Density-functional study of structural and electronic properties of Si(n)C(n) (n=1-10) clusters

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the structural and electronic structure of Si(n)C(n) (n=1-10) clusters. The geometries are found to undergo a structural change from two dimensional to three dimensional when the cluster size n equals 4. Cagelike structures are favored as the cluster size increases. A distinct segregation between the silicon and carbon atoms is observed for these clusters. It is found that the C atoms favor to form five-membered rings as the cluster size n increases. However, the growth motif for Si atoms is not observed. The Si(n)C(n) clusters at n=2, 6, and 9 are found to possess relatively higher stability. On the basis of the lowest-energy geometries obtained, the size dependence of cluster properties such as binding energy, HOMO-LUMO gap, Mulliken charge, vibrational spectrum, and ionization potential has been computed and analyzed. The bonding characteristics of the clusters are discussed.     

The structural and electronic properties of In(n)N(n = 1-13) clusters

The structural and electronic properties of In(n)N(n=1-13) clusters have been investigated by density-functional theory with the generalized gradient approximation. The results indicate that the equilibrium structures of In(n)N are linear for n=1,2, planar for n=3-5, and three dimensional for n=6-13. Maximum peaks were observed for In(n)N clusters at n=3,7,9 on the size dependence for second-order energy difference. These imply that these clusters possess relatively higher stability, which is consistent with the case of binding energy per atom. Moreover, the results show that the bonding in small In(n)N clusters has a little ionic character by Mulliken population analysis. The energy gap between the highest occupied and lowest unoccupied molecular orbitals, the vertical ionization potential and electron vertical affinity (VIP and VEA) form an even-odd alternating pattern with increasing cluster size. In general, the VIP tends to lower as the cluster size increases, while the VEA tends to increase as the cluster size increases.     

Density functional study of the structures and electronic properties of nitrogen-doped Ni(n) clusters, n = 1-10

We present a first-principles study of the equilibrium geometries, electronic structure, and related properties (binding energies, ionization potentials, electron affinities, and magnetic moments) of free-standing Ni(n) (n = 1-10) clusters doped with one impurity of N. Calculations have been performed in the framework of the density functional theory, as implemented in the SIESTA code within the generalized gradient approximation to exchange and correlation. We show that, in contrast to the molecular adsorption of N(2), the adsorption of a single N atom can dramatically change the structure of the host Ni(n) cluster, examples of which are Ni(5)N, Ni(7)N, and Ni(10)N, and that noticeable structure relaxations take place otherwise. Doping with a nitrogen impurity increases the binding energy as well as the ionization potential (except for Ni(6)N), which proves that N-doping works in favor of stabilizing the Ni clusters. We also find that the magnetic moments decrease in most cases upon N-doping despite the fact that the average Ni-Ni distance increases. The HUMO-LUMO gap for one spin channel strongly changes as a function of size upon N-doping, in contrast with the HUMO-LUMO gap for the other spin channel. This might have important implication in electronic transport properties through these molecular contacts anchored to source and drain electrodes.     

The structural and electronic properties of Ag-adsorbed (SiO2)n (n=1-7) clusters

Equilibrium geometries, charge distributions, stabilities, and electronic properties of the Ag-adsorbed (SiO(2))(n) (n=1-7) clusters have been investigated using density functional theory with generalized gradient approximation for exchange-correlation functional. The results show that the Ag atom preferably binds to silicon atom with dangling bond in nearly a fixed direction, and the incoming Ag atoms tend to cluster on the existing Ag cluster leading to the formation of Ag islands. The adsorbed Ag atom only causes charge redistributions of the atoms near itself. The effect of the adsorbed Ag atom on the bonding natures and structural features of the silica clusters is minor, attributing to the tendency of stability order of Ag(SiO(2))(n) (n=1-7) clusters in consistent with silica clusters. In addition, the energy gaps between the highest occupied and lowest unoccupied molecular orbitals remarkably decrease compared with the pure (SiO(2))(n) (n=1-7) clusters, eventually approaching the near infrared radiation region. This suggests that these small clusters may be an alternative material which has a similar functionality in treating cancer to the large gold-coated silica nanoshells and the small Au(3)(SiO(2))(3) cluster.     

