Comparison studies of fullerenes C72, C74, C76 and C78 by tight-binding Monte Carlo and quantum chemical methods

From C₇₂ to C₇₈, the top 20 low-energy isomers screened out from all isomers of each fullerene are optimized and computed by tight-binding Monte Carlo (TBMC), semi-empirical PM3, and ab initio B3LYP/6-31G*//HF/3-21G methods. The comparison results show that the TBMC method can efficiently optimize the structures and correctly predicate the low energy isomers. The relative energies computed by TBMC are in good agreement with the high-lever B3LYP calculation results. Our TBMC and B3LYP results show that the most energetically favorable structure of C₇₂ is not an isomer satisfying the isolated pentagon rule (IPR), which is different with the result by PM3. The symmetry of the most stable IPR isomer tends to low as the fullerene becomes large and several non-isolated-pentagon structures are found to have low symmetries and low energies close to the most stable isomer.     

An efficient approach for theoretical study on the low-energy isomers of large fullerenes C90-C140

An approach that consists of a molecular mechanics method based on the second generation reactive empirical bond order (REBO) potential and the more accurate semiempirical method PM3 (Parametric Method No. 3) was proposed to predict the energetically favored isomers of the fullerenes from C90 to C140 at the semiempirical level. All the 578,701 isolated-pentagon-rule isomers of fullerenes from C90 to C140 were enumerated from topological structures and systematically searched using an energy minimization method to select the best 100 low-energy isomers based on the REBO potential for each fullerene. Then these candidate isomers were further optimized by PM3 and ranked again to determine the top low-energy isomers. This approach was applied to calculate the energetically favored isomers of C90-C140. The results of C90-C120 are in good agreement with the published results by quantum-chemical methods. Furthermore, the top five low-energy isomers of C90-C120, as well as C122-C140 which have scarcely been systematically studied before, are also predicted with the approach. The analysis of the structures showed that the hexagon-neighbor rule is an important factor to the stability of C90-C140. The time cost for the systematical search based on the REBO potential was also discussed. It indicates that the approach proposed is efficient for predicting the energetically favored isomers of large fullerenes at the semiempirical level.     

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.     

Structures, stabilities, and electronic and optical properties of C62 fullerene isomers

The 2385 classical isomers and four nonclassical isomers of fullerene C62 have been studied by PM3, HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-31G(d)//B3LYP/6-31G(d). The Cs:7mbr isomer, with a chain of four adjacent pentagons surrounding a heptagon, is predicted to be the most stable isomer, followed by C2v:4mbr which is 3.15 kcal/mol higher in energy. C2:0032 with three pairs of adjacent pentagons is the most stable isomer in the classical framework. To clarify the relative stabilities of C62 isomers at high temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. Analyses reveal that Cs:7mbr prevails in a wide temperature range. The vibrational frequencies of the five most stable C62 fullerene isomers are also predicted at the B3LYP/6-31G(d) level, and the simulated IR spectra show important differences in positions and intensities of the vibrational modes for different isomers. The nucleus-independent chemical shift and the density of states of the three most stable isomers show that the square in C2v:4mbr and the adjacent pentagons in Cs:7mbr and C2:0032 possess high chemical reactivity. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and the sum-over-states mode. The intensity-dependent refractive index gamma(-omega; omega, omega, -omega) at omega = 2.3305 eV of Cs:7mbr is very large because of resonance with the external field. The second-order hyperpolarizabilities of the five most stable isomers of C62 are predicted to be larger than those of C60.     

Structures, stabilities, and electronic and optical properties of C52 fullerene, ions, and metallofullerenes

The 437 classical isomers of fullerene C52 have been studied by PM3, HCTH/3-21G, and B3LYP6-31G(d). C(2):029 with the least number of adjacent pentagons is predicted to be the most stable isomer. The investigations show that both the number of adjacent pentagons and the degree of aromaticity play important roles in the relative stabilities of fullerene isomers. To clarify the relative stabilities of the C52 isomers in a wide range of temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP6-31G(d) level. C(2):029 prevails in a wide temperature range. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and sum-over-states model. The static second-order hyperpolarizability of C(2):029 is 51% larger than that of C60. Furthermore, intensity-dependent refractive index gamma (-omega;omega,omega,-omega) (omega=1.1653 eV) of C(2):029 is 13 times larger than that of C60. The encapsulation of Ca atom in C52 fullerene is exothermic and the metallofullerene Ca-C52 is described as Ca2+-C52(2-).     

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).     

