Vibrational spectra of lanthanide endofullerenes with different symmetries of molecular structure

Quantum-chemical calculations of the geometric structure and vibrational spectra of lanthanide endofullerenes have been carried out. The vibrational frequencies of lanthanide atoms depend substantially on the symmetry of the molecular structure of the endofullerene and on the distance between the metal atom and the carbon cage. The infrared spectra of the endofullerenes M@C₆₀ contain vibrations that are forbidden by symmetry for the empty fullerene C₆₀. A change in the vibrational spectra due to the encapsulation of a metal atom in fullerenes with a C₆₀ cage is considerably more pronounced than that of the higher fullerenes. In the vibrational spectra, there are lines not characteristic of C₆₀, which indicates the presence of M@C₆₀ endofullerenes in a mixture with C₆₀ fullerenes.     

Structural and optical properties of the M@C59X cages (X=N,B and M=Li,Na)

Using B3LYP/6-31G* density functional level of theory, the structural and optical properties of the C₆₀ and M@C₅₉X cages have been investigated. Results indicate that the charge on C atoms and band gap of C₆₀ cage are changed dramatically with the substitution of one B or N atom at one of the C sites and the Li and Na atom encapsulations in the C₆₀ cage. The Mulliken analyses show that the charge is transferred completely between the alkali atoms and the C₅₉X cage. The substitutional and encapsulation doping (SED) reduce the optical gaps of the C₆₀ cage. Also, the oscillator strengths of the absorption peaks are dependent on dopant types.     

The compressive mechanical properties of Cn (n=20, 60, 80, 180) and endohedral M@C60 (M=Na,Al, Fe) fullerene molecules

The compressive mechanical properties of C_n (n = 20, 60, 80, 180) and endohedral M@C₆₀ (M = Na, Al, Fe) fullerene molecules are investigated using a quantum molecular dynamics (QMD) technique. Energy–strain curves, force–strain curves, endurance load, failure strain corresponding to the endurance load, and compressive stiffness of the fullerene molecules are obtained. The compressive mechanical properties of C₂₀, C₆₀, C₈₀, C₁₈₀ and M@C₆₀ (M = Na, Al, Fe) are discussed. The results show that the larger the magic number n of an empty fullerene, the higher its endurance load and compressive stiffness, but the lower its failure strain, and comparing to the empty C₆₀ fullerene, all the M@C60 molecules have greater endurance capability and failure strain.     

Novel metal-encapsulated caged clusters of silicon and germanium

We report the recent findings of metal (M) encapsulated clusters of silicon from computer experiments based on ab initio total energy calculations and a cage shrinkage and atom removal approach. Our results show that using a guest atom, it is possible to wrap silicon in fullerenelike (f) structures, as sp² bonding is not favorable to produce empty cages unlike for carbon. Transition M atoms have a strong bonding with the silicon cage that are responsible for the compact structures. The size and structure of the cage change from 14 to 20 Si atoms depending upon the size and valence of the M atom. Fewer Si atoms lead to relatively open structures. We find cubic, f, Frank-Kasper (FK) polyheral type, decahedral, icosahedral and hexagonal structures for M@Si_n with n = 12-16 and several different M atoms. The magic behavior of 15 and 16 atom Si cages is in agreement with experiments. The FK polyhedral cluster, M@Si₁₆ has an exceptionally large density functional gap of about 2.35 eV calculated within the generalized gradient approximation. It is likely to give rise to visible luminescence in these clusters. The cluster-cluster interaction is weak that makes such clusters attractive for cluster assembled materials. Further studies to stabilize Si₂₀ cage with M = Zr, Ba, Sr, and Pb show that in all cases there is a distortion of the f cage. Similar studies on M encapsulated germanium clusters show FK polyhedral and decahedral isomers to be more favorable. Also perfect icosahedral M@Ge₁₂ and M@Sn₁₂ clusters have been obtained with large gaps by doping with divalent M atoms. Recent results of the H interaction with these clusters, hydrogenated silicon fullerenes as well as assemblies of clusters such as nanowires and nanotubes are briefly presented.     

内掺过渡金属非典型富勒烯M@C22(M=Sc, Ti, V, Cr, Mn, Fe, Co, Ni) 几何结构、电子结构、稳定性和磁性的密度泛函研究

采用密度泛函理论中广义梯度近似对非典型富勒烯C₂₂和过渡金属内掺衍生物M@C₂₂(M=Sc,Ti,V,Cr,Mn,Fe,Co和Ni)的几何结构和电子结构进行计算研究.发现非典型富勒烯C₂₂的基态结构是含有一个四碳环的单重态笼状结构.过渡金属原子的掺入明显提高了体系的稳定性. C-M键既有一定共价性又有一定离子性.磁性、能级图、轨道分布和态密度图分析表明: M原子的3d轨道和碳笼的C原子的原子轨道之间存在较强的轨道杂化. Ti, Cr, Fe和Ni内掺的结构出现磁性完全猝灭现象. Sc和碳笼间是弱反铁磁作用, V,Mn和Co与碳笼间是弱铁磁作用.     