Structures and stabilities of small lead oxide clusters PbmOn (m=1-4,n=1-2m)

The structures and stabilities of small lead oxide clusters PbmOn with m=1-4, n=1-2m are systematically studied using density functional theory. It is found that the lowest-energy structures of all these clusters can be obtained by the sequential oxidation of small "core" lead clusters. For Pb-rich clusters (oxygen-to-lead ratio<1), oxygen atoms favor bridge sites for Pb2On and Pb3On and surface sites for Pb4On. The lead-monoxide-like clusters (PbO)i (i=1-4) have great stability because of their significant dissociation energies and highest occupied molecular orbital-lowest unoccupied molecular orbital gaps. This suggests that they could be adopted as the building blocks of cluster-assembled materials. For O-rich clusters (oxygen-to-lead ratio>1), the grouping of oxygen atoms usually appears. It is found that the structures with a grouping of more than two oxygen atoms are unstable.     

Density functional calculation of the structure and electronic properties of Cu(n)O(n) (n = 1-8) clusters

Ab initio simulations and calculations were used to study the structures and stabilities of copper oxide clusters, Cu(n)O(n) (n = 1-8). The lowest energy structures of neutral and charged copper oxide clusters were determined using primarily the B3LYP/LANL2DZ model chemistry. For n ≥ 4, the clusters are nonplanar. Selected electronic properties including atomization energies, ionization energies, electron affinities, and Bader charges were calculated and examined as a function of n.     

Geometries and electronic properties of the tungsten-doped germanium clusters: WGen (n = 1-17)

Geometries associated with relative stabilities, energy gaps, and polarities of W-doped germanium clusters have been investigated systematically by using density functional theory. The threshold size for the endohedral coordination and the critical size of W-encapsulated Gen structures emerge as, respectively, n = 8 and n = 12, while the fullerene-like W@Ge(n) clusters appears at n = 14. The evaluated relative stabilities in term of the calculated fragmentation energies reveal that the fullerene-like W@Ge(14) and W@Ge(16) structures as well as the hexagonal prism WGe(12) have enhanced stabilities over their neighboring clusters. Furthermore, the calculated polarities of the W@Ge(n) reveal that the bicapped tetragonal antiprism WGe(10) is a polar molecule while the hexagonal prism WGe(12) is a nonpolar molecule. Moreover, the recorded natural populations show that the charges transfer from the germanium framework to the W atom. Additionally, the WGe(12) cluster with large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, large fragmentation energy, and large binding energy is supposed to be suitable as a building block of assembly cluster material. It should be pointed out that the remarkable features of W@Ge(n) clusters above are distinctly different from those of transition metal (TM) doped Ge(n) (TM = Cu and Ni) clusters, indicating that the growth pattern of the TMGe(n) depends on the kind of doped TM impurity.     

Geometrical and electronic properties of neutral and charged cesium clusters Cs(n) (n=2-10): a theoretical study

We have investigated the structure and electronic properties of cesium clusters following all electron ab initio theoretical methods based on configuration interaction, second-order Moller-Plesset (MP2) perturbation theory, and density-functional theory. Becke's three-parameter nonlocal hybrid exchange-correlation functional (B3LYP) is found to perform best on the present systems with a split valence 3-21G basis function. We have calculated the optimized geometries of neutral and singly charged cesium clusters having up to ten atoms, their binding energy per atom, ionization potentials (IPs), and adiabatic electron affinity (EA). Geometry optimizations for all the clusters are carried out without imposing any symmetry restriction. The neutral clusters having up to six atoms prefer planar structure and three-dimensional structure is preferred only when the number of atoms in a cluster is more than six. There is a good agreement between the present theoretical and reported experimental IP values for the neutral clusters with cluster size n相似文献   

Structural and electronic properties of TaSi(n) (n=1-13) clusters: a relativistic density functional investigation

