Competition between supercluster and stuffed cage structures in medium-sized Ge(n) (n=30-39) clusters

We have performed an unbiased global search for the geometries of low-lying Ge(n) clusters in the size range of 30相似文献   

Competition among fcc-like, double-layered flat, tubular cage, and close-packed structural motifs for medium-sized Au n (n = 21-28) clusters

Using density functional theory calculations, we compared four kinds of possible structural motifs of the medium-sized Aun (n = 21-28) clusters, i.e., fcc-like, double-layered flat, tubular cage, and close-packed. Our results show strong competition between those structural motifs in the medium-sized gold clusters. Aun (n = 21-23) adopt fcc-like structure owing to the high stability of tetrahedral Au20. A structural transition from fcc-like to tubular occurs at Au24, and the tubular motif continues at Au27 and Au28. Meanwhile, a double-layered flat structure was found at Au25, and a pyramid-based structure at Au26. The relationship between electronic properties and cluster geometry was also discussed.     

Density-functional study of small neutral and cationic bismuth clusters Bi(n) and Bi(n) (+)(n=2-24)

Density-functional theory with scalar-relativistic pseudopotential and a generalized gradient correction is used to calculate the neutral and cationic Bi(n) clusters (2< or =n< or =24), with the aim to elucidate their structural evolution, relative stability, and magnetic property. The structures of neutral Bi clusters are found to be similar to that of other group-V elemental clusters, with the extensively studied sizes of n=4 and 8 having a tetrahedron and wedgelike structure, respectively. Generally, larger Bi clusters consist of a combination of several stable units of Bi(4), Bi(6), and Bi(8), and they have a tendency to form an amorphous structure with the increase of cluster sizes. The curves of second order energy difference exhibit strong odd-even alternations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizes are relatively stable in neutral clusters (cationic clusters). The calculated magnetic moments are 1micro (B) for odd-atom clusters and zero for even-atom clusters. We propose that the difference in magnetism between experiment and theory can be greatly improved by considering the orbital contribution. The calculated fragmentation behavior agrees well with the experiment, and for each cationic cluster the dissociation into Bi(4) or Bi(7) (+) subclusters confirms the special stability of Bi(4) and Bi(7) (+). Moreover, the bond orders and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital show that small Bi clusters would prefer semiconductor characters to metallicity.     

Molecular structures and energetics of the (TiO2)n (n = 1-4) clusters and their anions

The (TiO2)n clusters and their anions for n = 1-4 have been studied with coupled cluster theory [CCSD(T)] and density functional theory (DFT). For n > 1, numerous conformations are located for both the neutral and anionic clusters, and their relative energies are calculated at both the DFT and CCSD(T) levels. The CCSD(T) energies are extrapolated to the complete basis set limit for the monomer and dimer and calculated up to the triple-zeta level for the trimer and tetramer. The adiabatic and vertical electron detachment energies of the anionic clusters to the ground and first excited states of the neutral clusters are calculated at both levels and compared with the experimental results. The comparison allows for the definitive assignment of the ground-state structures of the anionic clusters. Anions of the dimer and tetramer are found to have very closely lying conformations within 2 kcal/mol at the CCSD(T) level, whereas that of the trimer does not. In addition, accurate clustering energies and heats of formation are calculated for the neutral clusters and compared with the available experimental data. Estimates of the titanium-oxygen bond energies show that they are stronger than the group VIB transition metal-oxygen bonds except for tungsten. The atomization energies of these clusters display much stronger basis set dependence than the clustering energies. This allows the calculation of more accurate heats of formation for larger clusters on the basis of calculated clustering energies.     

Theoretical prediction for the structures of gas phase lithium oxide clusters: (Li2O)n (n = 1–8)

We apply genetic algorithm combining directly with density functional method to search the potential energy surface of lithium‐oxide clusters (Li₂O)_n up to n = 8. In (Li₂O)_n (n = 1–8) clusters, the planar structures are found to be global minimum up to n = 2, and the global minimum structures are all three‐dimensional at n ≥ 3. At n ≥ 4, the tetrahedral unit (TU) is found in most of the stable structures. In the TU, the central Li is bonded with four O atoms in sp³ interactions, which leads to unusual charge transformation, and the probability of the central Li participating in the bonding is higher by adaptive natural density partitioning analysis, so the central Li is in particularly low positive charge. At large cluster size, distortion of structures is viewed, which breaks the symmetry and may make energy higher. The global minimum structures of (Li₂O)₂, (Li₂O)₆, and (Li₂O)₇ clusters are the most stable magic numbers, where the first one is planar and the later both have stable structural units of tetrahedral and C_4v. © 2012 Wiley Periodicals, Inc.     

