Second-order Energy Difference Research Articles

Geometrical and electronic structure of the Ba-doped Sin (n = 1–12) cluster: A density functional study

The structures, stabilities and electronic properties of BaSin and Sin+1 (n=1–12) clusters are systematically studied by density functional calculations using the B3LYP exchange–correlation potential. Extensive structure search based on large numbers of initial configurations has been carried out to identify the stable isomers of BaSin (n=1–12) clusters. We found that the most stable isomers of BaSin clusters are three-dimensional structures when n>3, and the most stable structures of BaSin clusters often can be created by adding Ba or substituting Si by Ba in pure silicon clusters. The stability has been analyzed based on the average binding energy, fragmentation energy and second-order energy difference. The calculated results indicate that BaSin clusters with n=2, 5, 8 and 10 have higher stability than other clusters. The analysis of the highest occupied molecular orbital and the lowest unoccupied molecular orbital suggests that the substitution of Ba atom reduce the gaps of the Sin+1 clusters. The Mulliken populations of the Ba atom in the BaSin clusters vary from 0.506 to 1.574, showing that the charges in BaSin clusters transfers from the Ba atom to Si atoms. Furthermore, the vertical ionization potential, vertical electron affinity, chemical hardness, infrared and Raman spectra are also analyzed.

Theoretical investigation on structural evolution, energetic stability trend and electronic properties of Au n Cd(n=1–12)

We systematically studied the geometrical structures, relative stabilities, electronic properties and chemical hardness of Au n Cd (n =1–12) clusters based on the framework of the density functional theory using relativistic all-electron methods. Low-lying energy structures include two-dimensional and three-dimensional geometries. Especially, all the lowest-energy structures of Au n Cd (n =1 −12) clusters are inclined to be planar geometries with slight distortion, in which the dopant Cd atom has higher coordination at n =2–6, but lower coordination at n =7–12. The fragmentation energies, second-order difference of energies, the highest occupied–lowest unoccupied molecular orbital gaps and chemical hardness of Au n Cd and Au n+1 exhibit a pronounced even–odd alternations phenomenon in the reverse order This result indicates that the geometrical, electronic and chemical stabilities of Au n Cd with even number of valence electrons are higher than those of the neighbouring Au n Cd with odd number of valence electrons and corresponding Au n+1 with odd number of valence electrons. Additionally, 4d valence electrons orbital of impurity Cd atom in Au n Cd hardly joins in the orbital interactions compared with 5d valence electrons of corresponding Au atom in Au n+1. Au–Cd bonds of Au n Cd clusters are weaker and have more obviously ionic-like characteristics than the corresponding Au–Au bonds of Au n+1. The impurity Cd atom can change the chemical stability pattern of pure gold clusters, namely the even-numbered Au n Cd are less reactive than the corresponding Au n+1 and neighbouring odd-numbered Au n Cd.

The geometries, electronic structures and magnetic properties of TM doped Cn(TM = Fe, Co, Ni, n = 9–15) clusters: a density functional theory investigation

The geometries, binding energies, electronic structures and magnetic properties of TMCn clusters (TM = Fe, Co, Ni, n = 9–15) have been systematically investigated with the generalized gradient approximation (GGA) based on all-electron density functional theory. Optimization results indicate that TMC9 clusters prefer linear structures with the TM atom at one end, while monocyclic planar structures are predicted to be the most favorable for TMCn (n = 10–15) clusters. The calculated second-order energy differences and fragmentation energies indicate that the magic numbers for stability appear at n = 10, 12, 14 for FeCn, and n = 11 and 14 for CoCn and NiCn, implying that these clusters possess relatively higher stability. Mülliken population analysis shows that charge always transfers from the TM atoms to C atoms. The magnetic moment of TMCn clusters mainly is located mainly on the TM atom. The 3d electrons in the TM atom play a dominant role in the determination of the magnetism of the TM atom.

