Geometric and electronic structures of AlnCum (n = 5–9, m = 1–3) clusters: genetic algorithm combined with ab initio models

The geometries, stabilities and electronic structures of Al _n Cu _m (n?=?5–9, m?=?1–3) clusters were explored by using the genetic algorithm combined with ab initio methods. The geometric structures are almost spherical when the valence electrons are around the magic number 20, otherwise the structures are oblate or prolate. The stabilities of the clusters are related to both the Cu/Al ratios and the electronic configurations. The clusters with lower Cu/Al ratios have high stabilities. The molecular orbitals are in accord with the shell structures predicted by the jellium model. The 3d orbitals of the Cu atoms are localised, although their orbital energies are between the 1P and 1D jellium orbitals. The Al₆Cu₂ with 20 valence electrons forms closed 1S²1P⁶1D¹⁰2S² shells, and shows large binding energy and removal energy, large ionisation potential and small electron affinity. For the no-magic clusters, the structure deformation leads to crystal-field-like splitting of the degenerate shells and stabilises the clusters.     

Electronic structures of Al–Si clusters and the magic number structure Al8Si4

The low-energy structures of Al₈Si_m (m = 1–6) have been determined by using the genetic algorithm combined with density functional theory and the Second-order Moller-Plesset perturbation theory (MP2) models. The results show that the close-packed structures are preferable in energy for Al–Si clusters and in most cases there exist a few isomers with close energies. The valence molecular orbitals, the orbital level structures and the electron localisation function (ELF) consistently demonstrate that the electronic structures of Al–Si clusters can be described by the jellium model. Al₈Si₄ corresponds to a magic number structure with pronounced stability and large energy gap; the 40 valence electrons form closed 1S²1P⁶1D¹⁰2S²1F¹⁴2P⁶ shells. The ELF attractors also suggest weak covalent Si–Si, Si–Al and Al–Al bonding, and doping Si in aluminium clusters promotes the covalent interaction between Al atoms.     

The electronic structures of the core and valence ion states of metal oxides

SCF-Xα SW MO calculations on metal core ion hole states and X-ray emission (XES) and X-ray photoelectron (XPS) transition states of the non- transition metal oxidic clusters MgO₆^10?, AlO₄^5? and SiO₄^4? show relative valence orbital energies to be virtually unaffected by the creation of valence orbital or metal core orbital holes. Accordingly, valence orbital energies derived from XPS and XES are directly comparable and may be correlated to generate empirical MO diagrams. In addition, charge relaxation about the metal core hole is small and valence orbital compositions are little changed in the core hole state. On the other hand, for the transition metal oxidic clusters FeO₆^10?, CrO₆^9? and TiO₆^8? relative valence orbital energies are sharply changed by a metal core orbital or crystal field orbital hole, the energy lowering of an orbital increasing with its degree of metal character. Consequently O 2p nonbonding → M 3d-O 2p antibonding (crystal field) energies are reduced, while M 3d bonding → O 2p nonbonding and M 3d-O 2p antibonding → M 4s,p-O 2p antibonding (conduction band) energies increase. Charge relaxation about the core hole is virtually complete in the transition metal oxides and substantial changes are observed in the composition of those valence orbitals with appreciable M 3d character. This change in composition is greater for e _g than for t_2g orbitals and increases as the separation of the e_g crystal field (CF) orbitals and the O 2p nonbonding orbital set decreases. Based on the hole state MO diagrams the higher energy XPS satellite in TiO₂ (at about 13 eV) is assigned to a valence → conduction band transition. The UV PES satellites at 8.2 eV in Cr₂O₃ and 9.3 eV in FeO are tentatively assigned to similar transitions to conduction band orbitals, although the closeness in energy of the crystal field and O 2p nonbonding orbitals in the valence orbital hole state prevents a definite assignment on energy criteria alone. However the calculations do clearly show that charge transfer transitions of the e_g bonding → e_g crystal field orbital type would generally occur at lower energy than is consistent with observed satellite structure.A core electron hole has little effect upon relative orbital energies and is only slightly neutralized by valence electron redistribution for MgO and SiO₂. For the transition metal oxides a core hole lowers the relative energies of M3d containing orbitals by large amounts, reducing O → M charge transfer and increasing M 3d crystal field → conduction band energies. Large and sometimes overcomplete neutralization of the core hole is observed, increasing from CrO₆^9? to FeO₆^10? to TiO₆^8?. as the O → M charge transfer energy declines.High energy XPS satellites in TiO₂ may be assigned to O 2p nonbonding → conduction band transitions while lower energy UV PES satellites in FeO and Cr₂O₃ arise from crystal field or O 2p nonbonding → conduction band excitations. Our “shake-up” assignment for FeO₆^10?, CrO₆^9? and TiO₆^8? are less than definitive because no procedure has yet been developed to calculate “shake-up” intensities resulting from transitions of the type described. However the results do allow a critical evaluation of earlier qualitative predictions of core and valence hole effects. First, we find that the comparison of hole or valence state ionic systems with equilibrium distance systems of higher nuclear and/or cation charge (e.g. the comparison of the FeO₆^10? Fe 2p core hole state to Co₃O₄) is dangerous. For example, larger MO distances in the ion states substantially reduce crystal field splittings. Second, core and CF orbital holes sharply reduce O → M charge transfer energies, giving 2e_g → 3e_g energy separations which are generally too small to match observed satellite energies. Third, highest occupied CF-conduction band energies are only about 4–5 eV in the ground states, but increase to about 7–11 eV in the core and valence hole states of the transition metal oxides studied. The energetic arguments presented thus support the idea of CF and/or O 2p nonbonding → conduction band excitations as assignments for “shake-up” satellites, at least in oxides of metals near the beginning of the transition series.     

