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.     

Computational studies of stable hexanuclear CulAgmAun (l + m + n = 6; l,m, n > 0) clusters

A DFT study was carried out on the ground state structures of ternary Cu_lAg_mAu_n (l + m + n = 6) clusters, with the aim of investigating changes of thermal and kinetic stabilities as an effect of composition, as well as the composition dependence of the electrostatic potential, of stable planar structures. DFT optimizations were performed using the PBE functional and the SDD basis set. All the optimized structures adopt planar geometries with bent triangular structures. Calculated binding energy values are in the range 1.5–1.9 eV/atom, which shows their thermal stability. The predicted HOMO‐LUMO energy gap values are in the semiconductor region, providing a qualitative indication of a moderate kinetic stability. NBO analyses indicate the existence of two mechanisms promoting planar structural stability, one due to bonding‐antibonding orbital interaction, and the other one due to the well‐known spd hybridization. Wiberg indices were obtained showing interatomic bonding. Electrostatic potential calculations show the existence of nucleophilic attack regions preferentially around silver and copper atoms located at the vertices while electrophilic attack regions are found in the vicinity of gold atoms over the cluster plane. Apparently, charge transfer occurs toward gold from silver and copper atoms when the concentration is favorable in the proximity of gold atoms. In particular, if the small ternary clusters discussed here contain only one gold atom, then a high electron density is observed at the site of this gold atom. © 2016 Wiley Periodicals, Inc.     

Ground State Structures,Electronic and Magnetic Properties of ScnFe (n=2–10) Clusters

The authors predict that the magnetic moment of the scandium clusters can not be efficiently enhanced with the encapsulation of Fe atom, which is different from previous works with Fe atom doped in B_n, Si_n, and Ge_n clusters. It was found that starting from n=6, the growth patterns of the ground state structures of the Sc_nFe clusters are dominated by the octahedron structures with Fe atom falling into the center of the host framework. The calculated results manifest that doping of the Fe atom contributes to strengthening the stabilities of the scandium framework. Maximum peaks are observed for clusters of n=3, 6 and 8 on the size dependence of the second‐order energy differences, implying that these clusters possess relatively higher stability. The HOMO‐LUMO gap of the Sc_nFe clusters exhibits an oscillational odd‐even character with the local peaks of n=4, 6 and 8. Especially, there is the largest oscillation of the gap with n=4 and 5. Additionally, the doped Fe atom exhibits the antiferromagnetic alignment at n=4, 5, 7 and 9. Also, the quench of the magnetic moments as n=6, 8 and 10 may be ascribed to the model of close‐shell electrons.     

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     

Theoretical investigation of the structures and spectroscopic properties of (H2O4)n (n = 1–4) clusters

Density functional theory and ab initio calculations were performed to elucidate the hydrogen interactions in (H₂O₄)_n (n = 1–4) clusters. The optimized geometries, binding energies, and harmonic vibrational frequencies were predicted at various levels of theory. The trans conformer of the H₂O₄ monomer was predicted to be the most stable structure at the CCSD(T)/aug‐cc‐pVTZ level of theory. The binding energies per H₂O₄ monomer increased in absolute value by 9.0, 10.1, and 11.8 kcal/mol from n = 2 to n = 4 at the MP2/cc‐pVTZ level of theory (after the zero‐point vibrational energy and basis set superposition error corrections). This result implies that the intermolecular hydrogen bonds were stronger in the long‐chain clusters, that is, the formation of the longer chain in the (H₂O₄)_n clusters was more energetically favorable.     

First-principle Study of AunSc (n=2～13) Clusters

The geometries, stabilities, electronic, and magnetic properties of Au_nSc clusters have been systematically investigated by density functional theory. The lowest energy structures of Au_nSc favor planar structure and the doped Sc atom does not disturb the frame of Au_nclusters with n≤11. For n≥12, Sc atom is fully encapsulated by the Au cages. From theanalysis of the second-order energy difference, the fragmentation energies, vertical ionizationpotential, vertical electron affinity, and HOMO-LUMO gap, the clusters with odd Au atoms possess relatively higher stabilities than their neighbor size. The doping of Sc atom can greatly improve the stability and change the sequence of chemical activity for Au_n. For n≤11, the total magnetic moments of Au_nSc appear the alternation between 0.00 and 1.00 μB. The total magnetic moments are quenched when Sc is trapped into the Au cages with n≥12.     

Search for the global minimum structures of AlB3H2n (n = 0 − 6) clusters

The global minimum structures of AlB₃H_2n (n = 0–6) clusters are determined using the stochastic search method at the B3LYP/6–31G level of theory. These initially specified geometries are recalculated using B3LYP and CCSD(T) methods using the 6–311++G^** basis set. The structural and electronic properties of the two lowest‐lying isomers are presented. The structural parameters obtained for aluminum borohydride are compared with the experimental and theoretical results. The H₂ fragmentation energies of the most stable isomers are investigated. Chemical bonding analyses for the global minimum of AlB₃H_2n (n = 0–6) clusters are performed using the adaptive natural density partitioning method. © 2014 Wiley Periodicals, Inc.     

