All-electron relativistic calculation on Au5X (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) clusters

All-electron scalar relativistic calculations on Au₅X (X = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Zn) clusters have been performed by using density functional theory with the generalized gradient approximation. Our calculation results indicate that all the lowest energy geometries of Au₅X clusters have planar structures; the doped X atoms prefer to occupy the fourfold coordination site. Except Au₅Fe, Au₅Co and Au₅Zn, for other clusters including pure Au₆ cluster, the HOMO are delocalized obviously with a contribution from all atoms in the cluster. On the contrary, the electron localization in Au₅Zn is very strong resulting in the least stability of this cluster. Au₅Cu cluster with six delocalized electrons being defined as magic number for two-dimensional system has the largest VIP and deepest HOMO energy level. With the substitution Au for X atoms, the metallicity of all Au₅X clusters is reinforced.     

All-electron scalar relativistic calculation on the interaction between nitric monoxide and small gold cluster

An all-electron scalar relativistic calculation on Au _n NO (n = 1–10) clusters has been performed by using density functional theory with the generalized gradient approximation at the PW91 level. The small gold cluster would like to bond with nitric and the nitric monoxide molecule prefers to occupy the on-top and single fold coordination site. The Au _n structures in all Au _n NO clusters are only distorted slightly and still keep the planar structures. With the bend of Au-N-O bond, the structures of Au _n NO clusters evolve from the 2D structure to 3D structure. The most favorable adsorption between small gold cluster and nitric monoxide molecule takes place in the case that nitric monoxide molecule is adsorbed onto an odd-numbered pure Au _n cluster and becomes odd-numbered Au _n NO cluster with even number of valence electrons. The scalar relativistic effect strengthens the Au–Au, Au–N interaction and weakens the N–O interaction, appearing as the shorter Au–Au, Au–N bond-length and the longer N–O bond-length. The differences between our work and previous work are believed to be the reflection of the scalar relativistic effect.     

Structural stability and electronic properties of Au5Hn (n=1–10) clusters

A systematic study on the geometrical structures, electronic and magnetic properties of Au₅H _n (n=1–10) clusters has been performed by using the all-electron scalar relativistic density functional theory with generalized gradient approximation at the PW91 level. It is found that all Au₅H _n clusters prefer to keep the planar structures like pure Au₅ cluster, the Au₅ structures in Au₅H₄, Au₅H₅ and Au₅H₆ clusters are distorted obviously. The adsorption of a number of hydrogen atoms enhances the stability of Au₅ cluster and all Au₅H _n clusters are more stable than pure Au₅ cluster energetically. The odd-even alteration of magnetic moment is observed in Au₅H _n clusters and may be served as the material with tunable code capacity of “0” and “1” by adsorbing odd or even number of H atoms. It seems that the most favorable adsorption between Au₅ cluster and a number of hydrogen atoms takes place in the case that the odd number of hydrogen atoms is adsorbed onto Au₅ cluster and becomes Au₅H _n cluster with even number of valence electrons.     

Density functional investigation on the structures and properties of Li atom doped Au20 cluster

Structures and properties of an Au₂₀ cluster doped with two Li atoms, Au₁₈Li₂, have been investigated using relativistic density functional theory within the framework of the zeroth-order regular approximation. Various initial structures have been generated and employed for geometry optimization followed by vibration analysis to check the stability of the final optimized structures. We have calculated various properties like binding energy, ionization potential, electron affinity and the HOMO–LUMO gap of these structures. It has been found that two dopant Li atoms favour occupying two different surface positions of the pyramidal Au₂₀ cluster. The binding energy of the surface-doped Au₁₈Li₂ cluster is 1.017?eV higher than that of the pure Au₂₀ cluster and the HOMO–LUMO gap (1.742?eV) is as high as a pure Au₂₀ cluster (1.786?eV). Interestingly, we observe that the HOMO–LUMO gap as well as the binding energy can be increased beyond those of the Au₁₈Li₂ cluster with the help of further Li atom doping. In fact, a doped tetrahedral Au₁₆Li₄ cluster, where all the dopants are at the surface sites, possesses a very high HOMO–LUMO gap of 2.117?eV. Geometric and energetic parameters indicate that the Au₁₆Li₄ cluster might be considered as a possible ‘superatom’ in the design of novel cluster-assembled materials.     

