The energy spectra and optical absorption spectra of isomers Nos. 1, 6, 16 and 46 of fullerene C90 are calculated. Due to the comparison of theoretical and experimental optical absorption spectra, three previously synthesized isomers of C90 fullerene have been identified. The calculations are carried out within the framework of the developed approach, taking into account the intra-node Coulomb interaction of ?-electrons, which plays a crucial role in the formation of the electronic and optical properties of fullerenes. Keywords: fullerene, intra-node Coulomb interaction, Hubbard model, Coulomb integral, energy spectrum, selection rules, optical absorption spectrum.

The energy spectra of ten isomers of trifluoromethyl derivatives of fullerenes C60(CF3)10 and C70(CF3)10 are calculated within the framework of the Hubbard model. Based on the obtained energy spectra, the optical absorption spectra of these compounds are modeled. The calculated optical absorption spectra are compared with the experimental spectra.

Taking into account the strong intra-node Coulomb interaction (10 eV), the energy spectrum of endohedral metallofullerene Sm@C80 is calculated. Based on the theoretical energy spectrum, the optical absorption spectrum of this compound is obtained. Comparison of the theoretical curves of the optical absorption spectrum obtained at different values of charge transfer from the embedded Sm atom with the experimental one with the corresponding experimental curve did not allow to establish the value of charge transfer. But despite this, the qualitative coincidence of the experimental curve with the theoretical ones indicates the adequacy of our model proposed for studying the electronic structure of endohedral fullerenes

Within the framework of Hubbard’s model using an approximation of static fluctuations, the electronic structure and optical properties of compounds of C90 fullerene isomers with chlorine atoms are investigated. The energy spectrum of π electron subsystem is shown to be divided into several unbound electronic subsystems when the number of the attached chlorine atoms becomes greater than (or about) 30. Each of subsystems behaves like a separate system in this case. The energy spectra and optical absorption spectra of ten different chlorine compounds C90@Cln have been calculated. Their optical properties are predicted.

The energy spectra of ten isomers of trifluoromethyl derivatives of fullerenes C 60 (CF 3 ) 10 and C 70 (CF 3 ) 10 are calculated within the framework of the Hubbard model. Based on the obtained energy spectra, the optical absorption spectra of these compounds are modeled. The calculated optical absorption spectra are compared with the experimental spectra. Keywords: trifluoromethyl derivatives, fullerene, Hubbard model, energy spectrum, optical absorption spectrum.

Within the framework of the Hubbard model, the energy spectra of the Cs and C3v isomers of C58 fullerene and dimers based on them are calculated. The obtained curves of the density of electronic states of these systems are compared with the experimental curves of the films, which were obtained by deposition of the Cs and C3v isomers of C58 fullerene on the (1,1,1) gold surface. A comparative analysis of the curves of the density of electronic states shows that in those sites through which a bond is formed between fullerenes, carbon is not in the sp2, but in the sp3 hybridized state.

Within the framework of the Hubbard model, the energy spectra of the C s and C 3v isomers of C 58 fullerene and dimers based on them are calculated. The obtained curves of the density of electronic states of these systems are compared with the experimental curves of the films, which were obtained by deposition of the C s and C 3v isomers of C 58 fullerene on the (1,1,1) gold surface. A comparative analysis of the curves of the density of electronic states shows that in those sites through which a bond is formed between fullerenes, carbon is not in the sp 2 , but in the sp 3 hybridized state. Keywords: fullerene, dimer, energy spectrum, Hubbard model, Hubbard subband, density of electronic states.

The energy spectra and optical absorption spectra of isomers Nos. 1, 6, 16 and 46 of fullerene C90 are calculated. Due to the comparison of theoretical and experimental optical absorption spectra, three previously synthesized isomers of C90 fullerene have been identified. The calculations are carried out within the framework of the developed approach, taking into account the intra-node Coulomb interaction of π-electrons, which plays a crucial role in the formation of the electronic and optical properties of fullerenes.

The article simulates the optical absorption spectra (OAS) of endohedral complexes Er2C2 @ C90 based on isomers No. 44 (C2) No. 21 (C1) of fullerene C90. For this purpose, the energy spectra of the indicated isomers have been calculated. The calculation was carried out within the framework of two models. Within the framework of the first model, which is traditional, only hops of π-electrons from site to site were taken into account (the integral of hopping to the nearest sites B ~ -2.6 eV). Within the framework of the second model, developed in a series of our works [1-5], in addition to hopping from site to site (the integral of hopping to the nearest sites B ~ -1.0 eV), the intrasite Coulomb interaction (ICCI) of π-electrons was also taken into account (the integral of the Coulomb interaction U ~ 7.0 eV). Comparison of the OSS curves obtained by us with the experimental data [5] convincingly indicates that the second model adequately describes the OSS of the endohedral Er2C2 @ C90 complexes based on the investigated isomers. The magnitude of charge transfer from the Er2C2 system to the fullerene shell turned out to be -4e.

