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.     

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.     

Quantum-Mechanical Study of Small Au2Pdn （n=1 ～ 4） Clusters

Gold-doped palladium clusters, Au2Pdn （n=1～4）, are investigated using the density functional method B3LYP with relativistic effective core potentials （RECP） and LANL2DZ basis set. The possible geometrical configurations with their electronic states are determined, and the stability trend is investigated. Several low-lying isomers are determined, and many of them are in electronic configurations with a high-spin multiplicity. Our results indicate that the palladium-gold interaction is strong enough to modify the known pattern of bare palladium clusters, and the lower stability as the structures grow in size. The present calculations are useful to understanding the enhanced catalytic activity and selectivity gained by using gold-doped palladium catalyst.     

First Principle Calculation on AunAg2 （n = 1 - 4） Clusters

The first-principles method based on density-functional theory is used to investigate the geometries of the lowest-lying isomers of AunAg2 （n = 1 - 4） clusters. Several low-lying isomers are determined, and many of them in electronic configurations with a high spin multiplicity. The stability trend of Ag-doped Aun dusters is compared to that of pure Aun clusters. Our results indicate that the inclusion of two Ag atoms in the clusters lowers the cluster stability, indicating higher stability as the structures grow in size. The bigger energy difference between the Aun and AunAg2 curves as the structures grows in size. This information will be useful to understanding the enhanced catalytic activity and selectivity gained by using silver-doped gold catalyst.     

A density functional theoretical investigation of RhSin（n = 1-6） clusters

This paper computationally investigates the RhSin （n = 1 6） clusters by using a density functional approach. Geometry optimizations of the RhSin （n = 1 6） clusters are carried out at the B3LYP level employing LanL2DZ basis sets. It presents and discusses the equilibrium geometries of the RhSin （n = 1-6） clusters as well as the corresponding averaged binding energies, fragmentation energies, natural populations, magnetic properties, and the energy gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital. Theoretical results show that the most stable RhSin（n = 1-6） isomers keep an analogous framework of the corresponding Sin＋1 clusters, the RhSi3 is the most stable cluster in RhSin （n = 1-6） isomers. Furthermore, the charges of the lowest-energy RhSin （n = 1-6） clusters transfer mainly from Si atom to Rh atom. Meanwhile, the magnetic moments of the RhSin（n = 1-6） arises from the 4d orbits of Rh atom. Finally, compared with the Sin＋1 cluster, the chemical stability RhSin clusters are universally improved.     

Ab initio calculations for the absorption spectra and polarizabilities of small sulfur clusters

Absorption spectra for Sn clusters （n=2...8） are calculated using an adiabatic time-dependent density functional formalism within the local density approximation （LDA）. We compare the calculated spectra with those computed using a simple LDA approach. The time-dependent LDA （TDLDA） spectra display a significant blue shift with respect to the LDA spectra. The calculated spectra present a variety of features that can be used for comparison with future experimental investigations. We also obtain a significant threshold absorption, which can distinguish between different ground states of the sulfur clusters. In addition, the polarizabilities of the clusters are calculated by using the higherorder finite-difference pseudopotential density functional method in real space. We find that the polarizabilities of the clusters considered are higher than the value estimated from the ＇hard sphere＇ model using the bulk static dielectric constant. The computed polarizabilities per atom tend to decrease with increasing cluster size. The polarizabilities are closely related to the HOMO-LUMO gaps and the geometrical configurations.     

Structural and bonding properties of ScSi_n~-(n=2～6) clusters:photoelectron spectroscopy and density functional calculations

Anion ion photoelectron spectroscopy and density functional theory (DFT) are used to investigate the electronic and structural properties of ScSi_n^- (n=2sim6) clusters and their neutrals. We find that the structures of ScSi_n^- are similar to those of Si_n+1^-. The most stable isomers of ScSi_n^- cluster anions and their neutrals are similar for n=2, 3 and 5 but different for n=4 and 6, indicating that the charge effect on geometry is size dependent for small scandium-silicon clusters. The low electron binding energy (EBE) tails observed in the spectra of ScSi_4,6^- can be explained by the existence of less stable isomers. A comparison between ScSi_n^- and VSi_n^- clusters shows the effects of metal size and electron configuration on cluster geometries.     

Density functional theory study of Mg2Nin （n = 1-8） clustersDensity functional theory study of Mg2Nin （n = 1-8） clustersDensity functional theory study of Mg2Nin （n = 1-8） clustersDensity functional theory study of Mg2Nin （n = 1-8） clustersDensity functional theory study of Mg2Nin （n = 1-8） clusters

The density functional theory B3PW91 with LANL2DZ basis sets has been used to study the possible geometries of Mg2Nin （n - 1-8） clusters. For the lowest energy structures of the clusters, stabilities, electronic properties, and natural bond orbital （NBO） are calculated and discussed. The results show that the doped Mg atoms reduce the stabilities of pure Ni clusters. The Mg2Ni2, Mg2Ni4, and Mg2Ni6 clusters are more stable than neighboring clusters. The system appears magic number characteristics. In addition, the hybridization phenomenon occurs, owing to the interaction of Mg and Ni. The result of charge transfer is that Ni atom is negative and the Mg atom is positive. We also conclude that the 3p and 4d orbitals of the Ni atom have an effect on the stabilities of the clusters.     

