Theoretical Study of the Molecular Electrostatic Potential of C_(50)

1 INTRODUCTION All fullerenes made so far obey the isolated pentagon (IPR)[1], which governs the stability of fullerenes comprising hexagons and exact 12 pen- tagons. Smaller fullerenes, which violate the IPR, are predicted to have high instability and especially difficult isolation due to their condensed pentagons and increased strain. The production of smaller fullerene C36 has been reported[2]. However, the definite characterization of a C36-based solid is in doubt. Moreover, variou…     

Comparative investigation on non-IPR C68 and IPR C78 fullerenes encaging Sc3N molecules

A computational study on the experimentally detected Sc(3)N@C(68) cluster is reported, involving quantum chemical analysis at the B3LYP/6-31G level. Extensive computations were carried out on the pure C(68) cage which does not conform with the isolated pentagon rule (IPR). The two maximally stable C(68) isomers were selected as initial Sc(3)N@C(68) cage structures. Full geometry optimization leads to a confirmation of an earlier assessment of the Sc(3)N@C(68) equilibrium geometry (Nature 2000, 408, 427), namely an eclipsed arrangement of Sc(3)N in the C(68) 6140 frame, where each Sc atom interacts with one pentagon pair. From a variety of theoretical procedures, a D(3h) structure is proposed for the free Sc(3)N molecule. Encapsulated into the C(68) enclosure, this unit is strongly stabilized with respect to rotation within the cage. The complexation energy of Sc(3)N@C(68) cage is found to be in the order of that determined for Sc(3)N@C(80) and exceeding the complexation energy of Sc(3)N@C(78). The cage-core interaction is investigated in terms of electron transfer from the encapsulated trimetallic cluster to the fullerene as well as hybridization between these two subsystems. The stabilization mechanism of Sc(3)N@C(68) is seen to be analogous to that operative in Sc(3)N@C(78). For both cages, C(68) and C(78), inclusion of Sc(3)N induces aromaticity of the cluster as a whole.     

富勒烯C72分子静电势以及Sc2@C72的理论研究

已制备出来的富勒烯都遵循分离五元环规则(IPR)。C72虽然满足五元环分离规则具有D6d对称结构,然而迄今为止还没有实现其宏观量的合成,人们称之为“遗失的碳笼”。但人们合成出了内掺金属M@C72(M=Ca,La等),证实了C72的存在[1-4]。最近用两步高性能液体色谱方法又成功地分离出La2     

13C NMR pattern of Sc3N@C68. Structural assignment of the first fullerene with adjacent pentagons

Sc3N@C68 is assigned to isomer Sc3N@C68:6140 on the grounds of relative energies, geometrical data, and its 13C NMR pattern. Sc3N@C68:6140 is an endohedral fullerene where each Sc atom is coordinated to the center of an equatorial pentalene unit. Static and dynamic computer simulations explain the different point groups observed in NMR and X-ray experiments. Computed and experimental 13C NMR pattern are in close agreement except for one low-intensity signal. The competing isomer Sc3N@C68:6275 is found to be 409 kJ/mol less stable and shows a different 13C NMR pattern.     

富勒烯结构B_(80)分子静电势的理论研究

在混合密度泛函B3LYP理论下,用6-31G*基函数对富勒烯结构B80分子的3个异构体(1个具有Ih对称性,2个具有Th对称性)构型进行优化和分子静电势计算.结果表明:3个异构体球内全部为正电势,球外五元环中心所对应的区域都为负电势,B80Ih,Th(A)和Th(B)球外静电势的最大负值分别对应于20个六元环中心的B原子,五元环中心和12个六元环中心的B原子周围,它们组成了化学反应中最可能的活性点.     

