Next generation interatomic potentials for condensed systems

The computer simulation of condensed systems is a challenging task. While electronic structure methods like density-functional theory (DFT) usually provide a good compromise between accuracy and efficiency, they are computationally very demanding and thus applicable only to systems containing up to a few hundred atoms. Unfortunately, many interesting problems require simulations to be performed on much larger systems involving thousands of atoms or more. Consequently, more efficient methods are urgently needed, and a lot of effort has been spent on the development of a large variety of potentials enabling simulations with significantly extended time and length scales. Most commonly, these potentials are based on physically motivated functional forms and thus perform very well for the applications they have been designed for. On the other hand, they are often highly system-specific and thus cannot easily be transferred from one system to another. Moreover, their numerical accuracy is restricted by the intrinsic limitations of the imposed functional forms. In recent years, several novel types of potentials have emerged, which are not based on physical considerations. Instead, they aim to reproduce a set of reference electronic structure data as accurately as possible by using very general and flexible functional forms. In this review we will survey a number of these methods. While they differ in the choice of the employed mathematical functions, they all have in common that they provide high-quality potential-energy surfaces, while the efficiency is comparable to conventional empirical potentials. It has been demonstrated that in many cases these potentials now offer a very interesting new approach to study complex systems with hitherto unreached accuracy.