Fullerenes electronic structure

An initial approach to fullerene enumeration was based on point-group symmetry (Fowler 1986 Fowler et al. 1988) and involved an extension of Coxeter s (1971) work on icosahedral tessellations of the sphere and of methods for the classification of virus structures (Caspar Klug 1962). This approach led to magic numbers in fullerene electronic structure (Fowler Steer 1987 Fowler 1990) and will be described briefly here. 

The other aspect of fullerene electronic structure which relates to their ability to accept electron density is the rehybridization of the carbon n atomic orbitals as a result of the curvature which is imposed on the conjugated carbon atoms by the shape of the molecules (Haddon et al. 1986a, b). The discussion of rehybridization effects is deferred to 6, and we begin with a treatment of the topological contribution to fullerene electronegativity within simple hmo theory. The presence of 12 conjugated 5MR in the fullerenes suggests that they will be biased towards reduction in their redox chemistry. 

This section deals with the overall qualitative features of fullerene electronic structure rather than with highly accurate calculations on specific cages. Some ab initio calculations are reviewed in Refs. 45 and 46. 

For a first survey of the electronic structures of the fullerenes, we take the position that all variation in Huckel parameters and all implicit or explicit treatment of o electrons is to be relegated to the steric factor and that the crude version of Huckel theory is taken to describe the pure 7t effects. The advantages of this approach for searching for formal rules of fullerene electronic structure will be made apparent in the following sections. It is also clear that the steric factor defined as above must be taken into account if realistic energies and energetic trends are to be obtained. Indeed, the steric factor seems to dominate relative stabilities of both lower and higher fullerenes, as will also become apparent later. 

The most extensive calculations of the electronic structure of fullerenes so far have been done for Ceo- Representative results for the energy levels of the free Ceo molecule are shown in Fig. 5(a) [60]. Because of the molecular nature of solid C o, the electronic structure for the solid phase is expected to be closely related to that of the free molecule [61]. An LDA calculation for the crystalline phase is shown in Fig. 5(b) for the energy bands derived from the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) for Cgo, and the band gap between the LUMO and HOMO-derived energy bands is shown on the figure. The LDA calculations are one-electron treatments which tend to underestimate the actual bandgap. Nevertheless, such calculations are widely used in the fullerene literature to provide physical insights about many of the physical properties. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

High-resolution transmission electron microscopy (HREM) is the technique best suited for the structural characterization of nanometer-sized graphitic particles. In-situ processing of fullerene-related structures may be performed, and it has been shown that carbonaceous materials transform themselves into quasi-spherical onion-like graphitic particles under the effect of intense electron irradiation[l 1],... 

Saito S, Umemoto K, Miyake T (2004) Electronic Structure and Energetics of Fullerites, Fullerides, and Fullerene Polymers 109 41-57 Sakata M, see TakataM (2004) 109 59-84... 

J. Cioslowski, Electronic Structure Calculations on Fullerenes and Their Derivatives... 

In contrast to carbon, which forms structures derived from both sp2 and sp3 bonds, silicon is unable to form sp2 related structures. Since one out of four sp3 bonds of a given atom is pointing out of the cage, the most stable fullerene-like structure in this case is a network of connected cages. This kind of network is realized in alkali metal doped silicon clathrate (19), which were identified to have a connected fullerene-like structure (20). In these compounds, Si polyhe-dra of 12 five-fold rings and 2 or 4 more six-fold rings share faces, and form a network of hollow cage structures, which can accommodate endohedral metal atoms. Recently, the clathrate compound (Na,Ba), has been synthesized and demonstrated a transition into a superconductor at 4 K (21). The electronic structure of these compounds is drastically different from that of sp3 Si solid (22). 

V.I. Sokolov, I.V. Stankevich. Fullerenes - new allotropic forms of carbon structure, electron structure and chemical properties. // Success in chemistry, 1993, v.62, N°5, p.455-473. 

Several effects can influence the electronic structure of Cjq upon metal complex formation. One is the removal of one double bond from the remaining 29 fullerene double bonds. As in any polyene system, this decreased conjugation is expected to raise the energy of the LUMO and therefore decreases the electron affinity of the system. Conversely, the d-orbital backbonding transfers electron density from the metal into n orbitals of the remaining double bonds, which also decreases the electron affinity. 

J. Cioslowski, Electronic Structure Calculations on Fullerenes and Their Derivatives, Oxford University Press, New York, 1995, Chapters 3, 4, and 5, and references therein. 

Under some simplifications associated with the symmetry of fullerenes, it has been possible to perform calculations of type Hartree-Fock in which the interelec-tronic correlation has been included up to second order Mpller-Plesset (Moller et al. 1934 Purcell 1979 Cioslowski 1995), and calculations based on the density functional (Pople et al. 1976). However, given the difficulties faced by ab initio computations when all the electrons of these large molecules are taken into account, other semiempirical methods of the Hiickel type or tight-binding (Haddon 1992) models have been developed to determine the electronic structure of C60 (Cioslowski 1995 Lin and Nori 1996) and associated properties like polarizabilities (Bonin and Kresin 1997 Rubio et al. 1993) hyperpolarizabilities (Fanti et al. 1995) plasmon excitations (Bertsch et al. 1991) etc. These semiempirical models reproduce the order of monoelectronic levels close to the Fermi level. Other more sophisticated semiempirical models, like the PPP (Pariser-Parr-Pople) (Pariser and Parr 1953 Pople 1953) obtain better quantitative results when compared with photoemission experiments (Savage 1975). 

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