Tight-binding density functional theory: An approximate Kohn-Sham DFT scheme

Gotthard Seifert Sr., Gotthard.Seifert@chemie.tu-dresden.de, Physikalische
Chemie, Technische Universitaet Dresden, Bergstr. 66, Dresden, D-01062, Germany

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, which 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.