Silicon monohydride clusters Si(n)H (n = 4-10) and their anions: structures, thermochemistry, and electron affinities

The molecular structures, electron affinities, and dissociation energies of the Si(n)H/Si(n)H- (n = 4-10) species have been examined via five hybrid and pure density functional theory (DFT) methods. The basis set used in this work is of double-zeta plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. The geometries are fully optimized with each DFT method independently. The three different types of neutral-anion energy separations presented in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). The first Si-H dissociation energies, D(e)(Si(n)H --> Si(n) + H) for neutral Si(n)H and D(e)(Si(n)H- --> Si(n)- + H) for anionic Si(n)H- species, have also been reported. The structures of the ground states of these clusters are traditional H-Si single-bond forms. The ground-state geometries of Si5H, Si6H, Si8H, and Si9H predicted by the DFT methods are different from previous calculations, such as those obtained by Car-Parrinello molecular dynamics and nonorthogonal tight-binding molecular dynamics schemes. The most reliable EA(ad) values obtained at the B3LYP level of theory are 2.59 (Si4H), 2.84 (Si5H), 2.86 (Si6H), 3.19 (Si7H), 3.14 (Si8H), 3.36 (Si9H), and 3.56 (Si10H) eV. The first dissociation energies (Si(n)H --> Si(n) + H) predicted by all of these methods are 2.20-2.29 (Si4H), 2.30-2.83 (Si5H), 2.12-2.41 (Si6H), 1.75-2.03 (Si7H), 2.41-2.72 (Si8H), 1.86-2.11 (Si9H), and 1.92-2.27 (Si10H) eV. For the negatively charged ion clusters (Si(n)H- --> Si(n)- + H), the dissociation energies predicted are 2.56-2.69 (Si4H-), 2.80-3.01 (Si5H-), 2.86-3.06 (Si6H-), 2.80-3.03 (Si7H-), 2.69-2.92 (Si8H-), 2.92-3.18 (Si9H-), and 2.89-3.25 (Si10H-) eV.     

Density functional study of the structures of lead sulfide clusters (PbS)n (n = 1-9)

The structures of (PbS)n (n = 1-9) clusters are investigated with density functional theory at the B3LYP level. Various pseudopotential basis sets on lead and the 6-31+G basis set on sulfur were employed. Full geometry optimization and extensive searches of the potential energy surface were carried out for clusters with n = 1-6. We find that even small PbS clusters (n > 2) start to take on the characteristic features of the rock salt structure of solid-state PbS (galena). The origin of some of the structural aspects of these crystals is shown to be associated with the partial covalent nature of the Pb-S bond. The magnitude of the HOMO-LUMO gap oscillates with increasing size of the clusters, in agreement with the observed behavior of the corresponding UV absorption bands of ultrasmall PbS quantum dots. Direct conformation of this oscillation was found by CIS(D) calculations, for which the absorption with the largest oscillator strength oscillates as the clusters grow from PbS to (PbS)9.     

Oxidation pattern of small silicon oxide clusters: structures and stability of Si6On (n = 1-12)

We have performed systematic ab initio calculations to study the structures and stability of Si(6)O(n)() clusters (n = 1-12) in order to understand the oxidation process in silicon systems. Our calculation results show that oxidation pattern of the small silicon cluster, with continuous addition of O atoms, extends from one side to the entire Si cluster. Si atoms are found to be separated from the pure Si cluster one-by-one by insertion of oxygen into the Si-O bonds. From fragmentation energy analyses, it is found that the Si-rich clusters usually dissociate into a smaller pure Si clusters (Si(5), Si(4), Si(3), or Si(2)), plus oxide fragments such as SiO, Si(2)O(2), Si(3)O(3), Si(3)O(4), and Si(4)O(5). We have also studied the structures of the ionic Si(6)O(n)(+/-) (n = 1-12) clusters and found that most of ionic clusters have different lowest-energy structures in comparison with the neutral clusters. Our calculation results suggest that transformation Si(6)O(n)+(a) + O --> Si(6)O(n+1)+(a) should be easier.     

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.     

Size- and charge-dependent geometric and electronic structures of Bi n (Bi(-)n) clusters (n=2-13) by first-principles simulations

Neutral and negatively charged bismuth clusters, Bi n and Bi(-)n (n=2-13), are investigated by first-principles simulations with the scalar-relativistic projector-augmented wave potential and the spin-polarized generalized gradient approximation. Both types of clusters show size-dependent odd-even oscillations in stability, density of states, and vertical and adiabatic electron affinities, in close agreement with experiment. The negative charge thoroughly reverses the oscillations and considerably influences the geometric structures, particularly of the odd-sized clusters. We note that most atoms in the ground states and the low-lying isomers are three coordinated with a quasilayerlike growth mode based on pentagon units, due to a weak s-p hybridization. The Bi12 cluster is found to prefer a small elongated tubelike structure with the surface consists of six curved-pentagon rings and two triangular facets, which may be the basis for the formation of bismuth nanotubes experimentally reported.     

