Comparison of the growth patterns of Si(n) and Ge(n) clusters (n = 25-33)

We performed an unbiased search for low-energy structures of medium-sized neutral Si n and Ge n clusters ( n = 25-33) using a genetic algorithm (GA) coupled with tight-binding interatomic potentials. Structural candidates obtained from our GA search were further optimized by first-principles calculations using density functional theory (DFT). Our approach reproduces well the lowest-energy structures of Si n and Ge n clusters of n = 25-29 compared to previous studies, showing the accuracy and reliability of our approach. In the present study, we pay more attention to determine low-lying isomers of Si n and Ge n ( n = 29-33) and study the growth patterns of these clusters. The B3LYP calculations suggest that the growth pattern of Si n ( n = 25-33) clusters undergoes a transition from prolate to cage at n = 31, while this transition appears at n = 26 from the PBE-calculated results. In the size range of 25-33, the corresponding Ge n clusters hold the prolate growth pattern. The relative stabilities and different structural motifs of Si n and Ge n ( n = 25-33) clusters were studied, and the changes of small cluster structures, when acting as building blocks of large clusters, were also discussed.     

Structures and stability of B-doped Al clusters: AlnB and AlnB2 (n=1-7)

Various structural possibilities for Al(n)B(m) (n=1-7, m=1-2) neutral isomers were investigated using B3LYP6-311G(d) and CCSD(T)6-311G(d) methods. Our calculations predicted the existence of a number of previously unknown isomers. The B atom favors to locate over/inside of all clusters in this series. All structures of the Al(n)B (n=2-7) may be derived from capping/putting a B atom over/inside the Al(n) cluster. All Al(n)B(2) (n=1-5) may be understood as two substitutions of Al atoms by B atoms in the Al(n+2) molecule. The strong B-B bond is a dominant factor in the building-up principle of mixed Al(n)B(2) neutral clusters. The second difference in energy showed that the Al(n)B(m) clusters with even n+m are more stable than those with odd n+m. Our results and analyses revealed that the mixed Al-B clusters exhibit aromatic behaviors.     

The structures and electronic states of zinc-water clusters Zn(n)(H2O)(m) (n = 1-32 and m = 1-3)

Ab initio and Density Functional Theory (DFT) calculations have been carried out for zinc-water clusters Zn(n)-(H2O)(m) (n = 1-32 and m = 1-3, where n and m are the numbers of zinc atoms and water molecules, respectively) to elucidate the structure and electronic states of the clusters and the interaction of zinc cluster with water molecules. The binding energies of H2O to zinc clusters were small at n = 2-3 (2.3-4.2 kcal mol(-1)), whereas the energy increased significantly in n = 4 (9.0 kcal mol(-1)). Also, the binding nature of H2O was changed at n = 4. The cluster size dependency of the binding energy of H2O accorded well with that of the natural population of electrons in the 4p orbital of the zinc atom. In the larger clusters (n > 20), it was found that the zinc atoms in surface regions of the zinc cluster have a positive charge, whereas those in the interior region have a negative charge with the large electron population in the 4p orbital. The interaction of H2O with the zinc clusters were discussed on the basis of the theoretical results.     

Structure and stability of (TiO2)n, (SiO2)n, and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] clusters

Structures, energetics, and vibrational spectra are investigated for small pure (TiO(2))(n), (SiO(2))(n), and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] oxide clusters by density functional theory (DFT). The BP86/ATZP level of theory is employed to obtain constitutional isomers of the oxide clusters. In accordance with previous studies, our calculations show three-dimensional compact structures are preferred for pure (TiO(2))(n) with oxo-stabilized higher hexavalent states, and linear chain structures are favored for pure (SiO(2))(n) with tetravalent states. However, the herein theoretically first reported mixed Ti(m)Si(n-m)O(2n) oxide clusters prefer either three-dimensional compact or linear chain structures depending upon the stoichiometry of the compound. Vibrational analysis of the important modes of some highly stable structures is provided. Coupled-cluster single and double excitation (with triples) [CCSD(T)] computed energy gaps for the TiO(2) dimers compare well with results from previous study. Excitation energies are computed by use of time-dependent (TD) DFT and equation-of-motion coupled-cluster calculations with singles and doubles (EOM-CCSD) for the most stable isomers.     

