C24和B12N12团簇的结构与稳定性

本文采用量子化学密度泛函理论的B3LYP/6-31G*方法,对C24和B12N12团簇的12种异构体进行了优化,并对它们的几何构型、振动频率、核独立化学位移(NICS)和结合能进行了理论探讨, 比较了C24和B12N12团簇结构的稳定性。研究表明:C24团簇的最稳定几何构型为类石墨结构d,B12N12团簇的最稳定结构为4/6笼状结构g。C24异构体的稳定性大小顺序为d > b > f > c > a > e。B12N12团簇异构体稳定性大小顺序为a > f> c> d > e >b。     

Structural and electronic properties of Al12X+ (X=C, Si, Ge, Sn, and Pb) clusters

Using the first-principles method with the generalized gradient approximation, the authors have studied the structural and electronic properties of Al(12)X(+) (X=C, Si, Ge, Sn, and Pb) clusters in detail. The ground state of Al(12)C(+) is a low symmetry C(s) structure instead of an icosahedron. However, the Si, Ge, Sn, and Pb atom doped cationic clusters favor icosahedral structures. The ground states for Al(12)Si(+) and Al(12)Ge(+) are icosahedra, while the C(5nu) structures optimized from an icosahedron with a vertex capped by a tetravalent atom have the highest binding energy for Al(12)Sn(+) and Al(12)Pb(+) clusters. The I(h) structure and the C(5nu) structure are almost degenerate for Al(12)Ge(+), whose binding energy difference is only 0.03 eV. The electronic properties are altered much by removing an electron from the neutral cluster. The binding strength of a valence electron is enhanced, while the binding energy of the cluster is reduced much. Due to the open electronic shell, the band gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital are approximately 0.3 eV for the studied cationic clusters.     

Cluster-assembled materials based on M12N12 (M = Al, Ga) fullerene-like clusters

We report the results of density functional theory calculations on cluster-assembled materials based on M(12)N(12) (M = Al, Ga) fullerene-like clusters. Our results show that the M(12)N(12) fullerene-like structure with six isolated four-membered rings (4NRs) and eight six-membered rings (6NRs) has a T(h) symmetry and a large HOMO-LUMO gap, indicating that the M(12)N(12) cluster would be ideal building blocks for the synthesis of cluster-assembled materials. Via the coalescence of M(12)N(12) building blocks, we find that the M(12)N(12) clusters can bind into stable assemblies by either 6NR or 4NR face coalescence, which enables the construction of rhombohedral or cubic nanoporous framework of varying porosity. The rhombohedral-MN phase is energetically more favorable than the cubic-MN phase. The M(12)N(12) fullerene-like structures in both phases are maintained and the M-N bond lengths between M(12)N(12) monomers are slightly larger than that in isolated M(12)N(12) clusters and the bulk wurtzite phases. The band analysis of both phases reveals that they are all wide-gap semiconductors. Because of the nanoporous character of these phases, they could be used for gas storage, heterogeneous catalysis, filtration and so on.     

Experimental and theoretical characterization of MSi16(-), MGe16(-), MSn16(-), and MPb16(-) (M = Ti, Zr, and Hf): the role of cage aromaticity

Silicon (Si), germanium (Ge), tin (Sn), and lead (Pb) clusters mixed with a group-4 transition metal atom [M = titanium (Ti), zirconium (Zr), and hafnium (Hf)] were generated by a dual-laser vaporization method, and their properties were analyzed by means of time-of-flight mass spectroscopy and anion photoelectron spectroscopy together with theoretical calculations. In the mass spectra, mixed neutral clusters of MSi(16), MGe(16), and MSn(16) were produced specifically, but the yield of MPb(16) was low. The anion photoelectron spectra revealed that MSi(16), MGe(16), and MSn(16) neutrals have large highest occupied molecular orbital-lowest unoccupied molecular orbital gaps of 1.5-1.9 eV compared to those of MPb(16) (0.8-0.9 eV), implying that MSi(16), MGe(16), and MSn(16) are evidently electronically stable clusters. Cage aromaticity appears to be an important determinant of the electronic stability of these clusters: Calculations of nucleus-independent chemical shifts (NICSs) show that Si(16)(4-), Ge(16)(4-), and Sn(16)(4-) have aromatic characters with negative NICS values, while Pb(16)(4-) has an antiaromatic character with a positive NICS value.     

