Theoretical Studies on Structures,Stabilities, NMR Spectra and Designing Methods of Dihedral Fullerenes of C3 Series

Using bowl shaped carbon intermediates to construct dihedral fullerenes is an advisable method. Assu- ming that cap shaped C21 extends the size through building pentagons and hexagons at the U and V clefts of the brims, a series of homologous carbon intermediates was generated, in which most of the members have been unknown up to now. The joins between these homologous intermediates gave the C3 dihedral series under the restriction of C3 sym- metrical axis. The investigations point out that the stabilities of these fullerenes not only relate to the shapes of cages and the co-planarities of polygons, but also associate with the equalizations of bond lengths and the pentagonal dis- tributions. The stabilities reveal that the pentagonal distribution in cages is not negligible to the Jr delocalization, be- sides the co-planarities of hexagons and pentagons. Analyzing the possible Stone-Wales（SW） rearrangements in those fullerenes with dehydrogenated pyracyclene units（DPUs） can help us to find out the highly stable isomers. Based on the geometrical optimizations, the calculations provided the theoretical chemical shifts of unknown fullerenes and the data reconfirmed the existence of members C78 and C84. The symmetry adaptation analyses for the frontier orbitals support the formative mechanism of consecutive pentagonal and hexagonal fusions, but the simulated routes are more complicated than the pentagon road（PR） mechanism, which include not only C2 but also C3 additive reactions.     

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。     

On the structure and relative stability of C50 fullerenes

The complete set of 271 classical fullerene isomers of C50 has been studied by full geometry optimizations at the SAM1, PM3, AM1, and MNDO quantum-chemical levels, and their lower energy structures have also been partially computed at the ab initio levels of theory. A D(5h) species, with the least number of pentagon adjacency, is predicted by all semiempirical methods and the HF/4-31G calculations as the lowest energy structure, but the B3LYP/6-31G* geometry optimizations favor a D3 structure (with the largest HOMO-LUMO gap and the second least number of adjacent pentagons) energetically lower (-2 kcal/mol) than the D(5h) isomer. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the HF/4-31G level for the first time. The computed relative-stability interchanges show that the D3 isomer behaves more thermodynamically stable than the D(5h) species within a wide temperature interval related to fullerene formation. According to a newly reported experimental observation, the structural/energetic properties and relative stabilities of both critical isomers (D(5h) and D3) are analyzed along with the experimentally identified decachlorofullerene C50Cl10 of D(5h) symmetry. Some features of higher symmetry C50 nanotube-type isomers are also discussed.     

Trifluoromethyl derivatives of insoluble small-HOMO-LUMO-gap hollow higher fullerenes. NMR and DFT structure elucidation of C2-(C74-D3h)(CF3)12, Cs-(C76-Td(2))(CF3)12, C2-(C78-D3h(5))(CF3)12, Cs-(C80-C2v(5))(CF3)12, and C2-(C82-C2(5))(CF3)12

Reaction of a mixture of insoluble higher fullerenes with CF3I at 500 degrees C produced a single abundant isomer of C74(CF3)12, C76(CF3)12, and C80(CF3)12, two abundant isomers of C78(CF3)12 and C82(CF3)12, and an indeterminant number of isomers of C84(CF3)12. Using a combination of 19F NMR spectroscopy, DFT calculations, and the structures and spectra of previously reported fullerene(CF3)n compounds, the most-probable structures of six of the seven isolated compounds were determined to be specific isomers of C2-(C74-D3h)(CF3)12, Cs-(C76-Td(2))(CF3)12), C2-(C78-D3h(5))(CF3)12), Cs-(C80-C2v(5))(CF3)12), C2-(C82-C2(5))(CF3)12), and C2-(C82-C2(3))(CF3)12) containing ribbons and/or loops of edge-sharing para-C6(CF3)2 hexagons. The seventh isolated compound is a C1 isomer of C78(CF3)12 containing two such ribbons. This set of compounds represents only the second reported isolable compound with the hollow C74-D3h cage and the first experimental evidence for the existence of the hollow fullerenes C76-Td(2), C78-D3h(5), C80-C2v(5), and C82-C2(5) in arc-discharge soots.     

