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.     

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.     

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.     

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.     

Effects of shape and dopant on structural,optical absorption,Raman, and vibrational properties of silver and copper quantum clusters: A density functional theory study

We investigate the effects of shape and single-atom doping on the structural, optical absorption, Raman, and vibra- tional properties of Ag13, Ag12CUl, CUl3, and Cul2Agl clusters by using the （time-dependent） density functional the- ory. The results show that the most stable structures are cuboctahedron （COh） for Ag13 and icosahedron （Ih） for CUl3, Agl2CUlcore, and Cul2Aglsur. In the visible-near infrared optical absorption, the transitions consist of the interband and the intraband transitions. Moreover, red shifts are observed as follows： 1） clusters change from Agl2CUlcore to Ag13 to Ag12Culsur with the same motifs, 2） the shapes of pure Agl3 and Agl2CUlcore clusters change from COh to Ih to decahe- dron （Dh）, 3） the shape of Agl2CUlsur clusters changes from Ih to COh to Dh, and 4） the shapes of pure CU13 and Cu12Agl clusters change from Ih to Dh to COb. All of the Raman and vibrational spectra exhibit many significant vibrational modes related to the shapes and the compositions of the clusters. The ranges of vibrational spectra of Ag13, Agl2CUl or CU13, and Cu12Agl clusters become narrower and the vibrational intensities increase as the shape of the clusters changes from Ih to Dh to COh.     

Tin-mZrmO2n(n=2-7，0≤m≤n)团簇结构和稳定性研究

应用密度泛函理论中的B3LYP方法对Tin-mZrmO2n (n = 2-7,0≤m≤n) 团簇的基态几何结构、相对稳定性和电子结构进行了理论研究.结果表明,与桥氧链接的Ti原子被Zr原子取代后形成的混合团簇较为稳定;在团簇尺寸一定的条件下（即n相同）,随着Zr原子数m的增加,团簇的结合能基本呈线性增大,团簇的稳定性增强;Ti、Zr、O原子之间发生了电荷转移现象,形成了稳定的Ti-O-Zr键.     

第一性原理比较研究MnPm(M=Al,Ga,In,2≤n+m≤3)团簇

利用密度泛函理论对MnPm (M=Al,Ga,and In,2≤n+m≤3)团簇的几何和电子结构性质及稳定性进行了研究.结果表明,三原子的MnPm团簇是二重态,而单体则是三重态.富P的MP2团簇是具有C2V对称性的等腰三角形结构,而富M的M2P团簇则是具有Cs对称性的三角形结构.在三原子磷化物团簇中,MP2团簇比M2P团簇稳定,而后者中M-P键的强度比前者强.对于这些小的磷化物团簇,电离势高于裂解能,表明裂解比电离占优势.Ga2P比Al2P和In2P的HOMO-LUMO能隙和电离势都高,归咎于在富金属的M2P团簇中,相对较强的Ga-P键.     

第一性原理比较研究MnPm (M=Al, Ga, and In,2≤n+m≤3)团簇

利用密度泛函理论对MnPm (M=Al,Ga,and In)团簇的几何和电子结构性质及稳定性进行了研究。结果表明,三原子的MnPm团簇是二重态,而单体则是三重态。富P的MP2团簇是具有C2V对称性的等腰三角形结构,而富M的M2P团簇则是具有Cs对称性的三角形结构。在三原子磷化物团簇中,MP2团簇比M2P团簇稳定,而后者中M-P键的强度比前者强。对于这些小的磷化物团簇,电离势高于裂解能,表明裂解比电离占优势。 Ga2P比Al2P和In2P的HOMO-LUMO能隙和电离势都高,归咎于在富金属的M2P团簇中,相对较强的Ga-P键。     

A density functional theory study of the electronic structures and magnetic properties of Fe（1-x）Cox alloy nanowires encapsulated in （10,0） carbon nanotubes

Under the generalized gradient approximation, the electronic structures and magnetic properties of Fe_(1-x)Co_x alloy nanowires encapsulated inside zigzag (10,0) carbon nanotubes (CNTs) are investigated systematically using firstprinciple density functional theory calculations. For the fully relaxed Fe_(1-x)Co_x/CNT structures, all the C atoms relax outwards, and thus the diameters of the CNTs are slightly increased. Formation energy analysis shows that the combining processes of all Fe_(1-x)Co_x/CNT systems are exothermic, and therefore the Fe_(1-x)Co_xalloy nanowires can be encapsulated into semiconducting zigzag (10,0) CNTs and form stable hybrid structures. The charges are transferred from the Fe_(1-x)Co_xnanowires to the more electronegative CNTs, and the Fe-C/Co-C bonds formed have polar covalent bond characteristics. Both the spin polarization and total magnetic moment of the Fe_(1-x)Co_x/CNT system are smaller than those of the corresponding freestanding Fe_(1-x)Co_xnanowire, and the magnetic moment of the Fe_(1-x)Co_x/CNT system decreases monotonously with increasing Co concentration, but the Fe_(1-x)Co_x/CNT systems still have a large magnetic moment, implying that they can be utilized in high-density magnetic recording devices.     

First-principles study on the structure,electronic and magnetic properties of HoSin （n=1-12, 20） clusters

The structure, electronic and magnetic properties of HoSin（n= 1 - 12, 20） clusters have been widely investigated by first-principles calculation method based on density flmctional theory （DFT）. From our calculation results, we find that for HoSin（n=1- 12） clusters except n = 7.10, the most stable structures are a replacement of Si atom in the corresponding pure Sin＋1 clusters by Ho atom. The doping of Ho atom makes the stability of Si clusters enhance remarkably, and HoSin（n = 2, 5, 8, 11） clusters are more stable than their neighboring clusters. The magnetic moment of Ho atom in HoSin （n = 1 - 12, 20） clusters mainly comes from of electron of tto, and never quenches.     