Investigation on Stability and Optical Properties of Zn<sub>n</sub>Se<sub>n</sub>(n=1~13) Nanocluster in CIGS-ZnSe Heterojunction Interface

ZnSe cluster is the main form of growth mechanism in CuInGaSe based solar cells as the buffer layer and the building blocks for larger bulk ZnSe materials as well. With the generalized gradient approximation in first principle all-electron calculations, a number of configurations and structural isomers of ZnnSen (n=1~13) nanoclusters has been geometrically optimized to get the lowest energy constructions of ZnnSen (n=1~13). Second-order energy difference were applied to investigate the stability of small ZnSe nanoclusters. And the nanocage Zn12Se12 cluster has been identified to be in rather stable state and can be the building block of larger ZnSe nanoclusters materials. Energy gap between lowest unoccupied molecular orbital and the highest occupied molecular orbital, Infrared Spectroscopy have also been investigated for further study on size and optical properties through testing methods.

Structural, Stabilities, and Electronic Properties of Bimetallic Mg2-doped Silicon Clusters

The equilibrium geometries, relative stabilities, growth patterns, and electronic properties of magnesium-doped silicon clusters Mg2Sin (n = 1 - 11) have been systematically investigated at the B3LYP/6-311G (d) level. A large number of initial configurations are optimized and the lowestenergy stable geometries of Mg2Sin (n = 1 - 11) clusters with different spin multiplicities are determined. The results indicate that the most stable configurations for Mg2Sin clusters favor the threedimensional structures at n = 3 - 11. The analyses of the averaged binding energies, fragmentation energies, second-order energy difference, and HOMO-LUMO gaps suggest that the Mg2Si4 and Mg2Si6 clusters have the stronger relative stability, and magnesium atoms doping enhances the chemical activity of the silicon framework. The natural population and natural electronic configuration analyses show that the charge transfer occurs from the 3s orbital of the magnesium atoms to the silicon atoms and 3p orbital of the magnesium atoms

Probing the geometries, relative stabilities, and electronic properties of neutral and anionic Ag(n)S(m) (n + m ≤ 7) clusters.

The geometry structures, relative stabilities, and electronic properties of neutral and anionic Ag(n)S(m) (n + m ≤ 7) clusters have been investigated systematically by means of density function theory (DFT). The results of geometry optimization show that the most stable configurations of binary Ag(n)S(m)⁰/⁻ clusters have an early appearance of 3D structure at n = 3, m = 1, differing from those of pure silver and sulfur clusters. Moreover, the ground-state structures prefer low spin multiplicity (singlet or doublet) except for S₂, Ag₂S₃, Ag₂S₄, Ag₄S₃, and Ag₂S₅. The calculated electron detachment energies (both vertical and adiabatic) are in good agreement with experimental data. This further lends considerable credence for the lowest-energy structures and the chosen computational method. By calculating the binding energies, fragmentation energies, second-order difference of energies and HOMO-LUMO energy gaps of neutral and anionic Ag n S m clusters, the relative stability and electronic property as a function of cluster size are discussed in detail. Further, in order to understand the nature of the bond in doped clusters and pure clusters, we have performed the contour maps of their HOMOs and analyzed their composition.

Geometries, stabilities and electronic properties of beryllium-silicon Be₂Si(n) clusters.

The equilibrium geometries, growth patterns, stabilities, and electronic properties of bimetallic Be₂Si(n) (n = 1-11) clusters are systematically investigated at the B3LYP/6-311G(d) level of theory. Harmonic vibrational analysis has been performed to assure that the optimized geometries are stable. The optimized results suggest that the three-dimensional structures are observed for the most stable isomers of Be₂Si(n) clusters when n > 2. The calculated vertical ionization potential for the lowest-energy isomers are comparable to the experimental values of Si(n+2). According to the averaged binding energy, fragmentation energy, second-order energy difference and HOMO-LUMO gaps calculations, we identify that the Be₂Si₂ and Be₂Si₅ clusters are more stable, and Be atoms doping enhance the chemical reactivity of the Si n host. The natural population and natural electron configuration analyses indicate that the Be atoms possess positive charge at n = 1-5 but negative charge at n = 6-11. The chemical hardness of Be₂Si(n) clusters show three local maxima at n = 2, 5, and 9, whereas three local minima are found for the corresponding chemical potential, meaning these clusters are more stable than their neighboring cluster sizes.

