Evolution of geometrical structures,stabilities and electronic properties of neutral and anionic Li n Cu λ (n = 1–9, λ = 0, −1) clusters: compare with pure lithium clusters

The structural evolution, stabilities, and electronic properties of copper-doped lithium Li _n Cu^λ (n?=?1–9, λ?=?0, ?1) clusters have been systematically investigated using a density functional method at PW91PW91 level. Extensive searches for ground-state structures were carried out, and the results showed the copper tends to occupy the most highly coordinated position and form the largest probable number of bonds with lithium atoms. By calculating the binding energies per atom, fragmentation energies and the HOMO-LOMO gaps, we found LiCu, Li₇Cu, LiCu^?, Li₂Cu^? and Li₈Cu^? clusters have the stronger relative stability and enhanced chemical stability. The content and pattern of frontier MOs for the most stable doped isomers were analysed to investigate the bond nature of interaction among Li and Cu atoms. The results show some σ-type and π-type bonds are formed among them, and with small admixture of the Cu d characters. To achieve a deep insight into the electron localization and reliable electronic structure information, the natural population analysis and electron localization function were performed and discussed.     

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,stabilities and electronic properties of boron-doped silicon clusters B3Sin (n=1–17) and their anions

The structures, stabilities and electronic properties of neutral and anionic B₃Si_n (n?=?1–17) clusters have been systemically investigated on the basis of density functional theory at the B3LYP/6-311?+?G(d) level and CALYPSO structure prediction method. The structural searches show that three boron atoms tend to form B₃ triangle encapsulated into Si_n cages with the increasing number of silicon atoms. Most of the lowest energy structures can be derived by using the squashed pentagonal bipyramid structure of B₃Si₄ and B₃Si₄^? as the major building unit. The relative stabilities are studied based on the calculated binding energies, second-order difference of energies and HOMO–LUMO gaps of the lowest energy structures. In addition, Hirshfeld, natural population analysis, Bader approaches and natural electronic configuration are performed to explore the charge transfer. At last, molecular orbital, magnetic properties, IR, Raman and UV–vis spectra are also, respectively, analysed for providing strong support for essential theoretical and experimental research.     

Geometries,stabilities, electronic and magnetic properties of small PdnIr (n = 1–8) clusters from first-principles calculations

The geometrical structures, relative stabilities, electronic and magnetic properties of small Pd_nIr (n = 1–8) clusters have been systematically investigated using density functional theory at the B3PW91 level. The optimised geometries show that the lowest-energy structures of Pd_nIr clusters prefer a three-dimensional configuration. The relative stability of these clusters was examined by analysis of the binding energies per atom, fragmentation energies, the second-order difference of energies and the HOMO–LUMO energy gaps as a function of cluster size. The obtained results exhibit that the Pd₂Ir, Pd₃Ir and Pd₅Ir clusters are more stable than their neighbouring clusters. The energy gap of the Pd₂Ir cluster is the largest of all the clusters (2.258 eV). In addition, the charge transfers, vertical ionisation potentials, vertical electron affinities and chemical hardness were calculated and discussed. The magnetism calculations indicate that the total magnetic moment of Pd_nIr clusters is mainly localised on the iridium atom for Pd_1–6Ir clusters. Meanwhile, the 5d orbital plays the key role in the magnetic moment of the iridium atom.     

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.     

Structures and energetics of BenGen (n = 1–5) and Be2nGen (n = 1–4) clusters

Cluster geometries and energies of Be_nGe_n (n = 1–5) and Be_2nGe_n (n = 1–4) have been examined in theoretical electronic structure calculations. Structure optimisations were carried out using DFT B3LYP/6-31G(2df) and the energies of the optimum geometries were ordered in QCISD(T) calculations. Be and Ge bond to each other and to other atoms of their own kind, creating a great variety of low-energy clusters in a variety of structural types. Comparisons of the germanide clusters with previously explored silicide and carbide structures reveal some structural similarities, but the germanides have much more in common with the beryllium silicides than with the carbides. However, germanide clusters show a greater tendency to form cage-like structures with potential in technological applications.     