Computational studies on nonlinear optical property of novel Wittig-based Schiff-base ligands and copper(II) complex

Hundred and forty-five novel molecules of Wittig-based Schiff-base (WSB), including copper(II) complex and precursors, were computationally screened for nonlinear optical (NLO) properties. WSB ligands were derived from various categories of amines and aldehydes. Wittig-based precursor aldehydes, (E)-2-hydroxy-5-(4-nitrostyryl)benzaldehyde (f) and 2-hydroxy-5-((1Z,3E)-4-phenylbuta-1,3-dien-1-yl) benzaldehyde (g) were synthesised and spectroscopically confirmed. Schiff-base ligands and copper(II) complex were designed, optimised and their NLO property was studied using GAUSSIAN09 computer program. For both optimisation and hyperpolarisability (finite-field approach) calculations, Density Functional Theory (DFT)-based B3LYP method was applied with LANL2DZ basis set for metal ion and 6-31G* basis set for C, H, N, O and Cl atoms. This is the first report to present the structure–activity relationship between hyperpolarisability (β) and WSB ligands containing mono imine group. The study reveals that Schiff-base ligands of the category N-2, which are the ones derived from the precursor aldehyde, 2-hydroxy-5-(4nitro-styryl)benzaldehyde and pre-polarised WSB coordinated with Cu(II), encoded as Complex-1 (β = 14.671 × 10^?30 e.s.u) showed higher β values over other categories, N-1 and N-3, i.e. WSB derived from precursor aldehydes, 2-hydroxy-5-styrylbenzaldehyde and 2-hydroxy-5-((1Z,3E)-4-phenylbuta-1,3-dien-1-yl)benzaldehyde, respectively. For the first time here we report the geometrical isomeric effect on β value.     

Structural,magneto and optical properties of BX − 1NXC and BXNX − 1C cages (X = 12, 24 and 36)

The effect of carbon doping on the structural, optical and magneto properties of the B_XN_X cages has been studied using the B3LYP/6-31G^* level of density functional theory. With replacing one B or N atom with one C atom on the B_XN_X cages, the structural and symmetric properties, the optical absorption spectra and the band gaps of the B_XN_X cages change and the B_XN_X cages become magnetic. Our calculations conclude that the B_{X ? 1}N_XC and B_XN_{X ? 1}C cages can be interesting candidates for application in optoelectronics and spintronics.     

Formation of metallofullerenes by laser ablation of externally doped fullerenes C60Mx (M=Sm, Pt and Ni)

Photofragmentation of metal fullerides C₆₀M_x (M=Sm, Pt and Ni) has been studied by excimer laser ablation–TOF mass spectrometry. Metallofullerenes of the type C_nM (n<60) have been observed in both the positive and negative ionic modes, with C₅₉M being the most prominent species. It is supposed that the metal atom is incorporated into the network of the fullerene cage to replace one carbon atom of the cage, forming substitutional metallofullerene. The occurrence of the C₅₉M, C₅₈M, C₅₇M clusters in the mass spectra is confirmed by the coincidence of the intensity distribution of the mass peaks with the isotopic abundance pattern calculated from the natural abundance of isotopes of C and M. Odd-numbered high-carbon clusters are observed in our laser ablation study of all the metal fullerides in the negative ion channel. The evolution of the mass spectra of these samples with laser irradiation shots indicates that the transformation process from an externally doped fullerene to the substitutionally doped fullerene involves the loss of metal carbide, MC. The structures of metallofullerenes C_2n+1M and C_2nM with even and odd total numbers of atoms respectively are discussed. Formation mechanisms with the participation of odd-numbered all-carbon fullerene clusters as intermediates are supposed. Received: 18 June 2001 / Accepted: 28 September 2001 / Published online: 2 May 2002     

A spectroscopic study of M@C82 metallofullerenes: Raman, far-infrared, and neutron scattering results

