A density functional theory study on size-dependent structures,stabilities,and electronic properties of bimetallic M_nAg_m(M=Na,Li;n + m≤7) clusters

The equilibrium geometries,relative stabilities,and electronic properties of Mn Agm(M=Na,Li;n + m ≤ 7) as well as pure Ag n,Na n,Li n(n ≤ 7) clusters are systematically investigated by means of the density functional theory.The optimized geometries reveal that for 2 ≤ n ≤ 7,there are significant similarities in geometry among pure Ag n,Na n,and Li n clusters,and the transitions from planar to three-dimensional configurations occur at n = 7,7,and 6,respectively.In contrast,the first three-dimensional(3D) structures are observed at n + m = 5 for both Na n Ag m and Li n Ag m clusters.When n + m ≥ 5,a striking feature is that the trigonal bipyramid becomes the main subunit of Li n Ag m.Furthermore,dramatic odd-even alternative behaviours are obtained in the fragmentation energies,secondorder difference energies,highest occupied and lowest unoccupied molecular orbital energy gaps,and chemical hardness for both pure and doped clusters.The analytic results exhibit that clusters with an even electronic configuration(2,4,6) possess the weakest chemical reactivity and more enhanced stability.     

First-Principles Study of Geometries,Stabilities and Electronic Properties of Ca2Sin （n=1-11） Clusters

The equilibrium geometries, relative stabilities, and electronic properties of Ca2Sin （n = 1-11） clusters have been systematically investigated by using the density function theory at the 6-311G （d） level The optimized geometries indicate that the most stable isomers have three-dimensional structures for n = 3-11. The electronic properties of Ca2 Sin （n = 1-11） dusters axe obtained through the analysis of the natural charge population, natural electron configuration, vertical ionization potential, and vertical electron affinity. The results show that the charges in corresponding Ca2Sin clusters transfer from the Ca atoms to the Sin host. Based on the obtained lowest-energy geometries, the size dependence of cluster properties, such as averaged binding energies, fragmentation energies, second-order energy differences, HOMO- LUMO gaps and chemical hardness, are deeply discussed.     

Structural, electronic, and magnetic properties of boron cluster anions doped with aluminum: BnAl- (2≤n≤9)

The geometrical structures, relative stabilities, electronic and magnetic properties of small B n Al (2 ≤ n ≤ 9) clusters are systematically investigated by using the first-principles density functional theory. The results show that the Al atom prefers to reside either on the outer-side or above the surface, but not in the centre of the clusters in all of the most stable B n Al (2 ≤ n ≤ 9) isomers and the one excess electron is strong enough to modify the geometries of some specific sizes of the neutral clusters. All the results of the analysis for the fragmentation energies, the second-order difference of energies, and the highest occupied-lowest unoccupied molecular orbital energy gaps show that B 4 Al and B 8 Al clusters each have a higher relative stability. Especially, the B 8 Al cluster has the most enhanced chemical stability. Furthermore, both the local magnetic moments and the total magnetic moments display a pronounced odd-even oscillation with the number of boron atoms, and the magnetic effects arise mainly from the boron atoms except for the B 7 Al and B 9 Al clusters.     

Density functional study on the bimetallic Ti_mZr_n(n+m ≤ 5) clusters and their interactions with H_2

Equilibrium geometries, stabilities, and electronic properties of small Ti_mZr_n(n + m ≤ 5) clusters were investigated using the density functional method. The ground states were determined, and it was found that the larger clusters and those consisting of more Zr atoms are more stable. The electronic properties of the clusters were discussed based on HOMO-LUMO gaps, vertical ionization potentials(VIP), and vertical electron affinities(VEA). Furthermore, we studied the interactions between those clusters and molecular hydrogen, and found that in all the cases dissociative chemisorptions occurred. According to the chemisorption energies, the pure Zr clusters are relatively more active towards H_2 when compared with the others except Ti_3Zr, which shows the highest activity. The magnetic moments of Ti_mZr_n and Ti_mZr_nH_2 were also compared, and the results show that the hydrogenated clusters have the same or decreased total magnetic moments with respect to the bare clusters except for Ti_3Zr_2.     

