Density functional theory empirical tight-binding

Methods particularly devoted to biomolecular processes are more frequently used than multipurpose semi-empirical molecular orbital methods like AMI and PM3. Self-consistent-charge density functional theory based tight-binding (SCC-DFTB), an efficient method derived from density functional theory, is well adapted for QM/MM studies of biomolecular systems."... 

New versions of AMBER software support the option of allowing part of the system to be described quantum mechanically in an approach known as a hybrid (or coupled potential) QM/MM simulation. Both semi-empirical and the Density Functional Theory-based Tight Binding (DFTB) Hamiltonian can be used. The system may contain both two non-bonded parts and covalently bonded QM and MM sub-systems (Case et al. 2010). 

The definition of the concept ab initio is somewhat fluid, but usually means essentially free of empirical parameters. Being ab initio is generally considered a quality stamp, but one should be aware that some approaches, which ru e formally parameter-free, e.g. Thomas-Fermi density functional theory or ab initio tight binding, fail miserably outside limited application ranges. 

Tlie suffices i and J refer to individual atoms and S and Sj to the species of the atoms involved. The summation over j extends over those neighbors of the atom i for which ry, the separation of atoms i and J, is within the cutoff radii of these potentials. The second term in Equation (la) is the attractive many-body term and both V and are empirically fitted pair potentials. A Justification for the square root form of the many-body function is provided in the framework of a second moment approximation of the density of states to the tight-binding theory incorporating local charge conservation in this framework the potentials represent squares of the hopping integrals (Ackland, et al. 1988). 

---