Threshold photoionization and density functional theory studies of the niobium carbide clusters Nb3C(n) (n = 1-4) and Nb4C(n) (n = 1-6)

We have used photoionization efficiency spectroscopy to determine ionization potentials (IP) of the niobium-carbide clusters, Nb3C(n) (n = 1-4) and Nb4C(n) (n = 1-6). The Nb3C2 and Nb4C4 clusters exhibit the lowest IPs for the two series, respectively. For clusters containing up to four carbon atoms, excellent agreement is found with relative IPs calculated using density functional theory. The lowest energy isomers are mostly consistent with the development of a 2 x 2 x 2 face-centered cubic structure of Nb4C4. However, for Nb3C4 a low-lying isomer containing a molecular C2 unit is assigned to the experimental IP rather than the depleted 2 x 2 x 2 nanocrystal isomer. For Nb4C5 and Nb4C6, interpretation is less straightforward, but results indicate isomers containing molecular C2 units are the lowest in energy, suggesting that carbon-carbon bonding is preferred when the number of carbon atoms exceeds the number of metal atoms. A double IP onset is observed for Nb4C3, which is attributed to ionization from the both the lowest energy singlet state and a meta-stable triplet state. This work further supports the notion that IPs can be used as a reliable validation for the geometries of metal-carbide clusters calculated by theory.     

Low-energy isomer identification, structural evolution, and magnetic properties in manganese-doped gold clusters MnAu(n) (n = 1-16)

The size-dependent electronic, structural, and magnetic properties of Mn-doped gold clusters have been systematically investigated by using relativistic all-electron density functional theory with generalized gradient approximation. A number of new isomers are obtained for neutral MnAu(n) (n = 1-16) clusters to probe the structural evolution. The two-dimensional (2D) to three-dimensional (3D) transition occurs in the size range n = 7-10 with manifest structure competitions. From size n = 13 to n = 16, the MnAu(n) prefers a gold cage structure with Mn atom locating at the center. The relative stabilities of the ground-state MnAu(n) clusters show a pronounced odd-even oscillation with the number of Au atoms. The magnetic moments of MnAu(n) clusters vary from 3 μ(B) to 6 μ(B) with the different cluster size, suggesting that nonmagnetic Au(n) clusters can serve as a flexible host to tailor the dopant's magnetism, which has potential applications in new nanomaterials with tunable magnetic properties.     

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.     

Structure and stability for (AlN)_n~+ and (AlN)_n~- (n=1-15) clusters

Using density functional theory (DFT) method with 6-31G* basis set, we have carried out the optimizing calculation of geometry, vibrational frequency and thermodynamical stability for(AIN)n+ and (AIN)n- (n =1-15) clusters. Moreover, their ionic potential (IP) and electron affinity(EA) were discussed. The results show that the electrical charge condition of the cluster has a relatively great impact on the structure of the cluster and with the increase of n, this kind of impactis reduced gradually. There are no AI-AI and N-N bonds in the stable structure of (AIN)n+ or (AIN)n-, and the AI-N bond is the sole bond type. The magic number regularity of (AIN)n+, and (AIN)n- is consistent with that for (AIN)n, indicating that the structure with even n such as 2, 4,6, … is more stable. In addition, (AIN)10 has the maximal ionization power (9.14 eV) and the minimal electron affinity energy (0.19 eV), which manifests that (AIN)10 is more stable than other clusters.     

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.     