Density functional study of structural and electronic properties of AlnN (1 ≤ n ≤ 12) clusters

Low‐lying equilibrium geometric structures of Al_nN (n = 1–12) clusters obtained by an all‐electron linear combination of atomic orbital approach, within spin‐polarized density functional theory, are reported. The binding energy, dissociation energy, and stability of these clusters are studied within the local spin density approximation (LSDA) and the three‐parameter hybrid generalized gradient approximation (GGA) due to Becke–Lee–Yang–Parr (B3LYP). Ionization potentials, electron affinities, hardness, and static dipole polarizabilities are calculated for the ground‐state structures within the GGA. It is observed that symmetric structures with the nitrogen atom occupying the internal position are lowest‐energy geometries. Generalized gradient approximation extends bond lengths as compared with the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps, the ionization potential, the electron affinity, and the hardness are more pronounced within the GGA. The stability analysis based on the energies clearly shows the Al₇N cluster to be endowed with special stability. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Density functional study of the structural,electronic, and magnetic properties of neutral and charged rhodium clusters up to tetramer

Model core potential computations were performed for Rh₂, Rh₃, and Rh₄ clusters and their respective cations and anions using the linear combination of Gaussian‐type orbital, nonlocal spin density method. The optimized geometries, electronic and magnetic structures, binding and fragmentation energies, adiabatic ionization potentials, and electron affinities were determined. Results show that the ionization potentials, electron affinities, binding energies, and magnetic moments decrease with the cluster size. For Rh₂ and Rh₃ the most stable structures exhibit ferromagnetic properties, while Rh₄ in its ground state is found to be paramagnetic. The structures of minimum energy for the charged species often differs from the corresponding neutral one. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Density Functional Theory Study on Electronic and Magnetic Properties of Mn-doped (MgO)n (n=2-10) Clusters

We study the geometries, stabilities, electronic and magnetic properties of (MgO)_n (n=2-10) clusters doped with a single Mn atom using the density functional theory with the gener-alized gradient approximation. The optimized geometries show that the impurity Mn atom prefers to replace the Mg atom which has low coordination number in all the lowest-energy MnMg_n-1O_n (n=2-10) structures. The stability analysis clearly represents that the aver-age binding energies of the doped clusters are larger than those of the corresponding pure (MgO)_n clusters. Maximum peaks of the second order energy differences are observed for MnMg_n-1O_n clusters at n=6, 9, implying that these clusters exhibit higher stability than their neighboring clusters. In addition, all the Mn-doped Mg clusters exhibit high total magnetic moments with the exception of MnMgO₂ which has 3.00 μB. Their magnetic be-havior is attributed to the impurity Mn atom, the charge transfer modes, and the size of MnMg_n-1O_n clusters.     

Double icosahedron‐based motif of Nin (n = 20−30)

A genetic algorithm (GA) coupled with a tight‐binding (TB) interatomic potential was used to search for the low‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters. The low‐energy candidate structures from the GA/TB search were further optimized by using the density functional theory calculations with the Perdew, Burke, and Ernzerhof exchange‐correlation energy functional. The obtained lowest‐energy structures of the medium‐sized Ni_n (n = 20?30) clusters are shown to exhibit double icosahedron‐based motif. The properties of the nickel clusters including binding energies, second differences in energy, and especially magnetic properties have also been studied. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Structural,Electronic and Tunable Magnetic Properties of Transition Metal Doped Rh<Subscript>8</Subscript> Cluster from First Principles Calculation

The configurations, electronic and magnetic properties of the Rh₇M (M?=?3d, 4d transition metal) are systematically investigated within the framework of the generalized gradient approximation density-functional theory (DFT-GGA). The results indicated that the ground state structures of Rh₇M (M?=?3d) clusters prefer to a bicapped octahedron configuration, while the Rh₇M (M?=?4d) clusters present a different degree of geometry reconstruction relative to the perfect cubic structure of Rh₈ cluster. In most cases, the doped clusters show relatively higher stability, indicating that impurity atoms could stabilize the pure Rh₈ cluster; the Rh₇M (M?=?3d, 4d) have smaller frontier orbital energy gaps in comparison to the host. The magnetic moments of Rh₇M (M?=?3d, 4d) exhibit a tunable magnetism with range from 3μ_B to 13μ_B and the Fe atom doping enhances the magnetic moment of mixed cluster.     

