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Detailed derivation of the analytical, reciprocal-space approach of Hessiancalculation within the self-consistent-charge density functional basedtight-binding framework (SCC-DFTB) is presented. This approach provides anaccurate and efficient way for obtaining the SCC-DFTB Hessian of periodicsystems. Its superiority with respect to the traditional numerical forcedifferentiation method is demonstrated for doped graphene, graphenenanoribbons, boron-nitride nanotubes, bulk zinc-oxide and other systems.

Analytical Approach to Phonon Calculations in the SCC-DFTB Framework