The Systems of Volume-Localized Electron Quantum Levels of Charged Fullerenes

Abstract

The existence of a system of short-lived, discrete, volume-localized electron quantum levels in positively charged fullerenes is theoretically and numerically demonstrated using the example of fullerenes C60 and C20. Unlike experimentally and theoretically well-studied electron states localized in a thin surface layer, these electron states are due to the flat part of the Coulomb potential of a positively charged fullerene sphere. The energy width of the system of such discrete volume-localized levels depends on the charge and increases with increasing charge. For C60+1, the energy width is 0.16 a.u. and increases up to 0.9 a.u. for fullerene C60+10. Thus, the electrons captured on these discrete levels of fullerene form a sort of short-lived superheavy “nanoatom” or “nanoion,” in which the electrons are localized inside a positively charged spherical “nucleus” with an atomic mass of 240 a.u. for C20 and 720 a.u. for C60. Numerous published papers have demonstrated theoretically and experimentally the existence of metastable positively charged C60 fullerenes with a charge of +10 or more, which suggests the possibility of experimental observation of the considering system of volume-localized electronic states. In conclusion, questions are discussed and estimates are made of the possibility of generating coherent radiation at these transitions.

Metastable One-Electron Excited States of Charged Fullerenes

“…The resulting potential is presented in Figure 1, where we show the cross-section passing through the center of the fullerene and the carbon atom and the section through the center of the fullerene and the center of the segment connecting two adjacent 2 Journal of Nanomaterials carbon atoms. Similar to the findings of our previous works [7,12], we observe that the value of the potential in the center is lower for the charged C 60 +2 than for the neutral fullerene. For the energies above the potential value at the center of the fullerene, we find both the well-studied surfacelocalized electron states (SLES) and volume-localized electron states (VLES).…”

“…At the same time, for transitions from SLES # 171, the lifetime is about 0.5 μs. These times are significantly greater than the characteristic values that were previously obtained on the basis of a simple estimate for the transition dipole moment [7].…”

“…Our calculations show that volume-localized electron states are metastable with the typical lifetimes of 1 μs. These times are essentially longer than the characteristic values that we previously obtained on the basis of a simple estimate for the transition dipole moment [7]. For example, the lifetime obtained with such a simple estimate was 0.1 ns for the transition energy of 10 eV, whereas now with the 3D numeric calculations for 10 eV, we find 0.1 μs.…”

“…In particular, a number of experimental studies demonstrate the existence of metastable cations C 60 +Z with charges Z up to +10 [4,5]. Earlier, by making use of analytical estimates in the approximation of a spherically symmetric model, it was shown that along with the well-known surface-localized electron states, there are volume-localized states for which the electron wave function has the maximum at the center of the fullerene [6,7]. The existence of volume-localized electron states for charged fullerenes was subsequently confirmed by means of the threedimensional numeric calculations with the help of the widely available QuantumEspresso software package for quantummechanical computations.…”

Numerical Simulation of Charged Fullerene Spectrum

“…More nontrivial shape of potential can be derived from the photoelectron intensity measurements for C 60 fullerenes [25,30]. The spectral computations were also done by taking into account of the actual fullerene's nonspherical geometry [33,39] for electrically neutral systems, and for the charged fullerenes the corresponding DFT computations [2] yield the qualitatively consistent results.…”