Abstract
The mathematical model of the electron spectrum of a charged fullerene is constructed on the basis of the potential of a charged sphere and the spherically symmetric potential of an uncharged fullerene. The electron spectrum is defined as the solution of the spectral problem for the one-dimensional Schr\"odinger equation. For the numerical solution of the spectral problem, piecewise-linear finite elements are used. The computational algorithm was tested on the analytical solution of the problem of the spectrum of the hydrogen atom. For solution of matrix spectral problems, a free library for solving spectral problems of SLEPc is used. The results of calculations of the electron spectrum of a charged fullerene C60 are presented.
Highlights
Fullerenes are known as one of allotropes of carbon, along with nanotubes, graphite, diamond, graphene and amorphous carbon
The mathematical model of the ground state electron spectrum of a charged fullerene is constructed on the basis of the potential of a charged sphere and the spherically symmetric potential of a neutral fullerene, derived in a singleelectron self-consistent field model approach
The electron spectrum is defined as the solution of the spectral problem for the one-dimensional Schrodinger equation
Summary
Fullerenes are known as one of allotropes of carbon, along with nanotubes, graphite, diamond, graphene and amorphous carbon. The electron spectrum is defined as the solution of the spectral problem for the one-dimensional Schrodinger equation. The computational algorithm was tested on the analytical solution of the problem of the spectrum of the hydrogen atom. The results of calculations of the electron spectrum of a charged fullerene C60 are presented.
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