Theoretical study of hydrogenated Mg, Ca@Al12 clusters

The studies on the structure and electronic properties of hydrogenated metal embedded Al(12) cage clusters have been performed by density functional theory calculations. We have investigated aluminum cluster hydrides with 12 and 14 hydrogen atoms, respectively. Insertion of the Mg, Ca alkali metals remarkably enhances the stability of the aluminum clusters. The hydrogen atom prefers to occupy on-top sites along the surface of the clusters. Mulliken population analysis indicates that significant charge transfer occurs between the Mg and Ca atoms and the Al atoms. Our computations suggest that these clusters appear to be physically and chemically stable.     

Structural and electronic properties of Si n, Si n+, and AlSi n-1 (n=2-13) clusters: theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n) (+), and AlSi(n-1) clusters (2< or =n< or =13) have been investigated using the ab initio molecular orbital theory under the density functional theory formalism. The hybrid exchange-correlation energy function (B3LYP) and a standard split-valence basis set with polarization functions [6-31G(d)] were employed for this purpose. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy (Delta (2)E) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si(n) clusters show similar structural growth. However, significant differences have been observed in the electronic structure leading to their different stability pattern. While for neutral clusters, the Si(10) is magic, the extra stability of the Si(11) (+) cluster over the Si(10) (+) and Si(12) (+) bears evidence for the magic behavior of the Si(11) (+) cluster, which is in excellent agreement with the recent experimental observations. Similarly for AlSi(n-1) clusters, which is isoelectronic with Si(n) (+) clusters show extra stability of the AlSi(10) cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. The ground state geometries of the AlSi(n-1) clusters show that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si(n) cluster. The fragmentation behavior of all these clusters show that while small clusters prefers to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size.     

The local electronic and magnetic properties of Fe impurity in Al clusters

The local magnetic property,d electronic structure and the charge transfer effect of Fe impurity in Al clusters have been studied by using a tight-binding model Hamiltonian in the unrestricted Hartree-Fock approximation, which includes intra-atomic and interatomic Coulomb interactions. We have obtained that local magnetic moment of Fe impurity in FeAl _N clusters decreases with increasing cluster size and convergences to zero (that of bulk given by Anderson) withN larger than 12, meanwhile, the local magnetic moment for smaller clusters depends on the clusters size and it is a monotonous descent function of cluster size. We have also found that the spin splitting of the localizedd states decreases as the cluster size increases, which mainly results from the interaction between the localized electrons of Fe atom and the delocalized electrons of Al atoms.     

Structural and electronic properties of Al12X+ (X=C, Si, Ge, Sn, and Pb) clusters

Using the first-principles method with the generalized gradient approximation, the authors have studied the structural and electronic properties of Al(12)X(+) (X=C, Si, Ge, Sn, and Pb) clusters in detail. The ground state of Al(12)C(+) is a low symmetry C(s) structure instead of an icosahedron. However, the Si, Ge, Sn, and Pb atom doped cationic clusters favor icosahedral structures. The ground states for Al(12)Si(+) and Al(12)Ge(+) are icosahedra, while the C(5nu) structures optimized from an icosahedron with a vertex capped by a tetravalent atom have the highest binding energy for Al(12)Sn(+) and Al(12)Pb(+) clusters. The I(h) structure and the C(5nu) structure are almost degenerate for Al(12)Ge(+), whose binding energy difference is only 0.03 eV. The electronic properties are altered much by removing an electron from the neutral cluster. The binding strength of a valence electron is enhanced, while the binding energy of the cluster is reduced much. Due to the open electronic shell, the band gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital are approximately 0.3 eV for the studied cationic clusters.     

