Relativistic effects on geometry and electronic structure of small Pdn species (n=1, 2, 4)

Relativistic effects on the properties of small neutral Pd_n species (n=1, 2, 4) and Pd₂⁻ have been examined for the first time at the all‐electron level by performing scalar‐relativistic and nonrelativistic density functional calculations using a gradient‐corrected density functional. Relativistic effects are found to be important: They lead to a contraction of bond lengths, increase of vibrational frequencies, and a significant enhancement of binding energies. While relativistic effects are quite uniform for several states of Pd₄, they vary for the states examined for Pd₂, leading to a change of ground state due to relativity. The calculated relativistic properties of Pd₂ and Pd₂⁻ are in good agreement with available experimental data from mass spectrometry and photoelectron spectroscopy. For Pd₄ three‐dimensional structures are found to be preferred to planar ones and many nearly isoenergetic isomers exist. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 74: 405–416, 1999     

Far‐Infrared Spectra of Yttrium‐Doped Gold Clusters AunY (n=1–9)

The geometric, spectroscopic, and electronic properties of neutral yttrium‐doped gold clusters Au_nY (n=1–9) are studied by far‐infrared multiple photon dissociation (FIR‐MPD) spectroscopy and quantum chemical calculations. Comparison of the observed and calculated vibrational spectra allows the structures of the isomers present in the molecular beam to be determined. Most of the isomers for which the IR spectra agree best with experiment are calculated to be the energetically most stable ones. Attachment of xenon to the Au_nY cluster can cause changes in the IR spectra, which involve band shifts and band splittings. In some cases symmetry changes, as a result of the attachment of xenon atoms, were also observed. All the Au_nY clusters considered prefer a low spin state. In contrast to pure gold clusters, which exhibit exclusively planar lowest‐energy structures for small sizes, several of the studied species are three‐dimensional. This is particularly the case for Au₄Y and Au₉Y, while for some other sizes (n=5, 8) the 3D structures have an energy similar to that of their 2D counterparts. Several of the lowest‐energy structures are quasi‐2D, that is, slightly distorted from planar shapes. For all the studied species the Y atom prefers high coordination, which is different from other metal dopants in gold clusters.     

Structures and electronic properties of the small rubidium‐doped silicon RbSin (n = 1–12) clusters

The geometries, relative stabilities, and electronic properties of small rubidium‐doped silicon clusters RbSi_n (n = 1–12) have been systematically investigated using the density functional theory at the B3LYP/GENECP level. The optimized structures show that lowest‐energy isomers of RbSi_n are similar with the ground state isomers of pure Si_n clusters and prefer the three‐dimensional for n = 3–12. The relative stabilities of RbSi_n clusters have been analyzed on the averaged binding energy, fragmentation energy, second‐order energy difference, and highest occupied molecular orbital‐lowest unoccupied molecular orbital energy gap. The calculated results indicate that the doping of Rb atom enhances the chemical activity of Si_n frame and the magic number is RbSi₂. The Mulliken population analysis reveals that the charges in the corresponding RbSi_n clusters transfer from the Rb atom to Si atoms. The partial density of states and chemical hardness are also discussed. © 2014 Wiley Periodicals, Inc.     

Observable Structures of Small Neutral and Anionic Gold Clusters

Since gold clusters have mostly been studied theoretically by using DFT calculations, more accurate studies are of importance. Thus, small neutral and anionic gold clusters (Au_n and Au_n^?, n=4–7) were investigated by means of coupled cluster with singles, doubles, and perturbative triple excitations [CCSD(T)] calculations with large basis sets, and some differences between DFT and CCSD(T) results are discussed. Interesting isomeric structures that have dangling atoms were obtained. Structures having dangling atoms appear to be stable up to n=4 for neutral gold clusters and up to n=7 for anionic clusters. The relative stabilities and electronic properties of some isomers and major structures are discussed on the basis of the CCSD(T) calculations. This accurate structure prediction of small gold clusters corresponding to experimental photoelectron spectral peaks is valuable in the field of atom‐scale materials science including nanocatalysts.     