Odd-even effect of the number of free valence electrons on the electronic structure properties of gold-thiolate clusters

ABSTRACT

It is essential to understand the intrinsic stability of the gold-thiolate clusters, which present extensive potential applications in many fields such as the catalysis, biomedicines and molecular machines. The electronic structures and aromaticity indexes of a series of Au_m(SH)_n (m, n?=?5–12) were comprehensively investigated through energetic, vibrational, magnetic, and electronic density properties, which are highly sensitive to the size and topological structure of the cluster. Generally, computational results of energy gap between the frontier molecular orbitals, normalized atomization energy (NAE), and electron localization function (ELF)-σ values exhibit the odd-even effect, in which clusters with the even number of free valence electrons, being reflected by the value of (m–n), possess relatively higher stability than the odd one. However, it is difficult to describe the stability of cluster with the sophisticated three-dimensional structure through one single aromaticity index such as the nucleus-independent chemical shift (NICS) value. Principal component analysis and clustering analysis of the calculation results of Au_m(SR)_n clusters suggest that the value of (m–n) and the Au₄ unit are important for predicting the stability of the Au clusters.     

Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

A systematic investigation of the geometries,electronic and magnetic properties of AlnAsq (q = −1, 0, +1; n = 1–16) clusters: a DFT calculation

The geometries, electronic and magnetic properties of Al_nAs^q (q = ?1, 0, +1; n = 1–16) clusters have been investigated systematically by using an unbiased CALYPSO structure searching method and density functional theory. The lowest energy structures show that the As atom prefers to occupy the peripheral position of Al_n+1 clusters instead of the endohedral position. For cationic and neutral clusters, the structural transition from bilayer-like structure to cage-like structure is observed at cluster size n = 12, while it occurs at n = 13 for anionic clusters. The calculated detachment energies (DEs), ionisation potentials (IPs) and electronic affinities (EAs) are consistent with the available experimental and theoretical results for small clusters, indicating that the calculated lowest energy structures are reliable. Furthermore, the DE, EA and IP values for cluster size n ≥ 6 are successfully predicted. A stability analysis shows that Al₅As and Al₁₂As⁺ clusters have relatively large HOMO–LUMO energy gaps, corresponding to the magic numbers of 20 and 40 valence electrons, respectively.     