Theoretical study of the structures, stabilities, and electronic properties of neutral and anionic Ca2Si n λ (n = 1–8, λ = 0, +1) clusters

The structures, stabilities and electronic properties of neutral and cationic, calcium-doped, small silicon clusters Ca2Si (n = 1–8, λ = 0, +1) have been systematically investigated by using the density functional theory method at the B3LYP/6-311G (d) level. The results show that the ground state optimal structures of the cationic and neutral clusters favour the three-dimensional structures for n = 3−8 respectively, and that the cationic Ca2Si + clusters have the lowest-energy structures similar to those of neutral Ca2Si n clusters with the exception of Ca2Si 6 + . The main configurations of the Ca2Si n isomers are not affected by removal of an electron, but the order of their stability is reversed. Based on the optimised geometries, the averaged binding energy (E b ), fragmentation energy (E f ), second-order energy difference (Δ 2 E), HOMO-LUMO energy gap (E gap ), adiabatic ionisation potential (AIP) and vertical ionisation potential (VIP) are analysed for the most stable structures. We found that Ca2Si5, Ca2Si7 and Ca2Si 7 + clusters have the strongest relative stability, and that the positive charged clusters are more stable than the corresponding neutral ones.

DFT and QTAIM studies on structure and stability of beryllium doped gold clusters

Impurity-doped clusters particularly the gold doped bimetallic clusters have received considerable attention in the last few years. The doped atoms can considerably alter the geometrical and electronic properties as well as the stability of gold clusters. Density functional theory (DFT) with B3LYP functional have been applied to study the geometrical structures and relative stabilities of small bimetallic neutral, cationic and anionic AunBe (n=1–6) and AunBe2 (n=1–5) clusters. For AunBe2 clusters, we obtained only planar structure whereas AunBe clusters show both planar and three dimensional structures. The relative stabilities of the clusters are compared on the basis of average binding energies, fragmentation energies and second order difference of energies. The fragmentation energies and second order difference of energies of all the three types of clusters shows the even–odd alternation phenomenon. The nature of bonding interaction is also investigated by using Bader’s quantum theory of atoms in molecules (QTAIM). Based on QTAIM results, we can suggest that the beryllium doped clusters are more stable than the pure gold clusters due to strong covalent interaction between the gold and beryllium metal centres.

Structural and electronic properties of the BnY (n=1-11) clusters

The geometric structures, electronic properties, average binding energies, second-order energy differences and energy gaps of BnY (n=1-11) clusters are systematically studied using the density functional theory (DFT) TPSSh method with 6-311+G(d) basis set for B atoms and Lanl2dz relativistic effective core potential basis set for Y atom. It is found that with the size increasing, the lowest energy structures of BnY (n=1-11) clusters gradually evolve from planar shape to cubic structure. With the atoms of B increasing, the average binding energies of the ground state of BnY (n=1-11) clusters increase. The second-order energy differences and the energy gaps of the ground states of BnY (n=1-11) clusters show that B3Y, B5Y and B7Y clusters possess relatively high stabilities. The polarization and the first static hyperpolarizability studied show that the plane structures of B5Y, B4Y, B3Y and B6Y clusters have larger nonlinear optical properties.

First-Principles Study of Geometries, Stabilities and Electronic Properties of Ca2Sin (n = 1–11) Clusters

The equilibrium geometries, relative stabilities, and electronic properties of Ca2Sin (n = 1–11) clusters have been systematically investigated by using the density function theory at the 6-311G (d) level. The optimized geometries indicate that the most stable isomers have three-dimensional structures for n = 3–11. The electronic properties of Ca2Sin (n = 1–11) clusters are obtained through the analysis of the natural charge population, natural electron configuration, vertical ionization potential, and vertical electron affinity. The results show that the charges in corresponding Ca2Sin clusters transfer from the Ca atoms to the Sin host. Based on the obtained lowest-energy geometries, the size dependence of cluster properties, such as averaged binding energies, fragmentation energies, second-order energy differences, HOMO-LUMO gaps and chemical hardness, are deeply discussed.