Search for suitable approximation methods for fullerene structure and relative stability studies: case study with C50

Local density approximation (LDA), several popular general gradient approximation (GGA), hybrid module based density functional theoretical methods: SVWN, BLYP, PBE, HCTH, B3LYP, PBE1PBE, B1LYP, and BHandHLYP, and some nonstandard hybrid methods are applied in geometry prediction for C60 and C70. HCTH with 3-21G basis set is found to be one of the best methods for fullerene structural prediction. In the predictions of relative stability of C50 isomers, PM3 is an efficient method in the first step for sorting out the most stable isomers. HCTH with 3-21G predicts very good geometries for C50, similar to the performance of B3LYP6-31G(d). The gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital from the predictions of all the density functional theory methods has the following descending order: E(gap)(half-and-half hybrid)>E(gap)(B3LYP)>E(gap)(HCTH)(GGA)>E(gap)(SVWN)(LDA).     

The way of stabilizing non-IPR fullerenes and structural elucidation of C(54)Cl(8)

Recently, a new non-IPR chlorofullerene C(54)Cl(8) was isolated experimentally (Science 2004, 304, 699). To explore the ways to stabilize non-IPR fullerenes, the authors studied all of the possible isomers of C(54) fullerene and some of the C(54)Cl(8) isomers at PM3, B3LYP/3-21G, and B3LYP/6-31G* levels. Combined with analysis of pentagon distributions, bond resonance energies, and steric strains, C(54):540 with the least number of 5/5 bonds was determined to be the thermodynamically best isomer for the C(54)Cl(8). Based on C(54):540, the most probable structure of the experimental C(54)Cl(8) was elucidated. The results suggested one of the necessary conditions of stabilizing non-IPR fullerenes: chemical derivatizations of either endohedral complexation or exohedral addition need to sufficiently stabilize all of the kinetically unstable 5/5 bonds of the cages.     

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.     

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     

Stability of Fullerene Cages： C30 to C70 and Their Dependence on Shared Pentagon Bonds

1 INTRODUCTION Since the discovery of buckministerfullerene (C60)[1], experimental and theoretical studies of the structure and properties of fullerenes have spread worldwide. Many experimental studies appeared on their syntheses[2], isolation[3], and characterization[4]. Theoretically, except studies on their chemical pro- perties[5], most of the work was concentrated on their interesting geometric[6～8] and electronic structures[9, 10]. For example, the ground state of C48 has C2 symme…     

Theoretical studies of structures and stabilities of a new odd-numbered fullerene dimer: C141

The possible isomers of a newly synthesized C(141) molecule are calculated using MNDO, AM1, PM3, B3LYP/3-21G, and B3LYP/6-31G(d) methods. The geometry optimizations showed that the isomer 8-8 has the lowest total energy in all 64 possible structures of C(141). Unlike those of C(130), C(140), etc., the C(141) 8-8 shows a new structure: two C(70) side cages open [6.6] ring junctions located at the equator (instead of cap) area to create new chemical bonds for the bridge atom. Theoretical measurements of the average length of the long and short axes of C(70) side cages in the C(141) molecule reveal that when two C(70) cages are connected with each other at the equators, their geometric shapes become more spherical compared with the pristine C(70); this leads to a reduction of the molecular polarizability. Analysis of the local and global strain indicates that the global strain of C(70) monomer in the C(141) 8-8 is greatly reduced compared to the pristine C(70). The stable C(70) derivatives that are formed with reacted C-C bonds in the equator area may put new insights into fullerene chemistry, in particular, for C(70) to react with a large molecule. The results are discussed together with the experimental data.     

Electronic structure and stability of fullerene C82 isolated-pentagon-rule isomers

All nine isolated-pentagon-rule isomers of fullerene C(82) were investigated by the DFT method with the B3LYP functional at the 6-31G, 6-31G*, and 6-31+G* levels. The distribution of single, double, and delocalized π-bonds in the molecules of these isomers is shown for the first time. The obtained results are fully supported by DFT quantum-chemical calculations of electronic and geometrical structures of these isomers. The molecules of isomers 7 (C(3v)), 8 (C(3v)), and 9 (C(2v)) contain some radical substructures (such as the phenalenyl-radical substructure), which indicates that they are unstable and cannot be obtained as empty molecules. Thus, there is a possibility of obtaining them only as endohedral metallofullerenes or exohedral derivatives. Isomers 1 (C(2)), 2 (C(s)), 4 (C(s)), 5 (C(2)), and 6 (C(s)) with closed electronic shell are supposed to be stable, resembling isomer 3 (C(2)), which has just been extracted experimentally as an empty fullerene. We assume they can be produced as empty molecules.     

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…     

C40异构体的结构和稳定性的理论研究

利用Gaussian98程序,采用密度泛函(DFT)方法中的B3LYP,选用6-31G基组对富勒烯(Fullerene)C40的6种异构体[D5d,Td,D2h,C3v,D2(Ⅰ),D2(Ⅱ)]进行了几何构型优化,其中,对于Td对称性的C40由于易发生Jahn-Teller畸变,则降低其对称性为D2d,再进行优化.对它们的平衡几何和电子结构进行了比较具体的分析,同时,根据计算得到的总能量推断出这6种异构体的稳定性顺序是D2(Ⅰ)>D5d>Td>C3v>D2h>D2(Ⅱ).     

