Density functional theory study of AunMn(n=1-8) clusters

Equilibrium geometries, relative stabilities, and magnetic properties of small Au_nMn (n=1-8) clusters have been investigated using density functional theory at the PW91P86 level. It is found that Mn atoms in the ground state Au_nMn isomers tend to occupy the most highly coordinated position and the lowest energy structure of Au_nMn clusters with even n is similar to that of pure Au_n+1 clusters, except for n=2. The substitution of Au atom in Au_n+1 cluster by a Mn atom improves the stability of the host clusters. Maximum peaks are observed for Au_nMn clusters at n=2, 4 on the size dependence of second-order energy differences and fragmentation energies, implying that the two clusters possess relatively higher stability. The HOMO-LUMO energy gaps of the ground state Au_nMn clusters show a pronounced odd-even oscillation with the number of Au atoms, and the energy gap of Au₂Mn cluster is the biggest among all the clusters. The magnetism calculations indicate that the total magnetic moment of Au_nMn cluster, which has a very large magnetic moment in comparison to the pure Au_n+1 cluster, is mainly localized on Mn atom.     

Density functional study of Al-doped Au clusters

The equilibrium geometries and electronic properties of Au_nAl, up to n=13, have been systematically investigated using the density functional theory. The results show that, for the Au_nAl clusters, two patterns are identified. Pattern one (n=2, 3, 8), the lowest-energy geometries prefer two-dimensional structures. Pattern two (n=4-7, 9--13), the lowest-energy geometries prefer three-dimensional structures. According to the analysis of the binding energy and the fragmentation energy, Au_nAl clusters with odd n are found to be more stable than those with even n. The same trend of alternation can be illuminated according to the computational results in the HOMO--LUMO gap, the ionization potential, and the electron affinities. The Al atom not only changes the structures of pure gold clusters, but also enhances their stabilities. NBO analysis indicates 6s orbital of Au atom hybridizes with 3p orbital of Al atom.     

Insights into the structures,stabilities, electronic and magnetic properties of X2Aun (X = La,Y, and Sc; n = 1–9) clusters: comparison with pure gold clusters

A systematic study of the X₂Au_n (X = La, Y, Sc; n = 1–9) clusters are performed by using the density functional theory at TPSS level. The structures, stabilities, electronic, and magnetic properties are investigated in comparison with pure gold clusters. The results show that the transition points of the doped clusters from two-dimensional to three-dimensional structure are obviously earlier than gold clusters. The impurity X atoms tend to occupy the most highly coordinated position and form the largest probable number of bonds with gold atoms. In addition, the impurity atoms can strongly enhance the stabilities of gold clusters. It indicates that the impurity atoms dramatically affect the geometries and stabilities of the Au_n clusters. The highest occupied molecular orbital–lowest occupied molecular orbital gap, vertical ionisation potential, and chemical hardness show that the X₂Au₆ clusters have higher stabilities than the others. In La₂Au_1–9, Y₂Au_1–7, and Sc₂Au_1–4 clusters, the charges transfer from X atoms to the Au_n frames. The total magnetic moments of X₂Au_n clusters exist distinctly odd–even alternation behaviours except for La₂Au₄ and Sc₂Au₄ clusters.     

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.     

Structures and magnetic properties of AunTi2+ (n $\leqslant$ 7) clusters

Base on the density-functional theory, the structural and magnetic properties of Au_nTi₂ ⁺ ( ) clusters are investigated. The two titanium atoms form a dimer in the gold clusters. The second-order energy differences and HOMO-LUMO gap provide a clear explanation of the abundance peaks and odd-even staggering observed recently in photofragmentation experiments. The magnetism of Au_nTi₂ ⁺ cluster shows an odd-even effect when n increases from 1 to 4 and drops to zero at n=5 and 7. The local magnetic moment and charge partition of Ti 4s, 3d orbitals are discussed. The peculiar magnetic properties are related to the structures and the hybridization between the Au 5d, 6s states and Ti 3d, 4s states.     

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.     

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.     

Geometrical,electronic, and magnetic properties of Au n V (n = 1–8) clusters: A density functional study

The geometrical, electronic, and magnetic properties of small Au _n V (n?=?1–8) clusters have been investigated using density functional theory at the PW91 level. An extensive structural search indicates that the V atom in low-energy Au _n V isomers tends to occupy the most highly coordinated position and the ground-state configuration of Au _n V clusters favors a planar structure. The substitution of a V atom for an Au atom in the Au _{n +1} cluster transforms the structure of the host cluster. Maximum peaks are observed for the ground-state Au _n V clusters at n?=?2 and 4 for the size dependence of the second-order energy differences, implying that the Au₂V and Au₄V clusters possess relatively higher stability. The energy gap of the Au₃V cluster is the largest of all the clusters. This may be ascribed to its highly symmetrical geometry and closed eight-electron shell. For ground-state clusters with the same spin multiplicity, as the clusters size increases, the vertical ionization potential decreases and the electron affinity increases. Magnetism calculations for the most stable Au _n V clusters demonstrate that the V atom enhances the magnetic moment of the host clusters and carries most of the total magnetic moment.     