A G3 study of the structure of carbon-nitrogen nanoclusters

Possible structures of the carbon-nitrogen clusters of the form C(m)N(n) (m = 1-4, n = 1-4, m + n = 2-5) were predicted for the neutral, anion, and cation species in the singlet, doublet, and triplet states, whenever appropriate. The calculations were performed at the G3, MP2(fc)/6-311+G*, and B3LYP/6-311+G* levels of theory. Several molecular properties related to the experimental data--such as the electronic energy, equilibrium geometry, binding energy, HOMO-LUMO gap (HLG), and spin contamination --were calculated. In addition the vertical electron attachment, the adiabatic electron affinity, and vertical ionization energy, of the neutral clusters were calculated. Most of the predicted lowest energy structures were linear, whereas bent structures became more stable with the increase of the cluster size and increase of the number of the N atoms. In most of the predicted lowest energy structures, the N atom prefers the terminal position with acetylenic bond. The calculated BE of the predicted clusters increases with the increase of the cluster size for the neutral and cation clusters but decreases with the increase of the cluster size for the anion clusters. The predicted clusters are characterized by high HLG of about 11 eV on the average, with that of the anion clusters is smaller than that for the neutral and cation clusters. It is concluded then that the anion clusters are less stable than the corresponding neutral and cation clusters. Finally, the N(2) loss reaction is treated.     

Geometries, stabilities, and electronic properties of small anion Mg-doped gold clusters: a density functional theory study

First-principle density functional theory is used for studying the anion gold clusters doped with magnesium atom. By performing geometry optimizations, the equilibrium geometries, relative stabilities, and electronic and magnetic properties of [Au(n)Mg]? (n = 1-8) clusters have been investigated systematically in comparison with pure gold clusters. The results show that doping with a single Mg atom dramatically affects the geometries of the ground-state Au(n+1)? clusters for n = 2-7. Here, the relative stabilities are investigated in terms of the calculated fragmentation energies, second-order difference of energies, and highest occupied?lowest unoccupied molecular orbital energy gaps, manifesting that the ground-state [Au(n)Mg]? and Au(n+1)? clusters with odd-number gold atoms have a higher relative stability. In particular, it should be noted that the [Au?Mg]? cluster has the most enhanced chemical stability. The natural population analysis reveals that the charges in [Au(n)Mg]? (n = 2-8) clusters transfer from the Mg atom to the Au frames. In addition, the total magnetic moments of [Au(n)Mg]? clusters exhibit an odd-even oscillation as a function of cluster size, and the magnetic effects mainly come from the Au atoms.     

Al7Ag and Al7Au clusters with large highest occupied molecular orbital-lowest unoccupied molecular orbital gap

The candidate structures for the ground-state geometry of the Al(7)M (M = Li, Cu, Ag, and Au) clusters are obtained within the spin-polarized density functional theory. Absorption energy, vertical ionization potential, vertical electron affinity, and the energy gap between the highest occupied molecular orbital (HOMO) level and the lowest unoccupied molecular orbital (LUMO) level have been calculated to investigate the effects of doping. Doping with Ag or Au can lead to a large HOMO-LUMO gap, low electron affinity, and increased ionization potential of Al(7) cluster. In the lowest-energy structure of the Al(7)Au cluster, the Al atom binding to the Al(6)Au acts monovalent and the other six Al atoms are trivalent. Thus, the Al(7)Au cluster has 20 valence electrons, and its enhanced stability may be due to the electronic shell closure effect.     

Geometry and stability of BenCm (n=1-10; m=1, 2, ..., to 11-n) clusters

Density functional theory B3PW91/6-31+G* calculations on BenCm (n=1-10; m=1, 2, ..., to 11-n) clusters have been carried out to examine the effect of cluster size, relative composition, binding energy per atom, HOMO-LUMO gap, vertical ionization potential, and electron affinity on their relative stabilities. The most stable planar cyclic conformations of these clusters always show at least a set of two carbon atoms between two beryllium atoms, while structures where beryllium atoms cluster together, or allow the intercalation of one carbon atom between two of them, generally seem to be the least stable ones. Clusters containing 1, 2, and 3 beryllium atoms (Be2C8, Be3C6, Be2C6, BeC6, Be2C4, BeC4, Be2C2, and BeC2) are identified as clusters of "magic numbers" in terms of their high binding energy per atom, high HOMO-LUMO gap, vertical ionization potential, and second difference in energy per beryllium atom.     