Role of four-membered rings in C32 fullerene stability and mechanisms of generalized Stone-Wales transformation: a density functional theory investigation

Density functional theory (DFT) methods have been applied to study C(32) fullerenes built from four-, five-, and six-membered rings. The relative energies of pure C(32) fullerenes have been evaluated to locate three most stable structures, 32:D(4d) with two squares, 1:D(3) without square and 5:C(s) with one square. Structural analysis reveals that there is a rearrangement pathway between the lowest energy classical isomer 1:D(3) and the lowest energy non-classical isomer 32:D(4d), and 5:C(s) behaves just as an intermediate between them. The kinetic processes of generalized Stone-Wales transformation (GSWT) with four-membered rings have been explored and two distinct reaction mechanisms are determined by all the transition states and intrinsic reaction coordinates with PBE1PBE/6-31G(d) approach for the first time. One mechanism is the concerted reaction with a rotating dimer closed to the cage surface and another is the stepwise reaction with a carbene-like sp(3) structure, whereas the latter is sorted into two paths based on four-membered ring vanishing before or after the formation of the carbene-like structure. It is indicated that there is no absolute preference for any mechanism, which depends on the adaptability of different reactants on the diverse mechanisms. Furthermore, it's found that the interconversion process with the participation of squares is more reactive than the rearrangement between C(60)_I(h) and C(60)_C(2v), implying some potential importance of non-classical small fullerenes in the fullerene isomerization.     

Insertion of C50 into single-walled carbon nanotubes: Selectivity in interwall spacing and C50 isomers

The structures and electronic properties of nanoscale "peapods," i.e., C(50) fullerenes inside single-walled carbon nanotubes (SWCNTs), were computationally investigated by density functional theory (DFT). Both zigzag and armchair SWCNTs with diameters larger than 1.17 nm can encapsulate C(50) fullerenes exothermically. Among the SWCNTs considered, (9,9) and (16,0) SWCNTs are the best sheaths for both D(3) and D(5h) isomers of C(50), corresponding to 0.32-0.34 nm tube-C50 distances. The orientation of C(50) inside nanotubes also affects the insertion energies, which depend on the actual tube-fullerene distances. The insertion of D(3) and D(5h) isomers of C(50) is somewhat selective; the less stable D(5h) isomer can be encapsulated more favorably inside SWCNTs at same tube-C(50) spacing. Because of the weak tube-C(50) interaction, the geometric and electronic structures of the peapods do not change greatly for the most stable configurations, but the selectivity in the interwall spacing and isomer encapsulation can be useful in separating various carbon fullerenes and their isomers.     

富勒烯C_(36)等电子体C_(34)BN异构体的结构及其相对稳定性理论研究

用半经验的AM1和MNDO方法优化了富勒烯C_(36)的等电子体C_(34)BN所有可能 异构体的构型,分析了各异构体相对稳定性与杂原子取代位置间的关系。另外,比 较了C_(36)碳笼上同位置地取代杂原子形成的C_34BN,C_(34)B_2和C_(34)N_2间的 电子结构,并分析了C_(34)BN最稳定异构体的振动模型。结果表明以C_(36):A (D_(6h))为母体形成的最稳定C_(34)BN异构体对应于碳笼赤道位置六元环中1,4- 取代产物,而以C_(36):B(D_(2d))为母体形成的最稳定C_(34)BN异构体对应于碳笼 近赤道位置的1,2-取代产物.C_(34)BN各异构体的稳定性可能主要由体系的共轭性 质决定。前线轨道能级表明B,N原子取代所得异构体的氧化-还原活性按以下顺序 递增：C_(34)B_2相似文献   