Assessing the validity of theoretical results

We present recent theoretical results for the V₃ and Au₄ clusters. Calculations of the V₃ doublet system indicate that the 6-311+G(d) basis set is sufficiently flexible to provide reliable minimum energy structures and vibrational frequencies, that these structures and frequencies are insensitive to spin contamination of the wave function when the BPW91 functional is used, and that changing to the B3LYP functional may result in very different structures and frequencies. A computationally less expensive scalar relativistic treatment of Au₄ clusters gives structural properties that are in good agreement with those obtained using a four-component method. Received 30 November 2000     

Probing the structural,electronic and magnetic properties of small Au4M (M = Sc–Zn) clusters

Density-functional method PW91 has been selected to investigate the structural, electronic and magnetic properties of Au₄M (M =Sc–Zn) clusters. Geometry optimisations show that the M atoms in the ground-state Au₄M clusters favour the most highly coordinated position. The ground-state Au₄M clusters possess a solid structure for M = Sc and Ti and a planar structure for M = V–Zn. The characteristic frequency of the doped clusters is much greater than that of pure gold cluster. The relative stability and chemical activity are analysed by means of the averaged binding energy and highest occupied molecular orbital and lowest unoccupied molecular orbital energy gap for the lowest energy Au₄M clusters. It is found that the dopant atoms can enhance the thermal stability of the host cluster except for Zn atom. The Au₄Ti, Au₄Mn and Au₄Zn clusters have relatively higher chemical stability. The vertical detachment energy, electron affinity and photoelectron spectrum are calculated and simulated theoretically for all the ground-state structures. The magnetism calculations reveal that the total magnetic moment of Au₄M cluster is mainly localised on the M atom and vary from 0 to 5 μ_B by substituting an Au atom in Au₅ cluster with different transition-metal atoms.     

Structural,electronic and magnetic properties of Au<Subscript>n</Subscript>Pt (n = 1−12) clusters in comparison with corresponding pure Au<Subscript>n+1</Subscript> (n = 1−12) clusters

An all-electron scalar relativistic calculation on Au _n Pt (n = 1−12) clusters has been performed by using density functional theory with the generalized gradient approximation at PW91 level. Our results reveal that all the lowest energy geometries of Au _n Pt  (n = 1−12) clusters may be generated by substituting Pt atom for one gold atom of the Au _n+1 cluster at the highest coordinated site. Compared with corresponding pure Au _n+1 cluster, the lowest energy geometries of Au _n Pt clusters are distorted slightly and still keep the planar structures due to the strong scalar relativistic effect in small gold cluster. The Au-Pt bonds are stronger and most Au-Au bonds far from Pt atom are weaker than the corresponding Au-Au bonds in pure Au _n+1 cluster. By substituting Pt atom for one gold atom of Au _n+1 cluster at the highest coordinated site, the relatively stable and inactive odd-numbered Au _n+1 cluster becomes the relatively unstable and reactive odd-numbered Au _n Pt cluster, and the relatively unstable and reactive even-numbered Au _n+1 cluster becomes the relatively stable and inactive even-numbered Au _n Pt  cluster chemically and electronically. All the Au _n Pt clusters prefer low spin multiplicity. The even-numbered Au _n Pt clusters are found to exhibit zero magnetic moment and the odd-numbered Au _n Pt clusters are found to possess magnetic moment with the value of 1 μ _B. The odd-even alterations of magnetic moments and electronic configurations for Au _n Pt clusters are very obvious and may be simply understood in terms of the electron pairing effect.     

A density functional theory study on the H2S molecule adsorption onto small gold clusters

An all-electron scalar relativistic calculation on Au_nH₂S (n = 1-13) clusters has been performed by using density functional theory with the generalized gradient approximation at PW91 level. The small gold cluster would like to bond with sulfur in the same plane and the H₂S molecule prefers to occupy the on-top and single fold coordination site in the cluster. The Au_n structures and H₂S molecule in all Au_nH₂S clusters are only slightly perturbed and still maintain their structural integrity. After adsorption, the S-H, H-H bond-lengths and most Au-Au bond-lengths are elongated, only a few Au-Au bond-lengths far from H₂S molecule are shortened. The reactivity enhancement of H₂S molecule is obvious and the strong gold-sulfur bond is observed expectedly. The most favorable adsorption takes place in the case that the H₂S molecule is adsorbed by an even-numbered Au_n cluster and becomes Au_nH₂S cluster with even number of valence electrons. It is believed that the strong scalar relativistic effect is favorable to H₂S molecule adsorption onto small gold clusters and is also one of the important reasons for the strong gold-sulfur bond.     