A density functional theory study on size-dependent structures, stabilities, and electronic properties of the bimetallic MnAgm (M=Na, Li; n+m ≤ 7) clusters

The equilibrium geometries, relative stabilities, and electronic properties of M_nAg_m (M=Na, Li; n+m≤ 7) as well as pure Ag_n, Na_n, Li_n (n≤ 7) clusters are systematically investigated by means of density functional theory. The optimized geometries reveal that for 2≤ n ≤ 7, there are significant similarities in geometry among pure Ag_n, Na_n, and Li_n clusters, and the transitions from planar to three-dimensional configurations occur at n=7, 7, and 6, respectively. In contrast, the first three-dimensional (3D) structures are observed at n+m=5 for both Na_nAg_m and Li_nAg_m cluters. When n+m ≥ 5, a striking feature is that the trigonal bipyramid becomes the main subunit of Li_nAg_m. Furthermore, dramatic odd-even alternative behaviours are obtained in the fragmentation energies, second-order difference energies, highest occupied and lowest unoccupied molecular orbital energy gaps, and chemical hardness for both pure and doped clusters. The analytic results exhibit that clusters with even electronic configuration (2, 4, 6) possess weakest chemical reactivity and more enhanced stability.     

A comparative study on geometries,stabilities, and electronic properties between bimetallic AgnX（X=Au,Cu;n=1-8）and pure silver clusters

Using the meta-generalized gradient approximation (meta-GGA) exchange correlation TPSS functional, the geo- metric structures, the relative stabilities, and the electronic properties of bimetallic Ag n X (X=Au, Cu; n=1–8) clusters are systematically investigated and compared with those of pure silver clusters. The optimized structures show that the transition point from preferentially planar to three-dimensional structure occurs at n = 6 for the Ag n Au clusters, and at n = 5 for Ag n Cu clusters. For different-sized Ag n X clusters, one X (X=Au or Cu) atom substituted Ag n+1 structure is a dominant growth pattern. The calculated fragmentation energies, second-order differences in energies, and the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps show interesting odd–even oscillation behaviours, indicating that Ag 2,4,6,8 and Ag 1,3,5,7 X (X=Au, Cu) clusters keep high stabilities in comparison with their neighbouring clusters. The natural population analysis reveals that the charges transfer from the Ag n host to the impurity atom except for the Ag 2 Cu cluster. Moreover, vertical ionization potential (VIP), vertical electronic affinity (VEA), and chemical hardness (η) are discussed and compared in depth. The same odd–even oscillations are found for the VIP and η of the Ag n X (X=Au, Cu; n=1–8) clusters.     

Structural,electronic, and magnetic properties of boron cluster anions doped with aluminum：BnAl-（2〈n〈9）

The geometrical structures, relative stabilities, electronic and magnetic properties of small BnAl-（2〈n〈9）clusters are systematicalyy investigated by using the first-principles density functional theory. The results show that the A1 atom prefers to reside either on the outer-side or above the surface, but not in the centre of the clusters in all of the most stable BnAl-（2〈n〈9） isomers and the one excess electron is strong enough to modify the geometries of some specific sizes of the neutral clusters. All the results of the analysis for the fragmentation energies, the second-order difference of energies, and the highest occupied-lowest unoccupied molecular orbital energy gaps show that B4A1- and B8A1- clusters each have a higher relative stability. Especially, the BsA1-cluster has the most enhanced chemical stability. Furthermore, both the local magnetic moments and the total magnetic moments display a pronounced oddeven oscillation with the number of boron atoms, and the magnetic effects arise mainly from the boron atoms except for the B7A1- and BgA1- clusters.     