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.     

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.     

Geometrical,energetic and electronic properties of Au_n-(C_3H_6O)_m complexes(n = 3,5,m≤n):A density functional theory study

<正>The interactions of acetone molecules with clusters of AU_3 and Au_5 are investigated by using a density functional theory(DFT) within a generalized gradient approximation(GGA).The geometries,adsorption energies and deformation electron density distributions are used to analyse these interactions.The present calculations show that more than one acetone molecule can be adsorbed onto small gold clusters,and this adsorption is different from that of single molecule absorption.The coordination number of the adsorption site on the gold cluster is the dominant factor responsible for the strength of the interactions.The effects of the Au-O bond lengths in the complexes on adsorption energies between Au clusters and acetone molecules are also examined.     

High stability of the goldalloy fullerenes：A density functional theory investigation of M_（12）@Au_（20）（M=Na,Al,Ag,Sc,Y,La,Lu,and Au） clusters

Discovering highly stable metal fullerenes such as the celebrated C 60 is interesting in cluster science as they have potential applications as building blocks in new nanostructures.We here investigated the structural and electronic properties of the fullerenes M 12 @Au 20（M=Na,Al,Ag,Sc,Y,La,Lu,and Au）,using a first-principles investigation with the density functional theory.It is found that these compound clusters possess a similar cage structure to the icosahedral Au 32 fullerene.La 12 @Au 20 is found to be particularly stable among these clusters.The binding energy of La 12 @Au 20 is 3.43 eV per atom,1.05 eV larger than that in Au 32.The highest occupied molecular orbital-lowest unoccupied molecular orbital（HOMO-LUMO） gap of La 12 @Au 20 is only 0.31 eV,suggesting that it should be relatively chemically reactive.     

A density functional theory study on the adsorption of CO and O2 on Cu-terminated Cu2O （111） surface

The adsorptions of CO and 02 molecules individually on the stoichiometric Cu-terminatcd Cu20 （111） surface are investigated by first-principles calculations on the basis of the density functional theory. The calculated results indicate that the CO molecule preferably coordinates to the Cu2 site through its C atom with an adsorption energy of-1.69 eV, whereas the 02 molecule is most stably adsorbed in a tilt type with one O atom coordinating to the Cu2 site and the other O atom coordinating to the Cul site, and has an adsorption energy of -1.97 eV. From the analysis of density of states, it is observed that Cu 3d transfers electrons to 2π orbital of the CO molecule and the highest occupied 5σ orbital of the CO molecule transfers electrons to the substrate. The sharp band of Cu 4s is delocalized when compared to that before the CO molecule adsorption, and overlaps substantially with bands of the adsorbed CO molecule. There is a broadening of the 2π orbital of the 02 molecule because of its overlapping with the Cu 3d orbital, indicating that strong 3d-2π interactions are involved in the chemisorption of the 02 molecule on the surface.     

First-principles study of the structural,mechanical and electronic properties of ZnX204 （X=Al,Cr and Ga）

This paper performs first-principles calculations to study the structural, mechanical and electronic properties of the spinels ZnA1204, ZnGa2O4 and ZnCr2O4, using density functional theory with the plane-wave pseudopotential method. Our calculations are in good agreement with previous theoretical calculations and the available experimental data. The studies in this paper focus on the evolution of the mechanical properties of ZnAl2O4, ZnGa2O4 and ZnCr2O4 under hydrostatic pressure. The results show that the cubic phases of ZnAl2O4, ZnCa2O4 and ZnCr2O4 become unstable at about 50 GPa, 40 GPa and 25 GPa, respectively. From analysis of the band structure of the three compounds at equilibrium volume, it obtains a direct band gap of 4.35 eV for ZnA1204 and 0.89 cV for ZnCr2O4, while ZnGa2O4 has an indirect band gap of 2.73 eV.     

The structural,elastic, and electronic properties of ZrxNbl-xC alloys from first principle calculations＊

The structural, elastic, electronic, and thermodynamic properties of ZrxNbl xC alloys are investigated using the first principles method based on the density functional theory. The results show that the structural properties of Zr~.Nb1 xC alloys vary continuously with the increase of Zr composition. The alloy possesses both the highest shear modulus （215 GPa） and a higher bulk modulus （294 GPa）, with a Zr composition of 0.21. Meanwhile, the Zr0.2! Nb0.79C alloy shows metallic conductivity based on the analysis of the density of states. In addition, the thermodynamic stability of the designed alloys is estimated using the calculated enthalpy of mixing.     

W_n Ni_m(n+m≤7;m=1,2)团簇电子结构与光谱性质的理论研究

采用密度泛函理论(DFT)中的B3PW91方法在LANL2DZ基组水平上对WnNim(n+m≤7;m=1,2)团簇的各种可能构型进行了几何结构优化,得出了它们的基态构型,并对其NBO、振动频率、光谱和极化率进行了理论研究.研究结果表明:W,Ni原子内部杂化现象较强,而在W-Ni原子之间杂化较弱;在W和Ni相互作用形成合金团簇的过程中,发生原子间的电荷转移,使得合金团簇中大多数Ni原子带正电荷W原子带负电荷;从光学上分析显示,W6Ni团簇的IR和Raman谱中的振动峰最多,W5Ni2的IR和Raman谱中的振动峰最强,W2Ni的IR谱中只有一个较强峰值;WnNim(n+m≤7;m=1,2)团簇中原子间的成键相互作用随W成分的增加而增强.     

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.