Computer simulations for the nano-scale

A review of methods for computations for the nano-scale is presented. The paper should provide a convenient starting point into computations for the nano-scale as well as a more in depth presentation for those already working in the field of atomic/molecular-scale modeling. The argument is divided in chapters covering the methods for description of the (i) electrons, (ii) ions, and (iii) techniques for efficient solving of the underlying equations. A fairly broad view is taken covering the Hartree-Fock approximation, density functional techniques and quantum Monte-Carlo techniques for electrons. The customary quantum chemistry methods, such as post Hartree-Fock techniques, are only briefly mentioned. Description of both classical and quantum ions is presented. The techniques cover Ehrenfest, Born-Oppenheimer, and Car-Parrinello dynamics. The strong and weak points of both principal and technical nature are analyzed. In the second part we introduce a number of applications to demonstrate the different approximations and techniques introduced in the first part. They cover a wide range of applications such as non-simple liquids, surfaces, molecule-surface interactions, applications in nano technology, etc. These more in depth presentations, while certainly not exhaustive, should provide information on technical aspects of the simulations, typical parameters used, and ways of analysis of the huge amounts of data generated in these large-scale supercomputer simulations. (author)