Stability of gold cages (Au<Subscript>16</Subscript> and Au<Subscript>17</Subscript>) at finite temperature

We have employed ab initio molecular dynamics to investigate the stability of the smallest gold cages, namely Au₁₆ and Au₁₇, at finite temperatures. First, we obtain the ground state structure along with at least 50 distinct isomers for both the clusters. This is followed by the finite temperature simulations of these clusters. Each cluster is maintained at 12 different temperatures for a time period of at least 150 ps. Thus, the total simulation time is of the order of 2.4 ns for each cluster. We observe that the cages are stable at least up to 850 K. Although both clusters melt around the same temperature, i.e. around 900 K, Au₁₇ shows a peak in the heat capacity curve in contrast to the broad peak seen for Au₁₆.      

Density-functional theory study of the geometries,stabilities, and electronic properties of Au n Rb (n = 1–10) clusters: comparison with pure gold clusters

The density functional method with the relativistic effective core potential has been employed to investigate systematically the geometric structures, relative stabilities, growth-pattern behavior, and electronic properties of small bimetallic Au _n Rb (n?=?1–10) and pure gold Au _n (n?≤?11) clusters. For the geometric structures of the Au _n Rb (n?=?1–10) clusters, the dominant growth pattern is for a Rb-substituted Au _{n +1} cluster or one Au atom capped on a Au _{n –1}Rb cluster, and the turnover point from a two-dimensional to a three-dimensional structure occurs at n?=?4. Moreover, the stability of the ground-state structures of these clusters has been examined via an analysis of the average atomic binding energies, fragmentation energies, and the second-order difference of energies as a function of cluster size. The results exhibit a pronounced even–odd alternation phenomenon. The same pronounced even–odd alternations are found for the HOMO–LUMO gap, VIPs, VEAs, and the chemical hardness. In addition, about one electron charge transfers from the Au _n host to the Rb atom in each corresponding Au _n Rb cluster.     

Interaction of gold and silver cluster cations with CH<Subscript>3</Subscript>Br: thermal and photoinduced reaction pathways

The reactions of free, size selected Au _n ⁺ (n = 1–3, 5, 7) and Ag₃ ⁺ clusters with CH₃Br as well as the photodissociation of the resulting complexes at 266 nm were studied in a radio frequency ion trap under multiple collision conditions. CH₃Br was found to interact more strongly with the gold clusters than with the silver clusters. All investigated metal clusters exhibited characteristic size dependent adsorbate coverages. Furthermore, the successive loss of methyl radicals was identified as a major thermal reaction channel of the adsorbed CH₃Br molecules. Photodissociation experiments were performed with the product complexes of the trimer clusters and revealed the strongly preferred light-induced fragmentation of Au₃Br₃ ⁺ and Ag₃Br₃ ⁺, respectively, over any other thermal reaction products. However, whereas in the case of the gold cluster complexes the bare Au₃ ⁺ was exclusively re-formed through laser irradiation, considerable photoinduced metal cluster fragmentation occurred in the case of Ag₃Br₃ ⁺.     

DFT calculations for aerobic oxidation of alcohols over neutral Au6 cluster

Lately, it was found that the Au nanoclusters stabilised by poly(N-vinyl-2-pyrrolidone) [PVP; (C₆H₉ON)_n], abbreviated to Au:PVP, can oxidise p-hydroxybenzyl alcohol selectively into the corresponding aldehyde in water without degradation. This observation indicates that Au cluster can exhibit high catalytic activity without any metal oxide supports. From previous works, it was found that the anionic Au clusters played an important role for the activation of oxygen molecule on the Au clusters. However, the catalytic activity of neutral Au clusters for the aerobic oxidation reaction of alcohol is not still investigated in detail. In order to examine the catalytic activity of neutral Au clusters, the aerobic oxidation of p-hydroxybenzyl alcohol to the corresponding aldehyde catalysed by Au₆ has been investigated quantum chemically using density functional theory with the PBE0 functional. Possible reaction pathways are investigated taking account of full structure relaxation of the model systems. From the calculation results, it was found that the formations of both a hydroperoxyl anion and a hydride were the important steps for the aerobic oxidation of p-hydroxybenzyl alcohol over Au₆ cluster.     