First-principle studies of the geometries and electronic properties of Cum Sin (2≤m+n≤7)clusters

The equilibrium geometries and electronic properties of CumSin （2 ≤m ＋ n ≤ 7） clusters have been studied by using density functional theory at the B3LYP/6-311＋G （d） level. Our results indicate that the structure of CuSin （n 〈6） keeps the frame of the corresponding Sin cluster unchanged, while for CunSi clusters, the rectangular pyramid structure of Cu4Si is shown to be a building block in many structures of larger CunSi clusters. The growth patterns of CumSin clusters become more complicated as the number of Cu atoms increases. Both the binding energies and the fragmentation energies indicate that the Si-Si bond is stronger than the Cu-Si bond, and the latter is stronger than the Cu-Cu bond. Combining the fragmentation energies in the process CumSin →Cu＋Cum-l Sin and the second-order difference △2E（m） against the number of Cu atoms of CumSin, we conclude that CumSin clusters with even number of Cu atoms have higher stabilities than those with odd rn. According to frontier orbital analyses, there exists a mixed ionic and covalent bonding picture between Cu and Si atoms, and the Cud orbitals contribute little to the Cu-Si bonding. For a certain cluster size （m ＋ n = 3, 4, 5, 6, 7）, the energy gaps of the most stable CumSin clusters show odd-even oscillation with changing m, the clusters with odd m exhibit stronger chemical reactivity than those with even m.[第一段]     

Density functional theory study of MgnNi2 （n=1-6） clusters

The geometries of Mg n Ni 2(n = 1-6) clusters are studied by using the hybrid density functional theory(B3LYP) with LANL2DZ basis sets.For the ground-state structures of Mg n Ni 2 clusters,the stabilities and the electronic properties are investigated.The results show that the groundstate structures and symmetries of Mg clusters change greatly due to the Ni atoms.The average binding energies have a growing tendency while the energy gaps have a declining tendency.In addition,the ionization energies exhibit an odd-even oscillation feature.We also conclude that n = 3,5 are the magic numbers of the Mg n Ni 2 clusters.The Mg 3 Ni 2 and Mg 5 Ni 2 clusters are more stable than neighbouring clusters,and the Mg 4 Ni 2 cluster exhibits a higher chemical activity.     

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.     

Structural,electronic,and magnetic properties in FeAlAu_n(n=1–6)clusters:A first-principles study

The geometries,electronic and magnetic properties of the trimetallic clusters Fe Al Aun(n = 1–6) are systematically investigated using density functional theory(DFT).A number of new isomers are obtained to probe the structural evolutions.All doped clusters show larger relative binding energies than pure Aun+2partners,indicating that doping with Fe and Al atoms can stabilize the Aun clusters.The highest occupied molecular orbital–lowest unoccupied molecular orbital(HOMO–LUMO) gaps,vertical ionization potentials and vertical electron affinities are also studied and compared with those of pure gold clusters.Magnetism calculations demonstrate that the magnetic moments of Fe Al Aun clusters each show a pronounced odd–even oscillation with the number of Au atoms.     

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.     

Structures and electronic properties of SimN8-m（0 〈 m 〈 8） clusters： a density functional theory study

The geometries, electronic structures and related properties of SimN8-m（0 〈 m 〈 8） clusters are studied using density functional theory （DFT） with hybrid functional B3LYP. The calculated results reveal several trends. For any stoichiometric clusters, the lowest energy isomers with an alteration of N and Si atoms are favourable in energy if the numbers of Si and N atoms are large enough to form ... Si N-Si-N... alternative chains. The bond lengths of single Si-N bonds are very close to the corresponding values of the bulk and other SiN clusters. The geometries for N-rich and Si4N4 clusters are planar structures, but three-dimensional structures are favourable in energy for Si-rich clusters. With the increase of m, the isotropic polarizability and average polarizability increase, the total binding energies generally decrease, the HOMO-LUMO gap and vertical ionization potential oscillate with increasing number of valence electrons, and their values with even valence electrons are larger than those with odd valence electrons. The atomic charges, IR and Raman properties are also reported.     

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.     