Evolution of structures,stabilities, and electronic properties of anionic [AunRb]− (n = 1–10) clusters: comparison with pure gold clusters

The geometric structures, stabilities, and electronic properties of small size anionic [Au_nRb]^? and Au_n+1^? (n = 1–10) clusters have been systematically investigated by using density functional theory. The optimised geometries show that the structures of [Au_nRb]^? clusters favour the three-dimensional structure at n ≥ 8. The Rb atoms tend to occupy the most highly coordinated position and form the largest probable number of bonds with gold atoms. One Au atom capped on [Au_n-1Rb]^? structures is the dominant growth pattern for n = 2–8 and Rb atom capped on Au_n^? structures for n = 9–10. The averaged atomic bonding energies, fragmentation energies, second-order difference of energies, and highest occupied molecular orbital–lowest unoccupied molecular orbital gaps exhibit a pronounced even–odd alternations phenomenon. The charges in [Au_nRb]^? clusters transfer from the Rb atoms to Au_n host. In addition, it is found that the most favourable dissociation channel of the [Au_nRb]^? clusters is to eject a Rb atom and the highest energy dissociation path is Rb^? anion ejection.     

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.     

Density functional study of AunCu (n=1-7) clusters

The possible stable geometrical configurations and the relative stabilities of the lowest-lying isomers of copper-doped gold clusters,Au n Cu (n=1-7),are investigated using the density functional theory.Several low-lying isomers are determined.The results indicate that the ground-state Au n Cu clusters have planar structures for n=1-7.The stability trend of the Au n Cu clusters (n=1-7),shows that odd-numbered Au n Cu clusters are more stable than the neighbouring even-numbered ones,thereby indicating the Au 5 Cu clusters are magic cluster with high chemical stability.     

DFT study on size-dependent geometries, stabilities, and electronic properties of AunM2 (M = Si, P; n = 1–8) clusters

The ab initio method based on density functional theory at the PW91PW91 level has been employed to systematically study the structures, stabilities, electronic, and magnetic properties of gold clusters with or without silicon/phosphorus doping. The optimized geometries show that the most stable isomers for Au _n Si₂ and Au _n P₂ (n = 1–8) clusters prefer a three-dimensional structure when n = 2 and n = 3 upwards, respectively, and they can be viewed as grown from the already observed Au _n−1M₂ (M = Si, P). The relative stabilities of calculated Au _n M₂ (M = Si, P) clusters have been analyzed through the atomic average binding energy, fragmentation energy, second-order difference of energy, and HOMO-LUMO gap. A pronounced odd-even alternative phenomenon indicates that the clusters with even-numbered valence electrons possess a higher stability than their neighboring ones. For both systems, natural population analysis reveals that electronic properties of dopant atoms in the corresponding configuration are mainly related to s and p states. We also investigated magnetic effects of clusters as a function of cluster size, however, their oscillatory magnetic moments were found to vary inversely to the fragmentation energy, second-order difference of energy, and HOMO-LUMO gap.     

Probing the structural and electronic properties of cationic rubidium–gold clusters: [AunRb]+ (n = 1–10)

Density functional theory has been applied to study the geometric structures, relative stabilities, and electronic properties of cationic [Au_nRb]⁺ and Au_{n + 1}⁺ (n = 1–10) clusters. For the lowest energy structures of [Au_nRb]⁺ clusters, the planar to three-dimensional transformation is found to occur at cluster size n = 4 and the Rb atoms prefer being located at the most highly coordinated position. The trends of the averaged atomic binding energies, fragmentation energies, second-order difference of energies, and energy gaps show pronounced even–odd alternations. It indicated that the clusters containing odd number of atoms maintain greater stability than the clusters in the vicinity. In particular, the [Au₆Rb]⁺ clusters are the most stable isomer for [Au_nRb]⁺ clusters in the region of n = 1–10. The charges in [Au_nRb]⁺ clusters transfer from the Rb atoms to Au_n host. Density of states revealed that the Au-5d, Au-5p, and Rb-4p orbitals hardly participated in bonding. In addition, it is found that the most favourable channel of the [Au_nRb]⁺ clusters is Rb⁺ cation ejection. The electronic localisation function (ELF) analysis of the [Au_nRb]⁺ clusters shown that strong interactions are not revealed in this study.     