Simulation of desorption of gold nanoclusters deposited on the (111) surface of Al and Au under bombardment with Au<Subscript>1</Subscript> ions and Au<Subscript>400</Subscript> clusters using the classical molecular dynamics method

The mechanisms of desorption of gold nanoclusters deposited on à substrate under low-energy bombardment with ions and clusters (in the mode of elastic stopping predominance) are analyzed. The classical molecular dynamics method is employed for computer simulation of both “direct” and “indirect” impact of bombarding particles (that is, when a projectile particle either directly interacts with the deposited cluster or penetrates into the substrate without hitting the cluster). Au₁ ions and Au₄₀₀ clusters with an energy of 38 keV and 0.18 keV/atom, respectively, are used as projectile particles. The spherical Au₆₀₅₁ gold nanocluster deposited on a substrate of Al(111) or Au(111) is applied as a target. It is shown that indirect impact does not lead to desorption of the nanocluster from the Al substrate in all considered cases; however, it can initiate desorption from the Au substrate. This phenomenon is quite efficient when the heat spike appearing upon penetration of a projectile particle involves the region of contact between the substrate and the nanocluster deposited on it. As this takes place, an intense flow of the sputtered substrate material transfers a sufficient-for-ejection momentum to the deposited nanocluster.     

The geometrical structure,electronic structure and magnetism of bimetallic Au<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>M<Subscript>2</Subscript> (<Emphasis Type="Italic">n</Emphasis>=1, 2; M=Y,Zr, Nb,Mo, Tc,Ru, Rh,Pd) clusters

The geometrical structure, stability, magnetism, and electronic structure of bimetallic clusters AuM₂ and Au₂M₂, where M are 4d transition metal elements, are investigated systematically by using the first-principles method based on density functional theory. The calculation results show that there is a large amount of low-energy isomers with the very similar structure. AuM₂ and Au₂M₂ clusters display dramatic magnetism. The magnetic moment of the 4d element is either enhanced or weakened with respect to the bulk value, which is largely dependent on the orbital exchange-splitting. Supported by the National Natural Science Foundation of China (Grant Nos. 10674015 and 10604035)     

Structural,electronic and magnetic properties of gold cluster doped with calcium: Au n Ca (n = 1–8)

The geometrical structures, relative stabilities, electronic and magnetic properties of calcium-doped gold clusters Au _n Ca (n?=?1–8) have been systematically investigated by employing density functional method at the BP86 level. The optimised geometries show that the ground-state structures are planar structures for Au _n Ca (n?=?3–8) clusters. Ca-substituted Au _{n +1} clusters, as well as Au-capped Au _{n ?1}Ca clusters, are dominant growth patterns for the Au _n Ca clusters. The relative stabilities of Au _n Ca clusters for the ground-state structures are analysed based on the averaged binding energies, fragmentation energies and second-order difference of energies. The calculated results reveal that the Au₂Ca isomer is the most stable structure for small size Au _n Ca (n?=?1–8) clusters. The HOMO-LUMO energy gaps as a function of the cluster size exhibit a pronounced even–odd alternation phenomenon. Subsequently, charge transfers and magnetic moment of Au _n Ca (n?=?1–8) clusters have been analysed further.     

AunY(n＝1—9)掺杂团簇的结构和电子性质研究

采用相对论有效原子实势(RECP)近似和密度泛函(B3LYP)方法，选择LANL2DZ基组，优化得到了Au_nY(n＝1—9)二元掺杂团簇稳定的基态结构和电子性质.研究结果表明，掺杂Y原子的Au_nY(n＝1—9)团簇随n的变化，其电离势、电子亲合能和费米能级与Au_n(n＝2—9)一样具有“奇-偶”振荡效应；团簇离子的稳定性具有“幻数”现象，Au₂Y⁺和Au₆Y⁺比其他团簇离子更稳定，与质谱实验结果一致；同一团簇中，团簇最稳定的异构体(基态)是趋于Y原子有最大的邻近的Au原子数. 关键词： Au-Y团簇 密度泛函 平衡几何结构 电子性质     

Chiral structures and tunable magnetic moments in 3d transition metal doped Pt6 clusters

