Abstract
Semi-empirical (SE) methods are derived from Hartree-Fock (HF) or Density Functional Theory (DFT) by neglect and approximation of electronic integrals. Thereby, parameters are introduced which have to be determined from reference calculations and/or by fitting to available experimental data. This leads to computational methods that are about 2-3 orders of magnitude faster than the standard HF/DFT methods using medium sized basis sets while being about 3 orders of magnitude slower than empirical force field methods (Molecular Mechanics: MM). Therefore, SE methods are most appropriate for a specific range of applications. These include the study of systems that contain a large number of atoms and therefore being too large for ab initio or DFT methods and also problems where dynamic or entropic effects are particularly important. In the latter case, the errors made by considering a very limited number of molecular structures or neglecting entropic contributions can be much larger than the accuracy lost due to the use of SE methods. Another area where SE methods are attractive concerns the analysis of systems for which reliable MM models are not readily available. Therefore, even in an era when rapid progress is being made in ab initio methods, there is considerable interest in further developing SE methods. We illustrate this point by focusing on the discussion of recent development and application of the Density Functional Tight Binding method.