Energy spectrum and optical properties of C 74 fullerene within the Hubbard model
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ONIC PROPERTIES OF SOLID
Energy Spectrum and Optical Properties of C74 Fullerene within the Hubbard Model A. I. Murzashev and T. I. Nazarova Mari State University, Ioshkar Ola, 424000 Russia email: [email protected] Received June 15, 2014
Abstract—The energy spectrum and the optical absorption spectrum of C74 fullerene are calculated within the Hubbard model with regard to strong Coulomb correlations. It is shown that, due to the strong correla tions, the energy spectrum is split into two 5.732 eV wide Hubbard subbands. The gap between these subbands is the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) and is equal to 1.268 eV. From the energy spectrum obtained, the optical absorption spectra of both pure fullerene and M@C74 metal fullerenes, where M is a metal of valence 1, 2, 3, or 4, are calculated. For M = Ca, Sr, Ba, or Eu, the optical absorption spectrum at wavelengths λ < 1000 nm well agrees with experimental data. DOI: 10.1134/S106377611411017X
1. INTRODUCTION Among the isomers of the C74 fullerene, there is only one that obeys the rule of isolated pentagons. According to this rule, the most stable fullerenes are those in which each pentagon is surrounded by hexa gons, i.e., such fullerenes whose structure does not contain pentagons adjacent to each other. This isomer belongs to the symmetry group D3h. Its Schlegel dia gram is demonstrated in Fig. 1. To all appearances, the C74 fullerene is unstable; it was not detected in its pure form, but its traces were seen in solutions and in car bon black [1]. In its pure form, this fullerene exists in macroscopic amounts only in endohedral metal fullerenes Eu@C74, Sc@C74, Sc2@C74, Ca@C74, Yb@C74, and Ba@C74 [2–5]. It is assumed that the insertion of a metal atom into a fullerene does not substantially change the energy levels of the latter; therefore, in a first approximation, the effect of the inserted atom is equivalent to the addition of extra electrons to the fullerene shell. Thus, to all appearances, the existence of the C74 fullerene solely in the form of endohedral complexes is associ ated with the fact that the presence of “redundant” electrons reduces the energy of the electron sub system, making it stable. Note that such a stabilization occurs not only in C74, but also in other fullerenes that are not observed in pure form but exist only in the form of endohedral complexes, for example, in Ca@C72 and in a number of isomers of the C80 fullerene. The stabi lization of unstable fullerenes through the encapsula tion of metals into their shells is obvious from empiri cal considerations. The point is that all fullerenes have positive affinity energy; i.e., the energy of fullerenes decreases under absorption of electrons [6], and,
hence, the insertion of metal atoms, which are usually donors with respect to fullerenes, into the shell of fullerenes stabilizes the system. In a number of studies, it was argued that the insta bility of the C74 fullerene is due to the fact that the gap betwe
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