Evolution of the geometrical and electronic structures of Gan(n=2-26) clusters: a density-functional theory study

Density-functional theory with generalized gradient approximation for the exchange-correlation potential has been used to calculate the lowest-energy geometries and electronic structure of neutral gallium clusters containing up to 26 atoms. Harmonic vibrational frequency analysis is undertaken to assure that the lowest-energy geometries are real local minima. With increasing cluster size, we find that the gallium clusters tend to adopt compact structures. The structures comprise triangular units that connect each other with different dihedral angles. The lowest-energy structure can be obtained by capping an atom on the structure of smaller one. The capping site occurs at a site where interactions with more atoms are available. The binding energy evolves monotonically with size, but Ga(8), Ga(14), and Ga(20) exhibit particularly higher stability. Except Ga(2) and Ga(4), all even-numbered gallium clusters we studied are closed-shell singlet states with a substantial highest occupied and lowest unoccupied molecular orbitals gap. The odd-numbered clusters are open shell with a small gap. The size dependence of cluster's ionization potentials and electron affinities is discussed and compared with available experiment.     

Au12M (M=Na,Mg, Al,Si, P,S, Cl)团簇的结构、稳定性和电子性质

采用基于密度泛函理论的第一性原理方法系统地研究了Au12M(M=Na,Mg,Al,Si,P,S,Cl)团簇的结构、稳定性和电子性质.对团簇的平均结合能、镶嵌能、垂直离化势、最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能级差、电荷布居分析、自然键轨道(NBO)进行了计算和讨论.对于Au12M(M=Na,Mg,Al)团簇,它们形成了内含M原子的最稳定的笼状结构.然而对于Au12M(M=Si,P,S,Cl)团簇,它们却形成了以M元素为顶点的稳定锥形结构.在这些团簇中发现Au12S团簇相对是最稳定的,这是由于Au12S团簇形成了稳定的满壳层的电子结构.自然电荷布居分析表明:对于所有的Au12M(M=Na,Mg,Al,Si,P,S,Cl)团簇电荷总是从Au原子转向M原子.自然键轨道和HOMO分析表明Au12M团簇中发生了Au原子的s-d轨道和M原子的p轨道间的杂化现象.     

Density functional embedding approach to the Mn impurities in NaBr crystals

We have performed density functional calculations for three 19‐atom clusters, two 25‐atom clusters, and one 18‐atom cluster, each embedded in a Madelung potential that takes into account the long‐range electrostatic interactions of the ion lattice of a NaBr crystal. One of the three 19‐atom and one of the two 25‐atom clusters model bulk crystalline NaBr; the others model a Mn²⁺ impurity trapped in a cubically symmetric crystalline electric field (CEF) site of the NaBr host. One of the latter has the NaBr bulk interatomic distance, while in the others relaxation of the Br atoms around the metallic impurity has been considered. The 18‐atom cluster models a relaxed Mn impurity Na vacancy system. All of our calculated clusters have a Na site at the center, and they all include at least first and second nearest‐neighbor host atoms. In the center of the doped clusters the Mn impurity replaces the missing Na ion. The electronic structure of the embedded impurity ion in its local environment was computed self‐consistently by means of all‐electron density functional theory (DFT) techniques. We have examined the lattice relaxation around the impurity and calculated the hyperfine coupling constants (HFCC). The results for the Mn electronic structure and for the HFCC are in agreement with experimental results using electron paramagnetic resonance measurements. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 34–46, 2000     

Electronic structure of Al,P, S,and Cl impurities in silicon

We report a fully self-consistent investigation of the electronic structure, relation between charge transfer and electronegativity, bonding characteristics, and alloying of Al, P, S, and Cl with silicon. The present study indicates that the charge transfer from the host Si atoms to the central impurity atom increases with electronegativity of the impurity element. The bonding between host Si atoms and the impurity atoms is ionic in nature. © 1996 John Wiley & Sons, Inc.     