Equilibrium geometries and electronic properties of BenLi （n=2-15） clusters from first principles

This paper studies the equilibrium geometries and electronic properties of Ben and BenLi clusters, up to n=15, by using density-functional theory（DFT） at B3LYP/6-31G（d） level. The lowest-energy structures of Ben and BenLi clusters were determined. The results indicate that a single lithium impurity enhances the stability and chemical reactivity of the beryllium clusters. It finds that the geometries of the host clusters change significantly after the addition of the lithium atom for n ≥8. The lithium impurity prefers to be on the periphery of beryllium clusters, and occupies vertex sites. Both Be4Li, Be9Li, and Be13Li were found to be particularly stable with higher average binding energy, local peaks of second-order energy difference and fragmentation energies. For all the BenLi clusters studied, we found charge transfers from the Li to Be site and co-existence of covalent and metallic bonding characteristics.     

Structure,stability and electronic properties of SrSin （n ： 1-12） clusters： Density-functional theory investigationStructure,stability and electronic properties of SrSin （n ： 1-12） clusters： Density-functional theory investigation

Geometric structures, stabilities, and electronic properties of SrSin （n = 1-12） clusters have been investigated using the density-functional theory within the generalized gradient approximation. The optimized geometries indicate that one Si atom capped on SrSin_ 1 structure and Sr atom capped Sin structure for difference SrSin clusters in size are two dominant growth patterns. The calculated average binding energy, fragmentation energy, second-order energy difference, the highest occupied molecular orbital, and the lowest unoccupied molecular orbital （HOMO-LUMO） gaps show that the doping of Sr atom can enhance the chemical activity of the silicon framework. The relative stability of SrSi9 is the strongest among the SrSin clusters. According to the mulliken population and natural population analysis, it is found that the charge in SrSin clusters transfer from Sr atom to the Sin host. In addition, the vertical ionization potential, vertical electron affinity, and chemical hardness are also discussed and compared.     

Structural evolutions and electronic properties of Au_nGd(n=6–15) small clusters: A first principles study

Structural, electronic, and magnetic properties of Au_nGd(n = 6–15) small clusters are investigated by using first principles spin polarized calculations and combining with the ab-initio evolutionary structure simulations. The calculated binding energies indicate that after doping a Gd atom Aun Gd cluster is obviously more stable than a pure Au_(n+1) cluster.Au_6Gd with the quasiplanar structure has a largest magnetic moment of 7.421 μ_B. The Gd-4 f electrons play an important role in determining the high magnetic moments of Au_nGd clusters, but in Au_6Gd and Au_(12) Gd clusters the unignorable spin polarized effects from the Au-6 s and Au-5 d electrons further enhance their magnetism. The HOMO–LUMO(here, HOMO and LUMO stand for the highest occupied molecular orbital, and the lowest unoccupied molecular orbital, respectively)energy gaps of Au_nGd clusters are smaller than those of pure Au_(n+1) clusters, indicating that Au_nGd clusters have potential as new catalysts with enhanced reactivity.     

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 MPt 6 (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 Pt 7 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 Pt 7 cluster. The magnetism calculations demonstrate that the variation range of the magnetic moments of the MPt 6 clusters is from 0 μ B to 7 μ B , revealing that the MPt 6 clusters have potential utility in designing new spintronic nanomaterials with tunable magnetic properties.     

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.     

Density-functional investigation of 3d,4d,5d impurity doped Au6 clusters

The general features of the geometries and electronic properties for 3d,4d,and 5d transition-metal atom doped Au 6 clusters are systematically investigated by using relativistic all-electron density functional theory in the generalized gradient approximation(GGA).A number of structural isomers are considered to search the lowest-energy structures of M@Au 6 clusters(M=3d,4d and 5d transition-metal atoms),and the transition metal atom locating in the centre of an Au 6 ring is found to be in the ground state for all the M@Au 6 clusters.All doped clusters,expect for Pd@Au 6,show large relative binding energies compared with a pure Au 7 cluster,indicating that doping by 3d,4d,5d transition-metal atoms could stabilize the Au 6 ring and promote the formation of a new binary alloy cluster.