Au12M (M=Na,Mg, Al,Si, P,S, Cl)团簇的结构、稳定性和电子性质

采用基于密度泛函理论的第一性原理方法系统地研究了Au12M(M=Na,Mg,Al,Si,P,S,Cl)团簇的结构、稳定性和电子性质.对团簇的平均结合能、镶嵌能、垂直离化势、最高占据分子轨道(HOMO)和最低未占据分子轨道(LUMO)的能级差、电荷布居分析、自然键轨道(NBO)进行了计算和讨论.对于Au12M(M=Na,Mg,Al)团簇,它们形成了内含M原子的最稳定的笼状结构.然而对于Au12M(M=Si,P,S,Cl)团簇,它们却形成了以M元素为顶点的稳定锥形结构.在这些团簇中发现Au12S团簇相对是最稳定的,这是由于Au12S团簇形成了稳定的满壳层的电子结构.自然电荷布居分析表明:对于所有的Au12M(M=Na,Mg,Al,Si,P,S,Cl)团簇电荷总是从Au原子转向M原子.自然键轨道和HOMO分析表明Au12M团簇中发生了Au原子的s-d轨道和M原子的p轨道间的杂化现象.     

Structural and electronic properties of Si n, Si n+, and AlSi n-1 (n=2-13) clusters: theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n) (+), and AlSi(n-1) clusters (2< or =n< or =13) have been investigated using the ab initio molecular orbital theory under the density functional theory formalism. The hybrid exchange-correlation energy function (B3LYP) and a standard split-valence basis set with polarization functions [6-31G(d)] were employed for this purpose. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy (Delta (2)E) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si(n) clusters show similar structural growth. However, significant differences have been observed in the electronic structure leading to their different stability pattern. While for neutral clusters, the Si(10) is magic, the extra stability of the Si(11) (+) cluster over the Si(10) (+) and Si(12) (+) bears evidence for the magic behavior of the Si(11) (+) cluster, which is in excellent agreement with the recent experimental observations. Similarly for AlSi(n-1) clusters, which is isoelectronic with Si(n) (+) clusters show extra stability of the AlSi(10) cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. The ground state geometries of the AlSi(n-1) clusters show that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si(n) cluster. The fragmentation behavior of all these clusters show that while small clusters prefers to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size.     

Adsorption of molecular hydrogen and hydrogen sulfide on Au clusters

The authors present theoretical results describing the adsorption of H2 and H2S molecules on small neutral and cationic gold clusters (Au(n)((0/+1)), n=1-8) using density functional theory with the generalized gradient approximation. Lowest energy structures of the gold clusters along with their isomers are considered in the optimization process for molecular adsorption. The adsorption energies of H2S molecule on the cationic clusters are generally greater than those on the corresponding neutral clusters. These are also greater than the H2 adsorption energies on the corresponding cationic and neutral clusters. The adsorption energies for cationic clusters decrease with increasing cluster size. This fact is reflected in the elongations of the Au-S and Au-H bonds indicating weak adsorption as the cluster grows. In most cases, the geometry of the lowest energy gold cluster remains planar even after the adsorption. In addition, the adsorbed molecule gets adjusted such that its center of mass lies on the plane of the gold cluster. Study of the orbital charge density of the gold adsorbed H2S molecule reveals that conduction is possible through molecular orbitals other than the lowest unoccupied molecular orbital level. The dissociation of the cationic Au(n)SH2+ cluster into Au(n)S+ and H2 is preferred over the dissociation into Au(m)SH2+ and Au(n-m), where n=2-8 and m=1-(n-1). H2S adsorbed clusters with odd number of gold atoms are more stable than neighboring even n clusters.     

Relativistic computational investigation: the geometries and electronic properties of TaSi(n)+ (n = 1-13, 16) clusters

The equilibrium geometries, stabilities, and electronic properties of the TaSi(n)+ (n = 1-13, 16) clusters are investigated systematically by using the relativistic density functional method with generalized gradient approximation. The small-sized TaSi(n)+ clusters with slight geometrical adjustments basically keep the frameworks that are analogous to the neutrals while the medium-sized charged clusters significantly deform the neutral geometries, which are confirmed by the calculated AIP and VIP values. Furthermore, the optimized geometries of the charged clusters agree with the experimental results of Hiura and co-workers (Hiura, H.; Miyazaki, T.; Kanayama, T. Phys. Rev. Lett. 2001, 86, 1733). The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gaps of the charged clusters are generally increased as the cluster size goes from n = 1 to 13; and the large HOMO-LUMO gaps of charged clusters resulting from the positive charge indicate that their chemical stabilities are stronger than their neutral counterparts, especially for n = 4, 6, and 7 clusters. Additionally, the contributions of the d orbitals of the Ta atom to the HOMO and LUMO reveal that the chemical activity of the d orbitals of the Ta atom decreases gradually as the number of silicon atoms increases. This interesting finding is in good agreement with the recent experimental results on the reactive activities of the H2O and transition-metal silicon clusters (Koyasu, K.; Akutsu, M.; Mitsui, M.; Nakajima, A. J. Am. Chem. Soc. 2005, 127, 4998). Generally, the positive charge significantly influences the electronic and geometric structures of the charged clusters. Finally, the most stable neutral and charged TaSi16 clusters are found to be fullerene-like structures and the HOMO-LUMO gap in charged form is detectable experimentally.     

