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A simple, computationally efficient method for the evaluation of structural and vibrational properties of carbon is presented. The scheme is based on the generalized tight-binding molecular dynamics technique applicable to covalent systems. The force constants for the evaluation of vibrational modes are obtained by employing analytic second derivatives of the electronic structure Hamiltonian matrix elements. This method, while providing better accuracy than conventional schemes, greatly expedites the determination of vibrational modes for large size clusters. The efficacy of the method is demonstrated by application to fullerenes and nanotubes. Good agreement is obtained with experiment for bond lengths and vibrational frequencies for these systems.
Menon et al. (1996) studied this question.