The DFTB method as an approximate KS-DFT scheme with an LCAO representation of the KS orbitals can be derived within a variational treatment of an approximate KS energy functional given by second-order perturbation with respect to charge density fluctuations around a properly chosen reference density. But it may also be related to cellular Wigner-Seitz methods and to the Harris functional. It is an approximate method, but it avoids any empirical parametrization by calculating the Hamiltonian and overlap matrices out of a DFT-LDA-derived local orbitals (atomic orbitals - AO’s) and a restriction to only two-centre integrals. Therefore, the method includes ab initio concepts in relating the Kohn-Sham orbitals of the atomic configuration to a minimal basis of the localized atomic valence orbitals of the atoms. Consistent with this approximation the Hamiltonian matrix elements can strictly be restricted to a two-centre representation. Taking advantage of the compensation of the so called “double counting terms” and the nuclear repulsion energy in the DFT total energy expression, the energy may be approximated as a sum of the occupied KS single-particle energies and a repulsive energy, which can be obtained from DFT calculations in properly chosen reference systems. This relates the method to common standard “tight-binding -TB” schemes, as they are well known in solid state physics. This approach defines the density-functional tight-binding (DFTB) method in its original (non-self-consistent) version. Its further development - e.g. including self-consistency - as well as the aspects of the computational realization and accuracy will be discussed. Finally, several examples for applications of the DFTB method will be shown.

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