Si4X(X=C,N,O,Si,P,S)原子簇结构的理论研究

在密度泛函B3LYP/6-311G*水平上, 对具有C3v对称的Si4X (X = C, N, O, P, S)原子簇进行了几何构型优化计算, 并讨论它们的热力学稳定性、动力学活性、Mulliken布居、SiX键长、占据价轨道的对称性以及HOMO能级位置等周期递变规律。     

Geometries and electronic properties of the tungsten-doped germanium clusters: WGen (n = 1-17)

Geometries associated with relative stabilities, energy gaps, and polarities of W-doped germanium clusters have been investigated systematically by using density functional theory. The threshold size for the endohedral coordination and the critical size of W-encapsulated Gen structures emerge as, respectively, n = 8 and n = 12, while the fullerene-like W@Ge(n) clusters appears at n = 14. The evaluated relative stabilities in term of the calculated fragmentation energies reveal that the fullerene-like W@Ge(14) and W@Ge(16) structures as well as the hexagonal prism WGe(12) have enhanced stabilities over their neighboring clusters. Furthermore, the calculated polarities of the W@Ge(n) reveal that the bicapped tetragonal antiprism WGe(10) is a polar molecule while the hexagonal prism WGe(12) is a nonpolar molecule. Moreover, the recorded natural populations show that the charges transfer from the germanium framework to the W atom. Additionally, the WGe(12) cluster with large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap, large fragmentation energy, and large binding energy is supposed to be suitable as a building block of assembly cluster material. It should be pointed out that the remarkable features of W@Ge(n) clusters above are distinctly different from those of transition metal (TM) doped Ge(n) (TM = Cu and Ni) clusters, indicating that the growth pattern of the TMGe(n) depends on the kind of doped TM impurity.     

Ionization thresholds of small carbon clusters: tunable VUV experiments and theory

Small carbon clusters (Cn, n = 2-15) are produced in a molecular beam by pulsed laser vaporization and studied with vacuum ultraviolet (VUV) photoionization mass spectrometry. The required VUV radiation in the 8-12 eV range is provided by the Advanced Light Source (ALS) at the Lawrence Berkeley National Laboratory. Mass spectra at various ionization energies reveal the qualitative relative abundances of the neutral carbon clusters produced. By far the most abundant species is C3. Using the tunability of the ALS, ionization threshold spectra are recorded for the clusters up to 15 atoms in size. The ionization thresholds are compared to those measured previously with charge-transfer bracketing methods. To interpret the ionization thresholds for different cluster sizes, new ab initio calculations are carried out on the clusters for n = 4-10. Geometric structures are optimized at the CCSD(T) level with cc-pVTZ (or cc-pVDZ) basis sets, and focal point extrapolations are applied to both neutral and cation species to determine adiabatic and vertical ionization potentials. The comparison of computed and measured ionization potentials makes it possible to investigate the isomeric structures of the neutral clusters produced in this experiment. The measurements are inconclusive for the n = 4-6 species because of unquenched excited electronic states. However, the data provide evidence for the prominence of linear structures for the n = 7, 9, 11, 13 species and the presence of cyclic C10.     

Correlations between bonding, size, and second hyperpolarizability (gamma) of small semiconductor clusters: ab initio study on Al(n)P(n) clusters with n=2, 3, 4, 6, and 9

A comprehensive investigation of the correlation between the second hyperpolarizability and the bonding and structural characteristics of stoichiometric aluminum phosphide clusters up to 18 atoms is presented. Several aluminum phosphide species displaying different types of configurations and bonding have been studied. The obtained ab initio and density functional finite field results suggest that the ionic AlP clusters are considerably less hyperpolarizable than the covalent bonded species. Other structural features such as symmetry, atoms' arrangement, and shape also play an important role on the hyperpolarizabilities of those species. However, they are only noticeable among clusters characterized by the same bonding patterns. Furthermore, the results of this study demonstrate that the bonding which is determined by the atoms' arrangement of a cluster has a more profound effect on the second hyperpolarizability than the cluster's composition or size. In addition, the mean second hyperpolarizability increases with the increasing number of atoms, assuming that the bonding characteristics among the clusters of increasing size are similar. On the other hand, the hyperpolarizability per atom rapidly decreases with the increase of atoms' number in the cluster and converges to values of approximately 900e(4)a(0)(4) and approximately 1300e(4)a(0)(4)E(h) (-3) at the HF/cc-pVDZ and MP2/cc-pVDZ levels of theory respectively. Lastly, this work provides the first systematic study on the hyperpolarizabilities of small aluminum phosphide clusters which, in their covalent forms, exhibit larger second order hyperpolarizabilities than the well studied small gallium arsenide clusters.     

