Second Energy Difference Research Articles

Comparison of Sn n (n=2–15) neutral and ionic structures

A large number of the isomers of neutral and ionic Snn(n=2–15) clusters have been designed and optimized at the level of MP2/LANL2DZ with the aid of the Gaussian 09 software package. The most stable geometric structures of ionic(cationic and anionic) Sn clusters have been compared with the corresponding neutral geometries. Most structures of Snn+ and Snn are similar to each other except for the structures of those with n=5, 11 and 15; while the anions Snn− are almost different from Snn clusters with n=9–15 except for Sn12− and Sn14−. The electronic properties have been calculated, including binding energy, second difference in energy, HOMO-LUMO gaps, ionization potentials, and electron affinities.

Structure and energetics of Li/Na, Li/K, and K/Na bimetallic hexamers

A systematic study of neutral mixed clusters, Li6−xNax, Li6−xKx and K6−xNax (x = 0–6), was performed within the framework of density functional theory. The aim of this work is to explore the geometry variation and the energy change of homonuclear hexamers (Li6 and K6) induced by impurities. It is found that the geometry of bimetallic hexamers varies with their compositions. The geometries of resulting clusters show evolution from D4h symmetry for Li6 to D3h symmetry for Na6 and K6. The stability of bimetallic hexamers has been also explained in terms of binding energy, excess energy, the second difference in energy, and the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) gaps. It is found that replacing each Li–Li bond with Li–Na or Li–K bonds decreases the cluster stability, while replacing each K–K bond by K–Na leads to stability enhancement. Examining the cluster stability, excess energy and second difference in energy reveal that among studied bimetallic hexamers, Li2Na4 is the most stable mixed hexamer.

Density Functional Study of H<sub>2</sub>S Adsorption on Small Ag<sub>n</sub> (<i>n</i> = 1–5)

The global-minimum geometries and electronic states of AgnH2S (n=1-5) clusters have been calculated using density-functional theory. Our calculations predicate that the stable geometries of AgnH2S clusters can be got by directly adding the H2S molecule on different site of Agn clusters, Agn (n=1-5) clusters would like to bond with sulfur atom and the H2S molecule is partial to hold the top location and single fold coordination site in the clusters. After adsorption, the structures of Agn clusters and H2S molecule keep the original structures and are only distorted slightly. The averaged binding energy reveals that adsorption of H2S molecule can strengthen the stabilities of AgnH2S clusters. The second difference in energy and the energy gaps between the HOMO and LUMO of Agn and AgnH2S have been studied.

Density Functional Study of Structural and Electronic Properties of AlP n (2 ≤ n ≤ 12) Clusters

Low-lying equilibrium geometric structures of AlPn (n = 2–12) 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 aluminum atom occupying the peripheral position are lowest-energy geometries. And the Al impurity in the most stable structures of AlPn clusters can be looked upon as a substitutional impurity in pure Pn+1 clusters or capping Al atom in the different peripheral positions of pure Pn clusters. Generalized gradient approximation extends bond lengths as compared to the LSDA lengths. The odd–even oscillations in the dissociation energy, the second differences in energy, the 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 AlP5 and AlP7 clusters to be endowed with special stabilities.

Density functional study on structures, stabilities, electronic and magnetic properties of NbnO (n = 3–10) clusters

The density functional theory has been employed to investigate the geometrical structures, relative stabilities, electronic and magnetic properties of NbnO (n=3–10) clusters. The ground state structure are obtained by adding one O atom to the Nbn clusters or by replacing one Nb atom by O atom in Nbn+1 clusters. The results of binding energy and the second difference in energy show Nb7O and Nb9O have strong stability. According to the natural population analysis, O atom attracts about 0.8 e charges from its neighboring Nb atoms. The magnetism of the NbnO clusters mostly stems from the contribution of 4d orbital of Nb atoms.