Structure, stability, and cluster-cage interactions in nitride clusterfullerenes M3N@C2n (M = Sc, Y; 2n = 68-98): a density functional theory study

Extensive semiempirical calculations of the hexaanions of IPR (isolated pentagon rule) and non-IPR isomers of C(68)-C(88) and IPR isomers of C(90)-C(98) followed by DFT calculations of the lowest energy structures were performed to find the carbon cages that can provide the most stable isomers of M(3)N@C(2n) clusterfullerenes (M = Sc, Y) with Y as a model for rare earth ions. DFT calculations of isomers of M(3)N@C(2n) (M = Sc, Y; 2n = 68-98) based on the most stable C(2n)(6-) cages were also performed. The lowest energy isomers found by this methodology for Sc(3)N@C(68), Sc(3)N@C(78), Sc(3)N@C(80), Y(3)N@C(78), Y(3)N@C(80), Y(3)N@C(84), Y(3)N@C(86), and Y(3)N@C(88) are those that have been shown to exist by single-crystal X-ray studies as Sc(3)N@C(2n) (2n = 68, 78, 80), Dy(3)N@C(80), and Tb(3)N@C(2n) (2n = 80, 84, 86, 88) clusterfullerenes. Reassignment of the carbon cage of Sc(2)@C(76) to the non-IPR Cs: 17490 isomer is also proposed. The stability of nitride clusterfullerenes was found to correlate well with the stability of the empty 6-fold charged cages. However, the dimensions of the cage in terms of its ability to encapsulate M(3)N clusters were also found to be an important factor, especially for the medium size cages and the large Y(3)N cluster. In some cases the most stable structures are based on the different cage isomers for Sc(3)N and Y(3)N clusters. Up to the cage size of C(84), non-IPR isomers of C(2n)(6-) and M(3)N@C(2n) were found to compete with or to be even more stable than IPR isomers. However, the number of adjacent pentagon pairs in the most stable non-IPR isomers decreases as cage size increases: the most stable M(3)N@C(2n) isomers have three such pairs for 2n = 68-72, two pairs for n = 74-80, and only one pair for n = 82, 84. For C(86) and C(88) the lowest energy IPR isomers are much more stable than any non-IPR isomer. The trends in the stability of the fullerene isomers and the cluster-cage binding energies are discussed, and general rules for stability of clusterfullerenes are established. Finally, the high yield of M(3)N@C(80) (Ih) clusterfullerenes for any metal is explained by the exceptional stability of the C(80)(6-) (Ih: 31924) cage, rationalized by the optimum distribution of the pentagons leading to the minimization of the steric strain, and structural similarities of C(80) (Ih: 31924) with the lowest energy non-IPR isomers of C(760(6-), C(78)(6-), C(82)(6-), and C(84)(6-) pointed out.     

Structures, stabilities, electronic, and optical properties of C64 fullerene isomers, anions (C64(2-) and C64(4-)), metallofullerene Sc2@C64, and Sc2C2@C64

The 3465 classical isomers of C(64) fullerene have been investigated by quantum chemical methods PM3, and the most stable isomers have been refined with HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-311G(d)//B3LYP/6-31G(d) level. C(64)(D(2):0003) with the lowest e(55) (e(55) = 2), the number of pentagon-pentagon fusions, is predicted to be the most stable isomer and it is followed by the C(64)(C(s):0077) and C(64)(C(2):0103) isomers within relative energy of 20.0 kcal/mol. C(64)(D(2):0003) prevails in a wide temperature range according to energy analysis with entropy contribution at B3LYP/6-31G(d) level. The simulated IR spectra and electronic spectra help to identify different fullerene isomers. All the hexagons in the isomers with e(55) = 2 display local aromaticity. The relative stabilities of C(64) isomers change with charging in ionic states. Doping also affects the relative stabilities of fullerene isomers as demonstrated by Sc(2)@C(64)(D(2):0003) and Sc(2)@C(64)(C(s):0077). The bonding of Sc atoms with C(64) elongates the C-C bond of two adjacent pentagons and enhances the local aromaticity of the fullerene cages. Charging, doping, and derativization can be utilized to isolate C(64) isomers through differentiating the electronic and steric effects.     

