Density-functional theory (DFT) has emerged as the premier quantum chem-istry tool for many chemical applications of small and intermediate size range. In the 1990's, break-throughs in DFT were realized with the development of gradient corrected exchange and correlations functionals, combined with considerable advantages in efficient computer programs for the solution of the Kohn-Sham (KS) equations, that caught the attention of the chemistry community. This opened a new field of applications for computational chem-istry and promised the treatment of large molecular and solid state systems with up to hundreds of atoms at new found accuracy. At the same time, the development of linear-scaling electronic structure methods offered promise that much larger systems, up to several tens of thousands of atoms, could be realized .
The last 10 years have led to a clearer and perhaps more balanced picture of strengths and weaknesses of DFT. For example, gradient corrected density functionals show clear limitations, e.g. in the description of vdW complexes, charge transfer excitations or isomerization reactions . Early attempts to overcome these difficulties seem to sacrifice computational efficiency, clos-ing the gap to the more involved ab initio approaches, e.g., MP2 or local MP2, CASSPT2 and CCSD(T).
It is now apparent that for many chemical applications, the bottleneck to high accuracy rests is the inability to properly model extremely complex con-densed phase environments and appropriately sample the necessary degrees of freedom to extract meaningful experimentally observable properties . The computational demands of even the most efficient full DFT methods pre-clude such applications in the foreseeable future. This is particularly true for large solvated biomolecules and macromolecular assemblies, adsorption studies of molecules or proteins on technical surfaces (simultaneously taking account of environmental electrochemical conditions) free energy simulations of molecular systems with hundreds of thousands of relevant configurations, computer aided drug and materials design or investigations of the properties of nanostructures with several thousands of atoms, couple to environmental conditions. Here, more approximate quantum methods and multiscale con-cepts can lead to valuable insights not accessible with more sophisticated and computationally intensive methods.
Recent examples in the literature have demonstrated that approximate quan-tum methods like semiempirical quantum chemistry (SE) or DFTB are today computationally fast enough to tackle macromolecular and/or condensed phase problems [6,7,8]. Their main bottleneck is now to obtain proper chemi-cal answers for such kind of systems since the parameters they use are generally obtained from experimental data of small gas-phase molecules. An urgent need has thus re-emerged to develop new approximate quantum models  that are orders of magnitude faster than their DFT counterparts, and that should allow access to a host of high-impact chemical problems within a multi-scale computational framework linking downscale to the more sophisticated theories and upscale to classical continuum and course-graining techniques. These ultra-fast quantum models are necessarily empirical, and originally bred from a long history more than 40 years successful semiem-pirical developments based on Hartree-Fock theory and more than 10 years approximate DFT. These methods include semiempirical NDDO-based methods such as OMx and OMx-D, PDDG/PM3, RM1, PM6, PM3-MAIS and PM3-PIF, AM1*, PM3BP and AM1/d-PhoT and others, and approximate DFT methods such as DFTB.