Structural, Electronic, and Magnetic Properties Of ConCum Nanoalloys (m + n = 12) from First Principles Calculations

Using the generalized gradient approximation (GGA) to density functional theory (DFT), we compute the electronic structure and related magnetic properties of free-standing Co(12-x)Cu(x) clusters (x = 0-12) with structures resulting from the optimization of those of the low-lying energy isomers of pure Co(12) and Cu(12) in which Co(Cu) were replaced by Cu(Co) atoms. Structural transitions for the lowest energy homotop are obtained as a function of the concentration, but in all cases, a clear surface segregation of Cu is found in the low concentration regime x < 5. The binding energy decreases monotonically when x increases. The dipole moment changes abruptly from 0.06 D for x = 2 to 0.59 D for x = 3 in coincidence with a structural change. The electronegativity of the lowest energy homotop exhibits minimum (maximum) value for x = 11 (x = 9). The x = 5, 9 clusters show local maxima of the hardness, of the excess energy, and of the second difference in energy, clear indicators of specially stable stoichiometries. The magnetic behavior of Co(12-x)Cu(x) is a monotonous function of the Co concentration, decreasing by steps of ≥2 μ(B) for every Co atom that is replaced by Cu, although for certain concentrations, different spin isomers, sometimes accompanied by structural transitions, are found close to the ground state. Ferromagnetic-like order is obtained as the ground state in all cases, contrary with the trend found in binary clusters of the same elements by other authors who predicted antiferromagnetic order. We analyze in detail the possible spin excitations in Co(12)Cu to demonstrate that local antiferromagnetic couplings can only exist as metastable spin states.

Structures and Stabilities: Quantum-Chemical Study of Aun (n = 2-2016) Nanoclusters by Extended Huckel and DFT Approaches

A fundamental understanding of the physical and chemical properties of gold clusters, namely, the size dependence of these properties, is necessary for developing wide range of gold clusters’ applications. Having this purpose in mind, the structural and energetic properties, such as binding energies, relative stability and band gaps ΔEHL (HOMOLUMO gaps) are evaluated. The gold clusters in a wide range of sizes, Aun (n=2 - 2016), were constructed and studied by Density Functional Theory and Extended Hückel Theory approaches. It was shown that the high values of ΔEHL for the clusters with n= 2, 6, 8, 20 correlate with the highest stability. This finding explains the existence of magic numbers for gold clusters. The 20 atom tetrahedral cluster stands out as particularly stable, comparing to the other small clusters. The binding energy EB is found to increase with the cluster size. The second difference in energy - Δ2E(n) value is used as the criterion of stability, in addition to ΔEHL and also shows a tendency to increase with the cluster size. This behavior suggests a transition of larger clusters towards bulk metallic properties. Both curves - Δ2E(n) and ΔEHL show sharp transformation from high values to close to 0 eV at n=252-504 cluster sizes (it relates to ca 2 nm cluster size).

Structures and Stabilities: Quantum-Chemical Study of Aun (n = 2-2016) Nanoclusters by Extended Huckel and DFT Approaches

A fundamental understanding of the physical and chemical properties of gold clusters, namely, the size dependence of these properties, is necessary for developing wide range of gold clusters’ applications. Having this purpose in mind, the structural and energetic properties, such as binding energies, relative stability and band gaps ΔEHL (HOMOLUMO gaps) are evaluated. The gold clusters in a wide range of sizes, Aun (n=2 - 2016), were constructed and studied by Density Functional Theory and Extended Hückel Theory approaches. It was shown that the high values of ΔEHL for the clusters with n= 2, 6, 8, 20 correlate with the highest stability. This finding explains the existence of magic numbers for gold clusters. The 20 atom tetrahedral cluster stands out as particularly stable, comparing to the other small clusters. The binding energy EB is found to increase with the cluster size. The second difference in energy - Δ2E(n) value is used as the criterion of stability, in addition to ΔEHL and also shows a tendency to increase with the cluster size. This behavior suggests a transition of larger clusters towards bulk metallic properties. Both curves - Δ2E(n) and ΔEHL show sharp transformation from high values to close to 0 eV at n=252-504 cluster sizes (it relates to ca 2 nm cluster size).

A DFT study on the structures and stabilities of As-doped Sin−1 (n = 2–15) clusters

The structures and relative stability of pure Sin and AsSin−1 (n=2–15) clusters have been investigated at the B3LYP/6-31++G(3d) level of density functional theory. In general, the As doping does not lead to fundamental changes in the geometry of the studied clusters; the effects are localized. Relative stabilities of these clusters have been analyzed based on the variation of their averaged binding energies (Eb), fragmentation energies (Ef), second differences in energy (Δ2E), and the highest occupied and the lowest unoccupied molecular orbital (HOMO–LUMO) gaps (ΔE) with cluster size (n). The calculated values of Ef, Δ2E, and ΔE shed light on the relatively high stability of clusters Si12 and Si14 in addition to the well-known magic numbers Si6 and Si10. According to Eb, Δ2E, and Ef results both Sin and AsSin−1 clusters with n=6, 10, 12, and 14 exhibit high stability when compared to their neighbors. This has been discussed in terms of their close-packed structures rather than electronic pairing effect. The analysis indicates that ΔE of AsSin−1 clusters are significantly smaller than those of the corresponding Sin clusters, especially for n>4, which means that the metallic characters of AsSin−1 clusters are enhanced by As doping.