正、负和中性TiP10团簇结构与电子性质的密度泛函研究

采用密度泛函理论的B3LYP方法研究了正、负和中性TiP10团簇的几何构型和电子结构. 计算结果表明, 中性TiP10团簇的基态构型为金属夹心结构, 正、负离子团簇同样具有该基态稳定结构. 通过对基态稳定结构的分子轨道分析表明, δ键对形成夹心结构起到重要作用. 理论计算得到的中性TiP10团簇的垂直和绝热电离能分别为7.84和7.68 eV, 垂直和绝热电子亲和势分别为3.18和3.35 eV.     

Experimental and theoretical studies of the conformational structures of the mixed clusters of 1-cyanonaphthalene with water

A concerted experimental (mass-selective, double-resonance laser spectroscopic technique) and theoretical (correlated quantum chemistry calculation) study of hydrogen-bonded clusters of 1-cyanonaphthalene (CNN) with water has been carried out to probe geometrical structures of the conformational isomers. The structures of the two low-energy conformers of CNN-H2O and CNN-(H2O)2, calculated at the MP2/cc-pVDZ level of theory, are consistent with the mass-selective infrared-ultraviolet double-resonance spectra and the partially resolved rotational band contours of the S1 <-- S0 origin bands. The facile loss of a neutral water molecule from the cluster ion of CNN-(H2O)2, relative to that of CNN-H2O, is in accord with the proposed structures of the clusters.     

Oxidation pattern of small silicon oxide clusters: structures and stability of Si6On (n = 1-12)

We have performed systematic ab initio calculations to study the structures and stability of Si(6)O(n)() clusters (n = 1-12) in order to understand the oxidation process in silicon systems. Our calculation results show that oxidation pattern of the small silicon cluster, with continuous addition of O atoms, extends from one side to the entire Si cluster. Si atoms are found to be separated from the pure Si cluster one-by-one by insertion of oxygen into the Si-O bonds. From fragmentation energy analyses, it is found that the Si-rich clusters usually dissociate into a smaller pure Si clusters (Si(5), Si(4), Si(3), or Si(2)), plus oxide fragments such as SiO, Si(2)O(2), Si(3)O(3), Si(3)O(4), and Si(4)O(5). We have also studied the structures of the ionic Si(6)O(n)(+/-) (n = 1-12) clusters and found that most of ionic clusters have different lowest-energy structures in comparison with the neutral clusters. Our calculation results suggest that transformation Si(6)O(n)+(a) + O --> Si(6)O(n+1)+(a) should be easier.     

Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.     

Size and charge effects on the binding of CO to late transition metal clusters

We report on the size and charge dependence of the C-O stretching frequency, nu(CO), in complexes of CO with gas phase anionic, neutral, and cationic cobalt clusters (Co(n)CO(-0+)), anionic, neutral, and cationic rhodium clusters (Rh(n)CO(-0+)), and cationic nickel clusters (Ni(n)CO(+)) for n up to 37. We develop models, based on the established vibrational spectroscopy of organometallic carbonyl compounds, to understand how cluster size and charge relate to nu(CO) in these complexes. The dominating factor is the available electron density for backdonation from the metal to the CO pi* orbital. Electrostatic effects play a significant but minor role. For the charged clusters, the size trends are related to the dilution of the charge density at the binding site on the cluster as n increases. At large n, nu(CO) approaches asymptotes that are not the same as found for nu(CO) on the single crystal metal surfaces, reflecting differences between binding sites on medium sized clusters and the more highly coordinated metal surface sites.     

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

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

Electronic structure, vibrational stability, and predicted infrared-Raman spectra of the As20, As @ Ni12, and As @ Ni12 @ As20 clusters

Recently an inorganic fullerine-like [As@Ni(12)@As(20)](3-) onion with near-perfect icosahedral symmetry in the crystalline phase was reported [M. J. Moses, J. C. Fettinger, and B. W. Eichhorn, Science 300, 778 (2003)]. This paper presents a detailed computational study in the framework of density functional theory on various aspects of this molecule. The electronic structure of the As@Ni(12)@As(20) is investigated in its neutral as well as -3 charged state together with its subunits As(20) and As@Ni(12) by the all electron linear combination of Gaussian-type orbitals method. The bonding is studied by examining the integrated charge within atomic sphere, the electron localization function, changes in the electron density distribution, and from vibrational modes. We find that strong covalent As-As bonds seen in isolated As(20) become weaker in the As@Ni(12)@As(20) and strong covalent As-Ni bonds are formed. The structural stability of all four clusters is examined by analyzing the energetics and by calculating the vibrational frequencies. Further, the infrared and Raman spectra is predicted for both the neutral and charged As@Ni(12)@As(20) clusters. Finally, the energy barrier for removal of a single arsenic atom is calculated for the neutral As@Ni(12)@As(20) cluster.