Empirical Methods and Coarse-Graining

Abstract

In the previous two chapters, we learned that atomistic- and electronic-scale simulations can be performed by means of ab initio or semi-empirical methods such as tight-binding. However, we learned also that these are, at present, still restricted in their capability with respect to both the number of atoms and the simulation timescale. In order to study longer-timescale phenomena of systems composed of larger numbers of particles, it becomes necessary to introduce much simpler but still atomic scale methods. If such methods are more or less based on the ab initio or semi-empirical total energies and they are not simplified too much, one may rely on them as a substitute. The important issue here is how to reduce the amount of necessary computation in such methods, and how to introduce parametrizations or fittings into the interatomic potentials without losing too much accuracy and reliability. In principle, it is possible to construct realistic classical potentials based on ab initio calculations. A possible methodology here is to determine classical potentials by, for example, fitting them to contour maps of the total energy, which may be obtained with an ab initio method by changing the position of one atom while fixing the coordinates of all other atoms. In this book, we do not go into the details of the applications of classical molecular dynamics, since readers can refer to many good reviews. Instead, a few examples are given of how classical potentials can be constructed from ab initio theories.KeywordsSingular Value DecompositionPair PotentialClassical PotentialCluster Variation MethodBare PotentialThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.