Ag4超原子在超原子分子中的SP3杂化特性

为了研究和原子类似的超原子也能用来组建分子和材料的这一特性,以正四面体的Ag₄团簇为例构建了一系列的超原子分子Ag₄X₄(X=H,Li,Na,K,Cu,Ag,Au以及F,Cl,Br)． 基于超级价键模型,可以将正四面体的Ag₄团簇视为4电子的超原子,通过比较Ag₄和C组成的代表分子Ag₄X₄(X=Au,Cl)和CX₄(X=H,Cl)的成键模式和分子轨道,可以发现Ag₄超原子与sp³杂化的C原子相似．能量计算显示超原子分子是稳定的,大能隙和高芳香性也进一步证实了它们的稳定性．     

C2和C2+,C2-的电子结构与势形共振

本文在独立电子近似的基础上,根据多重散射自洽场理论方法,计算了C₂和C₂⁺,C₂^-分子(离子)的电子结构,阐明了势形共振能量和上述分子(离子)电子数的关系,结果表明,随着电子数的减少,C原子2s-2p轨道杂化减弱,势形共振的能量将降低(如降低到阈值下,则势形共振消失)。 关键词：     

Density functional theory study of MgnNi2 (n=1-6) clusters

The geometries of Mg_nNi₂ (n=1-6) clusters are studied by using the hybrid density functional theory (B3LYP) with LANL2DZ basis sets. For the ground-state structures of Mg_nNi₂ clusters, the stabilities and the electronic properties are investigated. The results show that the groundstate structures and symmetries of Mg clusters change greatly due to the Ni atoms. The average binding energies have a growing tendency while the energy gaps have a declining tendency. In addition, the ionization energies exhibit an odd-even oscillation feature. We also conclude that n=3, 5 are the magic numbers of the Mg_nNi₂ clusters. The Mg₃ Ni₂ and Mg₅Ni₂ clusters are more stable than neighbouring clusters, and the Mg₄Ni₂ cluster exhibits a higher chemical activity.     

Structure and stability of neutral and cationic AlnO clusters

In this paper various structural possibilities for AlnO neutral and cationic isomers were investigated by using the B3LYP/6-311G（3df） method. Calculations of this paper predicted the existence of a number of previously unknown isomers. The stabilities of the AlnO （n = 2 - 7） clusters with even n are greater than those with odd n, however the stabilities Of cationic ions have the opposite odd-even alternation. The mass spectra observations of Al17O^＋ and Al19O^＋ ions support our theoretical predictions on their stabilities.     

Wn(n=3—27)原子团簇结构的第一性原理计算

使用密度泛函理论下的第一性原理方法,对W_n原子团簇(n=3—27)的结构特性进行了理论计算. 得到了W_n团簇(n=3—7)的最低能量结构和(n=8—27)的局域能量极小的典型结构. 使用凝胶模型,提出的电子组态1s²1p⁶1d¹⁰2s²1f¹⁴2p⁶3s ^{关键词： W团簇 结构性质 稳定性 从头计算}     

On the strength of electron correlations in high-T c superconducting copper oxides

We analyze the strength of electronic correlations in the half-filled antibonding Cu–O orbitals of high-T _c superconducting copper oxides by considering a Cu₁₂O ₁₇ ^n– cluster withn=8 or 10, respectively. The correlated ground state is calculated by the method of the local approach (LA) in a version which allows the treatment of stronger correlated electrons. As mean-field basis a semiempirical Hamiltonian of the ZDO (zero differential overlap) type has been adopted. It is found that the correlations are particularly strong in the Cu 3d _x ²–y² orbitals. The nonintegral orbital occupation allows for valence fluctuations between Cu⁺ and Cu²⁺ in spite of the remarkable correlations. According to the present model excess holes are located at the oxygen sites. The theoretical findings are compared with the results of spectroscopic investigations. The present electronic-structure analysis allows for a straighforward rationalization of previous experimental measurements. The strong connection between the importance of electronic correlations and the symmetry properties of the electronic wave function is emphasized.     