82 metallofullerenes have been studied at room temperature by Raman (for M=La, Y, Ce, Gd), far-infrared (FIR) (for M=La, Y, Ce), and inelastic neutron scattering (INS) (for M=La, Y) spectroscopy. Raman and FIR spectra suggest that these metallofullerenes have a common dominant, if not a single, structure of the C₈₂ cage and a similar bonding of the encapsulated metal ion, i.e. the bonding is primarily electrostatic and the metal atoms are in the same oxidation state (+3). The metal ion vibrations are located around 160 and 50 cm^-1. INS reveals no gap between internal vibrational and external vibrational and rotational modes in the range ∼50–200 cm^-1 as is typically observed for other fullerides and also predicted by our model calculations. Presumably this is due to strong intermolecular interactions between M@C₈₂ units in the bulk sample. The studied metallofullerenes are air sensitive, and degradation in air could be followed by changes in the Raman spectra. Received: 24 August 1997/Accepted: 26 September 1997     

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000     

内掺过渡金属富勒烯衍生物Ni@C20H20几何结构、成键和电磁性质的密度泛函计算研究

采用密度泛函理论中的广义梯度近似对Ni@C₂₀H₂₀的几何结构、成键和电磁性质进行密度泛函计算研究.结构优化发现位于偏离笼子中心三种位置处的Ni原子优化之后均回到笼子中心.结合能和能隙分析表明C₂₀H₂₀的中心位置是Ni原子热力学和动力学最稳定的位置.成键分析表明：Ni原子位于C₂₀H₂₀中心时,和C原子之间几乎没有相互作用,保持自己的孤立状态.电磁分析表明：原子磁矩为2关键词： 20H₂₀')" href="#">C₂₀H₂₀ 20H₂₀')" href="#">Ni@C₂₀H₂₀ 几何结构 成键 电磁性质 密度泛函理论     

M@C28(M=Ti,Zr,Hf)内裹配合物的电子结构及其稳定性

用B3-LYP赝势模型的密度泛函理论,对M@C₂₈(M=Ti,Zr,Hf)内裹配合物电子结构进行从头计算研究.计算包括确定稳定的几何结构参量的分子几何结构进行优化和自然键轨道分析.结果发现Ti与C₂₈基团的相互作用明显不同于Zr(Hf)与C₂₈的相互作用,表现在原子的电子组态、成键特征和电子态分布等诸多方面.另外,结合能估算表明,这三种内裹配合物均能稳定存在,但Zr@C₂₈和Hf@C₂₈比Ti@C     

FeBN(N≤6)团簇的结构与磁性

利用密度泛函理论中的广义梯度近似(GGA)，在考虑自旋多重度后，预测了FeB_N(N≤6)团簇的基态结构.结果表明基态团簇的自旋多重度分别为4，3，2，1，2和1，其中FeB₄团簇比较稳定.同时对FeB_N(N≤6)基态团簇的磁性做了系统地研究，发现除了FeB₅团簇外，FeB_N(N≤6)团簇的总磁矩和Fe原子磁矩随团簇尺寸的增大而减小. 关键词： N团簇')" href="#">FeB_N团簇 自旋多重度 磁矩     

N=2 affine superalgebras and Hamiltonian reduction inN=2 superspace

We constructN=2 affine current algebras for the superalgebrassl(n/n-1)⁽¹⁾ in terms ofN=2 supercurrents subjected to nonlinear constraints and discuss the general procedure of the hamiltonian reduction inN=2 superspace at the classical level. We consider in detail the simplest case ofN=2sl(2/1)⁽¹⁾ and show howN=2 superconformal algebra inN=2 superspace follows via the hamiltonian reduction. Applying the hamiltonian reduction to the case ofN=2sl(3/2)⁽¹⁾, we find two new extendedN=2 superconformal algebras in a manifestly supersymmetricN=2 superfield form. Decoupling of four component currents of dimension 1/2 in them yields, respectively,u(2/1) andu(3) Knizhnik-Bershadsky superconformal algebras. We also discuss how theN=2 superfield formulations ofN=2W ₃ andN=2W ₃ ⁽²⁾ superconformal algebras come out in this framework, as well as some unusual extendedN=2 superconformal algebras containing constrainedN=2 stress tensor and/or spin 0 supercurrents.     

Probe the accumulation modes of the Au–C22H14 dimer on the structure and NLO properties

In 2006, the Au–C₂₂H₁₄ with a covalent bond between an individual pentacene (C₂₂H₁₄) and a gold (Au) atom was synthesised and characterised, and its nonlinear optical (NLO) properties were explored. To further investigate the NLO properties from molecules to materials, three kinds of different dimers (Au–C₂₂H₁₄)₂ (2, 3 and 4) were designed to probe the monomer accumulation modes on the structures and NLO properties. The results indicate that Au atoms doping breaks the conjugate structures of the two pentacenes to different extent. On the other hand, their NLO properties investigated by three density functional theory methods Becke-Half-and-Half-LYP (BHandHLYP), Coulomb-attenuating method Becke-3-Lee–Yang–Parr (CAM-B3LYP) and Minnesota 2005 double the amount of nonlocal exchange (M05-2X) show the same order, and 2 has the largest first hyperpolarisability (β_tot) than the other molecules. At the same time, natural bond orbital analysis shows the Au atoms play a crucial role in pushing electron density. Meanwhile, the frontier molecular orbital analysis shows that charge transfer has occurred between the two pentacene molecules and Au atoms. As a result, the order of transition energy is opposite to the order of β_tot values. Because the pentacene is taken as a simplified fragment of the graphene, our present work may be beneficial to the development of high-performance NLO materials.     

