies and magnetic behaviors compared with pure Al_(n+1) counterpart. The calculated fragmentation energies and second-order difference of energies exhibit pronounced odd-even alternation behavior as a function of the cluster size when n = 3~13. In all Al_nZr clusters, there exits internal hybridization in both Al and Zr atoms and charge transfer from Al to Zr atom, which reflects the strong interactions between the two kinds of atoms. The magnetic property analysis shows that the 4d electrons of Zr atom are the main origin for cluster magnetism.     

Structures and energetics of electrosprayed uracil(n)Ca2+ clusters (n = 14-4) in the gas phase

Clusters of uracil (U) about a calcium dication, U(n)Ca(2+) (n = 14-4), have been studied in the gas phase by both experimental and theoretical methods. Temperature dependent blackbody infrared radiative dissociation (BIRD) experiments were performed on U(n)Ca(2+) clusters with n = 14-5 and the observed Arrhenius parameters are reported here. Master equation modeling of the BIRD kinetics data was carried out to determine threshold dissociation energies. Initial geometry calculations were performed using the B3LYP density functional and 3-21G(d) basis set. A sample of ten conformations per cluster was obtained through a simulated annealing study. These structures were optimized using B3LYP/6-31G(d) level of theory. Fragment-based hybrid many body interaction (HMBI) MP2/6-311++G(2df,2p)/Amoeba calculations were performed on representative conformations to determine theoretical binding energies. Results were examined in relation to cluster size (n). A significant increase in the energy required to remove uracil from U(6)Ca(2+) when compared to larger clusters supports previous reports that the calcium ion is coordinated by six uracil molecules in the formation of an inner shell. For clusters larger than n = 6, an odd-even alternation in threshold dissociation energies was observed, suggesting that the outer shell uracil molecules bind as dimers to the inner core. Proposed binding schemes are presented. Multiple structures of U(5)Ca(2+) are suggested as being present in the gas phase where the fifth uracil may be either part of the first or second solvation shell.     

Density functional study of small neutral and charged silver cluster hydrides

Small neutral, anionic, and cationic silver cluster hydrides AgnH and anionic HAgnH (n=1-7) have been studied using the PW91PW91 density functional method. It was found that the most stable structure of the AgnH complex (neutral or charged) does not always come from that of the lowest energy bare silver cluster plus an attached H atom. Among various possible adsorption sites, the bridge site is energetically preferred for the cationic and most cases of neutral Agn. For anionic Agn, the top site is preferred for smaller Agn within n相似文献   

Exploring the electronic structure of elemental lithium: from small molecules to nanoclusters, bulk metal, and surfaces

Clusters of lithium atoms ranging in size from Li4 to Li40 and bulk metallic solids, including surfaces, are investigated through first principles electronic structure calculations, which are based upon density functional theory and the electron localization function (ELF). It is found that large lithium ppi-type contributions in the electronic wavefunction cause the electrons to localize in interstitial regions, which leads to multicenter bonding for both the clusters and the solids, including their surfaces. For the smaller clusters these stabilizing ppi interactions also lead to short Li-Li interatomic distances, which in conjunction with the longer bonds induces "distance alternation" in the range from 2.45 A to 3.15 A. This consequence of the additional ppi interactions is absent in simple solids due to symmetry. The electronic structure of the clusters is topologically insensitive to deformations that do not affect their general shape, but changes significantly upon isomerization. The ramifications upon dynamic properties is that the clusters are quasi-rigid at low temperatures and retain their shape though the distance alternation pattern is suppressed. The picture which emerges for bonding in the bulk solid is that the metallic state arises from the presence of a large number of partially occupied multicenter bonds. For nanoscale clusters only the surface of these clusters exhibits strong localization, whereas their interiors display localization properties similar to the bulk metallic solid. On the other hand, localized states similar to those of the clusters ("dangling bonds") are found on the (001) surface of body-centered cubic (bcc) and face-centered cubic (fcc) lithium solids.     