Structure and stability of Ti2Bn (n=1-10) clusters: an ab initio investigation

Structures and stabilities of Ti2Bn (n=1-10) clusters have been systematically investigated by using the density-functional theory B3LYP method and ab initio CCSD(T) method. It is found that the ground state structures of the Bn clusters are substantially modified by doping two Ti atoms. Ti2Bn clusters have very clear growth patterns, namely to form bipyramid. All the most stable Ti2Bn can be visualized as bipyramids with the two Ti atoms located at the two apexes. Ti2B6, Ti2B7 and Ti2B8 are confirmed to be the magic number clusters based on the analysis of the second-order difference of energies. The dissociation energies, vertical ionization potentials and vertical electron affinities of Ti2Bn isomers are discussed. Ti2B6 cluster is found to be stable both kinetically and thermodynamically.

Structural and magnetic properties of small NinMn clusters

The effects of alloying on the structural and magnetic properties of NinMn (n=1–12) clusters are investigated using all-electron density functional theory. The results reveal that the most stable structures of NinMn (n=1–12) clusters are all similar to those of corresponding Nin+1 clusters. Maximum peaks of second-order energy difference are found at n=3, 5, 8 and 10, indicating that these clusters possess relatively higher stability than their respective neighbors. An enhancement in the magnetic moment is obtained for small binary Ni–Mn clusters compared to that of pure Ni clusters of same size except for Ni10Mn. In addition, the magnetic properties of the doped Mn atom exhibit the magnetic moment surface enhancement effect.

Geometries, stabilities, electronic and magnetic properties of small PdnIr (n = 1–8) clusters from first-principles calculations

The geometrical structures, relative stabilities, electronic and magnetic properties of small PdnIr (n = 1–8) clusters have been systematically investigated using density functional theory at the B3PW91 level. The optimised geometries show that the lowest-energy structures of PdnIr clusters prefer a three-dimensional configuration. The relative stability of these clusters was examined by analysis of the binding energies per atom, fragmentation energies, the second-order difference of energies and the HOMO–LUMO energy gaps as a function of cluster size. The obtained results exhibit that the Pd2Ir, Pd3Ir and Pd5Ir clusters are more stable than their neighbouring clusters. The energy gap of the Pd2Ir cluster is the largest of all the clusters (2.258 eV). In addition, the charge transfers, vertical ionisation potentials, vertical electron affinities and chemical hardness were calculated and discussed. The magnetism calculations indicate that the total magnetic moment of PdnIr clusters is mainly localised on the iridium atom for Pd1–6Ir clusters. Meanwhile, the 5d orbital plays the key role in the magnetic moment of the iridium atom.

Structure, stability and electronic properties of SrSin (n = 1–12) clusters: Density-functional theory investigation

Geometric structures, stabilities, and electronic properties of SrSin (n = 1–12) clusters have been investigated using the density-functional theory within the generalized gradient approximation. The optimized geometries indicate that one Si atom capped on SrSin–1 structure and Sr atom capped Sin structure for difference SrSin clusters in size are two dominant growth patterns. The calculated average binding energy, fragmentation energy, second-order energy difference, the highest occupied molecular orbital, and the lowest unoccupied molecular orbital (HOMO—LUMO) gaps show that the doping of Sr atom can enhance the chemical activity of the silicon framework. The relative stability of SrSi9 is the strongest among the SrSin clusters. According to the mulliken population and natural population analysis, it is found that the charge in SrSin clusters transfer from Sr atom to the Sin host. In addition, the vertical ionization potential, vertical electron affinity, and chemical hardness are also discussed and compared.

Structures, stabilities, and electronic properties of F-doped Sin (n = 1 ∼ 12) clusters: Density functional theory investigation

The geometries, stabilities, and electronic properties of FSin (n = 1 ∼ 12) clusters are systematically investigated by using first-principles calculations based on the hybrid density-functional theory at the B3LYP/6-311G level. The geometries are found to undergo a structural change from two-dimensional to three-dimensional structure when the cluster size n equals 3. On the basis of the obtained lowest-energy geometries, the size dependencies of cluster properties, such as averaged binding energy, fragmentation energy, second-order energy difference, HOMO—LUMO (highest occupied molecular orbital—lowest unoccupied molecular orbital) gap and chemical hardness, are discussed. In addition, natural population analysis indicates that the F atom in the most stable FSin cluster is recorded as being negative and the charges always transfer from Si atoms to the F atom in the FSin clusters.