The TaSi(n) (n=1-13) clusters with doublet, quartet, and sextet spin configurations have been systematically investigated by a relativistic density functional theory with the generalized gradient approximation available in Amsterdam density functional program. The total bonding energies, equilibrium geometries, Mulliken populations as well as Hirshfeld charges of TaSi(n) (n=1-13) clusters are calculated and presented. The emphasis on the stabilities and electronic properties is discussed. The most stable structures of the small TaSi(n) (n=1-6) clusters and the evolutional rule of low-lying geometries of the larger TaSi(n) (n=7-13) clusters are obtained. Theoretical results indicate that the most stable structure of TaSi(n) (n=1-6) clusters keeps the similar framework as the most stable structure of Si(n+1) clusters except for TaSi(3) cluster. The Ta atom in the lowest-energy TaSi(n) (n=1-13) isomers occupies a gradual sinking site, and the site moves from convex, to flatness, and to concave with the number of Si atom varying from 1 to 13. When n=12, the Ta atom in TaSi(12) cluster completely falls into the center of the Si frame, and a cagelike TaSi(12) geometry is formed. Meanwhile, the net Mulliken and Hirsheld populations of the Ta atom in the TaSi(n) (n=1-13) clusters vary from positive to negative, manifesting that the charges in TaSi(n) (n>/=12) clusters transfer from Si atoms to Ta atom. Additionally, the contribution of Si-Si and Si-Ta interactions to the stability of TaSi(n) clusters is briefly discussed. Furthermore, the investigations on atomic averaged binding energies and fragmentation energies show that the TaSi(n) (n=2,3,5,7,10,11,12) clusters have enhanced stabilities. Compared with pure silicon clusters, a universal narrowing of highest occupied molecular orbital-lowest unoccupied molecular orbital gap in TaSi(n) clusters is found.     

Structure and properties of Mn(n), Mn(n)-, and Mn(n)+ clusters (n = 3-10)

Electronic and geometrical structures of Mn(3)-Mn(10) together with their singly negatively and positively charged ions are computed using density functional theory with generalized gradient approximation. The ground-state spin multiplicities in the neutral series are 16, 21, 4, 9, 6, 5, 2, and 5, for Mn(3)-Mn(10), respectively. Thus, there is a transition from a ferromagnetic ground state to a ferrimagnetic ground state at Mn(5). The energy difference between ferrimagnetic and ferromagnetic states in Mn(n) grows rapidly with increasing n and exceeds 2 eV in Mn(10). The corresponding change from ferro- to ferrimagnetic ground state occurs at Mn(6)(-) and Mn(3)(+) in the anionic and cationic series, respectively. Beginning with Mn(6), the ion spin multiplicities differ from that of the neutral by +/-1 (i.e., they obey the empirical "+/-1 rule"). We found that the energy required to remove an Mn atom is nearly independent of the charge state of an Mn(n) cluster and the number of atoms in the cluster, except for Mn(3). The results of our calculations are in reasonable agreement with experiment, except for the experimental data on the magnetic moments per atom, where, in general, we predict smaller values than the experiment.     

Geometries, stabilities, and electronic properties of different-sized ZrSi(n) (n=1-16) clusters: a density-functional investigation

The ZrSi(n) (n=1-16) clusters with different spin configurations have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, growth-pattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of different-sized ZrSi(n) clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable ZrSi(n) (n=1-7) geometries, except ZrSi3, keep the analogous frameworks as the lowest-energy or the second lowest-energy Si(n+1) clusters. However, for large ZrSi(n) (n=8-16) clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transition-metal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowest-energy sandwich-like ZrSi12 geometry is not a sealed structure and appears irregular as compared with other TM@Si12 (TM = Re,Ni). The growth patterns of ZrSi(n) (n=1-16) clusters are concerned showing the Zr-encapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the ZrSi(n) (n=1-16) clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerene-like ZrSi16 is the most stable structure, which is in good agreement with the calculated atomic binding energies of ZrSi(n) (n=8-16) and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable ZrSi(n) (n=1-16) structures exactly varies from positive to negative at the critical-sized ZrSi8 cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small- or middle-sized clusters and metallic in character for the large-sized clusters. Finally, the properties of frontier orbitals and polarizabilities of ZrSi(n) are also discussed.     

Structures and energetics of Be(n)Si(n) and Be(2n)Si(n) (n = 1-4) clusters

The structures and energies of Be(n)Si(n) and Be(2n)Si(n) (n = 1-4) clusters have been examined in ab initio theoretical electronic structure calculations. Cluster geometries have been established in B3LYP/6-31G(2df) calculations and accurate relative energies determined by the G3XMP2 method. The two atoms readily bond to each other and to other atoms of their own kind. The result is a great variety of low-energy clusters in a variety of structural types.     

Structural and electronic properties of neutral and ionic Ga(n)On clusters with n = 4-7

We report the results of a theoretical study of neutral, anionic, and cationic Ga(n)On clusters (n = 4-7), focusing on their ground-state configurations, stability, and electronic properties. The structural motif of these small gallium oxide clusters appears to be a rhombus or a hexagonal ring with alternate gallium and oxygen atoms. With the increase in the cluster size from Ga4O4 to Ga7O7, the ground-state configurations show a transition from planar to quasi-planar to three-dimensional structure that maximizes the number of ionic metal-oxygen bonds in the cluster. The ionization-induced distortions in the ground state of the respective neutral clusters are small. However, the nature of the LUMO orbital of the neutral isomers is found to be a key factor in determining the ordering of the low-lying isomers of the corresponding anionic clusters. A sequential addition of a GaO unit to the GaO monomer initially increases the binding energy, though values of the ionization potential and the electron affinity do not show any systematic variation in these clusters.     