叠氮二氢硼多聚体结构和性质的理论研究(英文)

本文采用DFT-B3LYP方法,以不同基组对叠氮二氢硼多聚体(H2BN3)n (n=1-4)进行计算研究.二聚体(H2BN3)2(C2h对称性)中含B2N2平面四元环结构.船式(Cs对称性)和椅式(C3v对称性)三聚体(H2BN3)3的结合能相近(-122 和 -126 kJ·mol-1),其中均含B3N3六元环结构.拥有B4N4八元环结构的四个四聚体的结合能只有稍微差别.与单体相比,簇合物的结构参数变化较大.由ΔG0T可知,298.2 K下单体形成二聚体在热力学上是不利的,而形成三聚体和四聚体是有利的.     

二腈基衍生物的合成及其光限幅性质

设计并合成了一系列含不同末端给电子基团及共轭链长度的1,1-二腈基-2,2-二苯基乙烯类化合物(D1-D7),用核磁共振氢谱(1H NMR)、核磁共振碳谱(13C NMR)和高分辨质谱(HRMS)对分子结构进行了表征.选用N,N-二甲基甲酰胺(DMF)为溶剂,测定了它们的线性光物理性质,用光漂白法研究了它们的光稳定性,用热失重法测试了它们的热稳定性.研究了这7个化合物针对800 nm脉冲激光(掺钛蓝宝石激光器,脉冲宽度~130 fs,重复频率1000 Hz)的光限幅性质.结果表明:以二烷基氨基为给电子基团的4个化合物(D4-D7)对800 nm的飞秒脉冲激光均具有显著的光限幅性能,限幅机制为双光子吸收(2PA),而端基给电子能力较弱、共轭链长较短的D1-D3光限幅效果并不明显.此外,D4-D7都具有较好的热稳定性和光稳定性.而且,该系列化合物的双光子吸收截面、光稳定性和热稳定性都具有随分子结构中给电子基团增强或共轭链增长而增大或提高的趋势.D7具有最好的综合性能,是一个有应用潜力的光限幅材料.     

Theoretical investigation of C56 fullerene isomers and related compounds

All the 924 classical isomers of fullerene C(56) have been investigated by PM3, and some most stable isomers are refined with HCTH/3-21G and B3LYP6-31G(d) methods. D(2):003 with the least number of adjacent pentagons is predicted to be the most stable isomer at B3LYP/6-31G(d) level, while C(s):022 and C(2):049 possess nearly degenerate energies with relative energies of 0.03 and 3.90 kcal/mol, respectively. However, as to dianionic C(56)(2-) fullerene, C(2v):011 is predicted to be the most stable isomer. Investigations also show that the encapsulation of Ca atom in C(56) fullerene is exothermic and the metallofullerenes Ca@C(56) can be described as Ca(2+)@C(56)(2-). The computed relative stabilities show that the D(2):003 behaves more thermodynamically stable than other isomers in a wide temperature interval, and C(2v):011 should also be an important component. The electronic isomerization of C(56) (C(2v):011) and C(50) (D(5h):002) indicates that this phenomenon might be rather general in fullerenes and causes different properties, thus bringing about new possible applications of fullerenes. The static second-order hyperpolarizabilities of the three most stable isomers are slightly larger than that of C(60).     

