Ab-initio calculations of axially symmetric isolated carbon nanostructures: from linear chains to nanotubes
Marco Bianchetti - Università degli Studi di Milano - [2000]
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  • Abstract
    We have calculated the electronic structure and electromagnetic response of elongated carbon nanostructures of interest in several fields of physics, chemistry and astrophysics, in particular for linear carbon chains and incipient carbon nanotubes.
    The theoretical methods used here are based on the ab-initio density functional theory (DFT) for the ground state properties, and its time-dependent counterpart (TDDFT) for the excited state properties, both in the local density approximation (LDA and TDLDA, respectively).
    The corresponding equations have been written in an appropriate cylindrical basis, suitable for elongated structures, and have been numerically solved with the aid of new dedicated software.
    Regarding the ground state electronic structure, we have characterized the energy spectra and wavefunctions as a function of the chain length in the range 4< N < 31, and we have analyzed their one-dimensional character.
    Regarding the electromagnetic response, we have found that the systematic of the dominant longitudinal dipole modes, carrying a large fraction of the total energy weighted sum rule (EWSR), reproduces well the linear N dependence of the peak wavelength observed in the experiments, but shows a systematical blue-shift of the order of 15%. This may be due to a partial failure of the TDLDA.
    Furthermore, we have studied the microscopic structure of the wavefunctions associated with these states, and we have found that they show a collective character (plasmon), which we were able to work out in detail, along with the correlations of the ground state, due to virtual HOMO-LUMO excitations. This counterdicts the experimental literature, where these excited states are implicitely assumed to have a single-particle character.
    Finally, we have found that the calculated static polarizability as a function of N follows a scaling law of the form alpha_N = N^eta with eta approximately 2.3, indicating an intermediate behaviour between the free electron case (eta=3) and the strongly correlated electron case (eta=1), expected for finite 1-D systems. This fast scaling to large values of the polarizability has a simple interpretation in terms of sum rules, which confirms also the existence of non--negligible amount of ground state correlations, and has to be understood as a consequence of the strong delocalization of pi electrons in such sp hybridized systems. We suggest that this peculiar characteristic could be used as an experimental parameter useful to identify different structures with the same mass number, and to asses the stability of longer chains in electric fields.

    For further information see the web site: http://www.bianchetti.org...
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