Periodic boundary conditions, which rely on the assumption that the nuclei constitute an immobile grid with fixed periodicity, allow an efficient computational assessment of ideal macroscopic crystals. In real materials under realistic conditions, however, the nuclei are never immobile – not even at zero temperature due to the quantum mechanical zero point motion.
Accounting for this dynamics is essential to understand and to correctly describe a variety of effects which range from phase stability to charge and heat transport. In this lecture, we will first introduce the harmonic approximation, which allows to study the motion of the nuclei in a solid from first principles. In a second step, we will investigate the (often severe) limitations of this approximation and learn how to overcome them in an ab initio framework. In particular, we will discuss how these harmonic effects can and must be incorporated in a first-principle theory of charge and heat transport.