Polyhedral structures with three-, four-, and five fold symmetry in metal-centered ten-vertex germanium clusters

Studies using density functional theory (DFT) at the hybrid B3LYP level indicate that the relative energies of structures with three-fold, four-fold, and five-fold symmetry for centered 10-vertex bare germanium clusters of the general type M@Ge(10) (z) depend on the central metal atom M and the skeletal electron count. For M@Ge(10) clusters with 20 skeletal electrons the DFT results agree with experimental data on the isoelectronic centered 10-vertex bare metal clusters. Thus the lowest energy structure for Ni@Ge(10), isoelectronic with the known Ni@In(10) (10-), is a C(3v) polyhedron derived from the tetracapped trigonal prism. However, Zn@Ge(10) (2+) is isoelectronic with the known cluster Zn@In(10) (8-), which has the lowest energy structure, a D(4d) bicapped square antiprism. For the clusters Ni@Ge(10) (2-), Cu@Ge(10) (-), and Zn@Ge(10) that have 22 skeletal electrons the lowest energy structures are the D(4d) bicapped square antiprism predicted by the Wade-Mingos rules. For the clusters Ni@Ge(10) (4-), Cu@Ge(10) (3-), and Zn@Ge(10) (2-) that have 24 skeletal electrons the lowest energy structures are C(3v) polyhedra with 10 triangular faces and 3 quadrilateral faces derived from a tetracapped trigonal prism by extreme lengthening of the edges of the capped triangular face of the underlying trigonal prism. For the clusters Cu@Ge(10) (5-) and Zn@Ge(10) (4-) that have 26 skeletal electrons the lowest energy structures are the D(5d) pentagonal antiprisms predicted by the Wade-Mingos rules and the C(3v) tetracapped trigonal prism as a somewhat higher energy structure. However, for the isoelectronic Ni@Ge(10) (6-) the relative energies of these two structure types are reversed so that the C(3v) tetracapped trigonal prism becomes the global minimum. The effects of electron count on the geometries of the D(5d) pentagonal prism and D(4d) bicapped square antiprism centered metal cluster structures are consistent with the bonding/antibonding characteristics of the corresponding HOMO and LUMO frontier molecular orbitals.     

Some aspects of the symmetry and topology of possible carbon allotrope structures

Elemental carbon has recently been shown to form molecular polyhedral allotropes known as fullerenes in addition to the familiar graphite and diamond known since antiquity. Such fullerenes contain polyhedral carbon cages in which all vertices have degree 3 and all faces are either pentagons or hexagons. All known fullerenes are found to satisfy the isolated pentagon rule (IPR) in which all pentagonal faces are completely surrounded by hexagons so that no two pentagonal faces share an edge. The smallest fullerene structures satisfying the IPR are the known truncated icosahedral C₆₀ of I _h symmetry and ellipsoidal C₇₀ of D _5h symmetry. The multiple IPR isomers of families of larger fullerenes such as C₇₆, C₇₈, C₈₂ and C₈₄ can be classified into families related by the so-called pyracylene transformation based on the motion of two carbon atoms in a pyracylene unit containing two linked pentagons separated by two hexagons. Larger fullerenes with 3ν vertices can be generated from smaller fullerenes with ν vertices through a so‐called leapfrog transformation consisting of omnicapping followed by dualization. The energy levels of the bonding molecular orbitals of fullerenes having icosahedral symmetry and 60n ² carbon atoms can be approximated by spherical harmonics. If fullerenes are regarded as constructed from carbon networks of positive curvature, the corresponding carbon allotropes constructed from carbon networks of negative curvature are the polymeric schwarzites. The negative curvature in schwarzites is introduced through heptagons or octagons of carbon atoms and the schwarzites are constructed by placing such carbon networks on minimal surfaces with negative Gaussian curvature, particularly the so-called P and D surfaces with local cubic symmetry. The smallest unit cell of a viable schwarzite structure having only hexagons and heptagons contains 168 carbon atoms and is constructed by applying a leapfrog transformation to a genus 3 figure containing 24 heptagons and 56 vertices described by the German mathematician Klein in the 19th century analogous to the construction of the C₆₀ fullerene truncated icosahedron by applying a leapfrog transformation to the regular dodecahedron. Although this C₁₆₈ schwarzite unit cell has local O _h point group symmetry based on the cubic lattice of the D or P surface, its larger permutational symmetry group is the PSL(2,7) group of order 168 analogous to the icosahedral pure rotation group, I, of order 60 of the C₆₀ fullerene considered as the isomorphous PSL(2,5) group. The schwarzites, which are still unknown experimentally, are predicted to be unusually low density forms of elemental carbon because of the pores generated by the infinite periodicity in three dimensions of the underlying minimal surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nickel dithiolenes revisited: structures and electron distribution from density functional theory for the three-member electron-transfer series [Ni(S2C2Me2)2]0,1-,2-

