Laboratoire de Chimie et Physique Quantiques - UMR5626

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.