Effects of 5f-elements on electronic structures and spectroscopic properties of gold superatom model

5f-elements encaged in a gold superatomic cluster are capable of giving rise to unique optical properties due to their hyperactive valence electrons and great radial components of 5f/6d orbitals. Herein, we review our first-principles studies on electronic structures and spectroscopic properties of a series of actinide-embedded gold superatomic clusters with different dimensions. The three-dimensional(3D) and two-dimensional(2D) superatom clusters possess the 18-electron configuration of 1S21P61D10 and 10-electron configuration of 1S21P41D4, respectively. Importantly, their electronic absorption spectra can also be effectively explained by the superatom orbitals. Specifically, the charge transfer(CT) transitions involved in surface-enhance Raman spectroscopy(SERS) spectra for 3D and 2D structures are both from the filled 1D orbitals, providing the enhancement factors of the order of ～ 104 at 488 nm and ～ 105 at 456 nm, respectively. This work implies that the superatomic orbital transitions involved in 5f-elements can not only lead to a remarkable spectroscopic performance, but also a new direction for optical design in the future.     

Structural, electronic, and magnetic properties of boron cluster anions doped with aluminum: BnAl- (2≤n≤9)

The geometrical structures, relative stabilities, electronic and magnetic properties of small B n Al (2 ≤ n ≤ 9) clusters are systematically investigated by using the first-principles density functional theory. The results show that the Al atom prefers to reside either on the outer-side or above the surface, but not in the centre of the clusters in all of the most stable B n Al (2 ≤ n ≤ 9) isomers and the one excess electron is strong enough to modify the geometries of some specific sizes of the neutral clusters. All the results of the analysis for the fragmentation energies, the second-order difference of energies, and the highest occupied-lowest unoccupied molecular orbital energy gaps show that B 4 Al and B 8 Al clusters each have a higher relative stability. Especially, the B 8 Al cluster has the most enhanced chemical stability. Furthermore, both the local magnetic moments and the total magnetic moments display a pronounced odd-even oscillation with the number of boron atoms, and the magnetic effects arise mainly from the boron atoms except for the B 7 Al and B 9 Al clusters.     

Evolution of geometrical structures,stabilities and electronic properties of neutral and anionic Li n Cu λ (n = 1–9, λ = 0, −1) clusters: compare with pure lithium clusters

The structural evolution, stabilities, and electronic properties of copper-doped lithium Li _n Cu^λ (n?=?1–9, λ?=?0, ?1) clusters have been systematically investigated using a density functional method at PW91PW91 level. Extensive searches for ground-state structures were carried out, and the results showed the copper tends to occupy the most highly coordinated position and form the largest probable number of bonds with lithium atoms. By calculating the binding energies per atom, fragmentation energies and the HOMO-LOMO gaps, we found LiCu, Li₇Cu, LiCu^?, Li₂Cu^? and Li₈Cu^? clusters have the stronger relative stability and enhanced chemical stability. The content and pattern of frontier MOs for the most stable doped isomers were analysed to investigate the bond nature of interaction among Li and Cu atoms. The results show some σ-type and π-type bonds are formed among them, and with small admixture of the Cu d characters. To achieve a deep insight into the electron localization and reliable electronic structure information, the natural population analysis and electron localization function were performed and discussed.     