The complexes [Ni(S2C2Me2)2](z) (z = 0, 1-, 2-) have been isolated for the purpose of investigating their electronic structures in a reversible three-member electron-transfer series. Members are interrelated by reversible redox reactions with E(1/2)(0/1-) = -0.15 V and E(1/2)(1-/2-) = -1.05 V versus SCE in acetonitrile. The three complexes have nearly planar structures of idealized D(2)(h) symmetry. As the series is traversed in the reducing direction, Ni-S and C-S bond lengths increase; the chelate ring C-C bond length decreases from the neutral complex to the monoanion and does not change significantly in the dianion. Structural trends are compared with previous results for [Ni(S2C2R2)2)](1-,2-). Following the geometrical changes, values of nu(Ni)(-)(S) and nu(C)(-)(S) decrease, while the value of nu(C)(-)(C) increases with increased reduction. Geometry optimizations at the density functional theory (DFT) level were performed for all members of the series. Geometrical parameters obtained from the calculations are in good agreement with the experimental findings. The 5b(2g) orbital was identified as the LUMO in [Ni(S2C2Me2)2], the SOMO in [Ni(S2C2Me2)2](1-), and the HOMO in [Ni(S2C2Me2)2]2-. Unlike in the situation in the [M(CO)2-(S2C2Me2)2]z series (M = Mo, W; z = 0, 1-, 2-), the apparent contribution from the metal d orbital in the electroactive orbital is not constant. In the present series, the d(xz) contribution increases from 13 to 20 to 39% upon passing from the neutral to the monoanionic to the dianionic complex. Accurate calculation of EPR g-values of [Ni(S2C2Me2)2]1- by DFT serves as a test for the reliability of the electronic structure calculations.     

MP2 theory investigation on the halides of D6hC36:C36Xn (X=F,Cl,Br; n=2,4,6,12)

An investigation of C(36)X(n) (X=F,Cl,Br; n=2,4,6,12) formed from the initial C(36) fullerene with D(6h) symmetry has been performed using the MP2 theory. Their equilibrium structures, reaction energies, strain energies, lowest unoccupied molecular orbital-highest occupied molecular orbital (LUMO-HOMO) gap energies, and aromaticities have been studied. The calculation results showed that those addition reaction were highly exothermic and C(36)X(n) were more stable than C(36). Moreover, from the view of thermodynamics it should be possible to detect C(36)X(6). The LUMO-HOMO gap energies of C(36)X(n) were higher than D(6h)C(36) and the redox characteristics of C(36)X(n) were weaker comparing to D(6h)C(36). The analyses of pi-orbital axis vector indicated that the chemical reactivity of C(36) was the result of the high strain, and the nucleus independent chemical shifts research showed that the stabilities of the C(36)X(6) were correlative with the conjugation effect.     

Theoretical study on the small clusters of LiH, NaH, BeH(2), and MgH(2)