Optical properties of (GaAs)n clusters (n = 2-16)

The electronic and geometrical structures of the lowest triplet states of (GaAs) n clusters ( n = 2-16) are studied using density functional theory with generalized gradient approximation (DFT-GGA). It is found that the triplet-state geometries are different from the corresponding singlet-state geometries; for n = 2-8, 10, and 11, the triplets and singlets have different topologies, while the (GaAs) 9, (GaAs) 12, (GaAs) 15, and (GaAs) 16 triplets possess a reduced symmetry, due to Jahn-Teller distortions. Except for GaAs, the singlet states are the ground states. Excitation energies and oscillator strengths are computed for excitations from the ground state to ten singlet states of all (GaAs) n clusters using time-dependent density functional theory. The adiabatic singlet-triplet gap is compared to the vertical gap, and the difference in the eigenvalues of the highest-occupied and lowest-unoccupied molecular orbitals (the HOMO-LUMO gap). While these three values show large oscillations for small n, they approach each other as the cluster size grows. Thus, the HOMO-LUMO gap computed using the DFT-GGA approach presents a rather reliable estimate of the adiabatic singlet-triplet gap.     

Relativistic computational investigation: the geometries and electronic properties of TaSi(n)+ (n = 1-13, 16) clusters

The equilibrium geometries, stabilities, and electronic properties of the TaSi(n)+ (n = 1-13, 16) clusters are investigated systematically by using the relativistic density functional method with generalized gradient approximation. The small-sized TaSi(n)+ clusters with slight geometrical adjustments basically keep the frameworks that are analogous to the neutrals while the medium-sized charged clusters significantly deform the neutral geometries, which are confirmed by the calculated AIP and VIP values. Furthermore, the optimized geometries of the charged clusters agree with the experimental results of Hiura and co-workers (Hiura, H.; Miyazaki, T.; Kanayama, T. Phys. Rev. Lett. 2001, 86, 1733). The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gaps of the charged clusters are generally increased as the cluster size goes from n = 1 to 13; and the large HOMO-LUMO gaps of charged clusters resulting from the positive charge indicate that their chemical stabilities are stronger than their neutral counterparts, especially for n = 4, 6, and 7 clusters. Additionally, the contributions of the d orbitals of the Ta atom to the HOMO and LUMO reveal that the chemical activity of the d orbitals of the Ta atom decreases gradually as the number of silicon atoms increases. This interesting finding is in good agreement with the recent experimental results on the reactive activities of the H2O and transition-metal silicon clusters (Koyasu, K.; Akutsu, M.; Mitsui, M.; Nakajima, A. J. Am. Chem. Soc. 2005, 127, 4998). Generally, the positive charge significantly influences the electronic and geometric structures of the charged clusters. Finally, the most stable neutral and charged TaSi16 clusters are found to be fullerene-like structures and the HOMO-LUMO gap in charged form is detectable experimentally.     

Stability of small Pdn (n=1-7) clusters on the basis of structural and electronic properties: a density functional approach

Density functional calculations within the generalized gradient approximation have been used to investigate the lowest energy electronic and geometric structures of neutral, cationic, and anionic Pd(n) (n=1-7) clusters in the gas phase. In this study, we have examined three different spin multiplicities (M=1, 3, and 5) for different possible structural isomers of each neutral cluster. The calculated lowest energy structures of the neutral clusters are found to have multiplicities, M=1 for Pd(1), Pd(3), Pd(5), Pd(6), and Pd(7), while M=3 for Pd(2) and Pd(4). We have also determined the lowest energy states of cationic and anionic Pd(n) (n=1-7) clusters, formed from the most stable neutral clusters, in three spin multiplicities (M=2, 4, and 6). Bond length, coordination number, binding energy, fragmentation energy, bond dissociation energy, ionization potential, electron affinity, chemical hardness, and electric dipole moment of the optimized clusters are compared with experimental and other theoretical results available in the literature. Based on these criteria, we predict the four-atom palladium cluster to be a magic-number cluster.     