Density functional study of carbon monoxide adsorption on small cationic,neutral, and anionic aluminum nitride clusters

CO adsorption on small cationic, neutral, and anionic (AlN)_n (n = 1–6) clusters has been investigated using density functional theory in the generalized gradient approximation. Among various possible CO adsorption sites, an N on‐top (onefold coordinated) site is found to be the most favorable one, irrespective of the charge state of the clusters. The adsorption energies of CO on the anionic (AlN)_nCO (n = 2–4) clusters are greater than those on the neutral and cationic complexes. The adsorption energies on the cationic and neutral complexes reflect the odd–even oscillations, and the adsorption energies of CO on the cationic (AlN)_nCO (n = 5, 6) clusters are greater than those on the neutral and anionic complexes. The adsorption energies for the different charge states decrease with increasing cluster size. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

The Geometric Structure of Silver‐Doped Silicon Clusters

Cationic silver‐doped silicon clusters, Si_nAg⁺ (n=6–15), are studied using infrared multiple photon dissociation in combination with density functional theory computations. Candidate structures are identified using a basin‐hopping global optimizations method. Based on the comparison of experimental and calculated IR spectra for the identified low‐energy isomers, structures are assigned. It is found that all investigated clusters have exohedral structures, that is, the Ag atom is located at the surface. This is a surprising result because many transition‐metal dopant atoms have been shown to induce the formation of endohedral silicon clusters. The silicon framework of Si_nAg⁺ (n=7–9) has a pentagonal bipyramidal building block, whereas the larger Si_nAg⁺ (n=10–12, 14, 15) clusters have trigonal prism‐based structures. On comparing the structures of Si_nAg⁺ with those of Si_nCu⁺ (for n=6–11) it is found that both Cu and Ag adsorb on a surface site of bare Si_n⁺ clusters. However, the Ag dopant atom takes a lower coordinated site and is more weakly bound to the Si_n⁺ framework than the Cu dopant atom.     

Density functional study of hydrogen adsorption and dissociation on small Pdn (n = 1–7) clusters

Density functional theory has been performed to investigate the interaction of H₂ and Pd_n clusters (n = 1–7). The local minima configurations for different H₂ molecule approach modes towards Pd_n clusters are presented. Our results show that in some cases H₂ is physically adsorbed around Pd atom, and in other cases H₂ is dissociated to be H atoms. Except for PdH2, Pd_n clusters with H atoms dissociatively adsorbed are most stable. For these most stable PdnH2 clusters (n  2), the binding energy of hydrogen atom decreases as the number of Pd atom increases until n = 4, and when n  4, the binding energy almost keeps constant with the H atoms bound sites changing from Pd–Pd bonds to Pd triangle planes. Besides, the adsorption of H₂ on other low-lying isomers of Pd_n clusters is also discussed.     

Theoretical insight of nitric oxide adsorption on neutral and charged Pdn (n = 1–5) clusters

Density functional theory (DFT) calculations within the framework of generalized gradient approximation have been used to systematically investigate the adsorption of nitric oxide (NO) molecule on neutral, cationic, and anionic Pd_n (n = 1–5) clusters. NO coordinate to one Pd atom of the cluster by the end‐on mode, where the tilted end‐on structure is more favorable due to the additional electron in the π* orbital. On the contrary, in the neutral and cationic Pd₂ system, NO coordinates to the bridge site of cluster preferably by the side‐on mode. Charge transfer between Pd clusters and NO molecule and the corresponding weakening of N? O bond is an essential factor for the adsorption. The N? O stretching frequency follow the order of cationic > neutral > anionic. Binding energy of NO on anionic clusters is found to be greater than those of neutral and cationic clusters. © 2015 Wiley Periodicals, Inc.     