High-level ab initio molecular orbital theory is used to calculate the geometries, vibrational frequencies, atomic charges, and binding energies of the small clusters (LiH)(n), (NaH)(n), (BeH(2))(n), and (MgH(2))(n) (n = 1-4). For (LiH)(n) and (NaH)(n), there are planar cyclic structures when n = 2, 3. We have found the cubic structure T(d) in addition to the planar cyclic D(4)(h) when n = 4. The D(4)(h) is less stable than the T(d) geometry. For (BeH(2))(n) and (MgH(2))(n), when n = 3, there are three kinds of structures: chain C(2)(v), planar cyclic D(3)(h), and hat-like C(2)(v). The C(2)(v) geometry is more stable than the others. When n = 4, there are four kinds of structures: chain D(2)(h), cubic T(d), string-like C(2), and cubic transformation C(1). The most stable compounds in the families of (LiH)(n), (NaH)(n), (BeH(2))(n), and (MgH(2))(n) are cubic T(d), cubic T(d), chain D(2)(h), and string-like C(2) geometries, respectively, when n = 4. Calculated binding energies range from -24 to -37 kcal/mol for (LiH)(n) and --19 to -30 kcal/mol for (NaH)(n), (BeH(2))(n), and (MgH(2))(n). The hydrogen atoms in hydride clusters always have negative charges. The atomic charges of planar cyclic structures are weaker than those of cubic structures, and there is a tendency of reducing along with the increase of the cluster size. The vibrational frequencies of planar cyclic structures have consistent tendency, too. It indicates that the bond distance increases with the ionic character of the bond.     

The exohedral Diels-Alder reactivity of the titanium carbide endohedral metallofullerene Ti2C2@D(3h)-C78: comparison with D(3h)-C78 and M3N@D(3h)-C78 (M=Sc and Y) reactivity

The chemical functionalization of endohedral (metallo)fullerenes has become a main focus of research in the last few years. It has been found that the reactivity of endohedral (metallo)fullerenes may be quite different from that of the empty fullerenes. Encapsulated species have an enormous influence on the thermodynamics, kinetics, and regiochemistry of the exohedral addition reactions undergone by these species. A detailed understanding of the changes in chemical reactivity due to incarceration of atoms or clusters of atoms is essential to assist the synthesis of new functionalized endohedral fullerenes with specific properties. Herein, we report the study of the Diels-Alder cycloaddition between 1,3-butadiene and all nonequivalent bonds of the Ti(2)C(2)@D(3h)-C(78) metallic carbide endohedral metallofullerene (EMF) at the BP86/TZP//BP86/DZP level of theory. The results obtained are compared with those found by some of us at the same level of theory for the D(3h)-C(78) free cage and the M(3)N@D(3h)-C(78) (M=Sc and Y) metallic nitride EMFs. It is found that the free cage is more reactive than the Ti(2)C(2)@D(3h)-C(78) EMF and this, in turn, has a higher reactivity than M(3)N@D(3h)-C(78). The results indicate that, for Ti(2)C(2)@D(3h)-C(78), the corannulene-type [5,6] bonds c and f, and the type B [6,6] bond 3 are those thermodynamically and kinetically preferred. In contrast, the D(3h)-C(78) free cage has a preference for addition to the [6,6] 1 and 6 bonds and the [5,6] b bond, whereas M(3)N@D(3h)-C(78) favors additions to the [6,6] 6 (M=Sc) and [5,6] d (M=Y) bonds. The reasons for the regioselectivity found in Ti(2)C(2)@D(3h)-C(78) are discussed.     

Determining relative f and d orbital contributions to M-Cl covalency in MCl6(2-) (M = Ti, Zr, Hf, U) and UOCl5(-) using Cl K-edge X-ray absorption spectroscopy and time-dependent density functional theory

