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All the 924 classical isomers of fullerene C56 have been investigated by PM3, and some most stable isomers are refined with HCTH/3-21G and B3LYP/6-31G(d) methods. D2:003 with the least number of adjacent pentagons is predicted to be the most stable isomer at B3LYP/6-31G(d) level, while Cs:022 and C2:049 possess nearly degenerate energies with relative energies of 0.03 and 3.90 kcal/mol, respectively. However, as to dianionic C562- fullerene, C2v:011 is predicted to be the most stable isomer. Investigations also show that the encapsulation of Ca atom in C56 fullerene is exothermic and the metallofullerenes Ca@C56 can be described as Ca2+@C562-. The computed relative stabilities show that the D2:003 behaves more thermodynamically stable than other isomers in a wide temperature interval, and C2v:011 should also be an important component. The electronic isomerization of C56 (C2v:011) and C50 (D5h: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 C60. [ABSTRACT FROM AUTHOR]

The 437 classical isomers of fullerene C52 have been studied by PM3, HCTH/3-21G, and B3LYP/6-31G(d). C2:029 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 B3LYP/6-31G(d) level. C2:029 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 C2:029 is 51% larger than that of C60. Furthermore, intensity-dependent refractive index γ (-ω;ω,ω,-ω) (ω=1.1653 eV) of C2:029 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+-C522-. [ABSTRACT FROM AUTHOR]

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 B3LYP/6-31G(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: Egap(half-and-half hybrid)>Egap(B3LYP)>Egap(HCTH)(GGA)>Egap(SVWN)(LDA). [ABSTRACT FROM AUTHOR]

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 B3LYP/6-31G(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: Egap(half-and-half hybrid)>Egap(B3LYP)>Egap(HCTH)(GGA)>Egap(SVWN)(LDA). [ABSTRACT FROM AUTHOR]

Among all the 4478 classical isomers of C66, C66( C s:0060) with the lowest number of pentagon–pentagon fusions was predicted to be the most stable isomer, followed by isomers C66( C2 v:0011) and C66( C2:0083). The infrared spectra and aromaticity of the most stable isomers were predicted. The relative stabilities of C66 isomers change with charges or doping of metals. The structures and relative stabilities of the most stable metallofullerenes were delineated and compared with experiment. Sc2@C66( C2:0083) was predicted to be the most stable metallofullerene, although Sc2@C66( C2 v:0011) was observed. Charge-transfer from Sc2 to the fused pentagons and the bonding between these two moieties significantly decrease the strain energies caused by the pair of fused pentagons thereby stabilizing the fullerene cage. [ABSTRACT FROM AUTHOR]

The 3465 classical isomers of C64 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. C64(D2:0003) with the lowest e55 (e55 = 2), the number of pentagon-pentagon fusions, is predicted to be the most stable isomer and it is followed by the C64(Cs:0077) and C64(C2:0103) isomers within relative energy of 20.0 kcal/mol. C64(D2:0003) 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 e55 = 2 display local aromaticity. The relative stabilities of C64 isomers change with charging in ionic states. Doping also affects the relative stabilities of fullerene isomers as demonstrated by Sc2@C64(D2:0003) and Sc2@C64(Cs:0077). The bonding of Sc atoms with C64 elongates the C&bond;C bond of two adjacent pentagons and enhances the local aromaticity of the fullerene cages. Charging, doping, and derativization can be utilized to isolate C64 isomers through differentiating the electronic and steric effects. © 2008 Wiley Periodicals, Inc. J Comput Chem 2008 [ABSTRACT FROM AUTHOR]

Among all the 4478 classical isomers of C66, C66( C s:0060) with the lowest number of pentagon–pentagon fusions was predicted to be the most stable isomer, followed by isomers C66( C2 v:0011) and C66( C2:0083). The infrared spectra and aromaticity of the most stable isomers were predicted. The relative stabilities of C66 isomers change with charges or doping of metals. The structures and relative stabilities of the most stable metallofullerenes were delineated and compared with experiment. Sc2@C66( C2:0083) was predicted to be the most stable metallofullerene, although Sc2@C66( C2 v:0011) was observed. Charge-transfer from Sc2 to the fused pentagons and the bonding between these two moieties significantly decrease the strain energies caused by the pair of fused pentagons thereby stabilizing the fullerene cage. [ABSTRACT FROM AUTHOR]

The 2385 classical isomers and four nonclassical isomers of fullerene C62have 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:7mbrisomer, with a chain of four adjacent pentagons surrounding a heptagon, is predicted to be the most stable isomer, followed by C2v:4mbrwhich 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 C62isomers 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:7mbrprevails in a wide temperature range. The vibrational frequencies of the five most stable C62fullerene 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:4mbrand the adjacent pentagons in Cs:7mbrand 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 (−; , , −) at 2.3305 eV of Cs:7mbris very large because of resonance with the external field. The second-order hyperpolarizabilities of the five most stable isomers of C62are predicted to be larger than those of C60. [ABSTRACT FROM AUTHOR]