Density functional study of structural and electronic properties of maximum‐spin n+1Aun−1Ag clusters

The structures and relative stabilities of high‐spin ⁿ⁺¹Au_n?1Ag and ⁿAu_n?1Ag⁺ (n = 2–8) clusters have been studied with density functional calculation. We predicted the existence of a number of previously unknown isomers. Our results revealed that all structures of high‐spin neutral or cationic Au_n?1Ag clusters can be understood as a substitution of an Au atom by an Ag atom in the high‐spin neutral or cationic Au_n clusters. The properties of mixed gold–silver clusters are strongly sized and structural dependence. The high‐spin bimetallic clusters tend to be holding three‐dimensional geometry rather than planar form represented in their low‐spin situations. Silver atom prefers to occupy those peripheral positions until to n = 8 for high‐spin clusters, which is different from its position occupied by light atom in the low‐spin situations. Our theoretical calculations indicated that in various high‐spin Au_n?1Ag neutral and cationic species, ⁵Au₃Ag, ³AuAg and ⁵Au₄Ag⁺ hold high stability, which can be explained by valence bond theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Stability,Infrared Spectra and Electronic Structures of (ZrO2)n(n=3-6)Clusters:DFT Study

The stability, infrared spectra and electronic structures of (ZrO₂)_n (n=3–6) clusters have been investigated by using density‐functional theory (DFT) at B3LYP/6‐31G* level. The lowest‐energy structures have been recognized by considering a number of structural isomers for each cluster size. It is found that the lowest‐energy (ZrO₂)₅ cluster is the most stable among the (ZrO₂)_n (n=3–6) clusters. The vibration spectra of Zr? O stretching motion from terminal oxygen atom locate between 900 and 1000 cm^?1, and the vibrational band of Zr? O? Zr? O four member ring is obtained at 600–700 cm^?1, which are in good agreement with the experimental results. Mulliken populations and NBO charges of (ZrO₂)_n clusters indicate that the charge transfers occur between 4d orbital of Zr atoms and 2p orbital of O atoms. HOMO‐LUMO gaps illustrate that chemical stabilities of the lowest‐energy (ZrO₂)_n (n=3–6) clusters display an even‐odd alternating pattern with increasing cluster size.     

High Magnetic Moments in Manganese‐Doped Silicon Clusters

We report on the structural, electronic, and magnetic properties of manganese‐doped silicon clusters cations, Si_nMn⁺ with n=6–10, 12–14, and 16, using mass spectrometry and infrared spectroscopy in combination with density functional theory computations. This combined experimental and theoretical study allows several structures to be identified. All the exohedral Si_nMn⁺ (n=6–10) clusters are found to be substitutive derivatives of the bare Si_n+1⁺ cations, while the endohedral Si_nMn⁺ (n=12–14 and 16) clusters adopt fullerene‐like structures. The hybrid B3P86 functional is shown to be appropriate in predicting the ground electronic states of the clusters and in reproducing their infrared spectra. The clusters turn out to have high magnetic moments localized on Mn. In particular the Mn atoms in the exohedral Si_nMn⁺ (n=6–10) clusters have local magnetic moments of 4 μ_B or 6 μ_B and can be considered as magnetic copies of the silicon atoms. Opposed to other 3d transition‐metal dopants, the local magnetic moment of the Mn atom is not completely quenched when encapsulated in a silicon cage.     

Comprehensive understanding of size‐, shape‐, and composition‐dependent polarizabilities of SimCn (m,n = 1–4) clusters

We performed a comprehensive study of the size‐, shape‐, and composition‐dependent polarizabilities of Si_mC_n (m, n = 1–4) clusters on the basis of the density‐functional‐based coupled perturbed Hartree–Fock calculations. We found better correlations between the polarizabilities and both the binding energies (E_b) and change in charge distribution (Δq) than the energy gaps. The α values exhibit overall decreasing and increasing trends with increases in the E_b and Δq values, respectively. For isomers with the same E_b values and different polarizabilities, Δq can well explain the difference in polarizabilities. The π‐electron delocalization effect is the best factor for understanding the shape‐dependence. For a given m/n value, the linear clusters have an obviously larger polarizability than both the prolate and compact clusters, irrespective of the cluster size. We fit a quantitative expression [α = A ? (A ? B) × exp(?k(m/n))] to describe the composition‐dependent polarizabilities. © 2012 Wiley Periodicals, Inc.     