Size- and charge-dependent geometric and electronic structures of Bi n (Bi(-)n) clusters (n=2-13) by first-principles simulations

Neutral and negatively charged bismuth clusters, Bi n and Bi(-)n (n=2-13), are investigated by first-principles simulations with the scalar-relativistic projector-augmented wave potential and the spin-polarized generalized gradient approximation. Both types of clusters show size-dependent odd-even oscillations in stability, density of states, and vertical and adiabatic electron affinities, in close agreement with experiment. The negative charge thoroughly reverses the oscillations and considerably influences the geometric structures, particularly of the odd-sized clusters. We note that most atoms in the ground states and the low-lying isomers are three coordinated with a quasilayerlike growth mode based on pentagon units, due to a weak s-p hybridization. The Bi12 cluster is found to prefer a small elongated tubelike structure with the surface consists of six curved-pentagon rings and two triangular facets, which may be the basis for the formation of bismuth nanotubes experimentally reported.     

Density functional study of the interaction of chlorine atom with small neutral and charged silver clusters

Chlorine adsorption on small neutral, anionic, and cationic silver clusters Ag(n) (n=2-7) has been studied using the PW91PW91 density functional method. It was found that the adsorption of chlorine on the lowest-energy bare clusters does not always produce the lowest-energy complexes. In addition, the binding of chlorine can greatly change the geometries of the silver clusters in some cases. Among various possible adsorption sites, bridge site is energetically preferred for the neutral Ag(n) while top site is energetically more preferred for the anionic Ag(n) with n< or =6. For cationic clusters, adsorptions on bridge and face sites have similar binding energies, which are much larger than those on top sites. Natural bond orbital analyses show that irrespective of charge state, electrons always transfer from silver atoms to adsorbate and silver acts like alkali metals in the interaction with chlorine atom. Significant odd-even alternation patterns in the properties of the complexes have been observed: Even-electron clusters often have higher ionization energies, lower electron affinities, and higher dissociation energies than their odd-electron neighbors. It was also found that chlorine atoms bind more strongly with odd-electron bare clusters than with even-electron bare clusters. These patterns reveal that even-electron clusters are more stable than odd-electron clusters.     

Electron-gas clusters: the ultimate jellium model

The local spin-density approximation is used to calculate ground- and isomeric-state geometries of jellium clusters with 2 to 22 electrons. The positive background charge of the model is completely deformable, both in shape and in density. The model has no input parameters. The resulting shapes of the clusters exhibit breaking of axial and inversion symmetries; in general the shapes are far from ellipsoidal. Those clusters which lack inversion symmetry are extremely soft against odd-multipole deformations. Some clusters can be interpreted as molecules built from magic clusters. The deformation produces a gap at the Fermi level. This results in a regular odd-even staggering of the total energy per electron and of the HOMO level. The strongly deformed 14-electron cluster is semimagic. Stable isomers are predicted. The splitting of the plasmon resonance due to deformation is estimated on a classical argument.     

线形碳元素簇合物的成键性质

在ab initio 3-21G水平上, 用能量梯度法优化了线性碳元素簇合物C_n~e(n为成簇原子个数, e为电荷)的平衡几何结构. 所得的电离势随成簇原子个数的改变, 呈现出不同程度的奇偶交替变化趋势. 在ab initio计算基础上, 用Boys方法, 对其占据正则分子轨道进行定域化变换, 得到了它们的定域分子轨道. 对定域分子轨道性质的分析表明, 线性碳元素簇合物中, 主要键型有双中心σ和π健, 双中心弯键和三中心香蕉健, 以及多中心σ和π健. 这种键型的多样化可视为小元素簇的成健特征. 此外, 通过对其成键性质的分析, 讨论了线性碳元素簇的稳定性. 对于小碳元素簇, 化学键的共轭性对其稳定性具有十分显著的作用.     