Density functional study of structural and electronic properties of AlnAs (1 ≤ n ≤ 15) clusters

Energetically low-lying equilibrium geometric structures of AlnAs (n=1–15) 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 with 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 same method. The growth pattern for AlnAs (n=1–15) clusters is As-substituted the surface atom of Aln+1 clusters and it keeps the similar frameworks of the most stable Aln+1 clusters except for AlnAs (n=7, 8, and 15) clusters. The odd–even oscillations in the dissociation energy, the second differences in energy, the HOMO–LUMO gaps, the electron affinity, and the hardness are more pronounced. The stability analysis based on the energies clearly shows the clusters with an even number of valence electrons are more stable than clusters with odd number of valence electrons.

Density functional study of small cobalt–platinum nanoalloy clusters

The structural, energetic, electronic and magnetic properties of small bimetallic ConPtm (n+m≤5) nanoalloy clusters are investigated by density functional theory within the generalized gradient approximation. A plausible candidate for the ground state isomer and the other possible local minima, binding energies, relative stabilities, magnetic moments, the highest occupied and the lowest unoccupied molecular orbital energy gaps have been calculated. It is found as a general trend that average binding energies of Co–Pt bimetallic clusters increase with Pt doping. Planar structures of pure Co clusters become 3D with the addition of Pt atoms. CoPt2, Co2Pt2, Co3Pt2, and CoPt4 nanoalloys are identified as the most stable species since they have higher second finite difference in energy than the others. Pt doping decreases the total spin magnetic moment gradually. A rule for the prediction of the total spin moments of small Co–Pt bimetallic clusters is derived.

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

AbstractA genetic algorithm (GA) coupled with a tight‐binding (TB) interatomic potential was used to search for the low‐energy structures of the medium‐sized Nin (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 Nin (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

An ab initio calculation study of silicon and carbon binary clustersC7Sin (n = 1–7)

Binary C7Sin (n = 1–7) clusters are studied using density functional calculations at the level of B3LYP/6-311G(d).Lowest-energy structures have been determined theoretically and their properties such asbinding energies, second differences in energy and highest-occupied and lowest-unoccupiedmolecular orbital gaps have been analyzed. It is found that the lowest-energy structures of theC7Sin (n = 1–7) clusters change fromlinear to planar when n ≥ 3, and in the planar structures C atoms prefer to form five- andsix-membered rings surrounded by extra Si atoms in the form of theC2Si units.

Hydrogen storage capabilities of the most stable isomers of NanBm (m + n = 6) clusters

The most stable isomers of NanBm (m + n = 6) clusters and their hydrogen storage properties are investigated by means of density functional theory with a 6-311+G(d) basis set. To study the hydrogen storage properties, all of the stable structures of NanBmHx (m + n = 6) clusters have been optimized. It shows that boron atoms of NanBm are separated from the other boron atoms, and form satellite BHx (x = 3, 4) clusters around the centre, which attach to the system by a bridging bond of a hydrogen atom or an Na atom. Compared with the hydrogen storage capabilities, the Na3B3 has the highest hydrogen storage capacity among NanBm clusters. The binding energies, interaction energies of hydrogen atom with NanBm clusters and second difference in energy of Na3B3Hx clusters have been calculated. The results show that the stability of the NanBmHx clusters present an odd-even oscillatory effect, as the number of H atoms increases.

Structural, electronic and magnetic properties of GdSin ([formula omitted]) clusters: A density functional study

The geometries, stabilities, electronic and magnetic properties of GdSin (n=1–17) clusters have been investigated systematically by using density functional theory (DFT) with the generalized gradient approximation (GGA). We find that the Gd atom in the lowest-energy configuration gradually moves from convex to surface, and to the interior site as the number of Si atom varies from 1 to 17. Furthermore, from GdSi16, Gd atom in GdSi16 cluster completely falls into the center of the Si framework and forms a fullerene cage. On the basis of the atomic average binding energy [Eb(n)], the second difference in energy (Δ2E) and VIP, we predict that the magic number of GdSin (n=1–17) clusters should be 5, 11 and 16, and these clusters should be abundant in the mass spectra when n=5, 11 and 16. The magnetic moments of the GdSin clusters are also studied. It is found that the total magnetic moments and the magnetic moments on Gd of GdSin clusters are large, and they do not quench when Gd is encapsulated in Si outer framework cage, which is to a large extent due to the fact that the Gd 4f electrons hardly interact with the silicon cage.

