Fullerenes calculations

Certainly, it is not very good when fullerene concentration in C60/PVP complexes is rather low, but let us keep in mind that the acting antiviral dose of fullerene itself in this complex is not high. The active quantity of fullerene, calculated with the neglecting of the polymer vehicle, against the influenza vims is about 7pM (Piotrovskii et al., 2001). 

Fullerenes are highly symmetrical molecules free from any polar groups. For such types of molecules equations (13.7) and (13.8) give <5 = <5h = 0. Therefore, the solubility parameter of fullerenes calculated according to Van Krevelen (1990) can be calculated from equation (13.6). 

Table 2 shows that the size of microcrystalls is higher for precipitated fullerene than for C6o. The diffraction peak (111) has a shoulder at a lower angle, which is more pronounced for precipitated fullerene. According to [21] the asymmetric shape of (111) peak and the appearance of small peak marked by asterisk on the Fig. 2 could be associated with the distortion caused by the formation of two layer extrinsic hexagonal lattice in terchanged with normal fee lattice of C6o. The lattice parameter of precipitated fullerene calculated from the X-ray diffraction pattern a0 = 14.19 A is distinctly larger than that for pure C60 (a0 = 14.15 A). Most probably the gas atoms occupied octahedral lattice sites during crystallization and caused the lattice parameter increase observed in Ar, O2 or N2 fullerenes in comparison with pure C6o-... 

Table 2.6 Ionization potential (IP) and electron affinity (EA) of fullerenes (calculated for individual molecules).

Figure 1 TDDFT calculation and experiment for the electronic CD spectrum of fullerene Calculations were performed with the BP86 functional and an...

This behaviour also stands for functionalized [60]fullerene derivatives, with, however, a few striking differences. The most obvious parameter is the negative shift of the reduction potentials, which typically amounts to -100 mV. Secondly, the separation of the corresponding reduction potentials is clearly different. Wlrile the first two reduction steps follow closely the trend noted for pristine [60]fullerene, the remaining four steps display an enlianced separation. This has, again, a good resemblance to the ITOMO-LUMO calculations, namely, a cancellation of the degeneration for functionalized [60]fullerenes [31, 116, 117]. 

I he results of their calculations were summarised in two rules. The first rule states that at least one isomer C with a properly closed p shell (i.e. bonding HOMO, antibonding I. U.MO) exists for all n = 60 - - 6k (k = 0,2,3,..., but not 1). Thus Qg, C72, Cyg, etc., are in lhi-< group. The second rule is for carbon cylinders and states that a closed-shell structure is lound for n = 2p(7 - - 3fc) (for all k). C70 is the parent of this family. The calculations Were extended to cover different types of structure and fullerenes doped with metals. 

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... 

For C70, molecular orbital calculations [60] reveal a large number of closely-spaced orbitals both above and below the HOMO-LUMO gap [60]. The large number of orbitals makes it difficult to assign particular groups of transitions to structure observed in the solution spectra of C70. UV-visible solution spectra for higher fullerenes (C n = 76,78,82,84,90,96) have also been reported [37, 39, 72]. 

In the theoretical carbon nanotube literature, the focus is on single-wall tubules, cylindrical in shape with caps at each end, such that the two caps can be joined together to form a fullerene. The cylindrical portions of the tubules consist of a single graphene sheet that is shaped to form the cylinder. With the recent discovery of methods to prepare single-w alled nanotubes[4,5), it is now possible to test the predictions of the theoretical calculations. 

Azadienes 89, generated in situ by thermolysis of the corresponding o-aminobenzylalcohols, have been used for the derivatization of [60]-fullerene through C-N bond formation leading to tetrahydropyrido [60]-fullerenes [93]. Theoretical calculations predicted these cycloadditions to be HOMO azadiene-controlled (Equation 2.25). 

This paper is concerned with the structures of the simplest possible adducts of the Ceo and C70 fullerenes, namely the monohydrides, CmH and C H. These open shell species or radicals may be considered as the product of the addition of one atom of hydrogen or one of its isotopes, among which we include specifically the light pseudoisotope of hydrogen known as muonium. Mu = pfe. Although Ceo//has been observed [1], the stimulus for these calculations arose from the experiments on muon implantation in solid [2,3] and C70 [4]. 

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