A First-principles Calculation of Structures and Stability of Al13I Cluster

Using first-principles pseudo-potential plane wave method, the energetics, geometrical and electronic structures of three Al13I cluster isomers were calculated. The calculation results of the binding energy indicate Al13I cluster is more stable than Al13 cluster although its electrons are not a magic number as in Al13 cluster, and among Al13I cluster isomers the "Bridge" structure is the most stable, the second is the "Ontop" structure, and the worst is the "Hollow" structure. By analyzing the geometrical structures of Al13I cluster isomers, it is found that after I atom and Al13 cluster combine the geometrical structures of Al13 moieties are changed besides Al13IHollow cluster, in which the Al13 moiety is still a regular icosahedron. For Al13IOntop cluster, the Al13 moiety has a shrinking trend to I, whereas in Al13IBridge cluster it is distorted. Mulliken population analysis shows for the interaction of electrons between Al(I atoms in Al13I cluster not only there exists an ionic bonding but there is a covalent bonding. Part of electrons in the Al13 cluster transfer to I as Al13 cluster and I atom combine. The order of the strength of covalent bonding between Al13 moiety and I in Al13I cluster isomers is Al13IBridge>Al13IHollow>Al13IOntop. Further analysis of electric structures of Al13 and Al13I clusters indicates a higher stability of Al13I cluster than Al13 cluster can be attributed to the s-p hybridization of 3s and 3p electrons of Al in Al13 moiety induced by I doped, which leads to fewer electrons N(EF) at EF in Al13I and a larger energy gap ΔEH-L between HOMO and LUMO levels in Al13I cluster. The distinguish of structural stability of Al13I cluster isomers mainly originates from their different magnitudes in decrease of N(EF) and increase of ΔEH-L relative to Al13 cluster. The fewest N(EF) and the largest ΔEH-L are responsible for the high stability of Al13IBridge cluster .     

Special stability of cationic MPb12+ clusters and superalkali character of neutral MPb12 clusters (M = B, Al, Ga, In, and Tl)

The electronic structures and stabilities of cationic MPb12+ clusters (M = B, Al, Ga, In, and Tl) with 50 valence electrons are investigated within density functional theory. It is shown that, at the B3LYP/cc-pVDZ(-PP) and BPW91/cc-pVDZ(-PP) levels of theory, the structures of MPb12+ with icosahedra (I(h)) symmetry are energetically favorable, and their high stabilities may arise from the closed-shell nature of the pi subsystems which are subject to the 2(N(pi + 1)2 rule with N(pi = 1). In addition, the possessing of large nucleus-independent chemical shifts of the five kinds of clusters reflects the common aromatic character of these clusters. From the comparison of our studies on the binding energies and the highest occupied molecular orbital and the lowest unoccupied molecular orbital energy gaps, the cluster AlPb12+ has higher stability than the others and this is consistent with the recent mass-spectrometric discovery of Al-doped Pb(n)+ clusters, in which AlPb12+ is highly abundant. The same methods are used to search for the structures of the neutral MPb12 clusters. The calculations reveal that the most stable geometries of the BPb12 and GaPb12 clusters have I(h) symmetry, the AlPb12 and InPb12 clusters have T(h) symmetry, and the TlPb12 cluster has C5v symmetry. Furthermore, the vertical ionization potentials of the neutral MPb12 clusters are smaller than that of some alkali atoms, indicating that the neutral MPb12 clusters possess superalkali character.     

Hydrogen dissociative chemisorption and desorption on saturated subnano palladium clusters (Pdn, n = 2-9)

H(2) sequential dissociative chemisorption on small palladium clusters was studied using density functional theory. The chosen clusters Pd(n) (n = 2-9) are of the lowest energy structures for each n. H(2) dissociative chemisorption and subsequent H atom migration on the bare Pd clusters were found to be nearly barrierless. The dissociative chemisorption energy of H(2) and the desorption energy of H atom in general decrease with the coverage of H atoms and thus the catalytic efficiency decreases as the H loading increases. These energies at full cluster saturation were identified and found to vary in small energy ranges regardless of cluster size. As H loading increases, the clusters gradually change their bonding from metallic character to covalent character. For the selected Pd clusters, the capacity to adsorb H atoms increases almost proportionally with cluster size; however, it was found that the capacity of Pd clusters to adsorb H atoms is, on average, substantially smaller than that of small Pt clusters, suggesting that the catalytic efficiency of Pt nanoparticles is superior to Pd nanoparticles in catalyzing dissociative chemisorption of H(2) molecules.     