The structural, electronic, and magnetic properties of transition metal doped platinum clusters MPt6 （M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, and Zn） are systematically studied by using the relativistic all-electron density functional theory with the generalized gradient approximation. Most of the doped clusters show larger binding energies than the pure Pt7 cluster, which indicates that the doping of the transition metal atom can stabilize the pure platinum cluster. The results of the highest occupied molecular orbital （HOMO） lowest unoccupied molecular orbital （LUMO） gaps suggest that the doped clusters can have higher chemical activities than the pure Pt7 cluster. The magnetism calculations demonstrate that the variation range of the magnetic moments of the MPt6 clusters is from 0 μB to 7 μB, revealing that the MPt6 clusters have potential utility in designing new spintronic nanomaterials with tunable magnetic properties.     

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

We have systematically investigated the geometrical structures, relative stabilities and electronic properties of small bimetallic AunBe (n = 1, 2, . . . , 8) clusters using a density functional method at BP86 level. The optimized geometries reveal that the impurity beryllium atom dramatically affects the structures of the Aun clusters. The averaged binding energies, fragmentation energies, second-order difference of energies, the highest occupied-lowest unoccupied molecular orbital energy gaps and chemical hardness are investigated. All of them exhibit a pronounced odd-even alternation, manifesting that the clusters with even number of gold atoms possess relatively higher stabilities. Especially, the linear Au2Be cluster is magic cluster with the most stable chemical stability. According to the natural population analysis, it is found that charge-transferring direction between Au atom and Be atom changes at the size of n = 4.     

Ab initio calculation of the geometric,electronic and magnetic properties of neutral and anionic Au n Pd (n = 1–9) clusters

The ab initio method based on density functional theory at the B3PW91 level has been applied to study the geometric, electronic, and magnetic properties of neutral and anionic Au _n Pd (n?=?1–9) clusters. The results show that the most stable geometric structures adopt a three-dimensional structure for neutral Au₇Pd and Au₈Pd clusters, but for anionic clusters, no three-dimensional lowest-energy structures were obtained. The relative stabilities of neutral and anionic Au _n Pd clusters were analysed by means of the dependent relationships between the binding energies per atom, the dissociation energies, the second-order difference of energies, the HOMO–LUMO energy gaps and the cluster size n, and a local odd–even alternation phenomenon was found. Natural population analysis indicates the sequential transfer from the Pd atom to the Au _n frame in Au_1,2,3,5Pd and Au_2,3Pd^? clusters, and from the Au _n frame to the Pd atom in other clusters. Much to our surprise, irrespective of whether it is the total magnetic moment or the local magnetic moment, the magnetic moment presents an odd–even alternation phenomenon as a function of the cluster size n. The magnetic effects are mainly localized on the various atoms (Au or Pd) for different cluster size n.     

Chirality, defects, and disorder in gold clusters

Theoretical and experimental information on the shape and morphology of bare and passivated gold clusters is fundamental to predict and understand their electronic, optical, and other physical and chemical properties. An effective theoretical approach to determine the lowest-energy configuration (global minimum) and the structures of low energy isomers (local minima) of clusters is to combine genetic algorithms and many-body potentials (to perform global structural optimizations), and first-principles density functional theory (to confirm the stability and energy ordering of the local minima). The main trend emerging from structural optimizations of bare Au clusters in the size range of 12-212 atoms indicates that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest-energy ordered isomer. For example, chiral structures have been obtained as the lowest-energy isomers of bare Au₂₈ and Au₅₅ clusters, whereas in the size-range of 75-212 atoms, defective Marks decahedral structures are nearly degenerate in energy with the ordered symmetrical isomers. For methylthiol-passivated gold nanoclusters [Au₂₈(SCH₃)₁₆ and Au₃₈(SCH₃)₂₄], density functional structural relaxations have shown that the ligands are not only playing the role of passivating molecules, but their effect is strong enough to distort the metal cluster structure. In this work, a theoretical approach to characterize and quantify chirality in clusters, based on the Hausdorff chirality measure, is described. After calculating the index of chirality in bare and passivated gold clusters, it is found that the thiol monolayer induces or increases the degree of chirality of the metallic core. We also report simulated high-resolution transmission electron microscopy (HRTEM) images which show that defects in decahedral gold nanoclusters, with size between 1-2 nm, can be detected using currently available experimental HRTEM techniques.