DFT study on the stabilities of the heterofullerenes Sc3N@C67B, Sc3N@C67N, and Sc3N@C66BN

On the basis of calculations using density functional theory, we investigated the relative stabilities of all isomers of Sc3N@C67B and Sc3N@C67N as well as those of stable isomers of Sc3N@C66BN. As a result, we predict that Sc3N@C68 can be doped substitutionally with a boron atom much better than C60. This effect can be ascribed to the favorable electrostatic attraction between the encased Sc3N cluster and the polar C-B bonds of the fullerene cage, which show the important role played by the encapsulated atoms in stabilizing the fullerene. A difference in the interaction also determines the regiospecificity of Sc3N@C67B. On the contrary, N-doping of the fullerenes forming Sc3N@C67N is much less favorable than that in C60 or C70. A judicious choice of stable isomers of Sc3N@C66BN among a vast number of possible isomers indicates that Sc3N@C68 can also be doped with a pair of B and N atoms better than C60 under the simultaneous existence of B and N sources. Relative stabilities of various isomers of the BN-substituted fullerenes can be understood in terms of the combined electrostatic effects in the B- and N-substitutions of Sc3N@C68 complemented by a specific local preference in the N-substitution and the formation of a B-N bond.     

A facile route to the non-IPR fullerene Sc3N@C68: synthesis, spectroscopic characterization, and density functional theory computations (IPR=isolated pentagon rule)

Owing to the unique feature of the non-IPR D3 (isomer 6140) C68 cage (IPR=isolated pentagon rule), Sc3N@C68 has been attracting great interest in the fullerene community. Herein we report the first high-yield synthesis of Sc3N@C68 by the "reactive gas atmosphere" method and its facile isolation by single-step HPLC to a high purity (>or=99 %). Thus, Sc3N@C68 is isolated in sufficient quantities for its further spectroscopic characterization, while the high purity of the sample ensures the reliability of the spectroscopic data obtained. In particular, the electronic and vibrational structures of Sc3N@C68 were studied in detail experimentally and by theoretical computations. The assignment of the observed absorption bands to particular electronic transitions is given in detail on the basis of time-dependent DFT computations. Vibrational spectroscopy of Sc3N@C68 reveals good agreement between the measured spectra and the theoretically calculated spectra. A detailed assignment of the vibrational modes, including the Sc3N cluster modes, cage modes, and vibrations of the adjacent pentagons are discussed. This study reveals that the effect of Sc3N encapsulation in the cage is much more complicated than just a formal transfer of six electrons. Consequently the electronic and vibrational spectra of the carbon cage in Sc3N@C68 cannot be adequately understood on the basis of a C68 (6-) cage alone.     

Exohedral reactivity of trimetallic nitride template (TNT) endohedral metallofullerenes

[structures: see text] Fullerenes containing a trimetallic nitride template (TNT) within the cage are a particularly interesting class of endohedral metallofullerenes. Recently two exohedral derivatives of the Sc3N@C80 fullerene have been synthesized: a Diels-Alder and a fulleropyrrolidine cycloadduct. The successful isolation, purification, and structural elucidation of these metallofullerenes derivatives have encouraged us to understand how the chemical reactivity is affected by TNT encapsulation. First of all, we predicted the most reactive exohedral sites, taking into account the double bond character and the pyramidalization angle of the C-C bonds. For this purpose, a full characterization of all different types of C-C bonds of the following fullerenes was carried out: I(h)-C60:1, D3-C68:6140, D3-Sc3N@C68, D(5h)-C70:1, D(3h')-C78:5, D(3h)-Sc3N@C78, I(h)-C80:7 and several isomers of Sc3N@C80. Finally the exohedral reactivity of these TNT endohedral metallofullerenes, via [4 + 2] cycloaddition reactions of 1,3-butadiene, was corroborated by means of DFT calculations.     

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.     

Sc3N@C80: computations on the two-isomer equilibrium at high temperatures.

Reported herein are computations on the relative concentrations of the two experimentally known isomers of Sc3N@C80 , that is, those produced by encapsulation of Sc3N in two particular C80 cages that obey the isolated-pentagon rule, namely, with I(h) and D(5h) symmetries. The calculations are based on density functional methods and have been carried out using the Gibbs energy over a broad temperature interval. It has been computed that, if a relatively free motion of the encapsulate inside the cages is allowed, the observed populations of 10 and 17 % for the D(5h) Sc3N@C80 species are reached at temperatures of 2100 and 2450 K, respectively. The inclusion of the entropy term is essential as, if it is neglected, the D(5h) Sc3N@C80 population at a temperature of 2100 K would be a mere 1 %, owing to the relatively large interisomeric separation potential energy of 19 kcal mol(-1).     