Decay pathways of small gold clusters

The decay pathway competition between monomer and dimer evaporation of photoexcited cluster ions Au ⁺ _n, n = 2-27, has been investigated by photodissociation of size-selected gold clusters stored in a Penning trap. For n > 6 the two decay pathways are distinguished by their experimental signature in time-resolved measurements of the dissociation. For the smaller clusters, simple fragment spectra were used. As in the case of the other copper-group elements, even-numbered gold cluster ions decay exclusively by monomer evaporation, irrespective of their size. For small odd-size gold clusters, dimer evaporation is a competitive alternative, and the smaller the odd-sized clusters, the more likely they decay by dimer evaporation. In this respect, Au ⁺ ₉ shows an anomalous behavior, as it is less likely to evaporate dimers than its two odd-numbered neighbors, Au ⁺ ₇ and Au ⁺ ₁₁. This nonamer anomaly is typical for copper-group cluster ions M ⁺ ₉ (M = Cu, Ag, Au) and a similar behavior is found in the anionic heptamers M ^- ₇. It is discussed in terms of the well-known electronic shell closing at n _e = 8 atomic valence electrons. Received 2 November 2000     

密度泛函理论研究Hg与Auqn(n=1—6, q=0,+1,-1) 团簇的相互作用

采用密度泛函理论中的广义梯度近似对Hg与小团簇Au ^q_n (n=1—6, q=0, +1, -1)的相互作用进行了系统研究. 结果表明,除Au₅^+,-团簇外,前线分子轨道理论可以成功预测大部分Au _n Hg ^q 复合物的最低能量结构. Au_n团簇对Hg的吸附受团簇尺寸大小和团簇所携带电荷的影 关键词： 密度泛函理论 汞 金团簇 吸附能     

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.     

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.     

Geometric,stable and electronic properties of Aun-2Y2（n=3-8） clusters

Employing first-principles methods,based on the density function theory,and using the LANL2DZ basis sets,the ground-state geometric,the stable and the electronic properties of Aun-2Y2 clusters are investigated in this paper.Meanwhile,the differences in property among pure gold clusters,pure yttrium clusters,gold clusters doped with one yttrium atom,and gold clusters doped with two yttrium atoms are studied.We find that when gold clusters are doped by two yttrium atoms,the odd-even oscillatory behaviours of Aun-1Y and Aun disappear.The properties of Aun-2Y2 clusters are close to those of pure yttrium clusters.     

Structural properties and reactivity of bimetallic silver-gold clusters

Bimetallic silver-gold clusters are well suited to study changes in metallic versus ionic properties involving charge transfer as a function of the size and the composition. We present structures, ionization potentials (IP) and vertical detachment energies (VDE) for neutral and charged bimetallic Au_nAg_m ( 2(n + m)5) clusters obtained from density functional level of theory. In the stable structures of these clusters Au atoms assume positions which favor charge transfer from Ag atoms. In clusters with equal numbers of hetero atoms (n = m = 1- 4) heteronuclear bonding is preferred to homonuclear bonding, giving rise to large values of ionization potentials. For larger clusters (n=m=5, 10) stable structures do not favor neither hetero bonding nor segregation into the single components, although they exhibit more metallic than ionic features. This remains valid also for Au₈Ag₁₂ cluster characterized by strong charge transfer to gold subunit. The influence of doping of pure gold clusters with silver atoms on VDE and IP values is discussed in context of their reactivity towards O₂ and CO molecules. As a starting point we consider reactivity towards CO and O₂ molecules on the example of AgAu^- dimer. The results show that the catalytic cycle can be fullfilled.     

Geometrical, electronic, and magnetic properties of small AunSc (n=1-8) clusters

Geometrical, electronic, and magnetic properties of the Sc-doped gold clusters, Au_nSc (n=1-8), have been studied using the density-functional theory within the generalized gradient approximation. An extensive structural search shows that the Sc atom in low-energy Au_nSc isomers tends to occupy the most highly coordinated position. The substitution of a Sc atom for an Au atom in the Au_n+1 cluster markedly changes the structure of the host cluster. Moreover, we confirm that the ground-state Au₆Sc cluster has a distortion to a lower D_2h symmetry. The relative stabilities and electronic properties of the lowest-energy Au_nSc clusters are analyzed based on the averaged binding energies, second-order energy differences, fragmentation energies, chemical hardnesses, and HOMO-LUMO gaps. It is found that the magic Au₃Sc cluster can be perceived as a superatom with high chemical stability and its HOMO-LUMO gap is larger than that of the closed-shell Zr@Au₁₄ cluster. The high symmetry and spin multiplicity of the Au₃Sc and Au₆Sc clusters are responsible for their large vertical ionization potential and electron affinity. The magnetism calculations indicate that the magnetic moment of the Sc atom in the ground-state Au_nSc (n=2-8) clusters gradually decreases for even n and is completely quenched for odd n.