Numerical simulation of charged fullerene spectrum. (English) Zbl 1469.92005
Summary: 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 single-electron self-consistent field model approach. The electron spectrum is defined as the solution of the spectral problem for the one-dimensional Schrödinger 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 \(C_{60}\) are presented.
MSC:
| 92-10 | Mathematical modeling or simulation for problems pertaining to biology |
| 65L15 | Numerical solution of eigenvalue problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 82D80 | Statistical mechanics of nanostructures and nanoparticles |
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
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