Investigation of Size-Selective Zr(2)@Si(n) (n = 16-24) Caged Clusters

The size-selective Zr(2)Si(n) (n = 16-24) caged clusters have been investigated by density functional approach in detail. Their geometries, relative stabilities, electronic properties and ionization potentials have been discussed. The dominant structures of bimetallic Zr(2) doped silicon caged clusters gradually transform to Zr(2) totally encapsulated structures with increase of the clustered size from 16 to 24, which is good agreement with the recent experimental result (J. Phys. Chem. A. 2007, 111, 42). Two novel isomers, i.e., naphthalene-like and dodecahedral Zr(2)Si(20) clusters, are found as low-lying conformers. Furthermore, the novel quasi-1D naphthalene-like Zr(n)Si(m) nanotubes are first reported. The second-order energy differences reveal that magic numbers of the different sized neutral Zr(2)Si(n) clusters appear at n = 18, 20 and 22, which are attributed to the fullerene-like, dodecahedral and polyhedral structures, respectively. The HOMO-LUMO gaps (>1 eV) of all the size-selective Zr(2)Si(n) clusters suggest that encapsulation of the bimetallic zirconium atoms is favorable for increasing the stabilities of silicon cages.     

(CoMn)n(n=1～5)合金团簇的结构和磁性

All geometry structures of (CoMn)n (n=1-5) clusters were optimized, and the energy, frequence and magnetism of (CoMn)n (n=1-5) clusters were calculated by using the local spin density approximation and generalized gradient approximation of density functional theory. The same ground state structures of CoMn alloy clusters were confirmed in two methods, and magnetism of CoMn alloy ground state clusters was studied systemically. In order to understand structure and magnetism of CoMn alloy clusters better, Co2n (n=1-5) and Mn2n (n=1-5) clusters were calculated by the same method as alloy clusters, whose ground state structure and magnetism were confirmed. Moreover, the ground state structure and magnetism of clusters with the corresponding CoMn alloy clusters was compared. Results indicated that for (CoMn)n (n=1-4) clusters, geometry structures of CoMn alloy clusters are the same as the corresponding pure clusters still, (CoMn)3 and (CoMn)4 exhibit magnetic bistability, show ferromagnetic and anti-ferromagnetic coupling, local magnetic moment of Co, Mn atoms in CoMn alloy clusters almost preserves magnetism of pure clusters still.     

Time-resolved intraband electronic relaxation dynamics of Hg(n) (-) clusters (n=7-13,15,18) excited at 1.0 eV

Time-resolved photoelectron imaging has been used to study the relaxation dynamics of small Hg(n) (-) clusters (n=7-13,15,18) following intraband electronic excitation at 1250 nm (1.0 eV). This study furthers our previous investigation of single electron, intraband relaxation dynamics in Hg(n) (-) clusters at 790 nm by exploring the dynamics of smaller clusters (n=7-10), as well as those of larger clusters (n=11-13,15,18) at a lower excitation energy. We measure relaxation time scales of 2-9 ps, two to three times faster than seen previously after 790 nm excitation of Hg(n) (-), n=11-18. These results, along with size-dependent trends in the absorption cross-section and photoelectron angular distribution anisotropy, suggest significant evolution of the cluster anion electronic structure in the size range studied here. Furthermore, the smallest clusters studied here exhibit 35-45 cm(-1) oscillations in pump-probe signal at earliest temporal delays that are interpreted as early coherent nuclear motion on the excited potential energy surfaces of these clusters. Evidence for evaporation of one or two Hg atoms is seen on a time scale of tens of picoseconds.     