Structure and vibrations of Ga(n)N(n) (n = 3-10) clusters

The structure and harmonic vibrations of Ga(n)N(n) (n = 3-10) clusters have been investigated using the B3LYP (Becke 3-parameter-Lee-Yang-Parr) density functional theory. All structures are found to be cumulenic D(nh) rings (equal bonds, alternating angles), with one intense out of plane mode and three infrared-active degenerate modes, of which the highest one is extremely intense and asymptotically increases to 1029 cm(-1) for n = 10. Comparisons with C2n, B(n)N(n), and Al(n)N(n) clusters, the structure and bonding type for the Ga(n)N(n) (n=3-10) clusters are consistent with those of the C2n (n = 3, 5, 7, ...) clusters, the B(n)N(n) (n = 3-10), and Al(n)N(n) (n = 3-9) clusters.     

Trends in structural, electronic and energetic properties of bimetallic vanadium-gold clusters Au(n)V with n = 1-14

A systematic quantum chemical investigation on the electronic, geometric and energetic properties of Au(n)V clusters with n = 1-14 in both neutral and anionic states is performed using BP86/cc-pVTZ-PP calculations. Most clusters having an even number of electrons prefer a high spin state. For odd-electron systems, a quartet state is consistently favoured as the ground state up to Au(8)V. The larger sized Au(10)V, Au(12)V and Au(14)V prefer a doublet state. The clusters prefer 2D geometries up to Au(8)V involving a weak charge transfer. The larger systems bear 3D conformations with a more effective electron transfer from Au to V. The lowest-energy structure of a size Au(n)V is built upon the most stable form of Au(n-1)V. During the growth, V is endohedrally doped in order to maximize its coordination numbers and augment the charge transfer. Energetic properties, including the binding energies, embedding energies and second-order energy differences, show that the presence of a V atom enhances considerably the thermodynamic stability of odd-numbered gold clusters but reduces that of even-numbered systems. The atomic shape has an apparently more important effect on the clusters stability than the electronic structure. Especially, if both atomic shape and electronic condition are satisfied, the resulting cluster becomes particularly stable such as the anion Au(12)V(-), which can thus combine with the cation Au(+) to form a superatomic molecule of the type [Au(12)V]Au. Numerous lower-lying electronic states of these clusters are very close in energy, in such a way that DFT computations cannot clearly establish their ground electronic states. Calculated results demonstrate the existence of structural isomers with comparable energy content for several species including Au(9)V, Au(10)V, Au(13)V and Au(14)V.     

Structures and magnetic properties of CrSi(n) (-) (n = 3-12) clusters: Photoelectron spectroscopy and density functional calculations

Chromium-doped silicon clusters, CrSi(n) (-)(n = 3-12), were investigated with anion photoelectron spectroscopy and density functional theory calculations. The combination of experimental measurement and theoretical calculations reveals that the onset of endohedral structure in CrSi(n) (-) clusters occurs at n = 10 and the magnetic properties of the CrSi(n) (-) clusters are correlated to their geometric structures. The most stable isomers of CrSi(n) (-) from n = 3 to 9 have exohedral structures with magnetic moments of 3-5μ(B) while those of CrSi(10) (-), CrSi(11) (-), and CrSi(12) (-) have endohedral structures and magnetic moments of 1μ(B.).     

Equilibrium geometries, stabilities, and electronic properties of the bimetallic M2-doped Au(n) (M = Ag, Cu; n = 1-10) clusters: comparison with pure gold clusters

The density functional method with relativistic effective core potential has been employed to investigate systematically the geometrical structures, relative stabilities, growth-pattern behaviors, and electronic properties of small bimetallic M(2)Au(n) (M = Ag, Cu; n = 1-10) and pure gold Au(n) (n ≤ 12) clusters. The optimized geometries reveal that M(2) substituted Au(n+2) clusters and one Au atom capped M(2)Au(n-1) structures are dominant growth patterns of the stable alloyed M(2)Au(n) clusters. The calculated averaged atomic binding energies, fragmentation energies, and the second-order difference of energies as a function of the cluster size exhibit a pronounced even-odd alternation phenomenon. The analytic results exhibit that the planar structure Ag(2)Au(4) and Cu(2)Au(2) isomers are the most stable geometries of Ag(2)Au(n) and Cu(2)Au(n) clusters, respectively. In addition, the HOMO-LUMO gaps, charge transfers, chemical hardnesses and polarizabilities have been analyzed and compared further.