Second-order Energy Difference Research Articles

Geometries, stabilities, and electronic properties analysis in InnNi(0,±1) clusters: Molecular modeling and DFT calculations**Project supported by the Cultivating Program of Excellent Innovation Team of Chengdu University of Technology (Grant No. KYTD201704), the Cultivating Program of Middle-aged Backbone Teachers of Chengdu University of Technology (Grant No. 10912-KYGG201512), the National Natural Science Foundation of China (Grant No. 11404042), the Science Fund from

Density functional theory (DFT) with the B3LYP method and the SDD basis set is selected to investigate InNi, InNi, and InNi (–14) clusters. For neutral and charged systems, several isomers and different multiplicities are studied with the aim to confirm the most stable structures. The structural evolution of neutral, cationic, and anionic InNi clusters, which favors the three-dimensional structures for n = 3 – 14. The main configurations of the InNi isomers are not affected by adding or removing an electron, the order of their stabilities is also nearly not affected. The obtained binding energy exhibits that the Ni-doped In cluster is the most stable species of all different sized clusters. The calculated fragmentation energy and the second-order energy difference as a function of the cluster size exhibit a pronounced even–odd alternation phenomenon. The electronic properties including energy gap , adiabatic electron affinity (AEA), vertical electron detachment energy (VDE), adiabatic ionization potential energy (AIP), and vertical ionization potential energy (VIP) are studied. The total magnetic moments show that the different magnetic moments depend on the number of the In atoms for charged InNi. Additionally, the natural population analysis of InNi clusters is also discussed.

Another look at structure of gold clusters Aun from perspective of phenomenological shell model

Geometric, energetic and electronic properties of Aun clusters, n=2–20 are determined using DFT calculations (BB95/cc-pVTZ-PP). Global equilibrium structures were confirmed or found, and the growth mechanism was established. Au-clusters prefer 2D-geometries up to Au11 and are generated from the lowest-lying isomer of the smaller size by adding an extra gold atom. Transition from an oblate form to a pyramid is observed at Au17. Aun containing 17–20 atoms favor tetrahedral evolution by adding atoms to the Frank-Kasper 16-vertex. Binding energy per atom, second-order difference of energy, and one-step fragmentation energy show that Au6 and Au20 have high thermodynamic stability. Their valence electrons of generate magic numbers that can be understood using the phenomenological shell model. Due to Jahn-Teller effect, Au16 is characterized by oblate structure whereas the anion Au16-exhibits Frank-Kasper form.

Stabilities, electronic and magnetic properties of Cu-doped nickel clusters: a DFT investigation

ABSTRACTIn this paper, we investigate the electronic and magnetic properties of Cu-doped nickel clusters by means of density functional theory. The stabilities of these clusters have also been studied in terms of the binding energies, second-order difference of energies, fragmentation energies and HOMO–LUMO energy gaps. The obtained results reveal that the N4Cu, N5Cu and Ni7Cu clusters are found to be more stable that than all other clusters. Higher HOMO–LUMO gap was observed for Ni5Cu cluster (2.265 eV), indicating its higher chemical stability. A half-metallic behaviour has also been observed for the NinCu clusters, which suggests that these clusters can be employed as nanocatalysts for several catalytic processes, particularly for hydrogenation and dehydrogenation reactions. The magnetism calculations show that the magnetic moment is mostly located on the Ni atoms, and the contribution of the Cu atom to the total magnetic moment in the NinCu clusters is very small. Furthermore, partial density of states analysis indicates that the 3d orbitals in Ni atoms are mostly responsible for the magnetic behaviour of these clusters, and the s orbitals have a very little contribution to the total magnetic moment.