Magic-numbered Au(n) clusters protected by glutathione monolayers (n = 18, 21, 25, 28, 32, 39): isolation and spectroscopic characterization

Small gold clusters (<1 nm) protected by a glutathione (GSH) monolayer were fractionated into six components by polyacrylamide gel electrophoresis, and their chemical compositions were investigated by electrospray ionization mass spectroscopy. The results demonstrate isolation of a series of magic-numbered gold clusters, Au18(SG)11, Au21(SG)12, Au25+/-1(SG)14+/-1, Au28(SG)16, Au32(SG)18, and Au39(SG)23. Their optical absorption spectra are highly structured with clear absorption onsets, which shift toward higher energies with reduction of the core size. These molecular-like gold clusters exhibit visible photoluminescence. The results reported herein provide helpful guidelines or starting points for further experimental and theoretical studies on structures, stabilities, and optical properties of monolayer-protected gold clusters.     

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.     

Theoretical characterization of structures and energies of benzene-(H2S)n and (H2S)n (n=1-4) clusters

An ab initio study was performed in clusters up to four H(2)S molecules and benzene using calculations at MP26-31+G(*) and MP2/aug-cc-pVDZ levels. Differences between both sets of calculations show the importance of using large basis sets to describe the intermolecular interactions in this system. The obtained binding energies reflect that benzene has not the same behavior in H(2)S as in water, pointing to a higher solubility of this molecule in H(2)S than in water. The Bz-cluster binding energy was fitted to an asymptotic representation with a maximum value of the energy of -8.00 kcal/mol that converges in a cluster with 12 H(2)S molecules. The obtained intermolecular distance in the Bz-H(2)S dimer is similar to the experimental value; however, the difference is much larger for the angles defining the orientation. The influence of benzene produces a distortion of the (H(2)S)(n) clusters, so the intermolecular distances change with regard to the (H(2)S)(n) isolated clusters. Frequency shifts are larger in clusters with benzene than without it. In the smallest clusters the shift associated to the stretching of the S-H bonded to benzene is the largest one, but for the cluster with three H(2)S molecules this stretching is combined with the other S-H stretching of the molecule so the resulting shift is not the largest one.     

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.     

Theoretical study of Al(n) and Al(n)O (n = 2-10) clusters

The stable structures, energies, and electronic properties of neutral, cationic, and anionic clusters of Al(n) (n = 2-10) are studied systematically at the B3LYP/6-311G(2d) level. We find that our optimized structures of Al5(+), Al9(+), Al9(-), Al10, Al10(+), and Al10(-) clusters are more stable than the corresponding ones proposed in previous literature reports. For the studied neutral aluminum clusters, our results show that the stability has an odd/even alternation phenomenon. We also find that the Al3, Al7, Al7(+), and Al7(-) structures are more stable than their neighbors according to their binding energies. For Al7(+) with a special stability, the nucleus-independent chemical shifts and resonance energies are calculated to evaluate its aromaticity. In addition, we present results on hardness, ionization potential, and electron detachment energy. On the basis of the stable structures of the neutral Al(n) (n = 2-10) clusters, the Al(n)O (n = 2-10) clusters are further investigated at the B3LYP/6-311G(2d), and the lowest-energy structures are searched. The structures show that oxygen tends to either be absorbed at the surface of the aluminum clusters or be inserted between Al atoms to form an Al(n-1)OAl motif, of which the Al(n-1) part retains the stable structure of pure aluminum clusters.     

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.     

Stretching vibrations and structure of (HF) n (n=4–8) clusters

IR spectra of 24 structural isomers of (HF) _n (n=4–8) clusters were calculated in the framework of semiempirical theory of polyatomic molecule vibrations. Based on the results obtained and available experimental data it is proposed that (HF) _n associates comprising 3–5-membered cycles with attached monomeric HF units are present in molecular beams and gas phase.Ab initio calculations performed by the SCF method show the existence of local minima corresponding to such structures on the potential energy surface of (HF) _n clusters (n=4–6). Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 435–443, March, 1997.     

Ab initio and empirical energy landscapes of (MgF2)n clusters (n = 3, 4)

We explore the energy landscape of (MgF(2))(3) on both the empirical and ab initio level using the threshold algorithm. In order to determine the energy landscape and the dynamics of the trimer we investigate not only the stable isomers but also the barriers separating these isomers. Furthermore, we study the probability flows in order to estimate the stability of all the isomers found. We find that there is reasonable qualitative agreement between the ab initio and empirical potential, and important features such as sub-basins and energetic barriers follow similar trends. However, we observe that the energies are systematically different for the less compact clusters, when comparing empirical and ab initio energies. Since the underlying motivation of this work is to identify the possible clusters present in the gas phase during a low-temperature atom beam deposition synthesis of MgF(2), we employ the same procedure to additionally investigate the energy landscape of the tetramer. For this case, however, we use only the empirical potential.     

Time resolved photofragmentation of Au n + and Ag n + clusters (n = 9, 21)

Gold and silver cluster ions were produced by laser vaporization and stored in a Penning trap. After mass selection the cluster sizes of interest were illuminated by a laser pulse and electronically excited. Photoabsorption cross sections and fragmentation patterns were measured for photon energies of 2.3 eV to 5.2 eV. Unimolecular dissociation was observed time resolved on a microsecond to millisecond scale. Dissociation energies were deduced from the measured life times.