Dynamics of α-clusters in N = Z nuclei

The systematics for binding energies per α-particle in N = Z nuclei, E _Bα/N _α, are studied up to ¹⁶⁴Pb. It is shown that, although a geometrical model can be used to explain the systematics for light nuclei, the binding energy per α-particle exhibits structures which are due to the well-known shells of the mean field of nucleons in nuclei. The overall dependence of E _Bα/N _α on N _α in N = Z nuclei (for the ground-state masses) can be described in a liquid-drop model of α-particles. Conditions for a phase change with the formation of an α-particle condensate, a dilute Bose gas in excited compound nuclei are discussed for E _Bα/N _α = 0, at the thresholds. This is achieved when the binding energy per nucleon in nuclei is equal to or smaller than in the α-cluster. At somewhat smaller excitation energies the appearance of a Bose gas with a closed-shell core (N = Z, e.g. of ⁴⁰Ca) is proposed within the same concept. The experimental observation of the decay of such condensed α-particle states is proposed with the coherent emission of several correlated α-particles not described by the Hauser-Feshbach approach for compound-nucleus decay. This decay will be observed by the emission of unbound resonances in the form of ⁸Be and ¹²C ^* (0⁺ ₂) clusters.     

DFT studies on a high-energy density cage compound 1, 3, 5, 7, 9, 11-hexo(N(CH3)NO2)-2, 4, 6, 8, 10, 12-hexaazatetracyclo[5, 5, 0, 0, 0] dodecane

The infrared and Raman spectra, heat of formation (HOF) and thermodynamic properties were investigated by B3LYP/6-31G^** method for a new designed polynitro cage compound 1,3,5,7,9,11-hexo(N(CH₃)NO₂)-2,4,6,8,10,12-hexaazatetracyclo[5,5,0,0,0]dodecane. The detonation velocity (D) and pressure (P) were predicted by the Kamlet–Jacobs equations based on the theoretical density and condensed HOF. The bond dissociation energies and bond orders for the weakest bonds were analysed to investigate the thermal stability of the title compound. The computational result shows that the detonation velocity and pressure of the title compound are superior to those of hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), but inferior to those of 1,3,5,7-tetranitro-1,3,5,7-tetraazacyclooctane (HMX) and hexanitrohexaazaisowurtzitane (HNIW). And the analysis of thermal stability shows that the first step of pyrolysis is the rupture of the N₇–NO₂ bond. The crystal structure obtained by molecular mechanics belongs to the P2₁ space group, with the lattice parameters Z = 2, a = 11.8246 Å, b = 10.4632 Å, c = 15.9713 Å, ρ = 1.98 g cm^?3.     

Covariant first and second quantization of the N = 2, D = 10 Brink-Schwarz superparticle

Using a new type of harmonic superspace variables, we reduce the N = 2, D = 10 Brink-Schwarz (BS) superparticle to a system whose constraints are (i) first class, (ii) functionally independent and (iii) Lorentz covariant. We show that these features are essential for a correct covariant quantization. Q_BRST is first rank. By using it to second quantize the system, we obtain a covariant off-shell unconstrained superfield action of the linearized D = 10 type IIB supergravity. A corresponding procedure for the Green Schwarz (GS) superstring is conjectured.     

Prediction of the linear and nonlinear optical properties of tetrahydronaphthalone derivatives via long-range corrected hybrid functionals

The linear and nonlinear optical (NLO) properties of methoxybenzylidene (1) and thiophen-2-ylmethylidene (2) tetrahydronaphthalone derivatives are studied using long-range corrected density functional theory (LC-DFT). The calculated hyperpolarisabilities indicate that both compounds have measurable NLO properties (approximately one to two times the hyperpolarisability of p-nitroaniline). Charge-transfer indices and time-dependent DFT calculations suggest that the NLO properties are a result of a charge-transfer excitation, which is typical in conjugated donor–acceptor structures. The ultraviolet–visible spectra of 1 and 2 are also predicted using gap-fitting schemes, and these data are used to assess how accurately the hyperpolarisabilities of 1 and 2 could be estimated by the solvatochromic method.