Analytical time-dependent density functional derivative methods within the RI-J approximation, an approach to excited states of large molecules

Time-dependent density functional theory (TDDFT) is now well established as an efficient method for molecular excited state treatments. In this work, we introduce the resolution of the identity approximation for the Coulomb energy (RI-J) to excited state gradient calculations. In combination with nonhybrid functionals, the RI-J approximation leads to speed ups in total timings of an order of magnitude compared to the conventional method; this is demonstrated for oligothiophenes with up to 40 monomeric units and adamantane clusters. We assess the accuracy of the computed adiabatic excitation energies, excited state structures, and vibrational frequencies on a set of 36 excited states. The error introduced by the RI-J approximation is found to be negligible compared to deficiencies of standard basis sets and functionals. Auxiliary basis sets optimized for ground states are suitable for excited state calculations with small modifications. In conclusion, the RI-J approximation significantly extends the scope of applications of analytical TDDFT derivative methods in photophysics and photochemistry.     

Theoretical investigations on geometrical and electronic structures of silver clusters

Geometrical structures and ground and excited states of silver clusters are theoretically investigated using long-range corrected (LC) density functional theory (DFT) calculations. The discrepancy between HOMO-LUMO gaps and the vertical ionization potential minus vertical electron affinity values, which should be the same values, is explored to reveal the significance of long-range exchange effects on the electronic states of metal clusters. The difference between HOMO-LUMO gaps and HOMO-LUMO excitation energies, which is called “exciton binding energy,” is also tested. As a result, it is found that the long-range exchange effects are requisite in DFT calculations to quantitatively investigate the ground and excited states of metal clusters. © 2018 Wiley Periodicals, Inc.     

Understanding the dependence of the transitional properties of liquid crystal dimers on their molecular geometry

The characteristic feature of liquid crystal dimers, in which two mesogenic groups are linked by a flexible spacer, is often thought to be the strong odd-even effect exhibited by their transitional properties. That is, the nematic-isotropic transition temperature and the entropy of transition are large for dimers with an even number of groups in the spacer in comparison with those for neighbouring dimers with an odd number of groups. However, the magnitude of the odd-even effect along a homologous series of dimers is found to depend strongly on the nature of the link between the mesogenic group and the spacer. This dependence is thought to originate in the variation of the molecular geometry with the linking group, a view which is supported by detailed molecular field theory calculations involving all of the conformational states. Here we are concerned with developing a more transparent understanding of this geometrical effect using a simple model of the dimers in which all of the conformational states are replaced by just two, a linear and a bent conformer. The model has been found to exhibit a strong odd-even effect as well as a nematic-nematic transition when the bond angle is tetrahedral. We have used this model to explore the dependence of the transitional properties of liquid crystal dimers on their geometry by varying the bond angle of the bent conformer. The behaviour predicted by the model for the nematic-isotropic transition is found to be in qualitative agreement with experiment. In addition, the nematic-nematic transition is observed to exhibit a critical behaviour as the bond angle is increased. At the other extreme, when the bond angle is reduced to its limiting value of 90° there is a very strong first order transition between a discotic and a calamitic nematic.     

金镍二元团簇结构和电子性质的理论研究

在UBP86/LANL2DZ和UBP86/def2-TZVP水平下详细研究了AumNin (m＋n≤6)团簇的几何结构和电子性质. 详细地分析了团簇的结构特征, 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. 所有混合团簇中, 镍原子趋于聚集到一起, 形成最多Ni—Ni键, 金原子分布在镍原子聚集体周围以形成最多Au—Ni键. Ni原子较少团簇的电子性质与纯金团簇类似, 呈现一定奇偶振荡. 混合团簇中存在镍到金原子间的电荷转移. Ni原子较少团簇中, 自旋电子主要定域在Ni原子上, Ni原子较多团簇中, Au原子明显受到自旋极化. 混合团簇的分波态密度表明, AuNi混合团簇对小分子的反应活性要高于纯金团簇.     

Triaxial shapes of sodium clusters

A modified Nilsson-Clemenger model is combined with Strutinsky's shell correction method. For spherical clusters, the model potential is fitted to the single-particle spectra obtained from selfconsistent Kohn-Sham calculations. The deformation energy surfaces of sodium clusters with sizes of up toN=270 atoms are calculated for a combination of triaxial, quadrupole and hexadecapole deformations. The ground state shapes and energies are determined by simultaneous minimization with respect to the three shape parameters. A significant fraction of the clusters is predicted to be triaxial. The deviations from the axial shape do not generate any systematic odd-even staggering of the binding energies.     