(HBNH)n团簇的结构和稳定性

Structures and thermodynamic properties of the imidoboranes （HBNH）n （n=1-16） have been investigated theoretically at the B3LYP/6-31G^＊ level of theory. Needle-shaped oligomers that violate the isolated square rule were found to be more stable than cage isomers. The needle-shaped oligomer with n=16 was predicted to be exceptionally stable at low temperature, hexamer and octamer clusters dominated the gas phase at higher temperature. The highest oligomerization degree of the spontaneous cluster fomation has been estimated. It was concluded that generation of the gas phase （HBNH）n clusters with oligomerization degree n ≥24 was viable, making these species possible intermediates involved in the gas phase generation of BN nanoparticles.     

Optimization of bimetallic Cu–Au and Ag–Au clusters by using a modified adaptive immune optimization algorithm

A modified adaptive immune optimization algorithm (AIOA) is designed for optimization of Cu–Au and Ag–Au bimetallic clusters with Gupta potential. Compared with homoatom clusters, there are homotopic isomers in bimetallic cluster, so atom exchange operation is presented in the modified AIOA. The efficiency of the algorithm is tested by optimization of Cu_nAu_38‐n (0 ≤ n ≤ 38). Results show that all the structures with the putative global minimal energies are successfully located. In the optimization of Ag_nAu_55‐n (0 ≤ n ≤ 55) bimetallic clusters, all the structures with the reported minimal energies are obtained, and 36 structures with even lower potential energies are found. On the other hand, with the optimized structures of Cu_nAu_55‐n, it is shown that all 55‐atom Cu–Au bimetallic clusters are Mackay icosahedra except for Au₅₅, which is a face‐centered cubic (fcc)‐like structure; Cu₅₅, Cu₁₂Au₄₃, and Cu₁Au₅₄ have two‐shell Mackay icosahedral geometries with I_h point group symmetry. © 2009 Wiley Periodicals, Inc. J Comput Chem 2009     

Structure and stability of coinage metal fluoride and chloride clusters (MnFn and MnCln,M = Cu,Ag, or Au; n = 1–6)

Calculations in the framework of the density functional theory are performed to study the lowest‐energy isomers of coinage metal fluoride and chloride clusters (M_nF_n, M_nCl_n, M = Cu, Ag, or Au, n = 1–6). For all calculated species starting from the trimers the most stable structures are found to be cyclic arrangements. However, planar rings are favored in the case of metal fluorides whereas metal chlorides prefer nonplanar cycles. Calculated bond lengths and infrared frequencies are compared with the available experimental data. The nature of the bonding, involving both covalent and ionic contributions, is characterized. The stability and the fragmentation are also investigated. Trimers are found to be particularly stable when considering the Gibbs free energies. © 2012 Wiley Periodicals, Inc.     

Comparative DFT study of N2 and no adsorption on vanadium clusters Vn (n = 2–13)

Using gradient‐corrected density functional theory, we have comparatively studied the adsorption properties of diatomic molecules N₂ and NO on vanadium clusters up to 13 atoms. Spontaneous dissociation is found for N₂ adsorbing on V_n with n = 4–6, 12, and for NO with n = 3–12, respectively, whereas for the rest of the clusters, N₂ (NO) molecularly adsorbs on the cluster for all the possible sites. The incoming N₂ retains the magnetism of V_n except for V₂ and V₆ whose moments are quenched from 2 μ_B to zero. Consequently, the moments of V_nN₂ (n = 2–13) show even/odd oscillation between 0 and 1 μ_B. On the adsorption of NO, the magnetic moments of V_n with closed electronic shell are raised to 1 μ_B at n = 4, 8, and 10, and 3 μ_B at n = 12, whereas for open shell clusters, their magnetic moments increase for n = 5 and 9 and decrease for n = 2, 3, 5–7, 11, and 13 by 1 μ_B. These findings are rationalized by combinatory analysis from several aspects, for example, the geometry and stability of bare clusters, charge transfer induced by the adsorption, feature of frontier orbitals, and spin density distribution. © 2012 Wiley Periodicals, Inc.     

