Introduction

The DFTB parameters consist of two parts:

1. parameters entering the electronic part of the DFTB model
2. parameters for the repulsive energy contribution, which is a two-body force field like term.

Electronic part

This part contains atomic and diatomic comtributions which are both calculated from an atomic DFT program using either  LDA or GGA functionals.

• The atomic parameters are the atomic s,p,d,... Kohn-Sham eigenenergies, which enter as diagonal elements the (usually minimal basis) Hamilton matrix.  For the SCC-DFTB method additional atomic hardness values (Hubbard parameters) are calculated.
• The non-diagonal matrix (overlap matrix S and  Hamilton matrix H) elements are calculated in a two-center approximation for a neutral atomic reference density. They are distance dependent and are stored as a table for interatomic distances up to about 10 a.u..

Using these parameters the DFTB program does not have to perform any integral evaluation during the program runtime.

Repulsive part

The repulsive energy contribution is approximated as a sum of pair potentials, which are represented either by spline functions or by polynomials. They are derived by calculating bond stretching energies of selected bonds in a small set of molecules  or  using data from solid state calculations applying DFT calculations to get the total energy and the DFTB electronic part. In contrast to the diatomic parameters in the electronic part, the repulsive potentials are only needed for elements with a direct covalent bond.

For more details, have a look at the first three References on the page about dftb.

Slater-Koster files

The parameters are stored in files X-X, X-Y, Y-X and Y-Y, with X, Y being the available parametrized elements. They contain the diatomic parameters for the given interaction (tables for the H and S matrices and the repulsive contribution). The homonuclear X-X files additionally contain the atomic parameters for the given atom type.

Clearly, to get parameters for N elements is a N**2 effort. Therefore,  up to now only a small fraction of the desirable elements are available, in particular not all atom combinations are available. In some cases, the diatomic matrix elements X-Y and Y-X are missing and a program run is impossible, although the X-X and Y-Y files are available.

A detailed description of the Slater-Koster file format can be found here.

Documentation

Information about the parameters used in the generation of a particular Slater-Koster file is appended to each file in a documentation section. Here also benchmark results and known failures are provided. Publications for which the file at hand were utilized are also given. It is therefore highly recommended to read the documentation before performing a calculation. A detailed description of the documentation elements can be found here.