Chlorine K-edge X-ray absorption spectroscopy (XAS) and ground-state and time-dependent hybrid density functional theory (DFT) were used to probe the electronic structures of O(h)-MCl(6)(2-) (M = Ti, Zr, Hf, U) and C(4v)-UOCl(5)(-), and to determine the relative contributions of valence 3d, 4d, 5d, 6d, and 5f orbitals in M-Cl bonding. Spectral interpretations were guided by time-dependent DFT calculated transition energies and oscillator strengths, which agree well with the experimental XAS spectra. The data provide new spectroscopic evidence for the involvement of both 5f and 6d orbitals in actinide-ligand bonding in UCl(6)(2-). For the MCl(6)(2-), where transitions into d orbitals of t(2g) symmetry are spectroscopically resolved for all four complexes, the experimentally determined Cl 3p character per M-Cl bond increases from 8.3(4)% (TiCl(6)(2-)) to 10.3(5)% (ZrCl(6)(2-)), 12(1)% (HfCl(6)(2-)), and 18(1)% (UCl(6)(2-)). Chlorine K-edge XAS spectra of UOCl(5)(-) provide additional insights into the transition assignments by lowering the symmetry to C(4v), where five pre-edge transitions into both 5f and 6d orbitals are observed. For UCl(6)(2-), the XAS data suggest that orbital mixing associated with the U 5f orbitals is considerably lower than that of the U 6d orbitals. For both UCl(6)(2-) and UOCl(5)(-), the ground-state DFT calculations predict a larger 5f contribution to bonding than is determined experimentally. These findings are discussed in the context of conventional theories of covalent bonding for d- and f-block metal complexes.     

Structural and electronic trends among group 15 polyhedral fullerenes

We have investigated the structural and electronic characteristics of tetrahedral, octahedral, and icosahedral fullerenes composed of group 15 elements phosphorus, arsenic, antimony, and bismuth. Systematic quantum chemical studies at the DFT and MP2 levels of theory were performed to obtain periodic trends for the structural principles, stabilities, and electronic properties of the elemental nanostructures. Calibration calculations for polyhedral clusters with up to 20 atoms showed the applied theoretical approaches to be in good agreement with high-level CCSD(T)/cc-pVTZ results. By studying fullerenes up to P₈₈₈, As₅₄₀, Sb₆₂₀, and Bi₆₂₀, we found their structures and stabilities to converge smoothly toward their experimental bulk counterparts. The diameters of the largest studied cages were 4.8, 3.7, 4.8, and 5.1?nm for the P, As, Sb, and Bi fullerenes, respectively. Comparisons with the experimentally known allotropes of the studied elements suggest the predicted polyhedral cages to be thermodynamically stable. All studied group 15 polyhedral fullerenes were found to be semiconducting, and density of states analysis illustrated clear periodic trends in their electronic structure. Relativistic effects become increasingly important when moving from P to Bi and taking the spin?Corbit effects into account by using a two-component procedure had a significant positive effect on the relative stability of bismuth clusters.     

铝原子团簇Al5、Al5-和Al5+稳定结构的密度泛函理论研究

采用密度泛函理论的四种方法:杂化密度泛函B3LYP与B3PW91、Perdew-Wang91交换与相关泛函WP91PW91、局域自旋密度近似SVWN,研究了A15、Al5-和Al5+团簇的多种可能结构,找到了它们稳定的结构与自旋态,与已有的理论结果作了比较,并计算了Al5-的绝热与垂直电子离解能、Al5的绝热与垂直电离势,同有关的实验数据比较,符合较好.同时对四种密度泛函方法的计算结果作了一些比较与讨论.     

Strain energies due to nonplanar distortion of fullerenes and their dependence on structural motifs

Accurate strain energies due to nonplanar distortion of 114 isolated pentagon rule (IPR) fullerenes with 60-102 carbon atoms have been calculated based on B3LYP/6-31G(d) optimized structures. The calculated values of strain energy due to nonplanar distortion (Enp) are reproduced by three simple schemes based upon counts of 8, 16, and 30 distinct structural motifs composed of hexagons and pentagons. Using C180 (Ih) and CN (Ih) (N is very large) as test molecules, the intrinsic limitations of the motif model based on six-membered rings (6-MRs) as the central unit have been discussed. On the basis of the relationship between the contributions of motifs to Enp and the number of five-membered rings (5-MRs) in motifs, we found that IPR fullerenes with dispersed 5-MRs present smaller nonplanar distortions.