Probing structure, electronic property, and hydrogen adsorption for the alkali auride series

The structural evolution, relative stability, electronic property, and hydrogen adsorption of the alkali auride series, AunM (\( n = 1-8\)), \( {\rm M}= {\rm Li}\), Na, K, Rb, Cs), have been investigated using the density functional theory calculations at PW91 level. For the lowest-energy clusters, the dopant atom M prefers to occupy a peripheral or capped site in the host, and M-induced geometries become three-dimensional more easily. The average binding energy per atom, fragmentation energy, second-order difference of energy, and HOMO-LUMO energy gap show a pronounced odd-even oscillation with the number of Au atoms, and the enhanced relative stabilities are found in Au5M (\( {\rm M}= {\rm Li}\), Na, K) and Au3M (\( {\rm M}= {\rm Rb}\), Cs) clusters. In these clusters, the H2 molecule would like to bond with Au atom rather than impurity atom. After adsorption, the AunM structures and H2 molecule in all AunM-H2 clusters are hardly perturbed and still maintain their structural integrity. The geometrical and energetic information indicates a weak adsorption of H2 molecule.

Structural optimization of Fen-Ptm (5 n+m 24) alloy clusters based on an improved Basin-Hopping Monte Carlo algorithm

Alloy nanoclusters have received extensive attention because they can achieve bifunctional properties by making good use of the cooperative effect of two metals. In this paper, an improved Basin-Hopping Monte Carlo (BHMC) algorithm is proposed to investigate the structural stabilities of Fe-Pt alloy nanoclusters. Different cluster sizes and chemical compositions are considered. Moreover, a similarity function is introduced to analyze the structural similarity between the stable structures of alloy clusters and those of their monometallic clusters. Meanwhile, the atomic distributions of Fe-Pt alloy clusters are considered for their stable structures. The results indicate that for Fe-Pt alloy clusters with the size N 24, there is no significant structural evolution with the increase of cluster size. Fe atoms prefer to segregate at the peripheral positions of the clusters, while Pt atoms tend to occupy the interior. The same distribution result can be obtained for the structures of clusters with different compositions. With Fe composition increasing, this distribution trend is more pronounced for the Fe-Pt alloy clusters. In addition, by calculating the structural similarity function between alloy and monometallic clusters, we find that the stable structures of Fe-Pt alloy clusters gradually vary with composition ratio. Moreover, when the Fe atoms or Pt atoms are added into the Fe-Pt alloy system, they change the stable structures of Fe-Pt alloy clusters, resulting in a different structure from Fe and Pt monometallic ones. Also, the structural similarity is different when the Fe composition varies. Furthermore, the best stable structures of Fe-Pt clusters with different compositions and sizes are obtained by calculating the second-order finite difference in energy of Fe-Pt alloy clusters.

Global structural optimization and growth mechanism of cobalt oxide nanoclusters by genetic algorithm with spin-polarized DFT

Multi-convergence relaxation procedures within the genetic algorithm method refined by spin-polarized density functional theory were applied to search for the global and local minima of cobalt oxide nanoclusters ConOn (n = 3−7). The study found new global minimum structures for the Co5O5 and Co6O6 clusters, which are more stable than the best previous models. Through comparison with previous theoretical and experimental data, the genetic algorithm accurately predicted the global minima of Co3O3, Co4O4 and Co7O7, and the stability of the planar-like Co4O4 from the second-order energy difference calculation. Most interestingly, a new growth mechanism of ConOn from the planar-like to the compact as the global minimum structure was predicted that occurs at the Co5O5 cluster.

Evolution of the structural and electronic properties of small alkali metal-doped aluminum clusters