Optical absorption spectra (OASs) of endohedral Er2C2@C90 complexes, based on isomers nos. 44 (C2) and 21 (C1) of fullerene C90, have been simulated. To this end, the energy spectra of these isomers have been calculated. The calculations have been performed within two models. Within the first (conventional) model, only hoppings of π electrons between sites (nearest-neighbor hopping integral B ~ –2.6 eV) has been taken into account. Within the second model, intrasite Coulomb interaction (ISCI) of π electrons (Coulomb-interaction integral U ~ 7.0 eV) has been also taken into account along with intersite hoppings (nearest-neighbor hopping integral B ~ –1.0 eV). Comparison of the obtained OAS curves with the experimental data c-onvincingly indicates that the second model describes adequately the OASs of endohedral Er2C2@C90 complexes, based on the isomers under investigation. Charge transfer from the Er2C2 system to the fullerene shell was –4e.

The energy spectrum of isomer no. 181 (C2) of fullerene C96 is calculated within the approximation of static fluctuations taking into account the intrasite Coulomb interaction with parameter U ~ 10 eV, and its optical absorption spectrum is modeled based on the calculated energy spectrum. The obtained optical absorption spectrum is in a good qualitative agreement with the experimental curve. A similar curve obtained within a conventional model with the intrasite Coulomb interaction disregarded differs significantly from the experimental curve.

Abstract The energy spectra of isomers nos. 11 and 22 of C_84 fullerene is obtained with allowance for the intrasite Coulomb interaction. Based on the obtained spectra, the optical absorption spectra of these systems are simulated. The obtained optical absorption spectra qualitatively agree well with the available experimental data. In addition, the optical absorption spectra are also calculated on the base of the energy spectra of each of the systems calculated without considering the intrasite Coulomb interaction. The comparison of the results obtained in these different models strongly demonstrates the most important role of the Coulomb interaction in the formation of the electronic and optical properties of these systems.

The energy spectra of isomers nos. 11 and 22 of C 84 fullerene is obtained with allowance for the intrasite Coulomb interaction. Based on the obtained spectra, the optical absorption spectra of these systems are simulated. The obtained optical absorption spectra qualitatively agree well with the available experimental data. In addition, the optical absorption spectra are also calculated on the base of the energy spectra of each of the systems calculated without considering the intrasite Coulomb interaction. The comparison of the results obtained in these different models strongly demonstrates the most important role of the Coulomb interaction in the formation of the electronic and optical properties of these systems.

Taking into account the intrasite Coulomb interaction with the parameter U ~ 10 eV in the approximation of static fluctuations, the energy spectrum of the isomer N 181 (C2) of the C96 fullerene is calculated, based on which its optical absorption spectrum is modeled. The obtained curve of the optical absorption spectrum at a good qualitative level coincides with the experimental curve. The same curve obtained in the framework of the traditional model without taking into account the intranode Coulomb interaction differs significantly from the experimental curve. Keywords: fullerene, energy spectrum, optical absorption spectrum, π electron, Hubbard subband, optical transitions.

Within the framework of Hubbard’s model using an approximation of static fluctuations, the energy spectrum of the π-electron subsystem of an icosahedral C 80 fullerene isomer is obtained. Based on the energy spectrum, an optical absorption spectrum of metal-nitride complexes M 3 N@C 80 (M = Gd, Tm, Dy) is simulated. It is quite consistent with the respective experimental spectrum.

Energy spectrum of isomer No. 11 of С84 fullerene of С2 symmetry is calculated within the Hubbard model. Based on the obtained energy spectrum, the optical absorption spectrum is modeled taking into account not only allowed, but also forbidden symmetry transitions. Good qualitative agreement with the experimental data is obtained. This suggests that when studying fullerenes, the intra-site Coulomb interaction of electrons must be taken into account.

The rule of multiplicity of three according to which a nanotube has a metallic conductivity if the difference between the chiral indices is a multiple of three or behaves as a semiconductor or dielectric in the opposite case, is commonly used for interpretation of the physical properties of carbon nanotubes (CNTs). This rule is shown to have limited validity, for example, for single-walled CNTs considered as strongly correlated systems in terms of the perturbation theory, in which the state of individual atoms is a zero approximation and the electron site-to-site hopping is regarded as a perturbation. Due to a strong Coulomb interaction between p-electrons at one site, the energy spectrum is divided into two Hubbard subbands resulting in conditions when the rule of multiplicity of three does not work.

The energy spectrum of C 82 fullerene (isomer no. 3 of C 2 symmetry) is calculated within the Hubbard model in the approximation of static fluctuations. Based on the energy spectrum, optical absorption spectra of this isomer in neutral and anionic states with one, two, three, and four additional electrons are simulated. The calculated optical spectra in neutral and monoanionic states are compared with known experimental spectra.

В рамках модели Хаббарда в приближении статических флуктуаций вычислен энергетический спектр фуллерена C70 с учетом различия в длинах связей между неэквивалентными узлами. На основе полученного энергетического спектра смоделирован спектр оптического поглощения в ультрафиолетовом и видимом диапазоне. Обнаружено хорошее качественное согласие результата расчетов с экспериментально измеренным спектром поглощения, а также соответствие между экспериментальным и теоретическим значением щели между верхней заполненной и нижней свободной молекулярной орбиталью. DOI: 10.21883/FTT.2017.02.44071.474