Geometric and energetic properties of Al-doped Sin (n = 2–21) clusters: FP-LMTO-MD calculations

We have investigated the effect of aluminum impurity atoms on the geometric structures and stabilities of neutral and ionic Si_n (n = 2–21) clusters in detail by using full-potential linear-muffin-tin-orbital molecular-dynamics (FP-LMTO-MD) method. Our calculations suggest that most of the ground state structures for neutral and ionic Si_nAl (n = 1–20) clusters can be obtained by substituting one Si atom of their corresponding Si clusters with an Al atom. The neutral Si_n–1Al clusters with one Al atom have similar geometrical configurations to those of the pure Si_n clusters except for local structural distortion. But one Al impurity atom probably reverses the energy ordering of two isomers with small difference. Although, an Al heteroatom reduces the average binding energies for the mixed clusters, it would improve the bond strength between Si atoms in some mixed clusters. Our calculations also suggest that most of the ionic Si_n–1Al clusters adopt the same geometrical configurations as their neutral clusters. But for one selected mixed cluster, the charged structures probably have different energy ordering from the neutral clusters. The anionic Si_n–1Al⁻ clusters, which are isoelectronic to their corresponding pure Si_n clusters, show similar magic behavior.     

A density functional study of YnAl (n=1-14) clusters

The geometries, stabilities, and electronic and magnetic properties of Y(n)Al (n=1-14) clusters have been systematically investigated by using density functional theory with generalized gradient approximation. The growth pattern for different sized Y(n)Al (n=1-14) clusters is Al-substituted Y(n+1) clusters and it keeps the similar frameworks of the most stable Y(n+1) clusters except for Y(9)Al cluster. The Al atom substituted the surface atom of the Y(n+1) clusters for n<9. Starting from n=9, the Al atom completely falls into the center of the Y-frame. The Al atom substituted the center atom of the Y(n+1) clusters to form the Al-encapsulated Y(n) geometries for n>9. The calculated results manifest that doping of the Al atom contributes to strengthen the stabilities of the yttrium framework. In addition, the relative stability of Y(12)Al is the strongest among all different sized Y(n)Al clusters, which might stem from its highly symmetric geometry. Mulliken population analysis shows that the charges always transfer from Y atoms to Al atom in all different sized clusters. Doping of the Al atom decreases the average magnetic moments of most Y(n) clusters. Especially, the magnetic moment is completely quenched after doping Al in the Y(13), which is ascribed to the disappearance of the ininerant 4d electron spin exchange effect. Finally, the frontier orbitals properties of Y(n)Al are also discussed.     

Photoabsorption of Fe,Co, and Ni atoms embedded in Al-clusters near 3p-ionization threshold of impurity

Photoionization cross sections of Fe, Co, and Ni atoms inside Al jellium-clusters (containing up to 90 atoms) in the energy range near the 3p ionization threshold of the impurity atom are calculated using the time-dependent local spin-density approximation. The spectra are dominated by resonances and depend markedly on the cluster size. It is obtained that the resonances have an autoionization character and are caused by the interference between discrete electronic transitions from the 3p shell of the impurity atom to unfilled d shells of the jellium-cluster and ionization excitations ofd electrons. For comparison, within the same approach, photoionization cross sections of atomic Fe, Co, and Ni are computed.     

Influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters

With a gradient-corrected density functional method, we have studied computationally the influence of single impurity atoms on the structure, electronic, and magnetic properties of Ni5 clusters. The square-pyramidal isomer of bare Ni5 with six unpaired electrons was calculated 23 kJ/mol more stable than the trigonal bipyramid in its lowest-energy electronic configuration with four unpaired electrons. In a previous study on the cluster Ni4, we had obtained only one stable isomer with an O or an H impurity, but we located six minima for ONi5 and five minima for HNi5. In the most stable structures of HNi5, the H atom bridges a Ni-Ni edge at the base or the side of the square pyramid, similarly to the coordination of an H atom at the tetrahedral cluster Ni4. The most stable ONi5 isomers exhibit a trigonal bipyramidal structure of the Ni5 moiety, with the impurity coordinated at a facet, (micro3-O)Ni5, or at an apex edge, (micro-O)Ni5. We located four stable structures for a C impurity at a Ni5 cluster. As for CNi4, the most stable structure of the corresponding Ni5 complex comprises a four-coordinated C atom, (micro4-C)Ni5, and can be considered as insertion of the impurity into a Ni-Ni bond of the bare cluster. All structures with C and five with O impurity have four unpaired electrons, while the number of unpaired electrons in the clusters HNi5 varies between 3 and 7. As a rough trend, the ionization potentials and electron affinities of the clusters with impurity atoms decrease with the coordination number of the impurity. However, the position of the impurity and the shape of the metal moiety also affect the results. Coordination of an impurity atom leads to a partial oxidation of the metal atoms.     

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.