Range separated functionals in the density functional based tight binding method: Formalism

A generalization of the density-functional based tight-binding method (DFTB) for the use with range-separated exchange-correlation functionals is presented. It is based on the Generalized Kohn-Sham (GKS) formalism and employs the density matrix as basic variable in the expansion of the energy functional, in contrast to the traditional DFTB scheme. The GKS-TB equations are derived and appropriate integral approximations are discussed in detail. Implementation issues and numerical aspects of the new scheme are also covered.