Density functional theory study on the structure and properties of Si3N4 clusters

The hybrid density functional theory B3LYP with basis sets 6-31G＊ has been used to study on the equilibrium geometries and electronic structures of possible isomers of Si3N4 clusters. 24 possible isomers are obtained. The most stable isomer of Si3N4 is a 3D structure with 7 Si-N bonds and 2 N-N bonds that could beformed by 3 quadrangles. The bond properties of the most stable isomer was analyzed by using natural bond orbital method （NBO）, the results suggest that the charges on Si and N atoms in Si-N bonds are quite large, so theinteraction of N-Si atoms in Si3N4 cluster is of strongly electric interaction. The primary IR and Raman vibrational frequency located at 1033.40 cm^-1, 473.63 cm^-1 respectively. The polarizabilities and hyperpolarizabilities of the most stable isomer are also analyzed.     

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.     

Assignment of Photoelectron Spectra of MC2 （M= V, Cr, Fe, and Co）

Hybrid density functional theory （DFT） calculations are performed to study MC2 （M= V, Cr, Fe and Co） clusters in the neutral and anionic charge states. We find that the equilibrium geometries of MC2 and their anions are all cyclic structures with C2v symmetry, which agrees well with the previous theoretical studies. The Mulliken charge and spin populations of MC2 clusters and their anions are also calculated, and it is found that the electron charge transformations from anions to neutral molecules mainly take place on the M atoms. Time-dependent DFT is used to calculate the excited states, and a theoretical assignment for the features in the experimental photoelectron spectrum is given, which are in good agreement with the available experimental data.     

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

The equilibrium geometries, relative stabilities, and electronic properties of MnAgm（M=Na, Li; n ＋ m ≤ 7） as well as pure Agn, Nan, Lin （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 Agn, Nan, and Lin 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 NanAgm and LinAgm clusters. When n ＋ m ≥5, a striking feature is that the trigonal bipyramid becomes the main subunit of LinAgm. 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.     

Structures and Electronic Properties of CuN （N≤13） Clusters

A systematic study on the structures and electronic properties of copper clusters has been performed using the density functional theory. In the calculation, there are many isomers near the ground state for small copper clusters. Our results show that the three-dimensional isomers of copper clusters start from Cu7 cluster and then show a tendency to form more compact structures. The results of the formation energy and the second derivative of binding energy with duster size show that besides N = 8, N =11 is also a magic number. Furthermore, it is the first time to find that the ground state of 11-atom clusters is a biplanar structure as same as the 13-atom cluster. The clear odd-even alternation as cluster size for the formation energy indicates the stability of electronic close shell existed in the range studied.     

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.     

First Principle Calculation on Aun Ag2 (n = 1 ～ 4) Clusters

The first-principles method based on density-functional theory is used to investigate the geometries of the lowest-lying isomers of Aun Ag2 (n = 1 ～ 4) clusters. Several low-lying isomers are determined, and many of them in electronic configurations with a high spin multiplicity. The stability trend of Ag-doped Aun clusters is compared to that of pure Aun clusters. Our results indicate that the inclusion of two Ag atoms in the clusters lowers the cluster stability, indicating higher stability as the structures grow in size. The bigger energy difference between the Aun and Aun Ag2 curves as the structures grows in size. This information will be useful to understanding the enhanced catalytic activity and selectivity gained by using silver-doped gold catalyst.     

Time-Dependent Local Density Approximation Calculations for Absorption Spectra of Small Carbon Clusters

Absorption spectra for Cn clusters (n = 2-8) are calculated using an adiabatic time-dependent density functional formalism within the local density approximation (TDLDA). We compare the calculated spectra with those computed using a simple local density approximation approach. It is readily observed that the TDLDA spectra display a significant blue shift with respect to the Kohn-Sham eigenvalue spectra. The calculated spectra exhibit a variety of features that can be used for comparison against future experimental investigations. We also obtain a significant threshold absorption, which can distinguish different ground states of the carbon 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.     

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.     

Ab initio calculation on accurate analytic potential energy functions and harmonic frequencies of c^3∑g^＋ and B^1-Пu states of dimer 7Li2

The comparison between single-point energy scanning （SPES） and geometry optimization （OPT） in determining the equilibrium geometries of c^3∑g^＋ and B^1-Пu states of dimer 7Li2 is made at numerous basis sets by using a symmetryadapted-cluster configuration-interaztion （SAC-CI） method in the Gaussian 03 program package. In this paper the difference of the equilibrium geometries obtained by SPES and by OPT is reported. The results obtained by SPES are found to be more reasonable than those obtained by OPT in full active space at the present SAC-CI level of theory. And the conclusion is attained that the cc-PVTZ is a most suitable basis set for these states. The calculated dissociation energies and equilibrium geometries are 0.8818 eV and 0.3090 nm for c^3∑g^＋ state, and 0.3668 eV and 0.2932 nm for B^1-Пu state respectively. The potential energy curves are calculated over a wide internuclear distance range from about 2.5α0 to 37α0 and have a least-squares fit into the Murrell-Sorbie function. According to the calculated analytic potential energy functions, the harmonic frequencies （We） and other spectroscopic data （ωeXe, Be and αe） are calculated. Comparison of the theoretical determinations at present work with the experiments and other theories clearly shows that the present work is the most complete effort and thus represents an improvement over previous theoretical results.     

First-principles calculations for titanium monoxide clusters TinO （n=1-9）

Based on the density-functional theory, this paper studies the geometric and magnetic properties of TinO （n=1-9） clusters. The resulting geometries show that the oxygen atom remains on the surface of clusters and does not change the geometry of Tin significantly. The binding energy, second-order energy differences with the size of clusters show that Ti7O cluster is endowed with special stability. The stability of TinO clusters is validated by the recent time-of-flight mass spectra. The total magnetic moments for TinO clusters with n=1-4, 8-9 are constant with 2 and drop to zero at n=5-7. The local magnetic moment and charge partition of each atom, and the density of states are discussed. The magnetic moment of the TinO is clearly dominated by the localized 3d electrons of Ti atoms while the oxygen atom contributes a very small amount of spin in TinO clusters.