The atomic arrangement of Aln and AlnM clusters (n=2–14, M=Li, Na o K) was determined by combining both the basin hopping (BH) algorithm using the Gupta potential, and density functional theory (DFT) calculations. The BH yielded hundreds of structures that were refined by DFT using the PBE framework, and Ahlrichs-VDZ basis sets. Anions, neutrals and cations of Aln and AlnM clusters were calculated by DFT resulting in a set of ground state structures. These structures were considered for studying different stability criteria such as binding energy, dissociation energy, second-order difference of energies, and HOMO-LUMO gaps. Furthermore, the calculated ionization potential, and electron affinity of the clusters yielded values comparable to the experimental ones. A further bonding analysis of the clusters was carried out by the quantum theory of atoms in molecules (AIM) and by using the electronic localization function (ELF). Based on the stability criteria, we determinate the following clusters as relative stable against neighbors: Al7+, Al13−, Al2M−, Al4M−, Al6M−, and Al13M. Except by the Al4M− clusters, all clusters are closed shell structures and they follow the jellium model predictions. The high relative stability of the Al4M− clusters was attributable to their aromaticity. Moreover, AIM and ELF results revealed that when the size of the clusters increases then the transition from covalent to metallic AlAl bonding emerges. Otherwise, in the case of AlnM clusters, it was found that the nature of AlM bonds is modified with the size, from metallic for Al2M− to ionic when their size increases.

Density-Functional Study of Structural and Electronic Properties of the ZrnAl±m Clusters

<p>The geometries, stabilities, and electronic properties of Zr<em><sub>n</sub></em>Al<sup>±<em>m</em></sup> (<em>n</em> = 1 – 7 and <em>m</em> = 0, 1) clusters were investigated at the UB3LYP/LANL2DZ level. The variations of structural and electronic properties with the changes of <em>n</em> and <em>m</em> were probed. Several possible multiplicities of each cluster were tested. The multiplicity of the most stable neutral clusters is 4 instead of 2. For all the three differently charged of Zr<em><sub>n</sub></em>Al clusters, the lowest-energy geometry is in favor of three-dimensional structure when <em>n</em> ≥ 3. The Zr<sub>3</sub>Al<sup>+</sup>, Zr<sub>4</sub>Al<sup>–</sup>, Zr<sub>5</sub>Al<sup> +</sup>, Zr<sub>6</sub>Al<sup>– </sup>and Zr<sub>7</sub>Alclusters are more stable than their corresponding differently charged species of the same size. Moreover, the odd-even oscillations are found in the fragmentation energy and the second-order difference of total energies for Zr<em><sub>n</sub></em>Al<sup>– </sup>clusters. The Zr<sub>2</sub>Al<sup>+ </sup>cluster is more inert to chemical reaction than others judged by the HOMO-LUMO gaps. NBO analysis was done to analysis the electronic properties.</p>

Structural transformations in the carborane series: CnB6−nH6 (n = 0–6) upon substitution of boron by carbon

In this paper we examined a structural transition from three-dimensional to two-dimensional in the CnB6−nH6 (n=0–6) series. The searches for all the isomers of clusters were performed using the stochastic search algorithm at the B3LYP/6-31G level of theory. Subsequent geometry optimizations at the hybrid density functional B3LYP/6-311++G∗∗ level of theory along with single-point CCSD(T) calculations were carried out to estimate relative energies. We found that 3D-2D transition occurs at n=5 (C5BH6). Moreover, the stability of clusters is discussed on the basis of the binding energy per atom, second-order energy difference, adiabatic ionization potential, HOMO–LUMO energy gap and polarizability. Based on the simultaneous criteria of high binding energy, high band gap, high adiabatic ionization potential and low polarizability, it is found that C2B4H6 cluster has a higher stability.

Probing the structures, stabilities, and electronic properties of neutral and charged carbon-doped lithium CLi n μ (n = 2–20, μ = 0, ±1) clusters from unbiased CALYPSO method

The structural and electronic properties of the global minimum structures of neutral, anionic and cationic CLi (n = 2–20; μ = 0, ±1) clusters were systematically investigated using the unbiased CALYPSO structure searching method in conjunction with density functional theory calculations at the B3LYP/6-311+G* level of theory. It was found that the ground-state structures of neural CLi n clusters exhibit linear and planar configurations at n = 2 and 3, respectively, above which three-dimensional configurations are preferred with C and several Li atoms encapsulated into the Li n cages. There were only minor differences in the structure between the neutral and charged CLi n clusters, which is in accordance with the calculated results of ionization potential and electron affinity. However, the addition/removal of one electron to/from the neutral species had a significant effect on the stabilities of the resulting charged clusters. The averaged binding energy indicated that cationic CLi n clusters show relatively higher stabilities. Pronounced odd–even alternations were observed in the fragmentation energy, second-order energy difference and HOMO–LUMO energy gaps. Finally, detailed chemical bonding of the CLi 11 −1 cluster was analyzed based on the AdNDP method, and static polarizabilities of CLi clusters are discussed.