Density functional theory investigation on the structure and stability of Sc2Bn (n = 1–10) clusters

The geometries, stabilities, and electronic properties of Sc2Bn clusters, up to n=10, have been systematically investigated by using the density-functional B3LYP and CCSD(T) method. It was found that the ground state structures of the Bn clusters are substantially modified by the doping of Sc atoms. Sc2Bn clusters have very regular growth pattern, namely to form bipyramid. All the most stable Sc2Bn can be viewed as bipyramid (uncompleted when n⩽5) with two Sc atoms at the apexes. Sc2B7 and Sc2B8 are confirmed as the magic number clusters based on the analysis of the second-order difference of energies. The dissociation energies, vertical ionization potentials (VIP) and electron affinities (VEA) of Sc2Bn isomers are discussed. In most of the case, the Sc2Bn clusters have smaller HOMO–LUMO gap, VIP, VEA than the corresponding Bn clusters. There was no explicit correlation between the energetic stability and HOMO–LUMO gap, VIP or VEA.

Geometries, stabilities, and magnetic properties of AunTi (n = 1–9) clusters: A density functional study

The geometrical structures, relative stabilities, and magnetic properties of AunTi (n=1–9) clusters have been studied by using density functional method PW91. An extensive structural search shows that the Ti atom in low-energy AunTi isomers tends to occupy the most highly coordinated position. The ground state structures of AunTi clusters are different from that of Aun+1 clusters. The relative stabilities of ground state AunTi clusters are analyzed based on the averaged binding energies, second-order difference of energies, and HOMO–LUMO energy gaps. It is found that the substitution of a Ti atom for an Au atom in gold cluster enhances the stability of the host cluster. The AunTi clusters with even n exhibit higher stability over the clusters with odd n. The chemical activity of AunTi clusters is higher for odd n and lower for even n than that of the corresponding Aun+1 clusters. The Au4Ti cluster, which corresponds to a large energy gap, has a large VIP. The magnetism calculations indicate that the magnetic moment of the Ti atom in the ground-state AunTi (n=3–9) clusters is reduced to 0.75–1.15μB for odd n and is completely quenched for even n.

Probing the structural and electronic properties of bimetallic Group-III metal-doped gold clusters: AunM2 (M = Na, Mg, Al; n = 1–8)

Employing first-principles density functional theory at the PW91PW91 level, the equilibrium geometries, relative stabilities, and electronic properties of bimetallic Au n M2 (M = Na, Mg, Al; n = 1–8) clusters have been systematically investigated in comparison with pure gold clusters. The optimised results indicate that the doping atom Na trends to occupy a peripheral site in the host, while Mg and Al atoms favour the center site. Furthermore, Al-induced geometries become three-dimensional more easily. Much to our surprise, in the most stable isomers, doping with binary Group-III metal atoms markedly changes the geometries of the ground-state Aun+2 clusters, and higher average atomic binding energies are found in Al-doped clusters. The calculated fragmentation energies, second-order difference of energies, HOMO-LUMO energy gaps, and chemical hardness as a function of cluster size exhibit a pronounced odd-even alternating phenomenon, suggesting the clusters with closed electronic shells have higher relative stabilities. A natural population analysis has been performed to understand the effects of different doping atoms on electronic properties.

Geometry, stability, and isomerization of B n N2 (n = 1−6) isomers

We perform a systematic study on the geometry, stability, nature of bonding, and potential energy surface of low-lying isomers of planar and cyclic BnN2 (n = 1−6) at the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level. BnN2 (n = 2−4) clusters are structurally similar to pure boron clusters. The evolution of the binding energy per atom, incremental binding energy, and second-order difference of total energy with the size of BnN2 reveals that the lowest energy isomer of B3N2 has high stability. B5N2 and B6N2 possess π-aromaticity according to Hückel (4n + 2) rule. The aromaticity of some isomers of B4N2 and B6N2 is examined based on their valence molecular orbitals. At the CCSD(T)/6-311+G(d)//B3LYP/6-311+G(d) level, several B2N2, B3N2, B4N2, and B5N2 isomers are predicted to be stable both thermodynamically and kinetically, and detectable in future experiments. © 2013 Wiley Periodicals, Inc.