DFTB and modern DFT

Ben Hourahine, benjamin.hourahine@strath.ac.uk1, Bálint Aradi2, Simone Sanna,
sanna@phys.uni-paderborn.de3, Thomas A. Niehaus2, and Thomas Frauenheim,
frauenheim@phys.uni-paderborn.de2. (1) SUPA, Department of Physics, The
University of Strathclyde, John Anderson Building, 107 Rottenrow, Glasgow, G4
0NG, United Kingdom, (2) Bremen Center for Computational Materials Science,
Bremen University, Bibliotheksstrasse 1, Bremen, 28359, Germany, (3)
Theoretische Physik, Universität Paderborn, Warburger Str. 100, Paderborn,
Germany

The DFTB method can benefit substantially from a number of developments in
density functional theory while also providing an analytical proving ground for
new DFT extensions. In this contribution, variational energy expressions and
related self-consistency strategies are discussed in context of
SCC-DFTB. Suitable forms of the recent LDA+U functionals for DFTB and the
connection to self-interaction correction (SIC) are also discussed. This leads
to an efficient SIC method for DFTB, a parameter free LDA+U, and an improved
form of pseudo-SIC. The derivative discontinuity issue in Kohn-Sham-like
theories including DFTB is then discussed. In particular the observations that
non-self-consistent DFTB exhibits the correct form of band-gap and chemical
potential discontinuities is made, and the introduction of these discontinuities
into SCC and spin-DFTB is discussed. Illustrative examples will be presented
including strongly correlated transition metal and lanthanide systems, band-gaps
of semiconductors, and ionisation energies and electron affinities of molecular
systems.