Geometries,stabilities and electronic properties of small-sized Pd2-doped Sin (n = 1–11) clusters

The geometries, growth patterns, relative stabilities and electronic properties of small-sized Pd₂Si_n and Si_n+2 (n = 1–11) clusters are systematically studied using the hybrid density functional theory method B3LYP. The optimised structures revealed that the lowest energy Pd₂Si_n clusters are not similar to those of pure Si_n clusters. When n = 9, one Pd atom in Pd₂Si₉ completely falls into the centre of the Si outer frame, forming metal-encapsulated Si cages. On the basis of the optimised structures, the averaged binding energy, fragmentation energy, second-order energy difference and highest occupied–lowest unoccupied molecular orbital energy gap are calculated. It is found that the Pd₂Si₅ and Pd₂Si₇ clusters have stronger relative stabilities among the Pd₂Si_n clusters. Additionally, the stabilities of Si_n+2 clusters have been reduced by the doping of Pd impurity. The natural population and natural electronic configuration analysis indicated that the Pd atoms possess negative charges for n = 1–11 and there exist the spd hybridisation in the Pd atom. Finally, the chemical hardness, chemical potential, electrostatic potential and polarisability are discussed.     

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.     

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.     

Structures and its evolution of Ba n ( n =2 ∼ 14) clusters

We have studied the atomic structure and the electronic properties of Ba_n clusters by the ab initio molecular dynamics method. We find that a structural transition to the bulk-like structure begins at Ba₉ cluster, and the structures of the clusters are transferred to be icosahedral-like around n = 13. The relatively high stability for Ba₄, Ba₁₀ and Ba₁₃ clusters are observed. Received 1st December 2000     

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.     

Structures,stabilities, and electronic properties of F-doped Sin （n=1～12） clusters：Density functional theory investigation

The geometries, stabilities, and electronic properties of FSin （n=1～12） clusters are systematically investigated by using first-principles calculations based on the hybrid density-functional theory at the B3LYP/6-311G level. The geometries are found to undergo a structural change from two-dimensional to three-dimensional structure when the cluster size n equals 3. On the basis of the obtained lowest-energy geometries, the size dependencies of cluster properties, such as averaged binding energy, fragmentation energy, second-order energy difference, HOMO–LUMO （highest occupied molecular orbital–lowest unoccupied molecular orbital） gap and chemical hardness, are discussed. In addition, natural population analysis indicates that the F atom in the most stable FSin cluster is recorded as being negative and the charges always transfer from Si atoms to the F atom in the FSin clusters.     

Calculation on the CO2 influences on the structure,stability of (MgO)m (m = 1–6) clusters

ABSTRACT

The concentration of carbon dioxide (CO₂) has a significant influence on the morphology of thermal decomposition products of magnesite. So, structures, stabilities and adsorption mechanisms of (MgO)_m (m?=?1–6) clusters by one or two CO₂ molecules were calculated by the GGA-PW91 method. The results show that the stability of the considered clusters is (MgO)_m(CO₂)₂ clusters > (MgO)_m(CO₂) clusters > (MgO)_m clusters by the average binding energy. Certain low-lying isomers of (MgO)_m(CO₂) and (MgO)_m(CO₂)₂ clusters which have an isolated O atom are deviating from the cluster center which possess higher kinetic activity. (MgO)_m clusters prefer to adsorb a CO₂ molecule, while (MgO)₃(CO₂) clusters prefer to adsorb a CO₂ molecule rather than the neighbors. Magnesite is difficult to transit to (MgCO₃)₂ clusters at room temperature. However, magnesite will spontaneously transit to (MgO)₂ clusters and further transit to MgO crystal which need to adsorb more energy at 700?K.     

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.     

Spatial and electronic structures of the germanium-tantalum clusters TaGe n − (n = 8–17)

The results of optimizing the spatial structure and calculated electronic spectra of the TaGe _n ^? anion clusters (n = 8–17) have been presented. The calculations have been performed in terms of the density functional theory. The most probable spatial structures of clusters detected in the experiment have been determined by comparing the calculated and available experimental data.     

DFT study of CO adsorption on neutral and charged Pd<Subscript>n</Subscript>(n = 1–7) clusters

Density functional calculations have been performed to investigate CO adsorption on neutral, cationic and anionic Pd_n (n=1–7) clusters. From the results, it is observed that the binding of CO molecule to neutral and cationic palladium clusters takes place via 1-, 2- and 3-fold coordination. On the other hand, only terminal adsorption of CO molecule is possible in anionic clusters barring bridging adsorption in Pd₇ ^- cluster.