Rearrangement of the cyclohexadiene derivatives of C60 to bis(fulleroid) and bis(methano)fullerene: structure,stability, and mechanism

The cyclohexadiene derivative of C(60) rearranges photochemically to bis(fulleroid) (two [6,5] open structure) and bis(methano)fullerene (two [6,6] closed structure). During this process, a [6,5] open/[6,6] closed intermediate is observed. The isolated intermediate undergoes photochemical rearrangement to bis(fulleroid) and bis(methano)fullerene. On the other side, it undergoes retrorearrangement to the starting material in the dark. The structure and energetics of these C(60) derivatives have been studied at the AM1, PM3, RHF, and B3LYP levels of theory. It is found that bis(fulleroid) bearing four tert-butoxycarbonyl substituents is 5.8 kcal/mol (B3LYP) more stable than the corresponding bis(methano)fullerene. The isolated intermediate having the [6,5] open/[6,6] closed structure is 6.7 kcal/mol more favorable than the previously proposed two [6,5] closed intermediate, and the formation of this compound is well explained by the di-pi-methane rearrangement. (13)C NMR calculation at the B3LYP level reproduced the experimental chemical shifts with very good accuracy for each molecular system. Theoretical studies mainly at the unrestricted B3LYP level on singlet and triplet state potential energy surfaces on fullerene derivatives support the di-pi-methane rearrangement mechanism. The previously proposed symmetrical [4+4]/[2+2+2] and the novel proposed unsymmetrical di-pi-methane pathways may coexist during the reaction.     

DFT Study on the Structural, Electronic, and Spectroscopic Properties of the Highest Epoxygenated Fullerene C36O18

Theoretical investigation on the highest epoxygenated fullerene C36O18 formed from the initial C36 fullerene with D6h symmetry has been performed at the B3LYP/6-31G(d) level. Their equilibrium structures, thermal stabilities, electronic structures, vertical ionization potentials, vertical electron affinities, vibrational frequencies and 13C NMR chemical shifts have been studied. The calculation results showed that C36O18 isomers have higher LUMO-HOMO energy gaps than the fullerene C36 and should be more stable. Compared with C36 , it is less possible for C36O18 to accept or donate electrons from reduced VEAs and enhanced VIPs. It has been found that C36O18 isomers are not aromatic at all or antiaromatic on analyzing the NICS values. The present study will encourage further theoretical and experimental analyses of this system in future.     

Structure, stability, and NMR properties of lower fullerenes C38-C50 and azafullerene C44N6

A systematic survey of the complete set of isomers of fullerenes C(38), C(40), C(42), C(44), C(46), C(48), C(50) and azafullerene C(44)N(6) is reported. All isomeric structures were optimized using first-principle density functional theory at the B3LYP/6-31G level. The isomeric structures with the lowest energies are C(38):17, C(40):38, C(42):45, C(44):75, C(44):89, C(46):109, C(48):171, and C(50):270. The ground-state structure of the azafullerene C(44)N(6) in the framework of C(50):270 has D(3) symmetry. The (13)C NMR chemical shifts and nucleus-independent chemical shifts (NICS) for the stable isomers of each fullerene are presented.     

Unusual pentagon and hexagon geometry of three isomers (no 1, 20, and 23) of fullerene C84

Three isomers 23 (D_2d), 1 (D₂), and 20 (T_d) of fullerene C₈₄ have been investigated by PM3, HF/6‐31G*, and DFT methods with B3LYP functional at the 6‐31G and 6‐31G* levels. In this article we reveal for the first time that some distortion of hexagon (pentagon), measured as its maximal dihedral angles, caused by local molecular strains may serve as a new criterion of stability of fullerenes with closed shell. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

DFT Studies on Non-IPR C_(68) and Endohedral Fullerene Sc_3N@C_(68)

The structures and spectra of 20 possible isomers of C78(CH2)3 have been studied by using AM1,INDO/CIS and DFT methods. The results show that the most stable isomer is 1,2,3,4,5,6-C78(CH2)3 (A) with annulene structures,where three -CH2 groups are added to the 6/6 bonds located at the same hexagon passed by the shortest axis of C78 (C2v). Compared with that of C78 (C2v),the first absorption in the electronic spectrum of C78(CH2)3 (A) is blue-shifted because of its wider LUMO-HOMO energy gap. While the IR frequencies of the C–C bonds on the carbon cage are red-shifted owing to the formation of annulene structures and the extension of the conjugated system. The chemical shifts of the carbon atoms in 13C NMR spectra are moved upfield upon the addition.