Geometries and electronic properties of the neutral and charged rare earth Yb-doped Si(n) (n = 1-6) clusters: a relativistic density functional investigation

The neutral and charged YbSi(n) (n = 1-6) clusters considering different spin configurations have been systematically investigated by using the relativistic density functional theory with generalized gradient approximation. The total bonding energies, equilibrium geometries, Mulliken populations (MP), Hirshfeld charges (HC), fragmentation energies, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps are calculated and discussed. The optimized geometries indicate that the most stable YbSi(n) (n = 1-6) clusters keep basically the analogous frameworks as the low-lying Si(n)(+1) clusters, while the charged species deviate from their neutral counterparts, and that the doped Yb tends to occupy the substitutional site of the neutral and charged YbSi(n) isomers. The relative stabilities are investigated in terms of the calculated fragmentation energies, exhibiting enhanced stabilities for the remarkably stable neutral and charged YbSi2 and YbSi5 clusters. Furthermore, the calculated MP and HC values show that the charges of the neutral and charged YbSi(n) clusters transfer from the Yb atom to Si(n) atoms and the Yb atom acts as an electron donor, and that the f orbitals of the Yb atom in the neutral and charged YbSi(n) clusters behave as core without involvement in chemical bonding. The calculated HOMO-LUMO gaps indicate that the YbSi2 and YbSi4+ clusters have stronger chemical stabilities. Comparisons of the Yb-doped Si(n) (n = 1-6) with available theoretical results of transition-metal-doped silicon clusters are made. The growth pattern is investigated also.     

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.     

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.).     

Simulated annealing and density functional theory calculations of structural and energetic properties of the ammonium chloride clusters (NH4Cl)n, (NH4+)(NH4Cl)n, and (Cl-)(NH4Cl)n, n = 1-13

Simulated annealing Monte Carlo conformer searches using the "mag-walking" algorithm are employed to locate the global minima of molecular clusters of ammonium chloride of the types (NH(4)Cl)(n), (NH(4)(+))(NH(4)Cl)(n), and (Cl(-))(NH(4)Cl)(n) with n = 1-13. The M06-2X density functional theory method is used to refine and predict the structures, energies, and thermodynamic properties of the neutral, cation, and anion clusters. For selected small clusters, the resulting structures are compared to those obtained from a variety of models and basis sets, including RI-MP2 and B3LYP calculations. M06-2X calculations predict enhanced stability of the (NH(4)(+))(NH(4)Cl)(n) clusters when n = 3, 6, 8, and 13. This prediction corresponds favorably to anomalies previously observed in thermospray mass spectroscopy experiments. The (NH(4)Cl)(n) clusters show alternations in stability between even and odd values of n. Clusters of the type (Cl(-))(NH(4)Cl)(n) display a magic number distribution different from that of the cation clusters, with enhanced stability predicted for n = 2, 6, and 11. None of the observed cluster structures resemble the room-temperature CsCl structure of NH(4)Cl(s), which is consistent with previous work. Numerous clusters have structures reminiscent of the higher-temperature, rock-salt phase of the solid ammonium halides.     

The structure and energetics of (GaAs)n, (GaAs)n(-), and (GaAs)n+ (n=2-15)

Electronic and geometrical structures of neutral, negatively, and positively charged (GaAs)n clusters are computed using density functional theory with generalized gradient approximation. All-electron computations are performed on (GaAs)2-(GaAs)9 while effective core potentials (ECPs) are used for (GaAs)9-(GaAs)15. Calibration calculations on GaAs and (GaAs)9 species support the use of the ECP for the larger clusters. The ground-state geometries of (GaAs)n(-) and/or (GaAs)n+ are different from the corresponding neutral ground-state geometry, except for n=7, 9, 12, 14, and 15, where the neutral and ions have similar structures. Beginning with n=6, all atoms are three coordinate, except for (GaAs)10+ and (GaAs)13+. For the larger species, there is a competition between fullerenes built from hexagons and rhombi and geometrical configurations where Ga-Ga and As-As bonds are formed, which results in the formation of pentagons. As expected, the static polarizability varies in the order of anion>neutral>cation, but the values are rather similar for all three charge states. The thermodynamic stability for the loss of GaAs is reported.     

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.     

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.     

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.