Electron and Optical Properties of Fullerene C70 within ... - Springer Link

ISSN 1063-7834, Physics of the Solid State, 2017, Vol. 59, No. 2, pp. 423–427. © Pleiades Publishing, Ltd., 2017. Original Russian Text © B.V. Lobanov, A.I. Murzashev, 2017, published in Fizika Tverdogo Tela, 2017, Vol. 59, No. 2, pp. 409–413.

FULLERENES

Electron and Optical Properties of Fullerene C70 within the Conception of a Strongly Correlated State B. V. Lobanov and A. I. Murzashev* Mari State University, Yoshkar-Ola, 424000 Russia *e-mail: [email protected] Received December 21, 2015; in final form, July 22, 2016

Abstract—In the framework of the Hubbard model in the static fluctuation approximation, the energy spectrum of fullerene C70 with allowance for different lengths of the bonds between nonequivalent nodes is calculated. On the basis of the calculated energy spectrum, the optical absorption spectrum in the ultraviolet and visible region is simulated. A good qualitative agreement between the calculated and measured absorption spectra and between the measured and theoretical values of the gap width between the highest occupied and the lowest unoccupied molecular orbital is found. DOI: 10.1134/S1063783417020159

1. INTRODUCTION Fullerenes, which were discovered more than 30 years ago, still attract much attention from researchers. This circumstance is explained by their unique properties and big promises of their application in various branches of science-based engineering [1]. The electron structure, namely, the energy spectrum of any system carries most information on its properties. Knowing the energy spectrum enables one to explain many properties of the system and predict the areas of possible application of new materials. In [2– 7], on the example of fullerenes С60, С70, С72, С80, and С82, it was shown that the electron and optical properties of fullerenes can be consistently explained using the Hubbard model for calculating their energy spectrum. The reason is that, in the π-electron subsystem, in which, according to [8], the boundary between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is found, the on-site Coulomb interaction between electrons is strong. According to [9, 10], it can reach value about 10 eV. A convincing evidence in favor of the approach developed in [2–7] is as follows. The optical absorption spectrum of fullerene С60 measured in [11] contains absorption bands at 210 and 260 nm, which corresponds to transitions between electron states with the energy difference of ∼5–6 eV. This value is on the order of the bandwidth of π-electrons in fullerenes, which was obtained in the absence of the Coulomb interaction. Moreover, the absorption intensity at these wavelengths is 100–200 times higher than at the wavelengths corresponding to the visible and infrared (IR) region. This indicates that the absorption at the

wavelengths of 210 and 260 nm (5.9 and 4.8 eV) is connected with symmetry-allowed electron transitions and the absorption in the visible and IR region, with forbidden transitions that become allowed due to temperature distortions. It should be noted that our calculations are not ab initio and the exact values of the transition probability (and their difference from zero) require the exact knowledge of the wave functions of the corresponding states and matrix transition elements calculated from them. Therefore, our assertions that the transition intensity at large wavelengths is smaller by the factor of 100–200 are purely phenomenological and based on experimental data [11, 12]. The symmetry of fullerene C60 (symmetry group Ih) is such that, in its energy spectrum obtained in the framework of the classical Hückel calculation, symmetry-allowed transitions in which the energy different is about 5– 6 eV are absent. In [2], the presence of symmetryallowed transitions was explained by the fact that the strong on-site Coulomb interaction of π-electrons leads to dividing the energy spectrum of the system into two subzones each of width ~5–6 eV. Later, this result was refined in [13, 14]. In the latter work, the obtained optical absorption curves in regions of short (400 nm) wavelengths are in a good qualitative agreement with experimental ones. 2. PROBLEM STATEMENT In [3–7], within the Hubbard model, the energy spectra of fullerenes С70, С72, С74, С80, and С82 were obtained, on the basis of which their optical absorption spectra were simulated. The optical absorption spectra in those works were simulated at forbidden

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transitions, which become allowed due to temperature distortions of symmetry. The obtained optical absorption spectra exhibit a sufficiently good qualitative agreement with existing experimental data on these fullerenes in the region of wavelengths greater than 350 nm. The long-wavelength region was chosen because the available literature has no experimental data on the optical absorption spectra of higher fullerenes in the short-wavelength region (