Bridging the length and time scales: from ab initio electronic structure calculations to macroscopic proportions

Density functional theory (DFT) primarily provides a good description of the electronic structure. Thus, DFT primarily deals with length scales as those of a chemical bond, i.e. 10^-10 meter, and with time scales of the order of atomic vibrations, i.e. 10^-13 seconds. However, several interesting phenomena happen and/or become observable on different scales, namely meso- or macroscopic lengths and on time scales of seconds or even minutes. To bridge the gap between 10^-13 seconds and a second or between 10^-10 meter and 10 and more nano meters is one of the important challenges we are facing today. In this paper we show how we are overcoming these time and size problems for the example of crystal growth and the evolution of nano-scale structures. The key is a kinetic Monte Carlo approach with detailed input from DFT calculations of the relevant atomistic processes.