IntroductionThe tight-binding (TB) model has become a popular and convenient tool for total energy calculations and molecular dynamics simulations of complex systems. It offers a reasonable compromise between classical interaction potentials and ab initio electronic structure calculation methods, being rather close in efficiency to the former due to strong simplifications in the electronic structure calculations. In the last two decades much attention has been paid to development of different TB models. Now one can find successful applications of TB in physics, chemistry and biology. In spite of this, conventional TB models are not accurate enough yet to relay on them in the case of complex systems and unknown structures, particularly for the rich variety of possible nanostructures where the environment of the atoms is intermediate between the molecular and bulk environments. Development of conventional TB total energy calculation models has been mostly driven by the desire to have the simplest electronic structure based computational approach possible, while accuracy and transferability problems have been addressed by increasing the complexity of analytical formulas for terms of the TB total energy functional, as well as by increasing the number of fitting parameters and reference systems. This functional, introduced originally by Chadi [1] for simplified estimation of relaxation of silicon surface, is now widely accepted and most authors use and modify it without care about physical meaning of its terms. This work highlights the principal differences between conventional TB methods and a nonconventional tight-binding (NTB) method [2], which is based on more correct total energy functional with four easily interpretable energy terms that are initially defined in terms of individual characteristics of chemical elements: Slater exponents and energy of atomic orbitals (AO). Then the results of the application of NTB with improved parameterization [3] for silicon clusters will be presented, demonstrating the potential of tight-binding methods as a quantitative, predictive tool, provided they are based on an accurate total energy functional and exploit properly the individual properties of chemical elements, accounting for both intra-and inter-atomic charge redistributions.