C78 cage isomerism defined by trimetallic nitride cluster size: a computational and vibrational spectroscopic study

Molecular structures of Dy(3)N@C(78) and Tm(3)N@C(78) clusterfullerenes are addressed by the IR and Raman vibrational spectroscopic studies and density functional theory (DFT) computations. First, extensive semiempirical calculations of 2927 isomers of C(78) hexaanions followed by DFT optimization were applied to establish their relative stability. Then, DFT calculations of a series of M(3)N@C(78) (M = Sc, Y, Lu, La) isomers were performed which have shown that the stability order of the isomers depends on the cluster size. While the Sc(3)N cluster is planar in the earlier reported Sc(3)N@C(78) (D(3)h: 24,109) clusterfullerenes, relatively large Y(3)N and Lu(3)N clusters would be forced to be pyramidal inside this cage, which would result in their destabilization. Instead, these clusters remain planar in the nonisolated pentagon rule (non-IPR) C(2): 22,010 isomer making Y(3)N@C(78) and Lu(3)N@C(78) clusterfullerenes with this cage structure the most stable ones. Finally, on the basis of a detailed analysis of their IR and Raman spectra supplemented with DFT vibrational calculations, the recently isolated Tm(3)N@C(78) and the major isomer of Dy(3)N@C(78) are assigned to the non-IPR C(2): 22,010 cage structure. A detailed assignment of their experimental and computed IR and Raman spectra is provided to support this conclusion and to exclude other cage isomers.     

Synthesis, isolation, and addition patterns of trifluoromethylated D5h and I(h) isomers of Sc3N@C80: Sc3N@D5h-C80(CF3)18 and Sc3N@I(h)-C80(CF3)14

Sc(3)N@D(5h)-C(80) and Sc(3)N@I(h)-C(80) were trifluoromethylated with CF(3)I at 400 °C, affording mixtures of CF(3) derivatives. After separation with HPLC, the first multi-CF(3) derivative of Sc(3)N@D(5h)-C(80), Sc(3)N@D(5h)-C(80)(CF(3))(18), and three new isomers of Sc(3)N@I(h)-C(80)(CF(3))(14) were investigated by X-ray crystallography. The Sc(3)N@D(5h)-C(80)(CF(3))(18) molecule is characterized by a large number of double C-C bonds and benzenoid rings within the D(5h)-C(80) cage and a fully different position of the Sc(3)N unit compared to that in the pristine Sc(3)N@D(5h)-C(80). A detailed comparison of five Sc(3)N@I(h)-C(80)(CF(3))(14) isomers reveals a strong influence of the exohedral additions on the behavior of the Sc(3)N cluster inside the I(h)-C(80) cage.     

密度泛函理论和从头算方法对富勒烯分子静电势的比较研究

分别在Hartree-Fock和密度泛函B3LYP理论下,用6-31G*基组研究了C60和C70分子的静电势,比较了这方法计算得到上述分子静电势值的大小,静电势图形和静电势差值曲线,分析了富勒烯的电子相关效应.     

Sc2@C70 rather than Sc2C2@C68: density functional theory characterization of metallofullerene Sc2C70

Detailed study on Sc(2)C(70) series has been performed based on fully screening for C(70) tetra- and hexa- anions. With a combined methodology of quantum chemistry and statistical mechanics, our calculation results reveal that the Sc(2)C(70), which was proposed as the first metal-carbide endohedral metallofullerene with a non-isolated pentagon rule (non-IPR) cage (Sc(2)C(2)@C(68):6073_C(2v)), is in fact a C(70) non-IPR metallofullerene structure (Sc(2)@C(70):7854_C(2v)) with three pair of pentagon adjacency thanks to its significant thermodynamic and kinetic stability. According to the natural bond analysis and orbital interaction diagram, each scandium atom should only transfer two 4s electrons to the carbon cages and the valence state of Sc(2)@C(70) is (Sc(2+))(2)@C(70) (4-). In addition, the simulation of UV-Vis-NIR spectrum for Sc(2)@C(70):7854_C(2v) shows good accordance to the experimental spectrum.     