Structure and stability of high‐spin Aun(n = 2–8) clusters

The structures and relative stability of the maximum‐spin ⁿ⁺¹Au_n and ⁿAu (n = 2–8) clusters have been determined by density‐functional theory. The structure optimizations and vibrational frequency analysis are performed with the gradient‐corrections of Perdew along with his 1981 local correlation functional, combined with SBKJC effective core potential, augmented in the valence basis set by a set of f functions. We predicted the existence of a number of previously unknown isomers. The energetic and electronic properties of the small high‐spin gold clusters are strongly dependent on sizes. The high‐spin clusters tend to holding three‐dimensional geometry rather than planar form preferred in low‐spin situations. In whole high‐spin Au_n (n = 2–8) neutral and cationic species, ⁵Au₄, ²Au, and ⁴Au are predicted to be of high stability, which can be explained by valence bond theory. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Geometrical structures,electronic states,and stability of NinAl clusters

Density‐functional with generalized gradient approximation (GGA) for the exchange‐correlation potential has been used to calculate the energetically global‐minimum geometries and electronic states of Ni_nAl (n = 2–8) neutral clusters. Our calculations predict the existence of a number of previously unknown isomers. All structures may be derived from a substitution of a Ni atom at marginal positions by an Al atom in the Ni_n+1 cluster. Aluminum atom remains on the surface of the geometrical configurations. Moreover, these species prefer to adopt three‐dimensional (3D) spacial forms at the smaller number of nickel atoms compared with the pure Ni_n+1 (n ≥ 3) configuration. Atomization energies per atom for Ni_nAl (n = 2–8) have the same trend as the binding energies per atom for Ni_n (n = 3–9). The stabilization energies reveal that Ni₅Al is the relatively most stable in this series. In comparison with the magnetic moment of pure metal nickel (0.6 μ_B), the average magnetic moment of Ni atom increases in Ni Al clusters except the Ni₃Al. Moreover, except the case of Ni₅Al, Ni average magnetic moment decreases when alloyed with Al atoms than that in pure Ni clusters, which originate the effective charge transferring from Al to Ni atoms. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Structure and energetic of Bn (n = 2–12) clusters: Electronic structure calculations

The electronic and geometric structures, total and binding energies, first and second energy differences, harmonic frequencies, point symmetries, and highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps of small and neutral B_n (n = 2–12) clusters have been investigated using density functional theory (DFT), B3LYP with 6‐311++G(d,p) basis set. Linear, planar, convex, quasi‐planar, three‐dimensional (3D) cage, and open‐cage structures have been found. None of the lowest energy structures and their isomers has an inner atom; i.e., all the atoms are positioned at the surface. Within this size range, the planar and quasi‐planar (convex) structures have the lowest energies. The first and the second energy differences are used to obtain the most stable sizes. A simple growth path is also discussed with the studied sizes and isomers. The results have been compared with previously available theoretical and experimental works. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Chiral Self‐Discrimination and Guest Recognition in Helicene‐Based Coordination Cages

Chiral nanosized confinements play a major role for enantioselective recognition and reaction control in biological systems. Supramolecular self‐assembly gives access to artificial mimics with tunable sizes and properties. Herein, a new family of [Pd₂L₄] coordination cages based on a chiral [6]helicene backbone is introduced. A racemic mixture of the bis‐monodentate pyridyl ligand L¹ selectively assembles with Pd^II cations under chiral self‐discrimination to an achiral meso cage, cis‐[Pd₂ L^1P ₂ L^1M ₂]. Enantiopure L¹ forms homochiral cages [Pd₂ L^1P/M ₄]. A longer derivative L² forms chiral cages [Pd₂ L^2P/M ₄] with larger cavities, which bind optical isomers of chiral guests with different affinities. Owing to its distinct chiroptical properties, this cage can distinguish non‐chiral guests of different lengths, as they were found to squeeze or elongate the cavity under modulation of the helical pitch of the helicenes. The CD spectroscopic results were supported by ion mobility mass spectrometry.