Density functional theory study of the adsorption of NO on CunX (n = 2–8; X = Cu,K) clusters

Density functional theory calculations are performed to analyze the structure and stability of Cu and Cu-K clusters with 3 to 9 atoms. The results indicate that the stability of the clusters decreases after doping with a K atom. With the increase of cluster size, the stability of the clusters shows odd-even alternation. Cu₈ and Cu₇K clusters exhibit the highest stability. Next, different adsorption sites are considered to investigate the geometry of Cu_nNO and Cu_n−1KNO clusters. By calculating the adsorption energy and the HOMO-LUMO energy gap, it is determined that both types of reactions are exothermic processes, indicating stable adsorption of NO. Notably, the Cu_nK clusters are more active (stronger adsorption) for NO than the Cu_n clusters. The most chemically active clusters among Cu_nNO and Cu_n−1KNO clusters are Cu₈NO and Cu₇KNO clusters. Finally, electron transfer and Mayer bond order analysis of Cu₈NO and Cu₇KNO clusters reveal that the N O bond order decreases due to electron transfer when Cu/Cu-K clusters adsorb NO. In this process, the N atom is the electron donor and the Cu atom is the electron acceptor. Fundamental insights obtained in this study can be useful in the design of Cu/Cu-K catalysts.     

用密度泛函和遗传算法研究Cun (n≤20) 团簇的尺寸效应

结合遗传算法和Gupta多体势系统地搜索金属团簇Cu_n (n≤20)的几何结构, 并利用密度泛函方法进一步确定最稳定构型. 分析了平均键长、平均配位数、结合能、二阶差分能、电离势和电子亲和势等性质随着尺寸的变化规律. 发现在Cu₇处团簇最稳定构型从二维结构转向三维结构, Cu_n (n≤20)团簇的幻数为8, 13, 20. 团簇的键长、配位数和结合能属性随着尺寸的增长而递增最终接近相应的体相值; 而二阶差分能、电离势和电子亲和势随着尺寸增加出现奇偶交替, 说明偶数电子形成闭壳层结构, 比相邻团簇更稳定.     

Oxidation Effects on the Electronic Properties of Hydrogenated Silicon Clusters

The geometric and electronic properties of some hydrogenated silicon clusters in the presence of oxygen on the surface have been investigated.The density functional theory with generalized gradient approximation functional was applied in our calculations.By calculating the total energy,the double bond Si=O is shown to be more stable than the bridge bond Si-O-Si for large size oxidized clusters.The results of Mulliken population analysis indicate that a so-called passivation effect is enhanced by oxidization effects.From the energy band structures and density of states,we find that some localized states are induced by the p-orbital of O atom mainly and reduce the energy gaps substantially.     

Probing the structural and electronic properties of small vanadium monoxide clusters

The structural evolution and bonding of a series of early transition-metal oxide clusters, V(n)O(q) (n = 3-9, q = 0,-1), have been investigated with the aid of previous photoelectron spectroscopy (PES) and theoretical calculations. For each vanadium monoxide cluster, many low-lying isomers are generated using the Saunders "Kick" global minimum stochastic search method. Theoretical electron detachment energies (both vertical and adiabatic) were compared with the experimental measurements to verify the ground states of the vanadium monoxide clusters obtained from the DFT calculations. The results demonstrate that the combination of photoelectron spectroscopy experiments and DFT calculation is not only powerful for obtaining the electronic and atomic structures of size-selected clusters, but also valuable in resolving structurally and energetically close isomers. The second difference energies and adsorption energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The adsorption energies of one O atom on the anionic (6.64 → 8.16 eV) and neutral (6.41 → 8.13 eV) host vanadium clusters are shown to be surprisingly high, suggesting strong capabilities to activate O by structural defects in vanadium oxides.