Size effects on the structural, electronic, and optical properties of (5,0) finite-length carbon nanotube: An ab-initio electronic structure study

We use density functional computations to study the zero temperature structural, electronic, magnetic, and optical properties of (5,0) finite carbon nanotubes (FCNT), with length in the range of 4–44 Å. It is found that the structural and electronic properties of (5,0) FCNTs, in the ground state, converge at a length of about 30 Å, while the excited state properties exhibit long-range edge effects. We discuss that curvature effects enhance energy gap of FCNTs, in contrast to the known trend in the periodic limit. It is seen that compensation of curvature effects in two special small sizes may give rise to spontaneous magnetization. The obtained cohesive energies provide some insights into the effects of environment on the growth of FCNTs. The second-order difference of the total energies reveals an important magic size of about 15 Å. The optical and dynamical magnetic responses of the FCNTs to polarized electromagnetic pulses are studied by time dependent density functional theory. The results show that the static and dynamic magnetic properties mainly come from the edge carbon atoms. The optical absorption properties are described in terms of local field effects and characterized by Casida linear response method.

Properties of neutral and charged cobalt-doped arsenic CoAsn(0±1) (n = 1–15) clusters by density functional theory

The structural, electronic and magnetic properties of neutral and charged CoAsn (n=1–15) have been systematically investigated using spin polarized density functional theory to highlight the effects of a cobalt atom on properties of arsenic clusters. Compared with the neutral clusters, the ground state structures of CoAsn+ and CoAsn− were obviously rearranged due to the extraction or the addition of an electron. The optimized clusters reveal that the most stable structures and their corresponding isomers have three dimensional configurations. The relative stabilities have been studied in terms of the binding energies, fragmentation energies and second-order difference of energies for all CoAsn(0±1) structures. The values of HOMO–LUMO gaps have a decreasing tendency along with the increasing number of As atoms in the cluster. The HOMO–LUMO gaps decrease considerably in doped clusters which suggest an increase of metallic property. Total magnetic moment depends on the geometry, the position of Co atom in the cluster, the charge transfer and orbital hybridization. The vertical ionization potential (VIP), vertical electronic affinity (VEA), chemical hardness (η), adiabatic electronic affinity (AEA) and adiabatic ionization potential (AIP) have also been investigated and discussed.

Structures, stabilities, and magnetic properties of the FenAu (n = 1−12) clusters**Project supported by the National Natural Science Foundation of China (Grant No. 21301112) and the Ph. D. Program Foundation of the Education Ministry of China (Grant No. 20131404120001).

The configurations, stabilities, electronic, and magnetic properties of FenAu (n = 1−12) clusters are investigated systematically by using the relativistic all-electron density functional theory with the generalized gradient approximation. The substitutional effects of Au in Fen+1 (n = 1, 2, 4, 5, 10−12) clusters are found in optimized structures which keep the similar frameworks with the most stable Fen+1 clusters. And the growth way for FenAu (n = 6−9) clusters is that the Au atom occupies a peripheral position of Fen cluster. The peaks appear respectively at n = 6 and 9 for FenAu clusters and at n = 5 and 10 for Fen+1 clusters based on the size dependence of second-order difference of energy, implying that these clusters possess relatively high stabilities. The analysis of atomic net charge Q indicates that the charge always transfers from Fe to Au atom which causes the Au atom to be nearly non-magnetic, and the doped Au atom has little effect on the average magnetic moment of Fe atoms in FenAu cluster. Finally, the total magnetic moment is reduced by 3 μB for each of FenAu clusters except n = 3, 11, and 12 compared with for corresponding pure Fen+1 clusters.