Carbon-rich C 9Si n ( n = 1–5) clusters from ab initio calculations

The carbon-rich structures of C 9Si n ( n = 1–5) clusters were studied by first-principles density functional calculations using the B3LYP hybrid exchange–correlation energy functional and 6-311++G(2df) basis set. By systematic investigation of the structures and energies, we found that in the structures of the carbon-rich clusters C 9Si n ( n = 1–5), the C atoms were found to form linear ( n = 2), or single-ring ( n = 1 and 3) or double-rings ( n = 4 and 5) while the Si atoms prefer to attach to the carbon rings in the form of C 2Si units. Based on the lowest-energy structures obtained from our calculations, the properties of the clusters such as binding energy, second difference in energy, HOMO–LUMO gap, adiabatic ionization potential (AIP), adiabatic electron affinity (AEA), vibrational frequency, bond orders and NBO charge transfer have been calculated and analyzed.

Thermochemical properties, electronic structure and bonding of mixed lithium boron clusters (B nLi, n = 1–8) and their anions

The electronic structure and molecular properties of a series of small mixed lithium boron clusters B n Li ( n = 1–8) in both neutral and anionic states are investigated using quantum chemical methods. The lowest-energy structures are identified. Standard heats of formation, adiabatic electron affinities (EAs) and vertical detachment energies (VDEs) are predicted using coupled-cluster theory CCSD(T)/6-311+G(d) calculations. Addition of Li to B n to form B n Li clusters marginally distorts the geometries of the parent B n . The chemical bond in B n Li has a highly ionic character in which the positive charges are located on Li. MO analysis confirms a similar degree of aromaticity between B n Li and B n - . The relative stabilities of the clusters are evaluated using the average binding energy ( E b ), second order difference in energy (Δ 2 E), resonance energy (RE) and normalized resonance energy (NRE). Both REs and NREs quantities of the Li-doped boron clusters are consistently larger than those of the pure B n clusters. The B 3Li species exhibits a remarkably high stability within the B n Li series.

Molecular Structures, Energetics, and Electronic Properties of Neutral and Charged HgnClusters (n= 2−8)

The geometric and electronic structures of small mercury clusters, Hg(n), Hg(n)(+), and Hg(n)(-) (n </= 8) have been calculated using a density functional theory. The results indicate that as the cluster size increases, the lowest energy states of neutral and anionic mercury clusters prefer three-dimensional structure whereas those of cationic clusters are peculiarly linear structure due to s-p hybridization. This structural feature has influence on the energetic and electronic properties of cationic clusters which deviate from the characteristics of van der Waals cluster. As the cluster size increases, energetic properties, binding energies per atom and second order difference in total energy of cationic clusters consistently decrease, in contrast to the neutral and anionic clusters. However, neutral and charged mercury clusters show common features in terms of size dependent transition of bonding character, such as the decrease of band gap and vertical ionization potential, and the increase of vertical electron affinity. These various properties are also qualitatively and quantitatively in line with the available experimental and theoretical results, implying the reliability of the ground state geometries of these clusters.

Density functional study of structural and electronic properties of GaP n (2 ≤ n ≤ 12) clusters

Low-lying equilibrium geometric structures of GaPn (n = 2–12) 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 the gallium atoms of the symmetric ground-state structures prefer to occupy the peripheral positions. It is found that the relative ordering of the isomers is influenced by the nonlocal exchange-correlation effects for small clusters. Generalized gradient approximation extends bond lengths and widens the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), as compared to the LSDA gap. The odd–even oscillations in the dissociation energy, the second differences in energy, the 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 GaP5 and GaP7 clusters to be endowed with special stabilities.

Density functional theory study on Ni-doped MgnNi (n = 1–7) clusters

The possible geometrical and the electronic structures of small MgnNi (n = 1–7) clusters are optimised by the density functional theory with a LANL2DZ basis set. The binding energy, the energy gap, the electron affinity, the dissociation energy and the second difference in energy are calculated and discussed. The properties of MgnNi clusters are also discussed when the number of Mg atom increases.