Density function study transition metal chromium-doped alkali clusters: the finding of magnetic superatom

The structures, stabilities and magnetic properties of CrX_n (X = Na, Rb and Cs; n up to 9) clusters are studied using density functional theory to search for the stable magnetic superatoms. The geometrical optimisations indicate the ground-state structures of CrX_n evolve toward a close packed structure with an interior Cr atom surrounded by X atoms as the cluster size increase. Their stabilities are analysed by the relative energy, gain in energy (ΔE(n)) and the highest unoccupied molecular orbital and lowest unoccupied molecular orbital gaps. Furthermore, the magnetic moments of CrX_n clusters show an odd–even oscillation. Here, we mainly focus on the CrX₇ (X = Na, Rb and Cs) clusters due to the same valence count as the known stable magnetic superatoms VNa₈, VCs₈ and TiNa₉. Although these clusters all have a filled electronic configuration 1S²1P⁶ and large magnetic moment 5 μ_B, our studies indicate that only CrNa₇ is highly stable compared to its nearest neighbours, while CrRb₇ and CrCs₇ clusters are less stable. This suggests that Cr-doped Na₇ is most appropriate for filled electronic configuration and CrNa₇ is shown to be a stable magnetic superatom. More interesting, we find CrRb₈ and CrCs₈ with the filled electronic configuration 1S²1P⁶ have higher stability and large magnetic moment 6 μ_B in their respective series.     

Statistical measures and magic numbers in metal clusters

In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher-Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher-Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters.     

Structural and magnetic properties of Ti12M clusters (M=Sc to Zn)

The geometries, electronic, and magnetic properties of the 3d atom doped icosahedron (ICO) Ti₁₂M (M=Sc to Zn), where a dopant atom replaces either the centra l(Ti₁₂M^c) or surface (Ti₁₂M^s) Ti atom in ICO Ti₁₃ cluster, have been systematically investigated by using the density functional theory. The structures of all the optimized Ti₁₂M^c and Ti₁₂M^s clusters are distorted ICO. Sc, Ni, Cu, and Zn atoms prefer to displace surface Ti atom, V, Cr, Mn, and Fe atoms prefer to displace central Ti atom. The position of impurity atom depends on the strength of the interaction between the central atom and the surface atoms. As compared to the pure Ti₁₃ cluster, Ti₁₂M^c and Ti₁₂M^s (M=V, Fe, Co, and Ni) clusters are more stable, Ti₁₂M^c and Ti₁₂M^s (M=Sc, Cr, Mn, Cu, and Zn) are less stable. Both Ti₁₂Ni^s and Ti₁₂Ni^c are magic clusters, which originate from their electronic as well as geometric closed shells. Because the exchange interaction prevails over the crystal field in Ti₁₂M clusters, the valence electrons fill molecular orbitals in terms of Hund’s rule of maximum spin.     

Ba0.5Sr0.5TiO3电子结构和光学性质的第一性原理研究

利用第一性原理研究了Ba_0.5Sr_0.5TiO₃的能带结构和光学性质.结果表明,导带和价带都来源于钛原子3d轨道和氧原子2p轨道的杂化.导带主要由钛原子的3d轨道贡献,价带主要由氧原子的2p轨道贡献.吸收系数为10⁵ cm^-1量级,且吸收主要集中在低能区.折射率为n（0）=2.1,结果与实验符合. 关键词： 第一性原理 能带结构 光学性质     

Geometries, stabilities, and electronic properties of Be-doped gold clusters: a density functional theory study

We have systematically investigated the geometrical structures, relative stabilities and electronic properties of small bimetallic AunBe (n = 1, 2, . . . , 8) clusters using a density functional method at BP86 level. The optimized geometries reveal that the impurity beryllium atom dramatically affects the structures of the Aun clusters. The averaged binding energies, fragmentation energies, second-order difference of energies, the highest occupied-lowest unoccupied molecular orbital energy gaps and chemical hardness are investigated. All of them exhibit a pronounced odd-even alternation, manifesting that the clusters with even number of gold atoms possess relatively higher stabilities. Especially, the linear Au2Be cluster is magic cluster with the most stable chemical stability. According to the natural population analysis, it is found that charge-transferring direction between Au atom and Be atom changes at the size of n = 4.