Theoretical investigations on the superhalogen properties and interaction of PdOn (n = 1–5) species

Density functional calculations on the ground state geometries and stabilities of PdO_n species (n = 1–5) are performed in neutral as well as anionic forms. Calculations reveal that Pd can bind stably with four O atoms indicating the maximum oxidation state of Pd as high as +8. The electron affinities of PdO_n suggest that these species behave as superhalogens for n ≥ 2. The large electron affinities of PdO_n species along with stability of their anions point toward the synthesis of new class of compounds having unusual oxidizing capabilities. This possibility is explored by considering the interaction of PdO₂ superhalogen with Ca atom which forms a stable CaPdO₂ complex. In this complex, PdO₂ unit closely mimics the behavior of O atom when compared with CaO molecule. © 2013 Wiley Periodicals, Inc.     

Structures and basicity of LiNOH (N = 1 − 5) species

LiOH is one of the strong bases among neutral molecules. What about hydroxides of small Li_n (n = 2 ? 5) clusters? The addition of a single atom to a cluster sometimes has dramatic effects on its reactivity. This fact motivated us to perform an ab initio MP2/6‐311++G(d, p) investigation on Li_nOH species (n = 1 ? 5). These Li_nOH species are stabilized by both ionic as well as covalent interactions, and are found to be stable against elimination of LiOH and OH. We have determined their gas and aqueous phase basicity by considering hypothetical protonation reactions. The calculated proton affinities of Li_nOH (n ≥ 2) suggest their reduced basicity as compared to LiOH by 50–100 kJ/mol. The NBO charges and the highest occupied molecular orbitals also reveal the electride and alkalide characteristics of Li₂OH and Li₃OH, respectively. © 2016 Wiley Periodicals, Inc.     

Structural,electronic and magnetic properties of small gold clusters with a copper impurity

A set of all-electron scalar relativistic calculations on Au _n Cu (n = 1–12) clusters has been performed using density functional theory with the generalized gradient approximation at PW91 level. The lowest energy geometries of Au _n Cu clusters may be considered as assemblies of triangular Au₃ moieties substituted with one Cu atom at the highest coordinated site. All these lowest energy geometries of the Au _n Cu clusters are slightly distorted but retain the planar structures of the Au _n+1 clusters due to the strong scalar relativistic effects. The Au–Cu bonds are stronger, and a few Au–Au bonds far from the Cu atom are weaker, than the corresponding Au–Au bonds in pure Au _n+1 clusters. After doping with a Cu atom, the thermodynamic stability and chemical reactivity are enhanced to some extent. The odd-numbered Au _n Cu clusters with even numbers of valence electrons are more stable than the neighboring even-numbered Au _n Cu clusters with odd numbers of valence electrons. Odd–even alternations of magnetic moments and electronic configurations for the Au _n Cu clusters can be observed clearly and may be understood in terms of the electron pairing effect.     

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     

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.     

Geometries,stabilities, electronic and magnetic properties of small aluminum cluster anions doped with cobalt: A density functional theory study

The geometrical structures, relative electronic and magnetic properties of small Al_nCo^– (1 ≤ n ≤ 9) clusters are systematically investigated within the framework of density functional theory at the BPW91 level. The single Co doping can dramatically affect the ground state geometries of the 1 Al_n+1^- clusters. At the same time, the resulting geometries show that the lowest energy Al_nCo^– clusters prefer to be three dimensional structures. Here, the relative stabilities are investigated in terms of the calculated average binding energies, fragmentation energies, and second-order energy differences. Moreover, the result of the highest occupiedlowest unoccupied molecular orbital energy gaps indicates that Al₆Co^– clusters have the highest chemical stability for Al_nCo^– (1 ≤ n ≤ 9) clusters. Furthermore, the natural population analysis reveals that the charges in Al_nCo^– clusters transfer from the Al frames to the Co atom. Additionally, the analyses of the local and total magnetic moments of the Al_nCo^– clusters show that the magnetic effect mainly comes from the Co atom.     

Theoretical study on the interaction of neutral and charged Tin (n = 1–7) clusters with one oxygen molecule

The interactions between the neutral and charged (?2, ?1, +1, and +2) Ti_n (n = 1–7) clusters and one O₂ molecule were investigated by density functional theory. The calculated results show that the oxygen molecule is dissociative on the neutral Ti_n clusters. Geometrically, the two O atoms are distributed at the two sides across the neutral Ti_n cluster for n = 1–4 and the oxygen atom favors the three‐fold hollow site for n = 5, 6, and 7. The binding energy per atom (E_b) and energy gap (E_gap) show higher stability and lower chemical activity of the neutral Ti_nO₂ (n = 1–7) systems compared with the corresponding Ti_n clusters. The adsorption energies (E_ad) exhibit a continuously ascending tendency except for n = 4. The results of the addition of different charges (?2, ?1, +1, and +2) on the most stable neutral Ti_nO₂ (n = 1–7) systems indicate that their geometries are usually perturbed. The stabilities of the neutral Ti_nO₂ systems are enhanced by adding one negative charge. The strongest interaction of the charged Ti_n clusters (?2, ?1, +1, and +2) with O₂ molecule is found at charge +2. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011