Effect of alloying on the stabilities and catalytic properties of Ag–Au bimetallic subnanoclusters: a theoretical investigation

Density functional theory has been applied to study the geometric and electronic structures and the catalytic properties of Ag and AgAu clusters for CO oxidation. The calculated results suggest that the doping of Au atoms improve the stability of AgAu clusters. Correspondingly, the binding energy (BE) per atom of Ag n Au is larger than that of pure Ag n+1 cluster, due to strong hybridization between the d orbitals of Au and the s orbitals of Ag in Ag n Au clusters. With the increasing Au concentration, the BE of Ag13−n Aun(n = 1–8) clusters increase smoothly, while second-order difference of energies (Δ2 E) and fragmentation energies (ΔE) show an even–odd oscillation. The AgAu clusters containing an odd n umber of gold atoms (Ag13−n Au n , n = 3, 5, 7) are relatively stable compared to their neighbor. The CO and O2 adsorption properties on the Ag13, Ag10Au3, Ag8Au5, and Ag6Au7 clusters suggest that O2 is strongly activated by the clusters, while the activation of CO is much weak. Furthermore, the activation of O2 on AgAu cluster is stronger than that on pure Ag13 cluster, especially on Ag8Au5 cluster, due to the strengthened polarization of O–O bond. Compared to Ag13, Ag10Au3, and Ag6Au7 clusters, the lower energy barriers on Ag8Au5 cluster suggest a higher catalytic activity of Ag8Au5 cluster for O2 dissociation and CO oxidation reactions. The calculated results suggest that Ag8Au5 cluster could effectively reduce the carbon monoxide poisoning and exhibits the excellent catalytic performance for CO oxidation. Our study provides atomic-scale insights into the nature of the interfacial effects that determine CO oxidation on Ag–Au cluster catalysts.

Ab initio calculations of the structure, energetics and stability of AunTi (n = 1–32) clusters

The stability and structure of titanium doped gold clusters (AunTi; n=1–32) are studied by density functional theory calculations, as implemented in the first principles code SIESTA. The exchange and correlation effects were calculated within the generalized gradient approximation (GGA) parametrized by Perdew, Burke and Ernzerhof (PBE). We used norm conserving Troullier–Martins pseudopotentials for the 10-electron valence configuration of Ti and 11-electron valence configuration of Au. All calculations were spin-polarized. The global energy minimum geometries of the clusters were searched for by using the simulated annealing technique. The stability of the clusters is discussed on the basis of the binding energy per atom, second-order energy difference, vertical ionization potential, vertical electron affinities, HOMO–LUMO energy gap and vibrational frequencies. Based on the simultaneous criteria of high binding energy, high band gap, high vertical ionization potential, and low electron affinity, it is found that Au4Ti and Au14Ti clusters have a higher stability and are candidates for “magic clusters”, which confirms the already known results from previous works. The new result presented in this paper is that the Au20Ti and Au30Ti clusters have a higher stability too. In general, the clusters with even n are more stable than the clusters with odd n. Most of the clusters with even n are non-magnetic (total magnetic moment is zero). Our results also suggest that only the Au3Ti, Au7Ti and Au8Ti clusters have a planar structure.

Systematic theoretical investigation of structure and electronic properties of pure copper and lithium doped copper clusters

ABSTRACTThe pure copper and lithium-doped copper clusters are studied using the unbiased CALYPSO structure searching method and density function theory to understand the evolution of various structure and electronic properties. Theoretical results show the growth behaviours of doped clusters are organised as follows: Li capped Cun clusters or Li substituted Cun+1 clusters as well as Cu capped Cun-1Li clusters. Moreover, the lowest energy structures of CunLi favour planar structures for n ≤ 3 and three-dimensional structures for n = 4–12. In addition, the calculated averaged binding energies, fragmentation energies and second-order difference of energies exhibit obvious odd–even alternations as cluster size increasing. At last, the highest occupied-lowest unoccupied molecular orbital gaps, molecular orbital energy, magnetic property, natural population analysis, natural electron configurations, electrostatic potential, electron density difference, Infrared and Raman spectra and density of states are also, respectively, operative for characterising and rationalising the electronic properties of doped clusters.