A theoretical study on fullerene-dizincocene hybrids

Using the density functional theory, we investigated the possible formation of fullerene-dizincocene hybrids, specifically C(60)*-Zn-Zn-Cp*, C(60)*-Zn-Zn-C(60)*, C(70)*-Zn-Zn-Cp*, and C(70)*-Zn-Zn-C(70)*, where C(60)*, Cp*, and C(70)* represent C(60)(CH(3))(5), C(5)(CH(3))(5), and C(70)(CH(3))(5) radicals. Our calculation shows that these hybrids have HOMO-LUMO gaps which are larger than has been experimentally identified for C(60)*-Fe-Cp. In addition, the strength of the Zn--Zn bonds is similar to that in Cp*-Zn-Zn-Cp* which was also synthesized recently. Furthermore, heterohybrids, C(60)*-Zn-Zn-Cp* and C(70)*-Zn-Zn-Cp* are expected to exist in equilibria with homohybrids, C(60)*-Zn-Zn-C(60)* and C(70)*-Zn-Zn-C(70)*, in which heterohybrids are much more favored. On the other hand, another hybrid involving Sc(3)N@C(68) as a fullerene unit is not highly probable.     

Charged states of Sc3N@C68: an in situ spectroelectrochemical study of the radical cation and radical anion of a non-IPR fullerene

The redox behavior of Sc 3N@C 68 is studied systematically by means of electrochemistry, in situ ESR/Vis-NIR spectroelectrochemistry, and detailed theoretical treatment. Formation of the negatively and positively charged paramagnetic species for the same trimetallic nitride endohedral fullerene is demonstrated for the first time. The electrochemical study of Sc 3N@C 68 exhibits two electrochemically irreversible but chemically reversible reduction steps and two reversible oxidation steps. A double-square reaction scheme is proposed to explain the observed redox reaction at cathodic potentials involving the reversible dimerisation of the Sc 3N@C 68 monoanion. The spin state of the radical cation and the radical anion is probed by ESR spectroscopy, indicating that in both states, the large part of the unpaired spin is delocalized on the fullerene cage. The charged states of the non-isolated pentagon rule fullerene are characterized furthermore by in situ absorption spectroscopy. The interpretation of experimental data is supported by the density functional theory (DFT) calculations of the spin distribution in the anion and cation radicals of Sc 3N@C 68 and time-dependent DFT calculations of the absorption spectra of the charged species.     

Size effect of fullerene cages and encaged clusters in M<Subscript>3</Subscript>N@C<Subscript>2<Emphasis Type="Italic">n</Emphasis></Subscript>

Based on the calculated findings that the sizes of encaged clusters determine the structures and the stability of C₈₀-based trimetallic nitride fullerenes (TNFs), more extensive density functional theory calculations were performed on M₃N@C₆₈, M₃N@C₇₈ and M₃N@C₈₀ (M=Sc, Y and La). The calculated results demonstrated that the structures and stability undergo a transition with the increasing of the sizes of the cages and clusters. Sc₃N is planar inside the three considered cages, Y₃N is slightly pyramidal inside C₆₈-6140 and C₇₈-5 and planar inside I_h C₈₀-7, however, La₃N is pyramidal inside all the three cages. Those cages with pyramidal clusters inside deformed considerably, compared with their parent cages. In these cases, the bonding of metallic atoms toward the cages does not play an important role, and the encaged cluster tends to be located inside the cages with the largest M-M and M-C distances so that the strain energy can be released mostly. These calculations revealed the size effect of fullerene cages and encaged clusters, and can explain the position priority of M3N inside fullerene cages and the differences in yield of M₃N@C_2n . Supported by the Southwest University, China (Grant No. SWNUB2005002)