A density functional study of small neutral, anionic, and cationic indium clusters Inn, Inn−, and Inn+ (n = 2–15)

The density functional theory (DFT) is used to investigate the geometries, relative stabilities, electronic properties and natural population analysis for small neutral, anionic, and cationic indium clusters. From 2D to 3D structures of the neutral, anionic, and cationic indium clusters are studied. The optimized results indicate that the geometries of the anionic and cationic indium clusters exhibit large similarities from those of neutral indium. According to the calculations of the averaged binding energy, fragmentation energy, and second-order energy difference, we estimate the relative stabilities of Inn(0,±1) clusters. Odd–even alterations are found in the adiabatic electron affinity (AEA), vertical electron detachment energy (VDE), adiabatic ionization potential energy (AIP), and vertical ionization potential energy (VIP) for the neutral, anionic, and cationic indium clusters. In14 has the highest AEA, In10 has the highest VDE, In13 has the highest AIP, and In5 has the highest VIP. The HOMO–LUMO gaps are also calculated for the Inn(0,±1) clusters to investigate their electronic properties. Natural population analysis reveals that the sign of the charge are zero for Inn clusters, Inn− clusters occupy the negative charges and Inn+ clusters occupy the positive charges.

Theoretical study of geometry, stability and properties of Al and AlSi nanoclusters

Geometry, stability, and properties of Al n (n = 1–13) and Al n Si m (n + m = 5–7) nanoclusters were investigated by density functional theory. We found that while geometry of some clusters change significantly by substituting of Al atom(s) with Si atom(s) the geometry of some others remain without significant variation. The relative stability of clusters was discussed on the basis of binding energy per atom, fragmentation energy, and second-order difference of cluster energies. Our results reveal that Al7 is the most stable cluster among pure clusters. For Al n Si m clusters, it is observed that Al2Si3 (60 % Si), and Al4Si2 (33.33 % Si) are the most stable clusters. The reactivity of Al n and Al n Si m nanoclusters was also investigated on the basis of chemical hardness. The most important feature of chemical hardness is its oscillating behavior as a function of atomic percentage of Si indicating that the reactivity of Al n Si m clusters strongly depends on the composition of cluster.

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 n Co– (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 n Co– 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 n Co– (1 ≤ n ≤ 9) clusters. Furthermore, the natural population analysis reveals that the charges in Al n Co– clusters transfer from the Al frames to the Co atom. Additionally, the analyses of the local and total magnetic moments of the Al n Co– clusters show that the magnetic effect mainly comes from the Co atom.

Probing the structural and electronic properties of cationic rubidium–gold clusters: [AunRb]+ (n = 1–10)

ABSTRACTDensity functional theory has been applied to study the geometric structures, relative stabilities, and electronic properties of cationic [AunRb]+ and Aun + 1+ (n = 1–10) clusters. For the lowest energy structures of [AunRb]+ clusters, the planar to three-dimensional transformation is found to occur at cluster size n = 4 and the Rb atoms prefer being located at the most highly coordinated position. The trends of the averaged atomic binding energies, fragmentation energies, second-order difference of energies, and energy gaps show pronounced even–odd alternations. It indicated that the clusters containing odd number of atoms maintain greater stability than the clusters in the vicinity. In particular, the [Au6Rb]+ clusters are the most stable isomer for [AunRb]+ clusters in the region of n = 1–10. The charges in [AunRb]+ clusters transfer from the Rb atoms to Aun host. Density of states revealed that the Au-5d, Au-5p, and Rb-4p orbitals hardly participated in bonding. In addition, it is found that the most favourable channel of the [AunRb]+ clusters is Rb+ cation ejection. The electronic localisation function (ELF) analysis of the [AunRb]+ clusters shown that strong interactions are not revealed in this study.